I .I III “I III :Iq“. I :l I(III IIIII I.‘ "III “'- " IIIIII III II IIII IIII Ii“ II ”I .‘I MM'I'IIIIIII II ‘I II I I I I‘ III III IIIIISI IIIm II II I I III I“) "III IIIIIIIIIIIIIIIIH' III "II "I II IIII’l I'IIII I"' ‘_ ‘—.._ H {:4 "mi. . '1‘.‘ “flaw: x3; I Lu» ——... M1: _ v "fluff- . “A 221:“? :. . ; .. I, II T I IIIIII IIII.. 1! IIIII III . W ‘ u..- “M .—~—— W .. ‘ MI I" III {III . Mi: 1 I IIIIII IIIII‘fiI II ’ ' - ‘ a5}??? IIIII’ IIIII” ”I”. . ' ' ‘7 A‘ I I II 3I' III “IIIIIII I I I . . . 2.... " III1‘2I‘I'*IIIIII'II ' II“. II I III . I . . ‘I II IILI‘III‘I IrI'I. ‘ . H I IIIIHIIIIII:IIIIII‘IIIUIIII '; I1 . i IIIII;f|..;;I"-;‘::I.I H II .IIE I. III-II")? IIIIII'I;ITI"““ . I’ H "II III,I .I' I i. ’ ' '1 T"‘.I. Iii} I“ " II'MII : ”I" ‘I “III 1.1“" I I III ..~ I fig: I.“ II I..._ II .4 LIBRARY Mp.igan State Univ ”3519' This is to certify that the thesis entitled A MODEL FOR THE DISTRIBUTION AND ABUNDANCE OF THE CEREAL LEAF BEETLE IN A REGIONAL CROP SYSTEM presented by Alan J. Sawyer has been accepted towards fulfillment of the requirements for Ph.D. degree in ENTOMOLOGY (/rémoflm Major profesg Date 0%31j/77A/ 0-7639 OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to book drop to remove this checkout from your record. " E: l fl...» ommwefi sewir uao_ 1911 “Bar an») ”t ., emu": 11.2. a.” (I A‘! a 93:52: A MODEL FOR THE DISTRIBUTION AND ABUNDANCE OF THE CEREAL LEAF BEETLE IN A REGIONAL CROP SYSTEM BY Alan J. Sawyer A DISSERTATION Submitted to Michigan State University 3;. “Impartial fulfillment of the requirements for the degree of Department of Entomology 1978 ‘ 1 In ”17W 3“! 'L‘df‘h‘ “~42: ‘ ABSTRACT A MODEL FOR THE DISTRIBUTION AND ABUNDANCE OF THE CEREAL LEAF BEETLE IN A REGIONAL CROP SYSTEM BY Alan J. Sawyer .rg, qplayed by dispersal in the life history of this species. In this :fLJ‘ i u Alt of diffusive immigration and emigration. The validity of the ,9515 is evaluated and the factors affecting the dispersal rates idfih analysis of host crop preference and the nature of the dis- gyrocess in the cereal leaf beetle is carried out by relating Alan J. Sawyer Multivariate spatial analyses of beetle distribution and e in a regional crop system reveal a complex relationship 3}.r densities in individual fields and the structural features of lsurrounding environment. Field studies are discussed which lend further support to the spatial and temporal structure of the crop system in a 16 mi2 ion on the distribution and abundance of the insect. The model u‘sizes the importance of local uniqueness in producing spatial itch: in density. The simulations lead to surprising results v-rning‘the effects of resistant wheat, relative crop maturities, "1 crop acreages and field size, shape and location. To Marcia and Mariah sine qua non mum. .3 i c i. .;,n and an? n“zcircCTnui stimulation” 'lmy‘achnow ed gm the financial suopv;> '3‘. :2 WV 5m. Wfifi hf V . ACKNOWLEDGMENTS I wish to express my sincere appreciation to Dr. Dean L. ‘gn Haynes for his guidance and support while serving as my major pro- qufessor. His influence has shaped my development as a scientist and ‘fi‘ will continue to guide me in the years ahead. ‘ I also thank Drs. William E. Cooper, Stuart H. Gage, Ramamohan L. Tummala and Stanley G. Wellso for serving on my guidance committee :-:: and for the other contributions each has made, in his own way, to my ”pigraduate program. I I am appreciative also to Dr. James E. Bath, who, as department iqdhairman, provided an incredibly favorable atmosphere for my graduate computational matters, and to Dr. Robert L. Gallun for providing :the opportunity to participate in a unique research project. To my fellow students, Winston Fulton, John Jackman, Dick érande, Emmett Lampert, Kasumbogo Untung, Bill Ravlin and Ray 5 . thers, I express my gratitude for the intellectual stimulation ' §auaraderie we have shared. _‘V Jill?! ‘.’I‘ «Q1. M‘V'UF'L Wt if! L - 54 LL . "“ "Newton ushered in the Age of Reason, rgduring which it was the expectation of scholars that all problems would be solved by the accep- -gfq. fiance of a few axioms worked out from careful L,Lhmobservations of phenomena, and the skillful use A of mathematics. It was not to prove to be as ,easy as all that." «T ":31; ‘fi3x A.‘ Isaac.Asimov TABLE OF CONTENTS 'igélaurr OF TABLES. . . . . . . . . . . . . . . . . . . . . 5.§rrsr.or FIGURES . . . . . . . . . . :5 giinrkonucrron . . . . . . . . . . . . . . . . . . . . 'Afigirrenaruns REVIEW . . ‘fRELIMINARY ANALYSES . . . mu QHHB ROLE OF DISPERSAL IN POPULATION DYNAMICS . . . . . . V_ARTMENTAL ANALYSIS OF DISPERSAL AND MORTALITY . . Defining the Uniqueness of a Field . . . . . . . . Regression Analyses . . . . . . . . . . . . . . . . tar Analyses . . . . . . . . . . . . . . . . . . otorrelations . . . . . . . . . . . . . . . . E'lgras or DISPERSAL . . . . . . . . . . . . . . . o n o e o e c o o o e e a a a o I 0 e o o inApproach to Diffusion . . . . . . . . . Page 10 22 28 32 44 120 126 Other Components . . . . . . . . . . . . . . . . . . . . . . 136 Page Timing of Events . . . . . . . . . . . . . . . . . . . . 136 Crop Growth . . . . . . . . . . . . . . . . . . . . . . 138 Wheat Resistance . . . . . . . . . . . . . . . . . . . . 139 Spring Adult Emergence . . . . . . . . . . . . . . . . . 140 Sexual Maturation . . . . . . . . . . . . . . . . . . . 142 Oviposition . . . . . . . . . . . . . . . . . . . . . . 144 Adult Mortality . . . . . . . . . . . . . . . . . . . . 146 MODEL VALIDATION . . . . . . . . . . . . . . . . . . . . . . . . 148 ' Time Increment . . . . . . . . . . . . . . . . . . . . . . . 148 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . 148 Standard Parameters . . . . . . . . . . . . . . . . 150 Alternatives to Random Dispersal . . . . . . . . . . . . . . 158 SIMULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 162 The Effect of Resistant Wheat . . . . . . . . . . . . . . . 162 Temporal Patterns . . . . . . . . . . . . . . . . . . . . . 164 } CLB Emergence . . . . . . . . . . . . . . . . . . . 164 Planting Date of Oats . . . . . . . . . . . . . . . . . 166 f Wheat Growth . . . . . . . . . . . . . . . . . . . . . . 168 Spatial Patterns . . . . . . . . . . . . . . . . . . . . . . 170 l Absolute Acreages . . . . . . . . . . . . . . . . . . . 171 Relative Acreages . . . . . . . . . . . . . . . . . . . 172 Field Size and Shape . . . . . . . . . . . . . . . . . . 173 Field Locations . . . . . . . . . . . . . . . . . . . . 175 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 SUMMARYANDCONCLUSIONS.................... 183 LITERATURECITED........................ 186 APPENDICES Optimization Program for 1977 Compartmental Analysis . . 194 Data for Fields at Galien in 1976 and 1977 . . . . . . . 196 Remote Sensing Data . . . . . . . . . . . . . . . . . . . 200 Field Maps . . . . . . . . . . . . . . . . . . . . . . 222 Program SEARCH . . . . . . . . . . . . . . . . . . . . . 228 Contour Plots . . . . . . . . . . . . . . . . . . . . . . 233 Sticky Board Trap Data . . . . . . . . . . . . . . . . . 241 Spatial Dynamics Simulation Model . . . . . . . . . . . . 244 Spatial Configurations for Simulations . . . . . . . . . 252 Degree-day Accumulations Near Galien . . . . . . . . . . 278 vi LIST OF TABLES Table Page 1. Population parameters estimated for research plots at Gull Lake . . . . . . . . . . . . . . . . . . . . . . . 12 2. Examples of general (regional) and unique (local) factors affecting year-to-year (within-site) changes and site—to-site (within-year) differ— ences in density of a population, and the direction of influence which dispersal may have on the action of these factors . . . . . . . . . . . . 27 3. Weather variables considered in the analysis of crop preference at Gull Lake, 1967- 77 . . . . . . . . . 37 4. Regional total and mean density of eggs in suscep- tible wheat and oats in the Galien study area . . . . . 42 5. Intercrop dispersal and mortality rates (per °D > 48(F)) estimated by compartmental analysis, and the observed initial and mean values used in the analysis . . . . . . . . . . . . . . . . . . . . . . . . 49 6. The range and coefficient of variation of adult and egg densities in the fields in the Galien study area, 1975-77. Densities are number per 60 cm of grain row (1 ft ). Wheat is susceptible only . . . . . 55 7. Variables found to be significantly related to adult and egg densities in a multiple regression spatial analysis of the 1977 Galien data . . . . . . . . . . . . 67 environmental features using hierarchical cluster l l E 8. Final clustering of Galien-area fields based on their 1 analysis, and mean CLB densities within the clusters . . . . . . . . . . . . . . . . . . . . . . . . 74 f 9. Principal environmental variables contributing to the discrimination of the highest density class from all other classes . . . . . . . . . . . . . 79 10. The number of beetles that were to be released in plots of various sizes to attain various densities . . . . . . . . . . . . . . . . . . . . . . . 95 vii Table 12. 13. 14. 15. Bl. 32. C1. 31. Total daily catch of incoming and outgoing CLBs on sticky board traps in field 1022 S- wheat and 1024 R- wheat (16 traps per field) . . Vertical distribution of sticky board trap catch (proportion of total (n) caught on that side of trap) for both spring and summer beetles . Calculated mortality rates of adult CLBs in each crop . . . . . . . . . Adult density, change in total field population (AN), total mortality (M) and total immigrants (IN) and emigrants (OUT) estimated from sticky board trap catches, for frequent intervals in’field 1022 S-wheat. Also given are AN+M and IN-OUT . Relative density of cereal leaf beetles in each of five overwintering habitats at Galien, 1974- 77 (modified from Casagrande §t_al. 1977) Observed and predicted values of several validation criteria for run 11 of the simulation model (1977, high diffusion rates) Adult and egg densities in small grain fields at Galien in 1976, with field acreages, cell assignments in spatial analysis, and hierarchical cluster membership based on environmental features . . . . . . . . . . . . Adult and egg densities in small grain fields at Galien in 1977, with field acreages, cell assignments in spatial analysis, and hierarchical cluster membership based on environmental features . . . . . . . . . . . . Remote sensing data . . . . . . . . . . . . . . . . . . Catch by date of incoming and outgoing cereal leaf beetles on sticky board traps placed along each border of six fields at Galien in 1977 . . . . . . . . . . . . Degree-days > 48 (F) accumulated at Glendora, Michigan (Berrien County) during 1976 and 1977 . . . . . . . . . viii Page 102 104 105 107 141 154 196 198 200 241 278 10. 11-13. LIST OF FIGURES Page Egg and larval densities (log scale) in the Gull Lake research plots from 1989 to 1978 . . . . . . . 11 Key factor analysis of Gull Lake oat data (K: SG, k = larval survival, pupal survival, k = a ult survival and fecugdity, k = egg survival, k = survival from T. julis parasitism, k = survival from ichneumon parasitism) . . I . . . . . 16-18 The quadratic relationship between ln(SG) and ln(ASF) in oats at Gull Lake, 1967-77 . . . . . . . 20 The residual of E /Ew , after controlling for CR, WPREC and TEMP Byw multiple linear regression, plotted against the total regional egg popu— lation, T = To + Tw’ at Gull Lake during 1967- 77 . . . . . . . . . . . . . . . . . . . . . . . . . 40 A three compartment model of intercrop movement . . . 45 Solutions to the compartment models of intercrop movement at Galien, 1975- 77 . . . . . . . . 50-51 Aerial photograph of the research area near Galien, MI . . . . . . . . . . . . . . . . . . . . 58 Complete linkage hierarchical tree for the R— wheat fields at Galien in 1977, based on 76 environmental features . . . . . . . . . . 73 Ordination of the 1977 R-wheat fields on the two principal discriminant axes. Numbers refer to adult density classes (5 is highest). Stars indicate cluster centroids . . . . . . . . . . 82 Mean adult density at frequent intervals in three intensively sampled fields at Galien in 1977. 95% confidence intervals are indicated by (+) . . . 87-88 ix Figure 20. 21. £22. £23. 24 25m 26L 27. 2t}. Page Contour plots of adult density in R-wheat fields 722 and 236 and oat fields 235,613 and 612 (A- E, respectively) at Galien in 1977. Plotted daily beginning 10 May . . . . . . . . . . . . 92-93 Crop moisture in two of the fields used in the sticky board trap study . . . . . . . . . . . . . . 100 The path taken by a dispersing beetle in grass (1976 Gull Lake data from E. P. Lampert) . . . . . . 113 Diffusion rate (inz/min) in grains as a function of crop height . . . . . . . . . . . . . . . . . . . 116 Crop height in two of the fields used in the sticky board trap study . . . . . . . . . . 116 Block diagram of a model for the distribution and abundance of the cereal leaf beetle . . . . . . 124 Probability density for the location after t minutes of a beetle starting out in the center of a 10- acre field given1n a diffusion rate D such that 2Dt = 2 x 10 . . . . . . . . 129 Probability density for the location after t minutes of a beetle starting out half way toward each edge from the center of a 10- acre field given a diffusion rate D such that 2Dt = 2 x 1061 . . . . . . . . . . . . . . . 129 Probability density for the location after t minutes of a beetle starting out half way toward each edge from the center of a 10- -acre field given a diffusion rate D such that 2Dt = 4 x 106 m2 . . . . . . . . . . . . . . . . 130 Mean probability of being outside of a 10-acre cell as a function of time (t) and the dif- fusion rate (D) . . . . . . . . . . . . . . . . . . 131 Mean degree-day accumulations at Eau Claire, MI for the period 1931-60 . . . . . . . . . . . . . . 137 Crop growth curves for the standard simulation . . . . 137 Emergence of overwintered cereal leaf beetles as a function of °D > 48(F) . . . . . . . . . . . . . . 143 w— *——y ww—rw iv- Figure Page 33-34. Oviposition rates in wheat and oats as a function of °D > 9(C) since first egg . . . . . . . . . . . . 145 35. Instantaneous survival rate of adults as a function of temperature . . . . . . . . . . . . . . . . . . . 147 36. Total regional adult population in each crop in 1977 vs °D > 48, with simulation results using standard parameter values and high diffusion rates . . . . . . . . . . . . . . . . . . . . . 152 37. Observed and predicted total regional adult popu- lation in each crop in 1976 vs °D > 48 . . . . . 152 38. Observed and predicted adult densities in individ- ual S-wheat fields in 1977 . . . . . . . . . . . . . 155 39. The coefficient of variation of predicted adult densities in S-wheat fields through the season . . . 155 40. Total regional adult population in each crop in 1977, with simulation results using reduced absorptivities and lower diffusion rates in nonhost habitats . . . . . . . . . . . . . . . . . . 160 41. Total regional adult population in each crop in 1977, and simulation results with host crops attractive and diffusion rates reduced in other habitats . . . . . . . . . . . . . . . . . . . 160 42—43. CLB emergence shifted 50° D > 42 earlier and later . . . . . . . . . . . . . . . . . . . . . . 165 44—45. Oats planted 100°D > 42 earlier and later . . . . . . 167 46—47. Wheat growth advanced and delayed 100°D > 42 . . . . . 169 Dl-‘D6a Field maps 0 o o e o I o o o o o o o a e o e o o e o a 222-227 Fl-FIOB. Contour plots 0 I o o o o o o o o o o o o e e o e o a 233-240 11—126. Spatial configurations for simulations . . . . . . . . 252-277 xi wfi-Y‘Vvv‘v'vuw 'fi— INTRODUCTI ON The science of population dynamics broadly deals with the dis- txribution and abundance of organisms. Specifically, it is concerned saith the processes leading to changes in these attributes for a given population. Andrewartha and Birch (1954) have pointed out that "dis- tribution and abundance are but obverse and reverse aspects of the same problem." Several authors (Iwao 1971; Levin 1976; Watt 1962; Wiens 1976) have noted, however, that most theoretical and experi- mentzil approaches to population dynamics have ignored the spatial aspects of the problem, choosing to deal with populations as if they exisI:ed at single points in space. This has been true in the case of the (zereal leaf beetle, Qulgma melanopus (L.),1 an introduced pest 0f small grains which has received considerable research attention in recerrt years. Several population models of this species have been constructed (Ruesink 1972; Gutierrez §£_al. 1974; Tummala gt_al. 1975; Lee g£_31. 1976; Fulton 1978), but without exception they are Purely temporal models. The efforts directed by previous workers at understanding the adult dispersal process (Ruesink 1972; Casagrande 1975) reflect their reCognition of the importance of this phenomenon in the life history and Population dynamics of the cereal leaf beetle. The spatiotemporal ______________________ 1Coleoptera: Chrysomelidae dynamics of this species has not been systematically addressed, how- ever, and many questions remain unresolved. For example, Fulton (1978) recently emphasized the overriding influence of the rate of rnovement of adults from winter grains to spring grains on the synchrony <3f his within-generation population model with actual field events. lie noted that the lack of an understanding of this process rendered janractical the use of his model in an on—line control mode. This thesis discusses, with reference to the cereal leaf laeetle, the difficulties and deficiencies inherent in a purely tem- poral approach to population dynamics and suggests possible solutions to the problem. An hypothesis regarding the spatial dynamics of this species is proposed and is examined in light of existing data drawn fron1 many years of field research. Further analyses and field observations were conducted to supply missing information. An apprwaach to simulating the spatiotemporal dynamics of the cereal leaf beet 1e in a regional crop system is outlined, and the model's imple- mentrition and evaluation are described. The role of specific spatial and temporal structures of the environment in determining the dis- tribution of beetles throughout a region and their abundance in particular fields is examined via simulation. The model's application in a pest management program and its relevance to theoretical ques— tions in population dynamics are considered. The word "region," as used in this thesis, refers to a geo- graphical area of at least several square miles, encompassing many small grain fields as well as the overwintering habitats and inter- field environment of the beetle. The scope of this approach is ,;_ 7 3': in 3‘“ ‘ L‘ ,,_!1— 1.- "'-~'.‘ 1- ‘, 1 "“hm‘ufl . . .. ~F 48(F) (100 and 133°D > 8.9(C)), respectively, for eggs and larvae, as reported by Tummala gt_al. 1975.3 3Guppy and Harcourt (1978) have recently reported the develop- mental times to be 157 and 247°D > 48(F) (87 and 137°D > 8.9(C)). 10 r I I l ‘l l I I l 1 1 “ 1999 1989 1910 1911 1912 1913 1914 1915 1918 1911 1919 ‘ YEAR ’ “-333 and larval densities (loglo scale) in the Gull Lake re- . “search plots from 1967 to 1978. 12 Table 1.--Popu1ation parameters estimated for research plots at Gull [ Lake. L Year Eo Lo Po Sp STj SI EW Lw £ 1967 29.47 18.26 7.24 0.33 1.0 1.0 2.53 1.27 i 1968 91.82 69.57 51.13 .49 1.0 1.0 4.39 1.02 1 1969 318.12 170.66 34.31 .75 .993 1.0 346.94 142.00 ; 1970 167.48 118.11 21.62 .65 .783 .9997 167.13 63.51 I 1971 230.36 90.26 13.13 .66 .885 .998 20.75 1.30 1972 67.56 20.15 7.02 .43 .55 .987 9.06 3.84 ‘ (1973 8.96 3.71 1.13 .16 .26 .92 1.89 1.13 I 1974 16.59 5.84 0.63 .35 .47 .91 0.66 0.02 ' 1975 1.18 0.18 0.28 .65 .82 .88 0.95 0.26 1976 6.19 0.74 0.23 .28 .40 .88 0.41 0.26 1977 28.09 1.10 0.18 .20 .32 .91 9.09 2.64 E0 = eggs/ft2 in oats (seasonal total) L0 = larvae/ft2 in oats (seasonal total) P0 = pupae/ft2 in oats (seasonal total) (n p = pupal survival in cats (adults emerging/pupae, from soil samples) 51.5 = Survival from parasitism by I. julis (from soil samples) SI = Survival from parasitism by ichneumons (Diaparsis spp. and L. curtus) (from 5011 samples) 15' a eggs/ft2 in wheat Liv" larvae/ft2 in wheat WV W— vwv—vxw—v 13 Such density estimates are intended to represent the number of individuals entering the stage. This is true, in fact, only when any Inortality occurs at the end of the stage. When the mortality pattern is otherwise, the density estimates (and stage specific survival rates calculated from them) are in error. An analysis of the nature of these errors is given by Sawyer and Haynes (1979). Of the Gull Lake data, one might well ask why the density of larvae fluctuated so dramatically during the 11-year observation period. Could knowledge of the causes lead to predictions of the (direction and magnitude of population change? "Certainly there is 110 field of population management in which the forecast of densities is more vital than in applied entomology" (Voute 1971). As Watt (1961) has proposed, a model for a population in a closed system may take the form: N(t+1) = N(t)'Sl'Sz'°'Sn'Pf'F (1) where N(t+l) is the density of insects of a particular life stage in generation t+1, N(t) is the density of this same stage in generation t, the Si are the proportions surviving through the ith of n life stages, Pf is tme preportion of adults which are female, and F is the mean fecuruiity. A model of this form for the cereal leaf beetle is: L(t+l) = L(t)-SL-SP-ASF-SE (2) where L(t+1) and L(t) are the larval densities in years t+l and t, 3L. SP and SE are the survival rates for larvae, pupae, and eggs, and w ‘vwwv—vvw—w 14 ASP is a catch-all factor representing adult survival, sex ratio and fecundity. The selection of the larval stage as the one on which to base the model was not fortuitous. Watt (1961) recommended the adult stage and Morris (1963) preferred the egg stage in their applications. Actually, the life stage used to calculate the index should be that which is most effectively sampled and which provides a useful result. For the cereal leaf beetle, the larval stage is relatively numerous, immobile, and visible, and is more easily, accurately, and precisely sampled than other life stages. The larval stage is also of interest as it causes most of the economically important crop damage. Equation (2) may be rewritten as L(t+l)/L(t) = SL~SP-ASF-SE (3) which, in effect, decomposes the generation survival (SG), or trend index, L(t+1)/L(t), into a product of the survival rates for each life stage. Larval survival could be broken down further into the survival rates for each of the four larval instars, but reliable age- specific data are not available for the entire 11 year period at Gull Lake. The term ASF, which covers a time span of approximately July to April, could also be partitioned into its components, but, again, the necessary data are lacking. ASF was simply calculated as a "residual" term from a knowledge of summer adult density and resultant egg density in the spring: ASF = eggs produced/adults emerging from PMPation. The true significance of this factor will be examined in detail laelow. While pupal survival (SP) was estimated quite directly M‘fisfl. .' - .=._. .___v c v 15 by examining pupal cells from soil samples, egg and larval survival rates (SE and SL) were calculated as the ratio of density estimates for successive stages. These estimates are subject to complex errors related to the actual magnitude and timing of mortality within the stage (Sawyer and Haynes 1979). The model (3) can be transformed into an additive one by taking the logarithm of each side of the equation: ln(SG) = ln(SL) + 1n(SP) + ln(ASF) + ln(SE) (4) Two approaches may now be taken to analyze the relative con- tribution of variations in each of the survival components to vari- ation (and thus, prediction) of the trend index. The first comes from recognizing equation (4) as the key-factor relationship of Varley and Gradwell (1970): K=k1+k2+k3+k4 (5) Where K is the logarithm of the trend index, k = 1n(SL), etc. Key 1 factor analysis is essentially visual and subjective. Inspection of Figs. 2-7 shows that k3, representing ASF, appears to be the key factor, and k , or SL’ is also of some importance. Factors k5 (Fig. 6) l and ' ' ' 1 or k6 (Fig. 7) are 1n(STj) and ln(SI), where STj 15 the surV1va ( escape) from parasitism by the larval parasite I. julis and SI is 4 survival from ichneumons Diaparsis spp. and Lemophagus curtus TowneS- These parasites kill the pre-pupa after it forms its pupal cell in M 4Hymenoptera: Ichneumonidae 16 1,,vng and fecundit , k ““«Key factor analysis of Gull Lake oat data (K - S , k ‘ hasitism). 1I S LRRVRE ‘ K K1 ; l l 1 l I I I I 1 1 1968 69 10 11 ‘72 73 74 15 76 71 "t PUPRE .,, ."v,: ;‘5 K ,1 id 'K2 1 I l I I Y r I I I~ was as 70 'n 72 73 74 75 vs 77 . . = pupal survival, k Iadult surl.pnf = egg survival, 3k; a survival julis parasiti m, k6 = survival from ichneumon RDULTS 18 T. .JULIS ICHNEUMUN I 08 19 the soil, and their effects are actually already represented in SP' Factors k5 and k6 are not, therefore, additive contributors to K, but their relationship to K is of interest nonetheless. A criticism of key factor analysis is that it fails to account for intercorrelations among survival components. To avoid this prob- lem, at least in part, a partial correlation analysis (Nie e£_al. 1975) was performed on the components of equation (4). In partial correlation analysis, the effects of intervening variables are first removed from both the dependent and independent variables, by linear regression, before a correlation is determined. An assumption of correlation analysis is linearity in the bivariate relationships of the variables. Plots of the variables showed a nonlinear relationship only between ln(SG) and ln(ASF), namely, a quadratic one (Fig. 8), so the independent variable was transformed by (ln(ASF)—4.25)2 prior to analysis to linearize the relationship. The zero-order partial correlations of ln(SG) with ln(SL), ln(SP), (ln(ASF) — 4.25)2 and ln(SE) are, respectively, .757, -.071, .774 and .079 (significance levels are .006, .423, .004 and .414). Thus, the survival component most correlated with changes in the trend index is ASF. The factor With the highest first-order partial correlation with 86’ after con- trolling for ASF, is SL (r = .740, p = .011). No higher-order Partials were significant. The importance of these results is made clearer by looking at the simpler, within-generation analogue of equation (4), which omits the ASF term: 20 3’"? 3:0 410 LNI 93F) . 15.1113. 1967-77. l 5.0 emu relationship between ln(SG) and ln(ASF) in cats —-—~ Y“C~<—e -___~,_ V... ‘6‘: -.‘xr—---.‘.- R-~w- .— E E i 1 i : 21 ln(S w) = ln(SE) + ln(SL) + ln(Sp) (6) where SW is the within~generation survival (adults emerging from pupation/eggs laid in the same year). The simple correlations of ln(Sw) with ln(SE), ln(S , and ln(SP) are, respectively, .755, .578, L) and .728 (all significant at p < .05). Two points may be made about these reSults. First, the high correlation of Sw with SE indicates that egg parasitism by Anaphes flavipes Foerster5 may be as important in cereal leaf beetle population dynamics as is larval parasitism by the other three species of parasites (although certainly other factors enter into SE and SP). However, very little research has been done on the field biology or parasite/host dynamics of A: flavipes. It is not even known how the parasite overwinters or if it requires an alternate host late in the season, which seems likely. It has been suggested, on theoretical grounds, that Anaphes is a less effective parasite than I, luli§_(Haynes 1973), but the question is clearly not settled. Secondly, it is interesting that the two factors (ASP and 8L) most highly correlated with the population trend index, S , are not correlated with within—generation survival, G SW' Instead, SE Can be interpreted in terms of spatial effects and adult dispersal. and SP seem to influence SW the most. These results 5Hymenoptera: Mymaridae. F""‘. N < _' < _ W.“ B‘- _ . __ 4 . THE ROLE OF DISPERSAL IN POPULATION DYNAMICS Morris (1963) modified Watt‘s (1961) model (equation 1) by iricluding an additional term to consider losses from or additions to t116 system due to dispersal of the adult stage (spruce budworm moths): NE(t+1) = NE(t)'SE'SL'Sp°SA'Pf'F t ND (7) vfliere ND is the density of eggs added to or subtracted from the exPected NE(t+l) as a result of moth dispersal. This model has a difficulty in that it suggests that it is tile egg stage that disperses, since eggs are directly added to or Stflatracted from the system. A more realistic model would be: NE(t+1) = NE(t)-SE-SL-SP-SA'Pf'F-p + NA‘°SA'-Pf"F' (8) where p is the proportion of surviving adults which do ngt_disperse 01L11: of the system, and SA', Pf' and F' are defined as for equation (1) but: apply to NA' adults which disperse intg_the system. Clearly, as p becomes quite small and/or NA' becomes quite large, the character— istics of the immigrant segment of the population take on increasing importance and those of the "resident" portion of the population lose importance in determining the trend index, SG = NE(t+l)/NE(t). Further complexities are introduced if the immigrants are derived from a number of sources with each group possessing very different 22 fif ‘. -_-_ 23 characteristics or if some earlier life stage (or more than one life stage) disperses. In the case of the spruce budworm, three stages may disperse: lst instar larvae in the fall, 2nd instars in the spring, and adults in the summer. Morris' (1963) approach to the problem of dispersal was to incorporate the net effect of dispersal gains and losses into the age—specific survival rates peculiar to that site. Ultimately, even the additive term N was dropped from the model as D being inseparable from SA' Morris, then, did not take on the com— plexities of a spatial approach to dispersal in which the study site is but one component in a heterogeneous spatial matrix of sources and sinks for dispersing individuals. A recent modeling effort by Holling 33 El' (1976) takes dispersal among 265 spatial compartments into account, but at the cost of considerable within-site detail. Returning to the finding that ASP and SL are important deter- minants of the trend index for a single-site cereal leaf beetle popu- lation model at Gull Lake, while SE and Sp are most highly correlated Ivith within-generation survival, we can now understand these results iriterms of the life history of the species and the characteristics <>f its agricultural habitat. Summer adults leave the field from \VIIich they emerge from pupation, and move about in the environment-— ‘p<>ssib1e over a large area. Following an overwintering period in HIJOdlots, fence rows, etc., in spring the beetles again move about before entering grain fields. Meanwhile, the grain fields themselves h8Ve2"moved," because a field will not usually be planted to the same Crop in two successive years. Thus, the net effect of this thorough Mixing is that the entire population disperses out of a field and it '—— aw-“ _-_‘—,_.-—..- ~..... ‘, 24 may be an entirely different, heterogeneous, group of beetles which returns to the nearest field in the next year. This redistribution shows up as variations in the variable ASF. ASF actually represents several survival and redistributional components, as well as sex ratio and fecundity: ASF = Ssu-Rsu°Swi-SSP'RSP°Pf°F (9) where su, wi and sp subscripts indicate summer, winter and spring, 8' s are survival rates for the periods indicated, and R's are factors accounting for gains or losses due to redistribution occurring during the period indicated (this assumes that the regional population is homogeneous with respect to fecundity, sex ratio, and survivorship; heterogeneity in these components adds to the complexity). A knowledge of which of these factors are primarily responsible for observed variations in ASP is desired, but the values of these separate com— ponents are not available for the entire period 1967—77 at Gull Lake- Casagrande (1975) concluded that overwintering mortality in the $0.11 (Swi) was unrelated to cold exposure. It seems likely, then, that ASP is influenced primarily by events during the summer and spring dispersal and ovipositional periods. A multivariate analytical aPproach may shed some light on the identity of important factors, 131-R an understanding of the biological processes must come from experimental studies. Deductive submodels based on assumptions about the biological processes involved may be of use in guiding research and in constructing simulation models (Eberhardt 1970; Watson 1971; Watt 1962; Varley and Gradwell 1970). 25 Because all of the redistributional phenomena are incorporated into ASF, it is to be expected that ASF will be highly correlated with the trend index (measured at one place) of this species in which 100% of the population disperses. Another effect of total redistribution is to obscure, or minimize, the influence of processes operating on a field scale, such as egg and larval parasitism, on the year—to—year fluctuation in larval density in a given location. Because of spatial heterogeneity of both the parasite and cereal leaf beetle populations, parasitism may vary as much from field to field as from year to year.6 Para- sitism might, therefore, show little correlation with the change in beetle density after redistribution, even though it has a considerable impact on the within-generation (within-field) survival of the beetle. Larval survival, however, is not associated with parasitism and may be affected primarily by factors operating on a regional scale, such as temperature and rainfall. This survival component, then, should affect the entire regional population similarly. The factors, then, which determine the changes from year to year in the population density at a particular site may be visualized as falling into two categories: (1) those which are general, applying (n1 a regional scale (such as weather) and (2) those which are local, or unique to a particular field (such as local parasite density). Factors contributing to site to site differences in density in a 6In 12 oat fields in a 16 mi2 area of Berrien County in 1976, egg parasitism ranged from 6% to 50% (Sawyer 1976b) and in 1977 ranged from 13% to 80% in 7 fields (Sawyer 1978). Similar spatial variation was found for larval parasitism. 26 particular year may also be classified as being either general, such as the relative acreages of winter and spring grains in a region (Casagrande 1975, p. 50; Ruesink 1972, p. 29), or unique, such as a field's planting date or its nearness to overwintering sites. Dis- persal interacts with this complex of factors by tending to "homogenize the effects of local uniqueness" (Levin 1976), or, for some factors, by increasing the effects of local uniqueness. Dispersal may itself be density dependent, acting to increase or decrease density differ— ences from field to field through intraspecific attraction or repulsion. Dispersal may initially increase a field's population with immigrants from nearby population sources, but if dispersal continues to operate, site to site differences may become homogenized. 'These ideas are summarized in Table 2. General factors are able to contribute to site to site differences in density only through dis- laersal. In the absence of dispersal, the only factors contributing tc) site to site differences would be those affecting year to year fltictuations in density within the isolated fields. It is obvious that in the extreme case of total dispersal of a Slaecies inhabiting a patchy environment, such as the cereal leaf beetzle, Morris' (1963) approach to studying population dynamics is Partricularly unproductive. No amount of on-site study of survival rates will lead to an understanding of long—term population dynamics or tile ability to predict the density at that site even one generation into the future. Actually, in any situation, the appropriateness of Such a1: approach is simply a matter of degree depending on how much an Observed "survival" rate includes gains and losses to the system 35 a result of dispersal. 27 l§72.--Examples of general (regional) and unique (local) factors affecting year-to-year (within-site) changes and site-to- site (within;year) differences in density of a population, and the direction of influence which dispersal may have on the action of these factors: (-) indicates an averaging, countering, or minimizing influence, (+) indicates an emphasizing or maximizing influence. General Unique Weather Local parasitism and predation (-) Regional pest/ Food quality (-) parasite densities Population Quality Density (1) Relative crop acre- Attractiveness of ages in region site (+) Crop synchrony Location with respect to population sources (1) Previous population level (-) HYPOTHESES 0N CROP PREFERENCE AND DISPERSAL OF THE CEREAL LEAF BEETLE Ruesink (1972, p. 64) concluded, on the basis of surveying adult densities in all fields at Gull Lake in 1971, that Spring adults do not move from wheat to oats as has been assumed. It now seems clear that when beetles first emerge ; from overwintering, some portion of the population infests winter grains. The remainder stays in wild grasses or flies around in search of oats until the oats germinate and come up. Then the remainder infests oats. The portion in winter grains remains there, with the observed reduction in density primarily due to mortality not emigration. is not constant from year to year. It probably also varies between geographic regions. The primary factor affecting the portion entering winter grains seems to be the size of the ; plant as it comes through the winter. 1 I I I V i The portion of the population that infests winter grains He incorporated this hypothesis of a fixed preference of individual beetles for one crop or the other into his simulation lnodel of cereal leaf beetle population dynamics. The portion of the population preferring wheat immediately entered that crop upon 5 ‘ emergence, while the remaining ("oat") beetles were held aside until g Oats became available, at which point they were placed in that crop. He initially fixed the proportion preferring oats at .90, but found that the regional population trend index was sensitive to variations in this parameter, and also interacted with the relative acreages 0f tile two crops through density-dependent mortality effects. 28 29 Ruesink's (1972) assumption that there are two distinct types of beetles, those preferring oats and those preferring wheat (each type rejecting the other crop), seems an unnecessary complication (though not necessarily untrue: see discussion of host selection in Andrewartha and Birch 1954, pp. 509 and 691—3). A slightly more flexible assumption might have been that a population possesses a probability distribution of host preferences. For example, an average individual may tend_to prefer oats 3 to 1 over wheat or be 3 times more likely to enter oats than wheat. It can readily be shown that, under this assumption, the final distribution of beetles among cr0ps would be the same as if the population were composed of different proportions of individuals each with a fixed preference. The advan- tage to this probabilistic interpretation is that there is no need to hypothesize that different "kinds" of beetles exist. Each individ- ual may possess the same set of preferences or at least have prefer- ences drawn from a single distribution. Fulton (1978) made a different assumption about the crop Ixreference of beetles in his own simulation model, returning to the (alder picture of adults first entering winter grains and then moving 'to spring grains. He modeled this process by having the transfer from wheat to oats begin as soon as oats came up, and assumed that the rate of movement between crops followed a normal distribution with respect to degree-days. He found that the synchrony of observed and calculated density curves in oats was very sensitive to the Parameter determining when this movement occurred. 30 Actually, Fulton's (1978) model is equivalent to the proba- bilistic form of Ruesink's (1972) model, with a beetle possessing a fixed preference for wheat for a certain portion of its life, and then shifting to a fixed preference for oats for the remainder of its life. The portion of a beetle's life spent in oats in Fulton's model is equivalent to the expectation of entering oats in the former model, with both models making probabilistic statements about the overall distribution of activity in the two crops. The problem with both Ruesink's (1972) and Fulton's (1978) hypotheses about crop preference is that they propose a rigid rela- tionship (within a given year) describing the expected number of adults which will be found in each crop, irrespective of the spatial patterning of the crop environment. I propose as an alternative hypothesis that beetles not only move from wheat to oats, but may also move from oats to wheat. In ,general, they move continuously from field to field, most likely centering fields at random (as they chance to encounter them) and .leaving them at a rate related to their attractiveness.7 "Preference" :is thus seen not as an intrinsic property of the beetle, but rather 215 a property of the field. The beetle may respond, through its 7Fields, of course, may also be entered at a rate related to tflieir attractiveness, but studies have failed to find a chemical alrtractant for the cereal leaf beetle derived from the host crop (Jantz 1965). In a study with blowflies, MacLeod and Donnelly (1960) Observed random dispersal combined with a varying response to habitats entered by chance. An assumption of random movement greatly sim- plifies a simulation of the dispersal process. Even if there is some attraction to the crop, if the distance of attraction (area of discovery) is small compared to the size of a field and the spatial separation of fields, then an assumption of random dispersal should not lead to significant errors. 31 movements, to specific stimuli which vary from field to field, and the apparent preference for one crop over another is a function of the array of such stimuli that each crop presents. This array of stimuli, or "host quality," may vary from field to field as well as between crops (for example, planting dates of individual fields may vary). Since succulent young growth is more suitable for feeding and oviposition (Wilson and Shade 1966), spring oats will generally be a more "preferred" host than winter wheat. Beetles might then be expected to be less likely to leave oats, which would therefore act as a sink and accumulate higher densities. This hypothesis is simple in that it assumes only random inter—field movement and fixed behavioral responses to specific environmental stimuli, but allows for the possibility of dispersal interacting with environmental heterogeneity (the unique factors of 'Table 2) to produce the complex spatial pattern of densities observed over a large area. AN ANALYSIS OF HOST CROP PREFERENCE An analysis of crop preference and beetle dispersal can be Inade if the regional mean egg densities in oats and wheat are known. 'This analysis should be able to distinguish between the random-movement hypothesis of beetle dispersal and the hypothesis of a fixed crop preference or fixed sequence of movement from wheat to oats. The analysis deals with eggs rather than adult densities ‘because it is much simpler to establish total egg densities than 'total adult densities, since it is not known how long an adult is subject to sampling. It is assumed here that egg densities are directly related to adult densities. The total number of eggs in a region in oats and wheat are T = E0 X A (10) T = E x A w w w where T1 is the total regional number of eggs, Ei is the mean regional denSityof eggs and A1 is the acreage of crop i in the region. To/Tw isthe ratio of the two subpopulations. The ratio of densities in the two crops is 32 33 EO/Ew (TO/A0) / (TN/Aw) (To/Tw) x (Aw/A0) (TO/Tw) x CR where CR is the ratio of wheat acreage to oat acreage in the area. Rewriting this, we have CR = (ED/Ew)/(To/Tw). (11) Due to changing agricultural conditions, the crop ratio may vary from year to year, but the above relationship must always hold true. It is of interest to examine which component of the right-hand- side of equation (11) covaries most directly with CR. If CR increases from one year to the next, then either Eo/Bw must increase while To/Tw remains relatively constant, Eo/Ew must remain constant while To/Tw decreases, or there may be compensating changes in both com- ponents. Which of these situations actually occurs provides infor- mation on the nature of "crop preference" in the cereal leaf beetle. For example, if To/Tw remains constant despite a change in CR, it would imply that beetle distribution between the two crops is determined by some fixed preference of individual beetles for either Oats or wheat (i.e., there are "oat beetles" and "wheat beetles"). This would require some mechanism of attraction of the beetles to the proper crop, or would at least require that beetles entering the "wrong" crop leave without ovipositing. Thus, an increase or decrease in oat acreage relative to wheat would not affect the total number 0f beetles in oats or wheat. Such an acreage change would, however, 34 alter the density of beetles in the two crops, by concentration or dilution, so Eo/Ew would vary directly with CR. A similar pattern would result from the situation in which all beetles first entered wheat and then moved to oats. If the crop ratio changed, the relationship between the total number in each crop would not be altered, but the relationship between densities would. Alternatively, Eo/Ew may remain constant despite a change in CR. This would imply that beetles have no fixed preference for either crop, but rather disperse at random, entering and ovipositing in fields as they are encountered (this is not to say that the proba- bility of leaving a field, or the oviposition rate while in the field, lieed be the same for both crops). As oat acreage increases relative ‘to wheat (i.e., CR decreases), more beetles would chance to enter (bat fields and To/Tw would increase. The relative densities in the tnvo crops, however, would be unaffected as long as the relative Sanitabilities of the cr0ps remained constant. Thus, an inverse relationship between CR and To/Tw would be expected, with Eo/Ew remaining constant. While this analytical approach would seem to provide a neat Way of separating some of the hypotheses, such clear-cut results are urnlikely. If Ruesink's ”fixed" proportion preferring oats, or Ftnlton's time at which beetles moved from wheat to oats, or the relative suitability of the crops varied from year to year, then a Conflsination of varying TO/Tw and Eo/Ew could result for any of the tWpotheses. Factors contributing to variations might be the relative maturfiity of the two host crops and the synchrony of the insect with 35 its hosts. Some of the "background noise" in the analysis due to these factors might be controlled, statistically, by removing the correlation of the components of equation (11) with variables thought to affect these synchronies. Such variables might include degree- day accumulations above the developmental threshold of winter grain at various points early in the year, the difference in degree-day accumulations with respect to plant and insect developmental thres- holds, the amount of winter precipitation (which affects the growth of winter grains and planting date of spring grains), etc. After controlling for such effects, To/Tw should, theoretically, remain constant from year to year for both Ruesink's (1972) and Fulton's (1978) hypotheses. In contrast, EO/Ew should remain constant after adjustment if intercrop distribution is random. Two approaches may be taken in examining the components of variation in equation (11). One is to compare the relative variation in the two components To/Tw and Eo/Ew to determine which is more <:onstant. Another is to compare the partial correlation of CR with To/Tw and EO/Ew after controlling for the intervening environmental variables. The limiting factor in successfully making these analyses is; obtaining reliable estimates of the mean egg density for a large region for a number of years. The large-area study in Berrien County supplies such data for only three years, while the long-term data fromcull Lake are less extensive, representing just one or two fiefilds each year. For the purposes of this analysis it was assumed that: egg densities in the Gull Lake research plots at least reflected 36 the regional mean density, but interfield variation in densities is known to be large, and inferences about regional dynamics must be made cautiously. Gull Lake is located in the extreme northeast corner of Kalamazoo County, adjacent to both Barry and Calhoun Counties. The mean crop ratio for the three counties was used to represent the crop ratio for the Gull Lake area in any given year. These acreages were taken from various publications of the Michigan Crop Reporting Service. At Gull Lake from 1967 to 1977, the ratio of wheat acreage to oat acreage ranged from 1.3 to 3.3. For these same years, the coef- ficient of variation (C.V. = lOOS/i) for Eo/Ew was 89.6% and for Tony: it was 102.0%. Thus, neither Eo/Ew nor To/Tw was constant. Furthermore, neither quantity was significantly correlated with CR (r = .128 and r = -.255 for Eo/Ew and To/Tw, respectively).8 To adjust for variations in relative crop maturity and beetle/ host synchrony, a number of weather variables (Table 3) were considered in multiple regressions with Eo/Ew and To/Tw' Variables were chosen that were relevant to various aspects of crop development and beetle biology. For example, degree-days (°D) > 8.9 and 5.5 (C) represent meaningful time scales for the cereal leaf beetle and its hosts, respectively (Guppy and Harcourt 1978, Gage 1972), 55.5 and 111.1 °D > 8-9 (C) are points near the middle and end of spring adult emergence, etc. Some of the variables, such as JMAX, were recorded for other anaIYSes, but were included here also. Two variables were significantly related to variations in Eo/Ew: WPREC and TEMP. Together they accounted for 78% of the 8All correlation analyses were accompanied by examinations of r plots to check for violation of the necessary assumption that 1Variate relationships are linear. Scatt e the b 37 Table 3.--Weather variables considered in the analysis of crop prefer- ence at Gull Lake, 1967-77. Variable Description WPREC Total winter precipitation, Oct. - Mar. (cm) WAVG Mean winter temperature (Jan. - Mar.) (°C) WMIN Minimum winter temperature (Dec. - Mar.) (°C) SNOW Total days with snow on the ground :_2.54 cm (Oct. - May) FROST Last day of year in spring with min. temp. :_0°C TEMP Mean spring temp (April - June) (°C) RAIN Total spring precipitation (April - June) (cm) JMAX Max. temp., July of previous year (°C) SNOWAM Total days with snow on ground :_2.54 cm (April - May) AMINA Average min. Temp., April (°C) TEMPA Average temperature, April (°C) TEMPM Average temperature, May (°C) DDA Cumulative degree-days > 8.9 °C on April 1 DDM Cumulative degree-days > 8.9 °C on May 1 DDDA °D > 5.5 °C - °D > 8.9°C on April 1 DDDM °D > 5.5 °C - °D > 8.9°C on May 1 STR (TEMP/RAIN) JTR (TEMP/RAIN) DDSS °D > S.5°C at 55.5 0D > 8.9°C DD111 °D > s.s°c at 111.1 °D > 8.9°C 38 variation in Eo/Ew' The standard error of estimate, given by VMSE in the regression analysis, represents the standard deviation of the residuals of EO/Ew after controlling for WPREC and TEMP (Nie e£_313 1975, p. 331). Expressing this as a percent of the mean value of Eo/Ew yields a coefficient of variation (C.V.) for these residuals. The C.V. for EO/Ew after controlling for the two environmental factors was 47.2%. The partial correlation of EO/Ew with CR, after controlling for WPREC and TEMP, was .310 (p > .05, 7 df). Four climatological variables were significantly related to variations in To/Tw: WPREC, TEMP, DDDM and DDA. Together they accounted for 95% of the variation in To/Tw' The C.V. for To/Tw after controlling for these factors was 29.5%, and the partial correlation of To/Tw with CR was .165 (p > .05, 5 df). These results show that neither EO/Ew nor To/Tw is signifi- cantly correlated with CR, but suggests that Eo/Ew is possibly more ‘variable and more closely tied to variations in CR. These results :support the idea of a fixed crop preference, but are rather incon- cilusive. The problems of using single field density estimates to represent the mean regional density, and of using the mean crop ratio tfor'three counties to represent the ratio in the Gull Lake area, must be borne in mind. 'The relative suitability of a field, or entire crop, may be a furmmion of beetle density as well as crop maturity and other Variables. Casagrande (1975) developed this idea into a descriptive model of beetle distribution in wheat and oats as a function of the regicnial population level. He noted that negative interactions 39 between beetles (hypothesized by Helgesen in 1969) prevented the density of adults from exceeding some upper limit. In high density years these interactions would become important enough in the less pre- ferred wheat to drive a larger portion of the population into oats. In support of this, he pointed out that over a four-year period (1971-74) the highest ratio of adult density in oats to density in wheat occurred in the year with the highest population, and the lowest ratio occurred in the year with the lowest population. If Casagrande's (1975) model is correct, an examination of the Gull Lake data for 1967-77 might be expected to reveal a positive correlation between Eo/Ew and the total regional population, T = TO + Tw' This analysis was carried out by first regressing Eo/Ew on CR, WPREC and TEMP to control for their effects on variation in the dependent variable. At this point the partial correlation of .Eo/Ew with T was -.450 (p = .264, 6 df). The relationship, while .insignificant, is opposite to that predicted by Casagrande (1975). 111e residuals of Eo/Ew (after fitting CR, WPREC and TEMP), are plotted 111 Figure 9, where it is seen that any negative correlation is due tc> one year (1969) in which the densities were very high. For the 48(f). The equations were fitted to the data by supplying initial estximates of the unknown parameters, solving the system numerically bYeomputer, and comparing the curves generated to the actual data. New 13arameter values were then entered and a new solution obtained. 48 The parameters were varied systematically over their possible range (0.0 to 1.0) until the best set of parameter values was obtained. The criterion used for specifying the best fit was a weighted sum of squares. The deviation of each observed density from that predicted by the solution to equations (12) was squared and divided (weighted) by the mean density for that crop. The optimization function, U, was thus n A 2 _ 1 til (Xi(t) - xi(t)) /X1 (13) C II II MM i where n is the number of sample days, Xi(t) is the observed density in crop i on day t, ;i(t) is the predicted density, and ii = fi-tgl Xi(t). The parameter values were found which minimized U. Appendix A is a listing of the optimization program for 1977. For the other years (1975, 1976), the appropriate initial values (Xi(0)), arrays of observations (Xi(t)) and means (Ki) were substituted. In these ;years the model was converted into a two compartment model by setting C121 = 0‘12 = 0‘32 = 0‘23 = 0'0' The resulting parameter estimates are given in Table 5, and tire solutions to (12) are plotted in Figures ll-13 with the observed dtrtaw In both 1975 and 1976, the best fit to the data was obtained whtan G13 was set to 0.0, implying that no movement from oats to wheat ttnsk place. The rate of movement from wheat to oats was .15%/°D in 1975 and .19%/°D in 1976. The mortality rates were estimated to be .84%; and 1.04% per °D in 1975 and 1976, respectively. With 0L13 = 0.0, tfiuaciecline of the population in wheat simply follows an exponential Table 5.--Intercrop dispersal and mortality rates (per °D > 48(f)) estimated by compartmental analysis, and the observed initial and mean values used in the analysis. ——....._- 1975 1976 1977 012 - - .0003 021 - — .0017 613 0.0 0.0 .0023 631 .0015 .0019 .0024 023 - - 0.0 Q32 - - .0001 m .0084 .0104 .0048 to(°D > 48) 465 250 488 X1(o) 5.665 x 106 8.757 x 106 4.249 x 106 X2(o) - - 3.257 x 106 X3(o) 0.0 0.0 0.032 x 106 11 1.322 x 106 1.496 x 106 0.886 x 106 x2 - - 1.040 x 106 x 0.222 x 106 0.349 x 106 0.218 x 106 50 (D 1975 '0‘ a, e s-HHERT Z 53 + 0015 s a E .3 Cl: _. t— n O a... .J g C) N"1 c: w a: o r r I I 1 I 400 480 560 640 720 000 680 960 1040 DEGREE-DRYS > 48 (F) SH 1976 ‘0 .4 m 54: HHEHT 2 o 53 x cars .4 .J a: .3 Cl: .— D ,— _1 CE 2 O c: U m N D.4 l i l j 1 fi 300 400 500 600 700 000 900 1000 DEGREE-DRYS > 48 (F) Fig- Ila—13.--Solutions to the compartment models of intercrop movement at Galien, 1975-77. 51 ID 1977 (D 0 - Z 'd S HHERT E’. x 840158! -J u :1 + cars 2 _, u o m xl‘v .1 CE 8 u x x x x 5.. X _, m a . E g; m o—o X (D LLJ _- Q: * + u x ‘0' + + + u ‘ X x X + ' " .. ++ ‘EI‘ " “ - III 0 T l I fl I 400 500 600 700 800 900 1000 DEGREE-DRYS > 48 (F) Fig. ll-l3.--Continued. -“' "'T”T - - 1100 120 52 decay, with X1(t) = X1(0)e-(m + 0‘31”. In 1977, 013 was as large as 031, so beetles seemed as likely to move from oats to wheat as the reverse. Exchange between R-wheat and oats in either direction was minimal, as was movement from R-wheat to S-wheat, although the reverse was substantial. The mortality rate arrived at in 1977 was .48% per °D. The mortality rates obtained in the three analyses, .84%, 1.04%, and .48% per °D, agree well with those calculated by Casagrande (1975). In four years of field surveys at Gull Lake, the mortality rates, for the regional population as a whole, ranged from .368 to .710% per °D > 48. It must be remembered that a good fit of a model to the data does not ensure that the rates arrived at are correct, or that the hypothesized processes even occur. What this study shows is that the possibility of movement from oats to wheat cannot be ruled out, and that the rate of such transferral may be significant under certain conditions. These results support the dispersal and crop preference hypothesis presented earlier, and run counter to the model of beetles moving strictly from wheat to oats. It should be noted that if Ruesink's (1972) hypothesis is correct that "oat" beetles await the emergence of spring grains and then enter these directly, then the assumption of an initial pulse input to winter grains is violated. The subsequent input of beetles to spring grain could not be distinguished from transference from Winter grain. However, if Ruesink's hypothesis were true then a loss 0f beetles from wheat would be "primarily due to mortality not emi- graticnr'; one should not note an increased rate of loss with the aPPearance of spring grains. Exponential decay functions were fitted 53 to the 1976 S-wheat data for two periods: 205-262°D > 48, representing the time from peak density in wheat to the first observation of beetles in oats, and 262-570°D > 48, representing the period after beetles entered oats. Linear regressions of the form ln(y) = a + bx, where y is the regional population in S-wheat and x is degree-days, were highly significant (p < .001). The resulting decay rates were .48% and 1.40% per degree-day for the pre- and post-oats periods, respectively. This suggests that the beetles entering oats had come from wheat. SPATIAL ANALYSES OF REGIONAL DISTRIBUTION AND ABUNDANCE Defining the Uniqueness of a Field As discussed above, site to site differences in density within a particular year are due in large part to those factors which define a site's unique characteristics. To be sure, within-site fluctuations in population can lead to such differences if the separate fields are isolated and out of synchrony, but if dispersal plays a significant role in the dynamics then such asynchronies willbe minimized (Table 2). Instead, spatial and temporal features describing the uniqueness of the field will predominate and determine its density. The densities of cereal leaf beetles in the fields of the Galien study area (41.4 kmz) vary considerably (Table 6). The objec- tive of this analysis was to relate the seasonal total of adult activity (adult-°D) and egg density in individual fields to the principal spatial features of the environment immediately surrounding the fields, and to the relative maturity of the crop. It was hoped that this would lead to an understanding of the processes producing theeobserved variation in densities among the fields of a regional crop system. The data used are from the pubescent wheat pilot project con— chutted near Galien, MI. Only the 1976 and 1977 data were used, as 54 Table 6.--The range and coefficient of variation of adult and egg densities in the fields in the Galien study area, 1975- 1977. 2 Densities are number per 60 cm of grain row (1 ft ). Wheat is susceptible only. 1975 1976 1977 Wheat Fields: = 57 n = 50 n = 25 Adult-°Da Min. 3.3 5.7 44.0 Max. 599.8 203.2 245.7 C.V. 87.3% 93.4% 55.0% b Eggs/6O cm Min. 0.6 0.7 3.7 Max. 30.3 36.4 42.1 C.V. 89.6% 117.1% 87.3% Oat Fields: = 11 n = 12 n = 8 Adult-°D Min. 0.6 1.0 11.3 Max. 53.5 140.1 187.5 C.V. 84.5% 81.8% 87.9% Eggs/6O cm Min. 1.7 1.2 1.6 Max. 18.0 44.8 43.0 C.V. 67.4% 79.9% 116.1% aAdult-degree days, the area under the density vs. degree days > 48(F) curve, a measure of total activity. bArea under the curve divided by 180 °D > 48. 56 their analysis and summarization were more complete. Details of the data collection and analysis, the raw data and various summary statis- tics can be found in Sawyer (1976b, 1978). Appendix B gives the adult and egg densities in each field for the two years. The spatial features considered in this analysis were the size, boundary length, and shape of the field, the proportion of the total acreage surrounding the field belonging to each of several habitat types, and several measures of the heterogeneity of the surrounding environment. These will all be defined below. The measure of relative crop maturity was the crop height at the time of peak regional beetle activity in the grain fields, which corresponds very closely with the completion of beetle emergence from overwintering sites. Casagrande e£_31: (1977) described the principal overwintering habitats of the CLB. These were, in order of their importance at Galien: fence rows, woods edge, sparse woods, dense woods and crop- land. A detailed inventory of the spatial distribution of these habitats was needed from the Galien area for the present analysis. 'To this end, high altitude color-infrared (CIR) imagery was obtained on loan from the Southwest Michigan Regional Planning Commission in St. Joseph, MI. CIR photos (l:36,000) of the study area had been taken from a NASA RB-S7 aircraft on 3 June 1977. These photos were interpreted by the NASA Remote Sensing Office in the School of Urban Plaxniing and Landscape Architecture at Michigan State University under 57 the direction of W. R. Enslin.9 Figure 14 is a black and white copy of one of the photos which covered all but the westernmost 1/2 mile of the area. The 4 mi x 4 mi (6.4 km x 6.4 km) area was divided up into 1024 lO-acre (4 ha) cells .125 mi (.201 km) on a side. The area is thus represented by a matrix of 32 rows (N to S) and 32 columns (W to E). Each cell was further subdivided into 25 subcells of 0.4 acres (.162 ha). The imagery was examined with a microscope and each 0.4 acre subcell was classified by its dominant land use into one of five categories: (1) buildings, (2) water, (3) sparse woods, (4) dense woods and (5) cropland. The number (1 to 25) of subcells in each category was recorded for each lO-acre cell. Also measured and recorded were the total lengths (ft) of (6) fencerows and (7) edges of woodlots in each lO-acre cell. Appendix C gives the results of the photo interpretation. The habitat definitions given by Casagrande §£_a13 (1977) were slightly modified for this work. "Buildings" included roads and the yard-area around and between farm and resi- dential structures. Sparse woods were defined as wooded areas with a canopy closure of less than 75%, and shrubby old fields and idle areas. Dense woods had 75% or more canopy closure. Cropland com- prised all crops, pasture, grassy and weedy old fields, roadsides and field boundaries, and orchards. Fencerows included field boundaries and roadsides of trees or shrubs. Grassy fencerows were included with Funds for the interpretation were supplied by Dr. R. L. gallun (USDA, SEA and Department of Entomology, Purdue University) 113m monies granted for the pubescent wheat pilot project under USDA- ARS Project No. 3302-14800-001. 58 Fig. 14.--Aeria1 photograph of the research area near Galien, MI. 59 cropland, as these categories were difficult to distinguish on the photo and were considered to be similar habitats. An estimated mean width of 12 ft (3.7 m) was used to calculate the area occupied by fencerows; this area was subtracted from the cropland acreage. Woods edge was defined by Casagrande gt a1, (1977) as the perimeter of the woods, including 20 ft (6.1 m) into the woods. Accordingly, the area occupied by this habitat was calculated as its length x 20 ft and subtracted from the appropriate (sparse or dense) woodland. The distribution of habitat types for the entire 41.4 km2 area is: crop- land 69.6%, dense woods 14.3%, sparse woods 9.2%, woods edge 2.2%, fencerows 1.8%, water 1.7% and buildings 1.2%. For each of the years 1976 and 1977, the location of every small grain field was coded in terms of row and column coordinates. The acreage of a field was rounded to the nearest 10 acres (anything less than 10 acres was rounded up to 10), and an appropriate number of lO-acre cells were assigned to that field, approximating as closely as possible the location and shape of the field. These assignments are given in Appendix B and are mapped in Appendix D along with the locations of the woodland habitats and water. A computer program (Appendix E) was written to search around each field and calculate the total area occupied by each of the five overwintering habitats, S-wheat, R-wheat and oats within certain distances of the field's boundary. These distances, or radii, were .125, .250, .375 and .500 mi (.201, .402, .603 and .805 km). Acreages were tabulated separately for each of four quadrants, corresponding to the directions NW, NE, SW and SE so that directional effects, such 60 as that of wind, could be assessed. Thus 16 acreage values (4 radii x 4 quadrants) were calculated for each of the 8 habitats for the environment surrounding a field. If a field lay too near the edge of the study area, a search around the field would partially involve areas for which no habitat information was available. In such cases, if the missing area was 50% or less of the total for the quadrant and search radius in question, it was assumed that the habitat dis- tribution in the missing area was the same as that in the known portion. If the missing area was more than 50%, the habitat dis- tribution for that sector was declared unknown and coded as missing. Since the acreage within .500 mi also includes the acreage within .375 mi, and so on, these values are not independent. To correct this, the value for the next inner radius was subtracted from each value so that it represented only the area from one radius to the next. Since the area within a given distance of a field‘s boundary depends on the size of the field, all acreages were finally converted to proportions to characterize the distribution of habitat types. The independent variable set at this point consisted of 128 variables defining the habitat characteristics of the environment around each field. It was soon discovered that this exceeded the computational capacity of the computer programs available for analy- zing the data. The number of variables was therefore halved by com- bining radii .125 with .250, and .375 with .500 (mi). To this set were added the crop height at the time of peak regional adult activity, the acreage of the field, the length of its perimeter, and an index of "edge development" describing the degree -gwb—A—s 77777 61 of regularity of the field's boundary line. Edge development was defined as the ratio of the field's perimeter to the circumference of a circle having the same area as the field. That is, edge devel- opment = p/ZJEE where p is the perimeter and a is the area. This index is the same as the index of shore development used in lake morphometry (Welch 1948, p. 93). A circle has an edge development of 1.0 (the minimum). The higher the edge development index, the more irregular is the field's outline. The variables calculated thus far characterize the mean habi- tat pattern for any quadrant-distance sector. The variance of this pattern may also be important to CLB spatial dynamics. For this reason, several additional variables were considered. Spatial patterns have many properties, such as grain, patchiness, and connectedness (Pielou 1974, p. 193). Patchiness is a measure of pattern intensity, and is readily calculated from the remote sensing data set. Pattern intensity "is high if a wide range of densities is present; conversely, it is low if the density contrasts are slight" (Pielou 1974, p. 149). By density, I mean here the proportion of a lO-acre cell that is occupied by a given habitat. If woods occupied either 100% or 0% of any cell, then the contrast between cells is high, and woods may be considered a patchy habitat. If, instead, there were small pieces of woods in every cell, the contrast is low, and woods are not as patchy. Note that patchiness is therefore intimately tied to the size of the sample unit--here, a 10-acre cell. Pattern intensity is maximum when the mean patch size is the same as the size of the sample unit. Patchiness is, however, independent of density (Pielou 1974, p. 152). 62 That is, woods can be just as patchy when the total acreage of woods is high as when the total acreage is low. For a given density, however, patchiness is directly related to grain; a higher degree of patchiness must be associated with coarser grain, or larger patch size. Patchiness was defined for this study by Lloyd's index of patchiness (Pielou 1974, p. 150). It is the ratio of mean crowding (m) to density (m), where 3 ( 1) X. X.- $=j=1 J J (14) Q 2 x. i=1 3 Q 2 xj -J'=1 and m - Q (15). Q is the number of lO-acre cells in the area under consideration and xj is the acreage, in the jth cell, of the habitat for which patchiness is being calculated. The patchiness of sparse woods, dense woods and cropland were calculated for the areas within 0.25 mi of each field's boundary and between .25 and .50 mi. Patchiness was not defined on a directional basis, as were the habitat distributions, since this would have generated a prohibitively large number of variables. Furthermore, it was felt that measures of habitat variation, like patchiness, were not as likely to interact with wind or other direc- tional effects as were the mean amounts of various habitats, and the interpretation would be more difficult. 63 Some examples of the consequences of habitat patchiness are in order. Sparse woods is an important overwintering habitat, but makes up only 9.2% of the land area at Galien. If the distribution of this habitat was very patchy, then the probability of beetles finding sparse woods in which to overwinter might be reduced. For the more abundant dense woods and cropland habitats, a high degree of patchiness reflects uniformity within the 10-acre cells. For maximum patchiness of cropland, for example, each cell is either pure crop- land or it has none, creating a more homogeneous environment within the cells. Cropland, in such cases, will have fewer overwintering sites nearby. Woodlots are likely to be larger, denser, and have relatively less edge, therefore being less suitable for overwintering. Another measure of the spatial variability of the environment near a field is the habitat diversity. An appropriate measure of diversity in this situation is the Brillouin index (Pielou 1974, p. 304), H _ 1. log NT! ‘ 7" I I I I I NT 2 N1.N2.N3.N4.N5. (16) where N1 is the acreage (to the nearest integer) of the ith habitat 5 and NT = Z N.. The five habitats included were the usual woods i=1 edge, sparse woods, fencerows, cropland, and dense woods. The Brillouin index is used because the sum of acreages within a given distance of a field is finite, and this "collection” of acres is fully censused (Pielou 1974, p. 304). H was calculated for the areas within 0.25 mi and between .25 and .50 mi of each field's boundary, 64 as was Lloyd's index of patchiness. A high value of H would imply that the environment surrounding the field is more heterogeneous. A final measure of the spatial variability of the habitats around a field was the degree of ”woods edge development" (WED) within the same two annuli defined above. This was calculated in the same manner as edge development for the field itself. Thus, WED = L/Z/WF, where L is the total length of woods edge within the search area, and w is the total area occupied by woodlots, both sparse and dense. A high value for this index indicates that the woodlots are irregular in outline or are divided into small pieces. In either case, there is relatively more edge for a given acreage of woods. With these spatial variables in hand, two types of analyses were considered: multiple regression and cluster analysis. Regression Analyses The regression analyses were done first, before the data set had reached its final state. At this point the indices of patchiness, habitat diversity and woods edge development had not been added. The four radii had not been consolidated into 2, and the acreages had not been converted to proportions of the total area in each sector. Because there were too many variables (132) to consider all at once, different subsets of the variable set were dropped from the analysis, Iiepending on the crop under consideration. The decision on which ‘Variables to drop was based on preliminary runs with one of the radii excluded and which indicated that certain variables were unlikely to I”? important. When analyzing densities in S-wheat fields, the acreages 0f cr0puand and oats near the fields were omitted as independent 65 variables. When analyzing densities in R-wheat fields, cropland and dense woods were omitted. Note that for R-wheat only adult densities were analyzed since egg densities are strongly influenced by the degree of resistance the wheat in a particular field exhibits, which was observed to vary. Adult densities are less reduced by pubescence (Sawyer 1976b). When analyzing densities in oat fields, acreages of S-wheat and oats were omitted. The former was omitted because there was only one oat field within .5 mi of an S-wheat field in 1977. The objective of the multiple regression analysis was to find a small set of variables which accounted for the observed variation in adult and egg densities among the fields, and could be used to predict the density in particular fields. The regression analyses were done using the 1977 data to obtain the best fitting models, which then were tested with the 1976 data. Stepwise forward regres- sions were performed using the Statistical Package for the Social Sciences (SPSS) (Nie et_§1, 1975). A maximum of five variables were admitted for the analysis of wheat fields, and two for oat fields, to prevent saturation of the model, which occurs when too few degrees of freedom remain in the residual term. The results of the multiple regression analyses varied con- siderably depending on the dependent variable under consideration, and might best be described in general terms. In all cases it was pos- Sible to define a set of five or fewer independent variables which accounted for 80% or more of the variation in densities among the fields. All distances, from .125 to .500 mi, contributed significant independent variables. All directions contributed significant 66 variables, although the southwest was most often selected (Table 7). Wind velocity was recorded in 1977 when each sample was collected. Based on calculations of mean velocity x frequency of occurrence, the winds during April and May were mostly from the southwest, west, south, and southeast, in order of predomination. These general results suggest that beetles may move considerable distances to arrive at the host crop, and wind may possibly be a factor of influ- ence. More specifically, for S-wheat fields, sparse woods lying to the southwest contributed positively to both adult and egg densities (Table 7). Fence row acreage was also related to adult densities. Dense woods and woods edge nearby had a negative influence on egg densities, while if farther away they had a positive influence on both adult and egg densities. These results are at first confusing, but make sense in light of simulations described later. In these simulations, woods surrounding a field at some distance act as barriers to emigration, keeping beetles in the field later into the season. However, if too close to the field they may eliminate more important overwintering habitats from the area immediately around the field and thereby reduce early population levels. For R-wheat fields, the most important variables were acreages of S-wheat and oats. These may serve as sources of immigrants, partially countering the higher loss rate from the resistant host. Similarly, for oats, the most important variable was the acreage of R-wheat, a likely source of immigrants as the oats emerge (remember there were no S-wheat fields near oats). 67 Table 7.--Variables found to be significantly related (p < .05) to adult and egg densities in a multiple regression spatial analysis of the 1977 Galien data. gzgiggigt 13::Ezgiggt Distance (mi) Direction Influenceb S-wheat adults Sparse woods .375—.500 SW + Fence row .375-.500 SE + Sparse woods .250-.375 SW + Sparse woods 0—.125 NW + Dense woods .375-.500 NE + S-wheat eggs Sparse woods .375-.500 SW + Dense woods 0-.125 SW - Woods edge .125—.250 NW - Woods edge .250-.375 SW + Dense woods .250-.375 SW - R-wheat adults S-wheat .250-.375 NE + Oats .375—.500 SW + Woods edge .375-.500 NW + Crop height - - + Fence row .375-.500 NW - Oats adults R-wheat 0-.125 SW + Cropland .375—.500 NE - Oats eggs R-wheat .125-.250 NW + Woods edge .125-.250 SW - 8Ranked in order of partial F to remove. b Sign of regression coefficient. 68 The regression equations obtained with the 1977 data were tested for validity with the 1976 data. Since the regional mean population level may change from year to year, the criterion used for successful prediction was the correlation between predicted and observed densities, rather than a matching of the absolute levels. Of interest was the ability to predict relative densities within a year; i.e., to identify fields likely to have a high density, etc. The values of the required independent variables were obtained for every field in 1976 and were entered into the appropriate equation. For 44 S-wheat fields in 1976, the correlation between observed and predicted adult densities was r = .152 (p = .16); for eggs in 45 fields it was r = -.001 (p = .50). For adult densities in 8 R-wheat fields, r = .346 (p = .20). For adult densities in 10 oat fields r = .325 (p = .18); for eggs in 12 fields it was r = .325 (p = .15). There are many possible reasons for the failure of the regression models to predict the relative densities in 1976. Vio— lations of the assumptions underlying the use of multiple linear regression must be considered first. These assumptions are that the samples (densities) were drawn at random and independently of each other, that they are identically and normally distributed for fixed values of the independent variables, that the independent variables are not highly intercorrelated (multicollinear), and that the rela- tionship between density and each of the independent variables is linear. 69 Since the use of the analysis was not inferential, but, rather, was descriptive and predictive, the assumption of normality need not be met (Searle 1971, Ch. 3). The densities were estimated from every field in the region and all during the same year, so they are not independent random samples drawn from the population of all possible responses. This is perhaps the most likely reason for the failure. If, for example, wind patterns or crop synchronies differed in the two years, then the models would almost certainly fail in their predictions. Multicollinearity is unlikely to be a serious problem since correlations on the order of 0.8 must be present to cause computa- tional problems with inversion of the correlation matrix of the inde— pendent variables (Nie gt_gl: 1975, p. 340). Such high correlations are not expected due to the heterogeneity of the environment sur- rounding fields and the nature of the variables and their computation. A possible exception might be found within the smallest radius, since for a lO-acre field only 27.5 acres of habitat lie within .125 mi in one quadrant. In this small area, the acreage of cropland might be negatively correlated with the acreage of dense woods. The remaining assumption is that of linearity. This was assumed, but not carefully evaluated, as a first-order approximation. 'The large number of variables prevented a thorough investigation of this. If the work were pursued, clearly this assumption should be more closely examined, at least by analyzing the residuals. The fact that field densities were not closely related to any particular environmental condition which was measured could also 70 be due to biological causes. For example, if beetles are quite active and disperse widely, or if they move around considerably (among wild grasses, say) between emergence and entry into the fields, then the densities will become homogenized and the effect of a field's local features will be obscured. But in this case, between-field variation would not be expected to be as great as that observed (Table 6). This will be discussed more fully in relation to simu- lation results in a later section. The independent variables chosen may have been too specific and numerous. Thus, by chance alone, a subset was found which "explained” the 1977 data but was of no use with a different set of data. I attempted to prevent this by purposely limiting the number of independent variables included in the final model to a small fraction of the number of observations. Cluster Analyses Cluster analysis is a broadly descriptive term covering a number of multivariate statistical techniques (Anderberg 1973). The general goal of cluster analysis is to discover and describe the structure of a complex data set. Anderberg (1973, p. 3) defines the problem in cluster analysis as one of "finding the 'natural groups'" in the data. That is, "to sort the observations into groups such that the degree of 'natural association' is high among members of the same group and low between members of different groups." When the goal is exploration rather than rigorous analysis, few assumptions need to be made about the data for many of the techniques. 71 In the context of the current problem, the data units are fields. The observations on these units were the 76 spatial and temporal features: 64 variables describing the distribution of eight habitats in four quadrants and two distance ranges (.00 - .25 mi and .25 - .50 mi); ten variables characterizing patchiness of sparse woods, dense woods and cropland, habitat diversity and woods edge development in the two annuli; field size, and crop height at the time of regional peak densities. Oat fields were not included in these analyses because there were so few of them. Two approaches were taken in analyzing these data by cluster analysis. First, the fields were organized into natural groups as determined by their environmental features, and the groups, or clusters, were compared with respect to their mean CLB density. Where differences were found, the principal factors responsible for the grouping were identified. In the second approach, fields were first organized into classes based on their insect density. Then an effort was made to identify those environmental features which were best able to discriminate between the classes. In both cases the data were standardized prior to analysis by subtracting from each variable the overall mean of that variable and dividing by its standard deviation. This placed all variables on the same scale with a mean of 0.0 and standard deviation of 1.0, eliminating the artifact of measurement scale (Anderberg 1973, p. 102). An agglomerative hierarchical clustering procedure (Anderberg 1973, Ch. 6) was used to organize the fields into natural groupings. Starting with each data unit (field) as a cluster, clusters were 72 merged sequentially based on their similarity until there was one cluster containing all data units. The criterion of similarity used was Euclidean distance in the 76-dimensional feature space. The complete linkage method was used to define the distance from a newly formed cluster to any other cluster. This distance is defined as that separating the most distant members of the two clusters. Com- plete linkage tends to produce globular clusters with assurances that if two data units lie within the same cluster then they are at most a known distance apart. The outcome of hierarchical clustering, known as a dendrogram, can be depicted graphically as a tree (Figure 15). By visually examining the tree a number of fairly dis- tinct groups can usually be defined. For example, in Figure 15, at an intragroup distance of slightly more than 18 standardized units a well-defined group of seven fields (numbers 1228 to 413) joined all the rest of the fields. In the step before that, a cluster of three fields (348, 346 and 141) merged with a larger group to form a new cluster 16 units in diameter. The experience of the analyst and his knowledge of the problem at hand play a role in deciding how many clusters the final clustering will have. In difficult cases more objective methods can be devised to determine what constitutes a "good" or "natural" clustering. The final cluster memberships for the fields of each crop in 1976 and 1977 are given in Appendix B. Table 8 gives the final number of fields per cluster, and the mean and standard error for the densities within each cluster. Analyses of variance tested for significant differences between the clusters with regard to adult and 73 "“17 .J ou-r L "a 1417 n: I we IAXIIUI IITIAGIOUP DISIIICE Fig. 15.--Complete linkage hierarchical tree for the R-wheat fields at Galien in 1977, based on 76 environmental features. 74 Table 8.--Final clustering of Galien-area fields based on their environmental features using hierarchical cluster analysis, and mean CLB densities within the clusters. Cluster mem- berships are given in Appendix B. Adult densityb Egg densityc Year Crop Cluster Fields _ _ x SE x SE 1976 S-wheat l 2 9.80 26.80 5.84 4.58 2 11 49.61 11.43 5.62 1.95 3 6 88.16 15.47 13.36 2.64 4 14 24.45 10.13 2.80 1.73 5 17 47.00 9.19 6.06 1.57 1976 R-wheat 1 3 52.20 9.99 4.26 0.49 2 5 36.33 7.74 2.66 0.38 1977 S-wheat l 2 50.60 35.24 4.67 6.11 2 4 112.20 24.92 9.58 4.32 3 10 86.67 15.76 7.56 2.73 4 8 94.10 17.62 14.85 3.05 1977 R-wheat l 7 37.13 8.64 1.76 0.85 2 3 62.47 13.19 3.72 1.29 3 7 47.67 8.64 3.74 0.85 4 20 54.97 5.11 3.95 0.50 aNumber of fields for which density estimates were available. bAdult - °D > 48(F) for season. cEggs/60 cm, seasonal input. 7S egg densities. Where shown to be necessary by Bartlett's test, a logarithmic transformation was used to stabilize the variances (Sokal and Rohlf 1969, pp. 370, 382). Where significant differences in density were found among the clusters, discriminant analysis was used to identify features con- tributing to separation of the clusters. Discriminant analysis (Nie §t_al, 1975, Ch. 23) is a procedure which weights and linearly com- bines the features into discriminant functions in such a way that the predefined groups are as distinct as possible in their scores on these functions. The maximum number of discriminant functions derivable is one less than the number of groups, but satisfactory separation of the groups may be possible with fewer than this number of functions. The functions are ranked in order of their contribution to discrimination between groups. The relative importance of each variable to a discriminant function is given by the absolute value of its standardized weighting coefficient. The theoretical signifi- cance, if any, of the derived discriminant functions may thereby be assessed. All variables need not be included in each discriminant function. For the present work, the ten most significant features were selected for each function by a stepwise procedure which maxi- mized Wilk's lamda statistic, a measure of group discrimination (Nie §t_al, 1975, p. 447). The result of a discriminant analysis can be viewed as a projection of the data from a high, say 76, dimensional space to a space whose (lower) dimensionality is equal to the number of discriminant functions. Each function represents a dimension, or axis in this reduced space. 76 For S—wheat in 1976 there were significant differences (p = .02) in adult density among the five clusters. Specifically, cluster 1 had a lower density than all other clusters except cluster 4, and cluster 4 had a lower density than cluster 3. The discriminant analysis showed that cluster 4 was distinguished from cluster 3 by having a higher index of patchiness of sparse woods within .25 mi, greater acreage of S-wheat within .25 mi, and lower habitat diversity within .25 mi. By examining the aerial photo (Figure 14), it was seen that 13 of the 14 fields of this cluster all fell into two sets of neighboring fields located in areas of very few woodlots or tree lines. Unfortunately, the fields of cluster 1 all had missing data (habitat features found to be important discriminators) due to their location near the edge of the study area, and were not included in the discriminant analysis. However, cluster 1 was placed most closely to clusters 2 and 3 by the hierarchical clustering. It might be expected that its fields shared little in common with those of cluster 4, and that more than one set of conditions leads to low density. Indeed, by examining the aerial photo, it was seen that these fields were bordered by large areas of dense woods. There were no significant differences in egg density among the S-wheat fields in 1976 after transforming the data to stabilize the variances. Among the S-wheat fields in 1977 there was no clear definition of habitat groups. Four rough clusters were delimited, but analyses of variance of adult and egg densities showed no significant differ- ences between these groups. 77 The eight R-wheat fields in 1976 were separated by hierarchical clustering into two clusters. An analysis of variance showed that the mean egg density in group 2 was lower (p = .04). Because of the low number of fields, a discriminant analysis was not done, but inspection of the aerial photo showed that the fields of cluster 2 were near very few woodlots and fencerows. The R-wheat fields in 1977 were grouped into four fairly distinct clusters (Figure 15), but no significant differences among the clusters were evident for either adult or egg densities. The second approach to a cluster analysis of CLB densities and the spatial structure of the environment began with a classifi- cation of the fields into groups based separately on their adult and egg densities. This was done by plotting every field's density on a number line, and then breaking the line up into segments at points that gave a total of three to five groups and divided the line at naturally occurring gaps in the distribution of densities. It was possible to select breakpoints meeting these criteria and which also had the same value in both years. For adult densities (adult-°D/60 cm) the breakpoints were 62, 120 and 160 for S-wheat and 40, 55, 6S and 95 for R-wheat. Thus there were four density classes for S-wheat and five for R-wheat. As an example, an S-wheat field with a total seasonal adult activity of 70 adult-°D/60 cm would fall into density class 2 for that crop. For egg densities (eggs/60 cm) the breakpoints were located at 10 and 20 for S-wheat and 4.5 and 7 for R-wheat; there were thus three egg density classes in each crop. In this manner the 78 fields were divided up into groups based on their relative density, ranging from low through moderate to high. Discriminant analysis was then employed to determine if these density classes could be distinguished by any combinations of the spatial features describing a field's environment. To test the validity of any discriminant functions found, the analyses were first performed using one year's data to define the functions, then the other year's data set was "classified" using these results. Classifi- cation is the other, perhaps major, role of discriminant analysis, besides defining the relative importance of discriminating variables. Discriminant analysis provides classification functions which are used to calculate the probability of membership in each group for a new, unknown data unit. The procedure is commonly used in numerical taxonomy (Sneath and Sokal 1973). The success or failure of the analysis in defining meaningful functions was judged by the percentage of correct classifications of the "unknown" fields from the other year. In all cases, the validation procedure indicated a failure to identify a significant percentage of the unknown fields with their correct density class using the classification functions derived from the other year. This was true for both S-wheat and R—wheat fields, for both adult and egg density classes, and regardless of which year was used to construct the classification functions. Furthermore, the same variables were not given as those most important to discrimi— nation in the two years (Table 9). 79 Table 9.--Principal environmental variables contributing to the dis- crimination of the highest density class from all other classes. . . . Direc- % Contri- . b Year Crop Variable Distance (m1) tion bution Sign Adult density 1976 S-wheat Fencerows .00 - .25 NW 17 - Cropland .25 - .50 NE 14 + c Patchiness (l) of cropland .25 - .50 -- 11 + R-wheat .25 - .50 SW 11 — Fencerows .25 - .50 SW 11 + 64% 1977 S-wheat Sparse woods .25 - .50 SW 27 + R—wheat .00 - .25 NW 17 + (2) Crop height --- -- 11 - R-wheat .00 - .25 NE 9 - Fencerows .25 — .50 SW 9 - 73% 1977 R-wheat Woods edge .00 - .25 NW 16 + S-wheat .25 - .50 NE 13 + (2) Fencerows .00 - .25 NW 11 + Woods edge .25 - .50 NW 10 + Woods edge .00 - .50 SW 10 - 60% Egg density 1976 S-wheat Fencerows .00 - .25 NW 19 - Dense woods .25 - .50 NE 14 + (1) Cropland .25 - .50 SW 13 + S-wheat .00 - .25 NW 13 + Crop height --- -- 9 - 80 Table 9.--Continued. . . . Direc- % Contri- . b Y ear Crop Variable Distance (mi) tion bution Sign 1977 S-wheat Sparse woods .25 - .50 SW 23 + Woods edge .25 - .50 SE 16 + (3) Sparse woods .00 - .25 NE 13 + Oats .25 - .50 NE 13 - Cropland .OO - .25 NE 11 + 76% 1977 R-wheat Dense woods .25 - .50 SE 23 - Cropland .25 - .50 SE 19 — (3) R-wheat .00 - .25 SW 15 Crop height --- -- 13 + S-wheat .25 — .50 SW 8 + 78% aOf 10 variables included in the primary discriminant function, percent contribution by this variable to separation of groups along the axis represented by the function. b(+) means high score on variable moves classification toward highest density class along principal discriminant axis; (-) means high score moves classification away from highest density class. CNumber of fields in highest density class. 81 A major problem with the analysis was that the highest density class generally contained only one to three fields. This class was usually widely separated from the other classes along one of the discriminant axes (Figure 16). Discriminant analysis seeks, statistically, to minimize the ratio of within-group scatter to total scatter. A set of variables was probably found which, combined, uniquely described the few fields of the high density class. The group was then placed far from the others along the axis defined by a discriminant function made up of these variables, thereby greatly increasing the total scatter. In this way the fields in the highest density class dominated the analysis. The principal discriminant function, and the variables defining it, merely indicated how these few fields were different from all others. Apparently the factors responsible for creating unusually high densities in a couple of fields are not often the same. The principal features contributing to separation of the high density classes are given in Table 9. As in the regression analysis, all distances and directions contributed to discrimination of the high density fields, and the significant environmental features varied between crops and years. Again, a likely explanation is that the determinants of high density are many and are complexly inter- related, so that more than one set of environmental conditions leads to high densities. As Anderberg (1973, p. 192) notes, heterogeneity Within a group (such as "high density fields") can lead to failure of a discriminant analysis. Conditions associated with high density are likely to vary from one year to the next because of differences in 82 2a 0- 4 I -1. Fig. l6.--Ordination of the 1977 R-wheat fields on the two principal discriminant axes. Numbers refer to adult density classes (5 is highest). Stars indicate cluster centroids. 83 weather, planting times and other factors affecting CLB/host crop synchronies, wind patterns, and the spatial arrangement of the fields. There is little hope of unraveling these between-year relationships with data from only two years. In effect, all of the observations of a single year are reduced to a single point representing a set of conditions and a population response. To avoid the problem of having so few fields in the highest density class, the fields might better have been divided into just two groups, corresponding to above median and below median density. This however, may just aggravate the situation of intragroup hetero- geneity, if that is the problem. Autocorrelations If specific structural features of the environment are associ- ated with high CLB densities, then it might be expected that certain locations would continue to exhibit a tendency to have high densities year after year. It was noticed, in fact, that certain fields did seem to have unusually high densities in successive years. Corre~ lation analysis of 21 fields which were planted with the same crop in both 1975 and 1976 at Galien, and 14 fields planted with the same crop in both 1976 and 1977 showed that densities at the same site were indeed highly correlated in successive years. In a few cases the site in one year was not exactly the same as in the other, but was immediately adjacent and the surrounding habitat did not appear to be different in any way. Where heteroscedasticity resulted from the variance increasing with mean density, a logarithmic transformation was applied to the densities prior to analysis. The correlation 84 between adult densities (log transformed) in 21 fields in 1975 and 1976 was r = .43 (p = .05). For egg densities (no transform) in these years r = .68 (p < .01). For the 14 fields in 1976 and 1977, the logarithms of density were also significantly correlated: r = .63 (p < .05) and r = .74 (p < .01) for adults and eggs, respectively. Autocorrelation of densities could also account for the observed relationship between two successive years, rather than the nature of the site being responsible. That is, a high density at a site in one year may be followed by a similar density in the next year, just because the former provides the starting point from which the pOpulation level changes. The nature of autocorrelation is such, however, that its effect decreases as time progresses, and densities measured two years apart should be less correlated than those measured just one year apart. Unfortunately, not a single field was planted with the same grain in all Ehrgg years at Galien. A few fields were planted to S-wheat in both 1975 and 1977, with something else planted in the intervening year. Such a disruption of crop continuity would effectively eliminate any effect of autocorrelations, but would perhaps have little or no effect on a process in which a field's beetle density was determined by the surrounding environment of the field. Permanent habitats, such as woodlots, fencerows, etc., would be the same in both years. For eight fields for which adult densi- ties were available, and nine for egg densities, no significant correlations in densities two years apart were evident. Egg and larval densities in the wheat and oat research plots at Gull Lake over a 12-year period (1967-78) give similar results. 85 Here the sites were essentially the same each year. Twelve density estimates provide 11 pairs separated by one year, 10 pairs separated by two years, and 9 separated by three years. For both egg and larval densities, in both the wheat and oat plots, the correlation between pairs of estimates declined with each additional year of separation. These results suggest that the observed similarity in a field's density in two successive years is merely the result of autocorrelation and not necessarily because that site is consistently a favorable or poor one. This does not help to explain why a field's density is high or low to begin with. FIELD STUDIES OF DISPERSAL Fluctuations in Density The density of adult cereal leaf beetles in a field can change rapidly. Figures 17-19 show the mean and 95% confidence interval of density at frequent intervals in three fields that were intensively sampled at Galien in 1977. Except in very short grain, samples con- sisted of 20 randomly taken sets of 25 sweeps with a 15 in (38 cm) diameter sweepnet. Sweepnet counts were converted to density esti- mates using the model of Ruesink and Haynes (1973). When the crop height was less than 10 in (25 cm), samples consisted of 20 random visual counts along 10 ft (3 m) of two adjacent grain rows. The pre- cision of these estimates is high enough to show that the density may be significantly different on successive sampling days. What is interesting about this is that on occasion the density dropped one day and rose the next, showing rapid fluctuations rather than gradual changes. On 26 April 1977, (365°D > 48F) a low point was observed in the densities in fields 1022 and 1024. It had rained .25 in the day before, and the fields were still damp. The previous three days had been very cool, with only 1°D > 48 accumulating. The night before the minimum temperature had been 29°F (-l.7°C). At sampling time it was sunny, windless, and near noon. The maximum temperature that day 86 87 FIELD 1022 ‘ S-HHERT RDULTS/SOURRE FOOT O :4 2‘ o A °3oo 450 560 600 160 300 DEGREE-DRYS > 48 (F) 9 o- 22 FIELD 1024 R-HHERT RDULTS/SOURRE FOOT O fir V 300 GOO ' BOO GOO 760 800 DEGREE-DRYS > 48 (F) Fig. 17-19.--Mean adult density at frequent intervals in three intensively sampled fields at Galien in 1977. Ninety- five percent confidence intervals are indicated by (+). 88 ID 0') C o 3‘ FIELD 541 cars RDULTS/SOURRE FOOT ‘I t I I I I T I I T A —l 400 500 500 700 000 900 1000 1100 1200 1300 1400 DEGREE-DHYS > 48 (F) Fig. 17-19.--Continued. 89 was 58°F (l4.4°C). Neither the minimum temperature the night before nor cool weather earlier nor the rain adequately account for the low density, since on 29 April (381°D) the minimum was 26°F (-3.3°C), only 4°D had accumulated the previous two days, and .2 in of rain had fallen the day before. The density on 29 April, however, had just increased. It is difficult to account for the low population on 26 April. Similarly, on 3 May the population in field 1022 was again significantly lower than on either the previous or the following sampling day. It had been cloudy and had rained .25 in the day before but at the time of sampling it was sunny and near noon, the field was dry, and there was only a 6 mph wind (from the Northeast). The maxi— mum temperature that day was 70°F and the minimum the night before had been 49°F. Again, it is difficult to account for the drop in density in field 1022. Note that on this same day the density in adjacent field 1024 increased. On 5 May (458°D) the reverse occurred, with field 1024's population declining significantly while 1022's increased. In each case the two fields were sampled at the same time. The wind at the time of sampling on 5 May was from the West. Field 1024 was located directly west of 1022. Thus, wind might have carried beetles from 1022 to 1024 on 3 May, when winds were from the Northeast, and from 1024 to 1022 on 5 May. Problems with this interpretation are that there was a very dense tree row between the two fields, approxi- - mately 15 ft (4.6 m) thick, the wind at the time of sampling may not reflect the total wind pattern during the days when dispersal must have occurred, and on 26 April, when winds were very light, the entire 90 regional population exhibited the same sort of decline that the two study fields showed. Some other explanation must be sought for the fluctuations, at least on 26 April. I have no such explanation, but offered this example to make certain points. First, field densities in all crops fluctuate fre- quently and significantly. This shows that beetles do not stay in the field that they happen to enter, but instead are highly vagile and may move in or out of any crop at any time. I say the density fluctuations represent movement into and out of the fields rather than changes in sampling efficiency under different weather conditions for several reasons. The sweepnet model (Ruesink and Haynes 1973) makes some allowance for the influence of temperature, wind, and solar radiation on sampling efficiency, and the direct visual counts are little affected by these factors. The conditions at_£hg time 9: sampling were never particularly adverse anyway. The populations in the two adjacent fields changed in opposite directions on both 3 May and 5 May although sampling conditions were identical in the two fields. A second point demonstrated by the example is that while the rates of movement are undoubtedly affected by weather, these relation- ships are not obvious and are probably complex. Dispersal activity Inay be great even in cool, cloudy weather. The series of contour plots presented in Appendix F provides Inany examples of fluctuating densities in fields. The plots were drawn by computer, using the Surface 11 graphics package (Sampson 1975) and a Calcomp plotter. These maps represent the entire 41.4 km3 srtudy area of the pubescent wheat project in 1977. Each set of 91 concentric contours represents a field, or group of neighboring fields. The concentration of contour lines reflects the density of adult cereal leaf beetles in that field. Fields are located in terms of the same lO—acre cells used in the habitat analysis, above. Specific fields can be identified on the contour plots with the aid of the digital and traditional maps in Appendix D, and the cell assignments given in Appendix B. Plotted values are the estimated densities in every field at daily intervals, generated by interpolating from actual samples collected approximately twice weekly. It is not difficult to find examples among these plots of densities rapidly falling or rising, of some fields increasing while others decrease, and of apparent trans- fers of beetles from one field to a neighboring field. An interesting example of the latter is given by the sequence of events in fields 722, 236 (both R-wheat) and 235 (Oats) beginning on 10 May (plot No. 25). An enlargement of this group of fields (marked by an arrow in plot No. 25) is given in Figure 20. Oat field 235 is located between the two R-wheat fields. On 13 May the density in oats began to increase while those of the neighboring R-wheat fields declined, the latter apparently serving as a source for the beetles entering the oats. This continued until on 23 May the densities in the R-wheat fields were almost zero. On 24 May, however, the densi- ties in R-wheat began to increase again with oat field 235 the apparent source. Here, then, is an example which seems to show beetles trans- ferring from oats back to wheat. The evidence is circumstantial, of course, and only direct observation of the movement, say by marking individuals, could confirm the statement, but the suggestion is strong. 92 Fig. 20.--Contour plots of adult density in R-wheat fields 722 and 236 and oat fields 235, 613 and 612 (A-E, respectively) at Galien in 1977. Plotted daily beginning 10 May. 94 The number of spring adults in a field at any time t is given by N(t), the integrated difference of dispersal rates into and out of the field and losses due to mortality: t N(t) = I (IN — OUT - M)dT (17) o Quantification of these rates was sought in terms of environmental and biotic variables through three types of field studies: (1) field emptying rate studies, (2) sticky board trapping, and (3) the measure— ment of within field diffusion rates. Field Emptying Rates This experiment was directed toward defining a functional relationship between the rate of movement out of a field and such factors as crop species (wheat or oats), crop maturity and beetle density. While the experiment did not work out, I report the approach here to guide future work. Movement out of a field might be considered in two parts: movement within the field and movement across the field boundary, and these may take place at different rates. What lies outside the boundary may influence the rate of crossing, but this complication was eliminated here by plowing and discing a clear buffer space around the plots. It is not known what constitutes a "boundary" for the cereal leaf beetle--that is, the distance into the field at which the effect of the edge is no longer significant. Therefore, plots of various sizes in a geometric series were considered, ranging in size from 95 2 to 929 m2) (Table 10). It was hoped .25 ft2 to 10,000 ft2 (.023 m that the use of this series would give information on the effective width of a boundary so that further experiments could be restricted to the largest plot which could be considered "all boundary." Table 10.-—The number of beetles that were to be released in plots of various sizes to attain various densities. (For the smallest plots the number of beetles released is followed by the resulting densities.) —-— C.“ Area Adult Beetles/ft2 Side (ft) 2 ft Acres .03 .1 .3 1.0 3.0 .5 .25 .000006 1(4) 2(8) 3(12) 4(16) 5(20) 1.5 2.25 .00005 l(.44) 2(.9) 3(1.3) S(2.2) 7(3.I) 5.0 25 .0006 l(.04) 2 7 25 75 15.0 225 .005 7 22 68 225 675 50.0 2500 .O6 75 250 750 2500 - 100.0 10,000 .23 300 1000 3000 - - Plots were prepared by subdividing an existing winter wheat field at the Collins Road entomology research area in East Lansing, Michigan by plowing it on 23 May, 1976. Starting densities of adult CLBs were also to be in a geo- 2 to 3.0/ft2 (Table 10). Of course, metric series ranging from .03/ft in the smaller plots the lowest densities were not possible and in the larger plots the number of beetles required was prohibitive at high densities. A reasonable set of combinations required about 9000 beetles. Beetles were obtained by vacuuming a high-density wheat 96 field at Galien, Michigan on May 5, 1976 and later dates, but it proved impossible to collect more than about 6000 due to poor weather and declining densities. The beetles were transported to Collins Road and stored in a 13 x 19 ft field cage in wheat. By the time the plots were prepared the stock of beetles had dwindled due to mortality. Because they required fewer beetles, the smallest plots were used first. It was assumed that in these plots the number of beetles leaving per unit time could be measured directly by observing individ- ual flights. This assumption proved to be overly optimistic. For the larger plots the emptying rate was to have been inferred from the number remaining in the plot, estimated by sampling. The experiment failed for two reasons. First, the beetles were very inactive. They would sit in one place, crawl very slowly, or fall to the ground and either crawl into crevasses or away from the plot. Some beetles mated. Second, due to the inactivity of the beetles, very long observation times were required. It was impos- sible to be attentive enough to keep track of as few as four or five beetles in even the smallest plot (6 in x 6 in) and be sure one had not flown away. The difficulties may have been related to the lateness of the season when the experiment was begun (beetles were old, crop was tall) or to the artificially of such small plots affecting beetle behavior. Sticky Board Trapping During 1977 an attempt was made to quantitatively measure the rates of movement of adult cereal leaf beetles into and out of six grain fields in Berrien County, Michigan using sticky board traps. A 97 total of 120 sticky board traps were distributed around and within two susceptible and two resistant wheat, and two oat fields. The traps were 122 cm (4 ft) tall by 15.24 cm (6 in) wide, constructed of two pieces of .32 cm (1/8 in) thick tempered pegboard bolted to a 183 cm (6 ft) long stake and painted with "crescent yellow" exterior enamel latex paint (Silver Lead Co.). Unpublished data (Jantz 1965) showed that "canary yellow," a similar color, was the most attractive to adult CLBs of several colors tested, and it was desirable in this experiment to catch a large number of beetles on which to base an analysis (since it was not known what color of trap would be totally neutral, I decided that catching as many beetles as possible would be the next best situation). Four traps were placed, vertically, along each border of each field, and four in the interior of each field (20 traps per field) by pounding the stakes into the ground until the bottom of the trap was about 20 cm (8 in) above the ground. The border traps were placed so that one surface (labeled "B") faced the interior of the field and one surface (labeled "A") faced away from the field. These were assumed to monitor outgoing and incoming flight, respec- tively. The traps were coated with "Tacktrap," a sticky substance which entangles any insects flying into it, and were recoated as necessary. The traps were divided, vertically, into four sections of equal area to determine the vertical distribution of dispersal flight. Traps were examined twice a week. To relate trap catch to the actual number of beetles entering and leaving a field, accurate estimates of the change in density of adults in the field over the trapping interval were needed. Changes 98 in density must be due to the differential effects of mortality and beetles entering and leaving the field (in the absence of new beetles emerging from pupation). For a finite time interval this can be expressed as N2 = N1 - mortality + immigration - emigration or (N2 — N1) + mortality = immigration - emigration (16) or AN + M = IN - OUT. The change in the field's total population was estimated by sampling adults at frequent intervals, as described earlier. To estimate mortality rates, screened cages (30.5 cm high by 7.6 cm diam) (Casagrande 33 31. 1977) were used to hold adult CLBs on the host crop for a several-day period. Ten beetles, captured with a sweepnet in the same crop, were placed in each of five cages in one resistant and one susceptible wheat and one oat field. After several days the number which had died was recorded as well as the time elapsed. Many beetles escaped from the cages (between the foam plug and cage), so the number of remaining live beetles was also recorded. Mortality was calculated as the number dying divided by the sum of those dying and those live beetles which had not escaped. This :method probably overestimated mortality since it assumes that escape is independent of mortality, while in fact dead beetles can not escape but live ones can. The mortality over n days (Mn) was con— Verted to the rate of mortality per day (Md) by the equation 99 _ l/n Md - 1 - (1 - Mn) . (17) This rate was assigned to the midpoint of the test period and used to calculate the total number dying in a field over a sampling interval. At the end of the test period the beetles were discarded and the cages were moved and restocked with freshly caught beetles. On the average, two tests per week were conducted. Ultimately I wanted to relate the quantified rates of movement into and out of the field to such factors as beetle density, crop height, crop moisture, crop type (susceptible or resistant wheat, or oats), time and weather conditions. As a measure of crop moisture, four random samples of plant material were taken from fields 1022 (S-wheat) and 1024 (R-wheat) each week from 9 May to 27 June. The samples consisted of the above-ground portion of the crop plants in about 60 cm of row. The plants were put in tared paper bags and immediately weighed in the field on a portable balance. After oven drying (24 hr at 100°C) the samples and the empty bags were reweighed. Plant mois- ture was then calculated as percent, by weight, of fresh weight, and is shown in Figure 21. From equation (16), the quantity IN—OUT is equal to AN+M, which was measured in the field over each sampling interval, but the separate rates IN and OUT are unknown. These were thought to be estimated by sticky board trap catches on sides A and B, respectively, and related by some functions F and F - 1 2' IN = Fl(fN) (13) our = F2(ODT) 100 100 1 q 90 In FIELD 1022. S-HNERT o- I FIELD 1024. R-HHEHT PLFINT NRTER CONTENT. PERCENT 6 20 200 400 600 800 1000 12r00 1400 1600 DEGREE-DRYS > 40 (F) Fig. 21.--Crop moisture in two of the fields used in the sticky board trap study. 101 By assuming that the same function applies to trapping incoming and F(1N) - F(OUT) = F(IN-OUT) for a linear function, F, where F = F1 = F2. A regression of AN + M on IN - outgoing beetles, we have IN-OUT OOT should provide the function F, and from this the separate dispersal rates IN and OUT can be obtained. IN and ODT were determined from trap catches by using the stratified sampling estimator of a population total (Cochran 1963, Ch. 5): (19) where yh is the mean trap catch (on the appropriate side of the trap) along border h, and Nh is the length of the border in terms of trap units (border length/trap width). There were four traps along each of four borders in each field. The trap catches along the four borders of a field were usually quite different, often with a large number of beetles "entering" across one border and "leaving" across another border. A summary of the sticky board trap catches for the border traps of fields 1022 and 1024 is given in Table 11. The counts are the total number of CLBs caught on the entire "A" side (IN) and "B" side (OUT) of the 16 border traps in each field since the previous observation. The traps in these two fields caught a majority of the beetles (6870 out of the 8177 beetles caught in all six fields), so only these data are presented here for illustrative purposes. The raw data for these and the other four fields are given Table ll.--Tota1 daily catch of incoming and outgoing CLBs on sticky board traps in field 1022 S-wheat and 1024 R—wheat (l6 traps per field). Field 1022 Field 1024 Date In Out In Out 4/19 traps established 4/20 0 0 1 2 4/21 11 9 O 0 4/22 3 9 O 0 4/26 2 l 0 2 4/27 2 1 0 0 4/29 0 0 1 1 5/3 2 1 5 2 5/5 1 4 0 3 5/9 15 18 7 2 5/12 19 42 14 15 5/18 294 218 449 243 5/20 59 152 373 406 5/24 55 75 179 289 5/27 16 8 36 55 6/1 16 9 19 42 Spring total 495 547 1084 1062 6/8 9 l4 7 16 6/13 9 8 0 2 6/14 0 5 l 3 6/16 127 454 13 16 6/21 373 670 28 42 6/24 411 696 83 98 7/1 119 177 152 149 Summer total 1048 2024 284 326 Grand Total 1543 2571 1368 1388 -—- 103 in Appendix G. The data are separated at June 1 into spring adult activity and summer adult activity. The trap catch follows, in general, the buildup and decline of field densities and clearly shows a lull in activity between the spring and summer generations. This indicates that sticky board catch is, in some manner, related to beetle activity. The vertical distribution of trap catch for all six fields is given in Table 12. These data show that flight activity (as measured by sticky board trap catch in the air-space 1.4 M or less above the ground) declined above 1.0 M, with only 15% or so of the beetles being caught on the top section of the traps. Furthermore, the vertical pattern of activity is very similar for incoming and outgoing beetles (except in one oat field). There appeared to be a difference in vertical activity in the susceptible and resistant wheats, with a greater portion of the beetles in resistant wheat being caught closer to the ground. The reason for this is unknown. Table 13 gives the results of the mortality cage studies. The Inortality rates arrived at here are quite different from those reported ‘by Casagrande gt 31. (1977) for four years of research at Gull Lake, Idichigan, particularly in the rapid increase to very high mortality rates at the end of May. However, the current data may reflect the jpaxticular conditions existing in the study fields during the trapping jperiod, and were therefore the estimates used. Mortality over the period from 21 April to 20 May, for susceptible wheat, and 24 April ‘to 20 May, for resistant wheat, was rather low and constant. Average :rates of 1.0%/day and 0.5%/day were used for these periods in the two 104 .cofiuoom may» mo ofiwvws on pcsonw o>oam ucwwomw oma on. was. me. mow. mm owe. owm. com. omN. Mao on Hwo. Hes. Hmm. avm. mme coo. mNH. Nam. mom. Hem mumo no who. «am. aka. mow. 44 Mao. amm. 0mm. «we. mmm mama ooH. 0mm. mom. How. moms 42H. aea. 0mm. mom. «mam 048:2-m 0mm mHN. 4mm. saw. «ma. 4m Bea. mmm. Hmm. aka. NNm Hamm NVH. mam. mom. Ham. mema mmH. amm. amm. cam. mmoa 040:3-m aN.H om. co. mm. a~.~ co. co. mm. a flag “ammo: a «new “swam: afloaa mono Annoy m ovum mace < ovum .mofiwoon woeazm pcm wcwnmm :uon pow Amman mo ovwm Hosp :0 pnwsmu flay HmHOH mo :prpomopmv gonna use» chaos xxowum mo :0wuanwuumwp Hwowuao>II.NH oHnmh 105 Table l3.--Ca1culated mortality rates of adult CLBs in each crop. Datea No. beetlesb No. dying No. days Mprtaléty é/day Susceptible Wheat 4/21 16 0 2 0.00 5/1 43 l 5 0.47 5/8 40 4 6 1.74 5/13 39 3 5 1.59 5/18 45 l 4 0.56 5/21 41 33 3 42.00 5/24 48 38 l 79.17 5/28 86 85 3 77.34 5/30 48 46 1 95.83 Resistant Wheat 4/21 16 8 2 29.29 4/24 15 3 4 5.43 4/28 85 0 2 0.00 5/1 44 0 5 0.00 5/8 20 0 6 0.00 5/13 37 0 5 0.00 5/18 30 2 4 1.71 5/21 44 32 3 35.15 5/24 50 48 1 96.00 5/30 46 42 l 91.30 Oats 5/24 33 8 1 24.24 5/25 31 ll 3 13.59 5/27 28 13 6 9.88 5/28 32 31 3 68.50 5/30 38 36 l 94.74 aMidpoint of the test period. bAlive + dead at end of test (excludes escapes). cl-(l-d/n)“t where d is the number dying out of n beetles (alive + dead) not escaping after t days. 106 crops. From 24 May to 1 June the mortality was again rather constant, but very high. Average rates of 83%/day and 94%/day were used for this period in the two crops. Over the short interval from 20 May to 24 May, mortality rates increased rapidly. Appropriate rates for each day were obtained from a line drawn through a plot of the mortality rates for this period. A similar approach produced esti- mates for the period from 21 April to 24 April in resistant wheat, over which mortality declined. Mortality in oats started out quite high on 24 May, declined, and then became very high by 30 May. As will be seen, the modeling effort for the wheat fields was not very successful, so the analysis was not carried out with the less com- plete oat data, and these mortality rates were not used. Table 14 presents the calculated values of AN, M, IN and DOT for field 1022 (S-wheat), required for the quantification of trap catch. Similar calculations were done for the other three susceptible and resistant wheat fields, but are not presented here. For each sampling day, the density (no./6O cm) of adults is given, taken from Sawyer (1978, Table S1). These values were next converted to the total field population by considering the acreage of the field. The change, AN, in the population since the last sample was then obtained by sub- traction. Total mortality was estimated by applying the appropriate rate, in %/day, to the population. If more than one day elapsed between sampling dates, the mortality for intervening days was obtained ‘by estimating, by linear interpolation, what the total population was (Ml'these days. This method was only used when the mortality rate was ltnv (before 20 May) or if the population increased. At high rates of 107 oNo.N ooH.mH mom.m H-.o Hoo.oH Hoo.m- ooo o H\o oao.m Hoo.~H oHo.m moo.o oNN.o Ho~.m ooo. H~\m mmm.o- mmo.m- moa.om Hom.mm ooH.oH oam.oH- ooo. o~\m Hoo.om- omH.o Hoo.om oov.m~ mom Hoo.m oNo. om\m omm.om Hom.mo- Noo.mo ooo.oHH mmo.mH ooo.oa- HHo. oH\m ooo.o- HHo.mHNI wmm.oH Nmm.a omm.HH mmm.mo~- omH. ~H\m ooo- NHo.No omo.a oom.o HNH.mH Hmm.oo Ham. o\m on.HI ooo.NHN Hoo.H Ham omm.m ooo.oo~ Hoe. m\m ooo mmm.oa- Ham HHo ooo.o NHo.Ho- HHH. m\m o Hoa.om o o NoH.m oHo.Hm Hom. om\o Ham ooo.ooH Ham oma oam oHH.ooH NNN. H~\o Ham oma.omH- Ham oma oHo.o mam.mmH- moo. om\o NoN.NI HNH.NHHI mom.m HHH.H Hoo.m ooH.oHH- oom. -\o oma Hom.mo mom.m HoH.o moo.m o~m.~o oHo. Hm\o o o oom. om\o Hoe- 2H 2 + zo poo 2H 2 zo so oo\mpH:o< mono < /\ /\ l‘l ll." -. IIII 5-1. .HDOI zHw omH< .umoszI w NNoH pHon :H mHm>Hou=H ucozconm How .mocoumo< mmuu whoop xonum anm woumEHumo .Hesov mucmeHEo mam Hz 46 IF) Fi8~ 24.--Crop height in two of the fields used in the sticky board trap study. 117 border, as tested against the binomial distribution with a probability of 0.5 for moving in either direction. Thus, movement near the border seemed unaffected by proximity to the border. However, no beetle was ever observed to actually cross the border and leave a field in these studies. Exodus from Wheat The adult populations in fields 1022 (S-wheat) and 1024 (R- wheat) rapidly declined over the period 11 May to 19 May 1977 (500 to 650°D > 48) (Figures 17 and 18). The possibility that this was caused by some changing condition of the crops was examined, by looking at plant water content and height. The crop moisture is shown in Figure 21. Over the period of concern, water content of the above-ground plant material declined from about 83% to 79%. Water normally constitutes 80-90% of the fresh weight of most herbaceous plant parts (Kramer 1969, p. 5). It seems likely, then, that although the decline in water content was very slight and gradual, this point represented the beginning of dessic- cation in wheat. The physiological processes involved in heading may render the crop unsuitable to the cereal leaf beetle. A sudden increase in crop height may accompany heading, but Figure 24 gives no indication Of’this event occurring until perhaps 700°D, after the exodus was complete. During the interval from 500 to 650°D > 48, crop height increased gradually from 19 to 25 in. Unfortunately, the actual event of heading was not recorded. 118 Mortality rates at this time were quite low (Table 12), and did not begin their rapid increase until two days after the exodus was complete (21 May). Furthermore, the great increase in sticky board trap catch (Table 11) on 18 May in these fields support the idea that it was emigration, not mortality, which caused the decline in the population. It is interesting that almost as many beetles were caught on the outer faces of the traps as on the inner, indicating that the movement which ”emptied" the fields may still have been diffusive rather than directed, although at a greatly increased rate. A process which may account for both the exodus from 11 May to 19 May and the rise in mortality two days later is crop senescence. There are many physiological changes associated with the initiation of plant senescence (Salisbury and Ross 1969, p. 648). It may be that such changes (perhaps a decline in leaf water content below some threshold) signaled the beginning of crop maturation to the beetle, and emigration then began before the quality of the crop became so low as to be lethal. By 21 May any beetles confined to the crop in cages succumbed to starvation or other stresses associated with the low host quality. The weather both before and after 21 May was sunny, dry, and warm. The temperatures on 20 and 21 May were the warmest (92°F) yet recorded that year, but seem inadequate to account for the rapid increase in mortality following that date. That the kind of mortality observed at Galien in 1977 was not reported by Casagrande (1975) for four years at Gull Lake may be due to the extremely early maturation of crops at Galien in 1977. Wheat combining actually began in late June due to an early spring and a warm, dry season. 119 The hypothesis developed here to explain the observed exodus from wheat should be investigated further with specific behavioral and physiological experiments. Gutierrez ggngl. (1974) also observed a mass emigration of adults from oats and thought it was related to competition with large larvae. This is unlikely to have been respon- sible for the exodus from wheat observed in 1977, since densities and feeding damage were low. To summarize the field studies on dispersal, it was found that densities within and between fields are dynamic. Beetles enter and leave both wheat and oat fields throughout the season. These rates of movement are probably affected by weather conditions, but not in any simple way. Dispersal within a field and near its border appear to be similar in rate and lack of orientation. Diffusion rates in both wheat and oats are loosely related to crop height, and after adjusting for this influence, are probably not different. Beetles probably begin to leave wheat by an increase in their diffusion rate when it becomes unsuitable as a host. In 1977 this occurred when the wheat reached a height of approximately 20 in (51 cm). A SIMULATION MODEL Overview The need to consider a spatial approach to population dynamics leads to a familiar methodological dichotomy--namely, that of small plot, intensive studies versus large scale, extensive studies. The kind of research needed to gain a detailed understanding of age- specific survival rates generally requires intensive work done on small plots, including frequent and precise determinations of density, age distribution, parasitism rates, etc. Varley and Gradwell (1970) considered this type of study to be of prime importance. However, the type of research needed to understand the redis- tribution process of an insect like the cereal leaf beetle requires extensive work done in a number of fields over a large area. The time and labor involved in each approach preclude combining them into a single effort except in unusually well-funded, short-lived projects. Even so, the resulting data are bound to be unwieldy. Experiments designed to test hypotheses about a large and com- plex system's behavior under specific conditions or to evaluate alter- native control measures and system designs may not be feasible in the real world. They may be too costly, time consuming, or even physically impossible to perform (Watt 1966). What, for example, would be the effect of doubling the wheat acreage in an entire region on the mean 120 121 density of beetles in wheat? Properly controlled and replicated experiments on this scale are difficult to achieve in the field. A logical solution to these problems is to use simulation techniques, where the results of separate studies which have taken different approaches are synthesized into a model whose behavior hope- fully compares well with that of the whole system. Some general comments on the use of systems analysis in ecology are given by Arnold and deWitt (1976), Levin (1975), Patten (1972) and Watt (1966). The role of computer modeling is aptly described by Watt (1968): ”A . difficulty in the description and analysis of dispersal phenomena is the sheer complexity of the bookkeeping because of the number of variables involved, the number of different points in space involved, and the number of different times at which we must record the variate values for the several variables at each point in space. We are led inexorably to computers." Levin (1976) reviewed the topic of population dynamics models for heterogeneous environments, illustrating the construction of models for two situations: a patchy environment of discrete habitats, and an environment continuously varying in space. Examples of models of the former type are given by Kitching (1971) and Levin and Paine (1974). Population models in which space is treated continuously include those of Bailey (1968), Richardson (1970) and Scotter §t_§1, (1971). A combination of discrete and continuous spatial approaches Inust be taken in simulating cereal leaf beetle spatial dynamics in order to capture the essential features of dispersal for this species. 122 The habitat of the cereal leaf beetle is inherently discontinuous, or patchy (see maps, Appendix D). It may be assumed that some bio- logical processes, such as feeding and oviposition, occur primarily in grain fields. However, if dispersal between fields is random, as hypothesized, then dispersing beetles may not be treated as if they move directly from patch to patch; a continuous model of dispersal, such as Bailey's (1968), is needed. Furthermore, the inter-patch, noncrop environment plays a vital role in processes such as mortality and in imposing varying time delays on dispersal between the discrete sites. The spatiotemporal spruce budworm model of Holling 25.31: (1975) suffers from a lack of detail and realism in the within-site submodel. The reason for this is given by the authors themselves (Holling ggflgl. 1976, p. 31): "Even though the previous steps of bounding may seem to have led to a highly simplified representation, the number of state variables generated is still enormous. The 79 variables (of which only one represents the insect population) in each site are replicated 265 times to give a total of 20,935 state variables. Thus even this drastic simplification . . . leads to a system that is enormously complex." Due to the limitations that the complexities of an ecosystem impose on a simulation model, the intended use of the model must govern the structure that it will have, and the resolution with which the system is simulated (Arnold and DeWitt 1976). Models describing the within-field dynamics of the cereal leaf beetle have already been constructed (Gutierrez gt_§13 1974; Fulton 123 1978; Lee EE.E£- 1976; Tummala gt 3}, 1975). Since it is only the adult which disperses, a spatiotemporal model need only include this stage, and can be linked to the detailed single—site models of the other authors by a single variable: the egg input to specific fields. Fulton's (1978) model, for example, required this information for initialization. To deal adequately with the spatial complexity of the system, then, and because within-generation population models of the cereal leaf beetle already exist, the spatiotemporal model developed here is limited in temporal scope to the period from spring emergence of overwintered adult beetles to oviposition in the host crop. It has a high degree of temporal resolution to capture the dynamics of dis- persal. Its spatial scope is a region of 16 miz, with a spatial resolution of ten acres. An overall block diagram for a spatiotemporal model of the cereal leaf beetle in a regional crop system is given in Figure 25. As mentioned, the within-generation dynamics component was not incor- porated into the model developed here, and the host crop component is very simply represented by the height and relative suitability of each crop. The components within the box drawn with a dashed line represent the aggregate of regional processes; the solid arrows represent vectors of flow rates between sites. The components out- side the dashed line represent within-site processes--name1y, the integration of net dispersal and mortality rates to arrive at adult density, oviposition within the field, and the process by which the probability of leaving the site is determined. The letters S, T and 124 I7 :- ------------- 1 Qua/3P0 I H : n : I} : If- I I S 9 Inter-aite I out: + (it ff 222::tion I T 9 :iaperaal ‘ rate Population . H 9 roceaa : - Dyn-ica I I .l\ ' I hold” : danaity larval I ' 1 feeding I an t | 7* rate ' I I I I I 8’ I I N ' 31“ Plant ' , 2x1: crop Growth 5 w : 0D > 9 I Proceaa auitability DeveloplIent ‘ , I l mergence : T l, I I H L ____________ J Fig. 25.--Block diagram of a model for the distribution and abundance of the cereal leaf beetle. 125 W stand for spatial, temporal, and weather factors which affect these processes, and M denotes mortality. In the simulation model, the 16 mi2 area is represented by a 32 x 32 grid of lO-acre cells. The simulated area can be patterned after the pubescent wheat study area near Galien by using the habitat data from the remote sensing work to assign a dominant habitat to each cell. These habitats are (1) S-wheat, (2) R-wheat, (3) oats, (4) nonhost cropland, (5) sparse woods, (6) dense woods and (7) water. To determine the initial locations of overwintering adults, the dis- tributions of woods edge and fencerows are also utilized, but in the model these small habitats occupy no space and have no effect on dis- persal rates. Prior to oat emergence, oat fields are treated as non- host cropland. State variables which are kept track of by the model include the number of adults and eggs in every cell, the cumulative total of emerged beetles and of sexually mature beetles, the height of each host crop, the time, in days, since 1 April, and the degree—day accu- mulations above 42°F (5.5°C) and 48°F (8.9°C). Input variables include the daily degree-days above both bases, the mean daily temperature, and the size of the overwintering population. Fixed design parameters are the numerical distribution of overwintering adults among the different overwintering habitats, the emergence rate of adults as a function of °D > 48, the maturation delay for female adults as a function of temperature, the adult :mortality rate as a function of temperature, the oviposition rate in 126 each crop as a function of beetle age, the diffusion coefficient in the host crops as a function of crop height, and the maximum height of each host crop and its rate of growth as a function of °D > 42. Tunable design parameters, or those which can be varied to evaluate alternate system designs, are the spatial pattern of nonhost habitats, the crop pattern for the year, in terms of the size, shape, location and variety of each small grain field, the degree of resis- tance for the pubescent wheat, the relative synchrony of the beetle with its host crops, the synchrony of winter and spring grains, the diffusion rate in each nonhost habitat, the degree to which each habitat acts as a barrier to diffusion or is attractive to dispersing beetles, the height at which wheat becomes unsuitable as a host and the degree of this unsuitability. A listing of the FORTRAN computer program for the simulation model is given in Appendix H. Mathematical Approach to Diffusion The probability of a diffusing particle being outside of a bounded area after a fixed length of time, given that it started out within the area, is related to the diffusion coefficient. Two dimen— sional diffusion without drift is described by the partial differential equation 2 2 3t 2 2 3X BY where ¢(x,y,t) gives the probability that at time t the particle will be at position (x,y) and D is the 2-dimensional diffusion coefficient 127 introduced earlier (Pielou 1977, p. 170). The solution to this equation can be shown to be the bivariate normal distribution, ¢(x,y,t) = 5%62 e-ch - x0)2 + (y - y012]/202 (22) where (x0, yo) is the initial position and 02 = var(x) = var(y) = ZDt. For the simulation model we need to know the probability that a diffusing beetle will be outside of (has left) a 10-acre cell at time t. For a fixed time span and cell size, this probability depends only on the values of D and (x0, yo). By assuming that the popu- lation is uniformly distributed within the cell, we can find the mean probability of leaving10 the cell for the population as a whole. This will depend only on D. To do this the probability density function (22) must be integrated over the range of x and y coordinates representing the field, as we let (x0, yo) range uniformly over the entire cell. This integral gives the probability of being inside the cell, so its value subtracted from 1.0 gives the desired quantity. Thus, the probability of leaving the cell is 1 a a a a - —3—I(x- )2 + I - )2] P = 1.0 - TEEQEDI.'f f f f e 4Dt u y V dxdydudv (23) -a-a-a-a 10Actually, the probability of leaving the cell is not the same as the probability of being outside after some interval, since the beetle may return. The probability wanted for the model is the latter, and its derivation is given, although for convenience I may refer to this as the probability of leaving the cell. 128 where (0,0) is the center of the cell which is 2a x 2a in size and (u,V) gives the initial location of an individual in the cell. Figure 26 shows the probable location of a beetle starting out in the center of a lO-acre cell after t minutes given a mean diffusion rate D such that 2Dt = 2 x 106 inz. For example, if D = 500 inz/min, then t = 2000 min, or 33 hr. The volume under the bell- shaped surface is the probability of being inside the field, in this case .74. Thus the probability of being outside is .26. Figure 27 shows the probability density function for a beetle starting out half way from the center toward each edge of the cell, with the same value for 2Dt. Clearly, there is a higher probability of being out- side of the cell. Equation (23) gives the mean probability for all possible starting locations. Figure 28 shows the same density function as in Figure 27 but with ZDt twice as large. That is, after twice as long a time or with twice the diffusion rate. The probable locations are obviously spread farther in all directions. Although P in equation (23) depends only on 2Dt for a fixed cell size, there is no closed solution to the equation; it must be solved by numerical integration. This was done for a 10-acre cell, and the resulting solution is shown in Figure 29. The equation, LOGlo(Y) = -3.688 + 0.4958 LOGlo(X), (24) where Y is the probability of being outside of the field (averaged over all possible starting locations) and X = 2Dt, fits the calculated points extremely well except for very high values of 2Dt. This is because equation (23) is asymptotic at 1.0, but equation (24) goes to 129 Fig. 26.--Probability density for the location after t minutes of a beetle starting out in the center of a 10-acre field given a diffusion rate D such that 2Dt = 2 x 106 inz. Fig. 27.--Probability density for the location after t minutes of a beetle starting out half way toward each edge from the center of a lO-acge field given a diffusion rate D such that 2Dt = 2 x 10 in . Fig. 28.--Probability density for the location after t minutes of a beetle starting out half way toward each edge from the center of a lO-acre field given a diffusion rate D such that 20: = 4 x 106 inz. Mun) 130 I -:. a. n..:. - - - .v _, ’ -.- .:..::.~ - 131 0.30 TEN HCRE FIELD 1 0.20 L LOOIYI = -3.688 9 0.4958 LOGIX) PROBHBILITY OF LERVING FIELD .00 I I ”’1 S 1.0 1.6 2.0 ZDT (MILLION SOUHRE INCHES) 0 ”’T 000 0. Fig. 29.--Mean probability of being outside of a 10-acre cell as a function of time (t) and the diffusion rate (D). 132 infinity. The maximum point plotted, however, represents a fairly high diffusion rate or long time interval, say D = 1000 inz/min and t = 1000 min 16.7 hr. The simulation model requires daily rates (15 hr day), so the maximum point plotted represents one day of diffusion at a continuous rate higher than normally observed (Figure 20). Bailey (1968) has developed equations to express the change in the size of a spatially distributed population with stochastic birth, death, and migration processes. The simplifying assumptions are made that the birth, death, and migration rates, A, u and v are constant through both time and space. Bailey hypothesizes a popu- lation existing at the nodes of a square lattice, and permits migration to lattice point (i,j) only from its four nearest neigh- bors (i+1, j), (i-l, j), (i, j+l) and (i, j-l). He gives the rate of change in the mean value, mij’ of the random variable xij(t)’ the colony size at (i,j) at time t, as dm.. 1 = - - dt (4 “ °)mij + V/4 (mi,j+1 + mi,j-l + (25) ). mi+1.j + mi-1.j Bailey (1968) then deve10ps equations for the explicit solution to (25). For the present simulation model, the explicit solution is of little use, since the parameters A, u and v are not constants, but vary in time and space (in different habitats). These complexities are easily handled in a computer simulation by solving an equation such as (25), with variable parameters, numerically. 133 Bailey's (1968) differential equation (25) was modified to incorporate the possibility of nonrandom exchange between neighboring cells. This was done to evaluate alternative assumptions about the nature of the dispersal process. These assumptions are, in order of stringency: (l) neutrality (random exchange), (2) repulsion (habitats may act as barriers to dispersal) and (3) attraction. These variations were incorporated by introducing an absorptivity constant, A, associ- ated with each habitat type. An absorptivity of A = 0.0 signifies a perfect barrier: no dispersing beetles enter such a habitat. This was used for the boundary surrounding the simulated region, for water, and for dense woods. A nonabsorptive habitat may be regarded as a perfect reflector, also. Beetles that might have entered that habitat are, in effect, turned back. By placing a perfectly reflecting barrier along the boundary of the region, mirror-image symmetry is accomplished: losses from within the region are exactly balanced by gains from outside. An absorptivity of A = 1.0 gives a neutral model, such as Bailey's (1968). When 0 < A < 1, partially reflective barriers are created, where the probability of exchange between the two sites is A times the probability for a neutral model. When A is greater than 1, a habitat is attractive, and the probability of an individual entering the site from a neighboring cell is also A times the random probability. Repulsion is considered to be a less— demanding assumption because it does not necessarily involve action at a distance. It simply states that a portion of those beetles which would otherwise have crossed the boundary are turned back. For attraction to be operative, beetles which would not have approached 134 the boundary must be drawn to and across it. Comparison of the model's behavior under the various assumptions permits their validity to be evaluated. In general, the simplest hypothesis which explains the observed behavior should be made. The rate of change of a cell's population of adults is thus given by the following modification of equation (25): dm.. 1]: - . dt Eij (“ * vijNBij)mij + AiJ/4 (mi, j+l Vi, j+l (26) mi. j-l Vi. j—1 * “1+1, 3 V1.1, j * mi-l. j v1-1. I)- All rates are expressed on a per-day basis. Eij is the rate of emergence from overwintering sites within the cell, u is the daily mortality rate of adults, Vij is the probability of leaving the cell in one day by random diffusion (from equation 24), NBij is the non- barrier portion of the cell's boundary, and is given by the mean absorptivity of its four neighboring cells. For example, if all absorptivities are 1.0, then emigration is the same as for random diffusion. If dense woods, a perfect barrier, borders the cell on two sides, then NBij = (l + l + 0 + 0)/4 = .5, and the loss rate from the cell is reduced by half. If one neighboring cell is attractive, say with A = 2.0, then NBij = (1 + 1 + 1 + 2) = 1.25, and the rate of loss from the cell is increased. If the cell in question is, itself, reflective (Aij < 1.0), then immigration from neighboring cells is reduced accordingly. The model outlined here is essentially the same as Bailey's (1968), except the population is located in cells which cover the 135 region rather than at the nodes of a grid. Furthermore, by allowing parameters to differ in the various habitats, the heterogeneity of the cereal leaf beetle's environment is taken into account. Bailey's explicit solution involved a probability of exchange between each site and 311_others, however distant. This poses computational difficulties. By solving (26) numerically and considering rates of change in sufficiently small time steps, only exchange between neighboring cells need be considered. This is, in effect, a random— walk approximation to diffusion (Karlin and Taylor 1975). The standard values used initially in the model were A = 1.0 for host crops and nonhost cropland, A = 0.5 for sparse woods, and A = 0.0 for dense woods, water and the boundary of the region. The standard diffusion coefficients, which determine the probability of leaving a cell by random dispersal, were D = 584 for nonhost cropland, grain fields prior to emergence of the seedlings, and water. This was the mean value in grasses and stubble fields at Gull Lake in 1976. Cells dominated by water, although perfect barriers, require an associated diffusion rate because they may con- tain minor acreages of other habitats. Overwintered beetles emerging from these habitats must be permitted to disperse out of the cell. For lack of any information, the diffusion rate in sparse and dense woods was arbitrarily set to 500. In the host crops, the diffusion coefficient was calculated as D = 4230/HT - 148.3, where HT is the crop height in inches (Figure 23). To simulate the exodus of beetles from maturing wheat, a critical height can be specified at which point the diffusion rate and/or absorptivity of wheat may be altered. 136 In the standard simulation, this height was 20 inches (the height at which the exodus in 1977 was observed to begin), and the diffusion rate at this point was changed to that of nonhost cropland. The absorptivity remained unaltered at 1.0. Other Components Timing_of Events The model simulates events over the period 1 April to 15 July. All rates are calculated on a daily basis, but may be functions of degree-days or mean daily temperature. Rates of plant growth are related to °D > 42(F) (5.5°C), while those affecting the CLB are in terms of °D > 48(F) (8.9°C). Degree-day accumulations by date are given in the model by the 30-year mean accumulations at Eau Claire, Michigan (Berrien County) over the period 1931-60 (Figure 30). These were obtained, by interpolation, from accumulations reported by Van Den Brink gt_§13 (1971) for the bases 40, 45 and 50°F. Van Den Brink calculated °D > 42 as (Max + Min)/2 - 42, where (Max + Min)/2 is a good approximation to mean daily temperature. Mean daily temperature (°F) was therefore back-calculated in the model as TEMP = DD42 + 42. This overestimates the temperature slightly early in the season, since Van Den Brink set °D > 42 to zero when the mean daily temperature was less than 42. Degree-day accumu- lations were stored as arrays and a table look-up function retrieved the current accumulation. It would be an easy matter to input actual field temperatures to calculate degree-day accumulations and mean temperatures, if 137 §1 ERU CIHIRE. HICHIoHN N I DISC 42 IF) I DOSE 4. IF) JULY 15 CUHULHTIVE DEDREE-DHYS ‘¥°° 8H 0 8H ' I I I U I °bo I60 120 140 130 I00 200 DRY 0F YERR Fig. 30.--Mean degree-day accumulations at Eau Claire, M1 for the period 1931-60. INCHES 2? ID 20 l 1 CROP HEIGHT. D L O HHEHI I DRY! T I I 1 I I l I too «no :00 too 1000 I200 1400 I300 I000 DEGREE-OBIS > 42 IF) Fig. 3l.--Cr0p growth curves for the standard simulation. 138 desired. The goals of the simulation work were general, however, and such detail was unnecessary. The model was used to evaluate the influence of general spatial and temporal patterns on beetle dis- tribution and abundance, and for this purpose average temperature conditions were an appropriate simplification. Crop Growth Crop growth was simulated by defining functional relationships between crop height and accumulated °D > 42 (DD42). No variation in height between fields was incorporated, again because of the general goals of the current work. The mean height of wheat on each sampling date in 1977 at Galien is shown in Figure 31. A cubic regression was fitted to the data to describe the relationship: 3 HTW = -1.55 + 9.57 x 10‘ 0042 + 3.58 x 10’5 (0042)2 (27) -1.89 x 10'8 (0042)3 where HTW is the mean wheat height, in inches. The 1977 data were used to develop the wheat equation because, due to the early season, a fairly complete growth was observed. Only eight oat fields provided data for 1977, however, and they were planted over a wide range of dates. A plot of mean oat height for this year was therefore very atypical. For this reason, the 1976 mean oat height data were used. These are shown in Figure 31, translated ZOO°D > 42 later to give the wheat and oat growth curves a temporal relationship which seemed typical of other years. The cubic regression for oat height is: 139 HTO = -21.2 + .0563 x -2.82 x 10‘5 x2 (28) + 8.18 x 10'9 x3 where HTO is the mean oat height in inches and X = DD42 - 200. Oats were permitted to reach a maximum height of 30 in, the maximum attained by wheat. To evaluate the effect of varying the synchrony between the beetle and its hosts, or between winter and spring grains, the two crop growth curves can be independently shifted earlier or later by any °D > 42 value using the parameters DWX and DOX. Wheat Resistance There are three means of simulating resistance in wheat in the model. Adult densities can be reduced by increasing the diffusion rate (and hence, emigration rate) in R-wheat by multiplying the D value for S-wheat by a factor, DINCR. Adult densities can also be reduced by setting the absorptivity, A, to less than 1.0 to make R-wheat a partially repulsive crop. Neither of these options was used in the standard run. There is no evidence for the latter phe- nomenon. The mean diffusion rate measured in R-wheat at Galien in 1977 was not significantly different from that in S-wheat. In 1977 the mean density of adults was lower in R-wheat, but in 1976 it was inOt (Sawyer 1976b, 1978). Thus, in the standard run, DINCR = 1.0 and A for R-wheat = 1.0. The other way to incorporate resistance is by reducing the cWiposition rate per female by a factor, OVRED. There is ample eVidence for this phenomenon (Sawyer 1976b, 1978; Gallun ital. 1966; 140 Schillinger and Gallun 1968; Hoxie gt_§13 1975; Casagrande and Haynes 1976b). For the standard run, OVRED = 0.68, the observed reduction in eggs laid per adult-°D at Galien in 1977. Spring Adult Emergence Casagrande gt 31. (1977) reported the relative density of cereal leaf beetles in the five overwintering habitats at Galien, based on two years' (1974-75) trapping data. Data from 1976 and 1977 (Sawyer 1976b, 1978) were added to the earlier information, and updated distributions (Table 15) were calculated by the method described by Casagrande gt_§1, (1977). Let T be the sum of the mean densities/yd2 of emerging beetles in the five habitats. Then the last row of Table 15 gives the expected density in each habitat as a percent of T. The actual acreage of each habitat in each cell at Galien was available from the remote sensing data. T was entered as an input variable. For each cell (i,j), the total number of adults emerging was calculated as: 5 = 29 AEij 48,400 hil Ahij db? ( ) where A is the relative area occupied by habitat h in cell (i,j), hij th is the mean regional density of emerging beetles in habitat h, and 48,400 is the number of yd2 in 10 acres. The daily rate of emergence was related to °D > 48 using data afki the approach given by Casagrande (1975, pp. 20—22). Regressions Of' the probit of cumulative proportion emerged on the logarithm of °D 3> 48 were calculated separately for Casagrande's 1971, 1973 and 141 Table 15.-—Re1ative density of cereal leaf beetles in each of five overwintering habitats at Galien, 1974-77 (modified from Casagrande §t_al. 1977). Habitat Crop Dense Sparse Woods Fence T t 1 Land Woods Woods Edge Rows O a 1974 Traps 3 5 7 6 8 29 Density/yd2 .333 .800 1.429 1.500 5.125 8.854 % of Total 3.761 9.035 16.140 16.941 57.883 1975 Traps O 12 12 12 12 48 Density/ydz — 1.917 6.417 6.583 4.833 19.750 % of Total - 9.706 32.491 33.331 24.470 1976 Traps 26 18 30 30 23 127 Density/yd2 1.346 0.111 0.667 2.067 3.565 7.756 % of Total 17.354 1.431 8.600 25.650 45.964 1977 Traps 20 30 20 16 14 100 Density/yd2 1.050 0.200 1.800 2.063 1 500 6.613 % of Total 15.879 3.025 27.221 31.198 22.684 Weighted i 15.920 4.279 18.917 28.129 37.394 104.639 Adjusted i 15.214 4.089 18.078 26.882 35.736 100 142 1974 data. The average slope and intercept, weighted for each year's number of data points, gave the following equation: PROBIT (Proportion) = -7.772 + 6.098 LDD48 (30) where LDD48 is the common logarithm of °D > 48. This equation is equivalent to a log-normal probability density function (pdf) with mean u = (5-intercept)/slope = 2.094 and standard deviation 0 = l/slope = 0.164 (Finney 1971, p. 24). The point of 50% emergence is given by 10U = 124.3°D > 48. The cumulative proportion emerged is found by integrating the density function over time (log °D scale). Figure 32 shows the emergence of overwintered adults where the log—normal pdf has been integrated in increments of one °D > 48. In the model the emergence curve can be shifted earlier or later by any specified °D > 48 using the parameter DEM. Sexual Maturation Once beetles have emerged they begin to disperse through the environment, but do not begin to oviposit until they have undergone a temperature-dependent maturation process. A slight modification of Fulton's (1978) approach to modeling the process was used here. Maturation is represented by a time varying distributed delay (Manetsch and Park 1977, as modified by Fulton 1978), the length of which is a decreasing function of temperature (Yun 1967). The relationship between maturation time and temperature, and the prop- erties of the delay process, are exactly as in Fulton (1978, p. 16). The input to the delay is the emergence rate. The output is the 143 92 GULL LHKE. 1971. 73. 74 ° (DERIVED FROH cnsnoRnIIDE 1975) PERCENT EHERGENCE PER DEG-DRY Y Y Y Y ' *T Y V f f 1 T I I ’7‘ t v 100 200 v 300 400 DEGREE-DRYS > 48 (F) Fig. 32.--Emergence of overwintered cereal leaf beetles as a function of °D > 48(F). 144 rate of maturation. These two rates are integrated through time, and the ratio of cumulative maturation to cumulative emergence gives the proportion of emerged adults which are sexually mature. Using this factor it is an easy matter to calculate the number of sexually mature, hence ovipositing, females present in each cell. A sex ratio of 50:50 was assumed. Oviposition Unpublished data of S. G. Wellso were used to relate the ovi- position rate of females to their age in terms of °D > 9(C) since the first eggs are laid in the crop. For wheat, the "zero-age" was taken to be when 5% of the emerged females had sexually matured. For oats, the starting point was when oats emerged. These points were assumed because in Wellso's (1976) experiment beetles were confined in a field cage until the first eggs appeared, then observations on the oviposition rate were begun. Twenty-two beetles were used in wheat, so one mature beetle is about 5%. For oats, I assumed beetles are already mature and begin ovipositing as soon as they enter the crop, which is as soon as it emerges. Probit regressions were fitted to Wellso's data on cumulative eggs/female vs °D > 9(C). The best fitting equations gave the normal curves shown in Figures 33 and 34, generated at intervals of 1°D > 9. The normal equations have parameters u = 144, 02 = 27,321 for wheat and u = 146, 02 = 48,968 for oats. Daily oviposition rates are cal- culated in the model by integrating the probability functions over One-day intervals. 145 E. LENSING HHEHT. 1972 (HELLSO. UNPUBL. DHTHI EGGS/FEHRLE/DEOREE-DRY : T I I I I o 100 200 300 400 600 CUHULRTIVE DEGREE-DRYS > 9 (C) e- N E. LENSING ORTS. 1972 I ' (HELLSO. UNPUBL. DRTR) 9‘ as 4 6:4 % . EGGS/FEHRLE/DEGREE-DRY T I Y Y T 100 200 Y 300 ' 400 600 000 CUHULQTIVE DEGREE-OBIS > 9 (C) a CI 0 Fig. 33-34.—-Oviposition rates in wheat and oats as a function of °D > 9(C) since first egg. 146 Adult Mortality Adult mortality in the model is a function of temperature. The approach taken by Fulton (1978) was used here. Upon consulting his data source (Casagrande 1975, p. 28), however, it was discovered that several points were apparently calculated erroneously by Fulton (1978, Figure 6), so the original data were reworked here. Figure 35 shows the regression of instantaneous survival (per day) on tempera- ture (°C), which differs only slightly from Fulton's (1978) equation. The equation is: a = .00194 - .00206 (TEMP) (31) where a is the instantaneous survival rate and TEMP is the mean temperature (°C) over the period for which the mortality applies. The daily mortality rate is given by l-exp(a) in the model since exp(a) is the proportion surviving through one day (Fulton 1978). 147 I 0.02 I ‘0002 0.00 i -0004 L -0006 L B Q L I = 0.00194 - 0.00206 x I!2 = 0.180. r > 0.10 (HDDIFIED FROH FULTON. 1978) -0-08 1 INSTRNTRNEOUS SURVIVRL (l/OHY) -0-10 -D-12 1 I I I I’ I ’1 10 12 I4 16 18 20 22 24 TENPERRTURE (C) 0‘0-14 Fig. 35.--Instantaneous survival rate of adults as a function of temperature. MODEL VALIDATION Time Increment Before evaluating the model it was necessary to check the stability of the output as the time increment, dt, was varied. A small dt produces smaller integration errors and avoids instability in the delays and feedback loops, but increases the cost of executing the program. The output from the standard run was examined as dt was given the values .025, .05, .1, .2, .25, .5 and 1.0 day. Instability resulted at dt = 1.0 (that is, the output changed dramatically as dt was changed from 0.5 to 1.0), and the cost of execution increased rapidly for dt < 0.2. A value of 0.25 day was used in all subsequent simulations. One run of the program takes 75 seconds of central processor time on the CDC 6500 computer, and costs $2.50 (excluding printing) at the lowest priority rate. Evaluation Criteria The model's output was compared to observations made at Galien in 1976 and 1977. The model was essentially constructed inde- pendently of these observations, but certain initializing parameters had to be set. These included, obviously, the spatial configuration (bf land use for each year and the regional mean overwintering density. l\lso, needed, however, were parameters adjusting the timing of beetle Eflnergence and crop growth, because these events vary somewhat in their 148 149 occurrence even on the appropriate degree-day scale. For example, the height of winter wheat early in the year may be related to the amount of winter precipitation, the planting date of oats depends on field conditions and the farmers' work schedules, and the emergence of cereal leaf beetles may be either early, as in 1972 at Gull Lake (Casagrande 1975) or late, as in 1977 at Galien (Sawyer 1978) on a °D > 48 scale if the spring is unusually cool or warm. Until these phenomena are better understood and can be modeled, initial obser- vations must be made to establish the timing of events. In the simulations, the values of DWX, DOX and DEM were adjusted so that the simulated rates of wheat growth, oat growth and spring adult emergence, respectively, were in agreement with the timing of these events as observed in the field. These constants were added to or subtracted from the °D > 42 and °D > 48 accumulations serving as 'the independent variables in equations describing the growth and ennergence curves, thus "shifting" the curves earlier or later. The degree of resistance shown by R-wheat varies, too, depending on the vzxriety used, etc., so OVRED was set from its observed value. The criteria used to judge the success of the model in pre- dixrting actual events in 1977 included the total adult degree-days and egg input for the year in each crop (total number and density per éicre), the peak adult population in small grains and the time Of itds occurrence, the total adult activity and egg densities in each field, and the general correspondence between model and Obsermration in the pattern of population trends through time in each 150 crop (a graphical evaluation). For 1976 only the graphical output was evaluated. Standard Parameters For the standard 1977 simulation, the absorptivities, critical wheat height (signaling maturation of the crop), degree of R-wheat resistance, and timing of growth curves for wheat and oats were all set as discussed above. The point of 50% emergence of overwintered adults was shifted 100°D > 48 later, since in this year with a warm, early spring the median emergence point was not until about 224°D > 48. The peak regional populations estimated by the model with these parameter values were too low, and, contrary to observation, the peak regional population was greater in R-wheat than in S-wheat. Apparently, dispersing beetles were spending too much time in nonhost habitats compared to small grains, and since R-wheat and S—wheat were :identical except for the oviposition rate, the larger number of Iaeetles in R-wheat simply reflected a greater acreage of this crop. Since the diffusion rates in nonhost crops have not been standied (except for a small number of observations by Lampert), these values had been set rather arbitrarily in the model. They were row adjtisted upward until the peak population in S-wheat was near the Observed value. To reduce the population in R-wheat, DINCR was increased until the peak population in that crop was also near its Obseifived value. The values arrived at were D = 8000 inZ/min for all licrnhost habitats and for wheat taller than the critical height, and DINCR = 10.0. 151 Figure 36 shows the regional population in 1977 in each crop vs °D > 48. The correspondence between predicted and observed is fairly good except at three points. The field data show a large drop in population at around 350 to 400°D. This has already been discussed in relation to weather factors in an earlier section. The decline may be related to cool weather, but it is not certain. The second point of discrepancy is for R-wheat from 600 to 700°D. This crop did not exhibit the rapid decline in population which S-wheat experienced. The reason for this is unclear, but may be due to a difference in the rate of crop maturation. Finally, the populations in all crops remained too high at the end of the season in the model. This is probably due to a late-season acceleration in mortality and crop senescence in the field but unaccounted for by the model. Figure 37 shows the results of the 1976 simulation. The same parameter values were used except T, the sum of the mean overwintering (densities in five habitats, was 6.66, OVRED, the reduction in the (Jviposition rate in R—wheat, was 0.58 as observed in 1976, and DINCR Iwas set at 2.0. The adult emergence curve was shifted 50°D > 48 later than standard, the wheat growth curve was shifted 200°D > 42 eaJfllier, and the oat growth curve was shifted 30°D > 42 earlier to estnablish the prOper timing of these events as discussed above. No _eValuation of the 1976 results were made other than to note the fairly good correspondence between observed and predicted populations in Ffiigure 37. All further discussion of validation applies to the 1977 simulation. 152 m7 I 61 1977 HIGH DIFFUSION RFITES ‘é’ ,4 0 s—IIHEIII C - x R—HHERI _J 4 d + ORTS 1: -I I .J E I '5 0 xxx x F- d x _1 N a x CI 2 . o u H X 8 4 . m d #§ 4 4' T + F + G X \ + u . +9”: :1 I :I'" I I 0 200 400 600 800 1000 1200 DEGREE-DRYS > 48 IF) Fig. 36.--Total regional adult population in each crop in 1977 vs °D > 48, with simulation results using standard parameter values and high diffusion rates. 2‘1 I a, 1976 STRNDRRD RUN w _ U S-HHERT €23 ‘9 “ x R-HHEHT 3 4 4 DRIS .1 H t d . (D .J CE 4 .— O 0... fi _’ Q CI 2 a 4 H (D In .1 (z w I \ O I ' I I O 200 400 600 000 1000 1200 DEGREE-DRYS > 48 (F) Fig: 5372--Observed and predicted total regional adult population in each crop in 1976 vs °D > 48. 153 The high value (10.0) required for DINCR in order to reduce the population in R-wheat sufficiently was surprising, since no such difference in the diffusion rates for R-wheat and S-wheat was observed in the field studies. The effect of decreasing the absorp- tivity of R—wheat is examined below. Table 16 lists the observed and predicted values for some validation criteria. The correspondence is very good for most vari- ables on the regional scale except in oats, where the seasonal totals are too high but the peak population is too low (this is also evident in Figure 36). For the individual fields, however, the model generally fails to predict densities accurately. In particular, the wide range of densities found in the field is not duplicated by the model. For example, actual adult densities in S-wheat ranged from 44 to 246 adult-°D/ft2, while the model produced densities ranging only from 66 to 122 (Figure 38). The coefficient of variation in adult densi- ties was 55.1% in the field, but only 13.8% in the model. For S-wheat at least, there was a significant correlation between observed zand predicted densities of both adults and eggs (r = .435, p = .03 :Eor adults, and r = .395, p = .05 for eggs). In this crop the model Ivas correct in its identification of the field with the highest athilt density, and nearly correct about the field with the lowest density. For the other crops, however, the model failed entirely to Predict appropriate densities. That the mean densities produced by the model are fairly ac1Curate, that there was a significant correlation, although slight, 15 4 Table l6.--Observed and predicted values of several validation criteria for run 11 of the simulation model (1977, high diffusion rates). S-wheat R-wheat Oats obs. model obs. model obs. model I. Seasonal Totals Adult-°D/Region (x109) 1.25 1.61 1.35 1.63 .242 .388 Adult-°D/Acre 3.59 4.03 2.26 2.71 3.10 4.85 Eggs/Region 1.24 1.78 0.91 1.26 .427 .686 Eggs/Acre 3.57 4.45 1.53 2.10 5.47 8.57 Eggs/Adult-°D .100 .110 .068 .078 .176 .177 11. Regional Totals Peak adults 4.32 3.63 3.27 3.12 .889 .423 °D > 48 at peak 496 496 488 496 636 816 III. Individual Fields, Seasonal Production No. fields 25 37 7 Min. Adult-°D/ft2 44.0 66.3 24.4 50.4 12.7 103. Max. Adult-°D/ft2 246. 122. 115. 74.3 187. 125. i Adult-°D/ft2 88.6 97.2 50.8 62.1 86.0 113. C.V. (%) 55.1 13.8 45.6 8.50 77.8 6.69 rxy .435* .162 .201 Min. Eggs/ft2 3.72 7.41 0.87 3.80 1.65 18.4 Max. Eggs/ft2 42.1 13.6 10.6 5.80 43.0 22.1 i Eggs/ft2 9.94 10.7 3.49 4.82 13.1 19.9 C.V. (%) 87.4 13.1 66.2 8.94 109. 6.24 rxy .395* .081 -.430 *p < .05 250 J RDULI 00/60 CH INODELI 150 L 155 1977 S-HHERT. HIGH DIFFUSION RHTES I f Y W 50 100 150 200 Y 250 HDULI 00/60 cn (OBSERVED) Fig. 38.—-Observed and predicted adult densities in individual S-wheat fields in 1977. Fig. 39. COEFFICIENT OF VHRIRTION HDULTS/RCRE IN S-HHERT. 1977 (STRNDHRD RUN) I fl 1 I I f T I 200 400 000 000 1000 1200 1400 1800 DEGREE-DRYS > 48 (F) --The coefficient of variation of predicted adult densities in S-wheat fields through the season. 156 between observed and predicted densities in S-wheat, and that by the other validation criteria the model performs fairly well all suggest that the model may be basically correct. It simply fails to account for the between-field variation in densities observed, particularly for fields with high densities. There are two possible reasons why the model's predicted densities are too uniform. The first has to do with the nature of the dispersal process. As noted earlier, the effect of dispersal is to homogenize the effect of local uniqueness. While dispersal per- mits nearby population sources (such as a fence row) to contribute to a field's high density, continued dispersal tends to smooth out spatial variation. This is illustrated in Figure 39, which shows the coefficient of variation (C.V.) of predicted adult densities in S-wheat fields as it changes through the season (these are simula- ‘tion results, not observed values). The C.V. initially declines (A to B) due to diSpersal homogenizing the original differences in density related to the spatial distribution of overwintering sites. It then increased beginning at the time of peak emergence (B) to a maximum at the time of highest field populations (C). This may be due to the effects of continued emergence from the heterogeneous overwintering sites again overcoming the smoothing effect of dis- Persal, as the emigration rate from the host crops declines with increasing crop height. When the exodus from wheat begins, the high diffiision rate again homogenizes densities (C to D) until the C.V. reacflies a minimum (D). The subsequent increase from D to E seems to berelated to the effects of neighboring habitats. A nearby oat field, 157 for example, acts to decrease a wheat field's population because it acts as a sink. With the declining diffusion rate in oats as they get taller, beetles entering that crop will remain, and not reenter neighboring wheat. A nearby dense woodlot, on the other hand, acts as a barrier and serves to preserve higher densities in the wheat field. These last ideas were confirmed by an examination of the habitat surrounding fields with particularly low or high predicted densities. Thus, there are two opposing forces at work regulating rates of population buildup and declinezdispersal, which has an homogenizing influence, and local uniqueness, which has the opposite effect. The high diffusion rates used in the simulation to drive beetles out of the nonhost habitats and into small grains may be responsible for excessive uniformity in the resulting densities. This is examined in the next section. A second possible reason for the failure of the model to pre—~ dict an adequate range of densities is also related to the property of local uniqueness. As noted earlier, between-field differences in crop height were not incorporated into the model. In fact, the only contributors to local uniqueness that were incorporated were differ- ences in the habitats surrounding the fields. There may be other attributes of fields with high density which were not considered in ‘the model. Four possibilities are (l) the relative crop maturity (planting date, growth rate) of the field; (2) some environmental Condition (such as soil type, topography, soil moisture, wind patterns) CH? interaction not accounted for by the model; (3) heterogeneity, or aggregation, in the overwintering populations within a given habitat, 158 resulting from the existence of "hot spots" of high beetle density created by chance, by aggregation behavior of the beetle, or by specific combinations of habitats being particularly favorable over- wintering sites; and (4) density dependent effects. Levin (1976, p. 294) notes that "density-dependent factors in dispersal or recolon- ization success can lead . . . to spatio-temporal patterning." Several of these factors were checked for the 12 S-wheat fields with the highest observed adult densities in 1977. These fields were not atypical with respect to soil type, slope, or crop height at any point in the season. The hierarchical clustering discussed earlier showed no grouping together of these 12 fields based on the measured habitat features. Alternatives to Random Dispersal As mentioned above, the high diffusion rates used in the simulation may have led to the homogeneous resultant densities. To test this idea, the diffusion rate was lowered to 4000 inz/min in nonhost cropland and in oats prior to germination, and to 6000 in woods. The absorptivity of nonhost cropland was changed to 0.5. At the critical height in wheat, the diffusion rate was changed to 6000 .and the absorptivity was dropped to 0.25. These measures were intended to reduce the proportion of the population in nonhost habi- ‘tats, thereby maintaining appropriate numbers in the host crops, while iPermfitting the use of lower dispersal rates in an attempt to lessen the homogenizing influence of dispersal. The result, instead, was a Smaller coefficient of variation of adult densities in S-wheat fields (13.4%), and a lower, now insignificant, correlation between observed 159 and expected densities (.381). Furthermore, these new parameter values led to a poorer match of model output to observation for the regional total in oats, and a smaller difference between the peak population in S-wheat and R—wheat (Figure 40). The effect of making the host crops attractive to the cereal leaf beetle was examined by increasing the absorptivity of S-wheat and oats to 2.0, and of R-wheat to 1.5. The absorptivity of nonhost cropland was again set at 0.5. The diffusion rate in cropland was lowered to 2000, and in woods to 4000. At the critical wheat height the absorptivity of S-wheat and R-wheat was changed to 0.25 and the diffusion rate to 4000. The result (Figure 41) was a better fit of the population total curves to observed values in S-wheat and R- wheat, but a much worse fit in oats. The C.V. of adult densities in S-wheat was slightly higher (15.5%), but the correlation between actual and predicted adult densities was lower still (.318). In conclusion, reducing the diffusion rate did not lead to less homogeneity in adult densities in the host crops. Making other habitats less absorptive and making the host crops more attractive did increase the number of beetles found in small grains, but at the expense of reduced correspondence between observed and predicted densities in the individual fields. The simplest assumption regarding dispersal among the various habitats, namely, random diffusion, seems .adequate to account for regional population patterns, and gives better Single-field predictions than the assumptions of repulsion from Ianhosts or attraction to hosts. All subsequent simulations were run REGIONRL TOTHL. HILLIONS 160 1977 REDUCED HBSORPTIVITY g , (RUN 13) x R-NHERT + OBIS If A‘ I 1* n I 200 400 800 000 1000 1200 1400 1800 DEGREE-DHYS > 48 (F) Fig. 40.--Tota1 regional adult population in each crop in 1977, with HILLIONS REGIONRL TOTHL. simulation results using reduced absorptivities and lower diffusion rates in nonhost habitats. 1977 HOST CROPS ATTRACTIVE g IRUNI4) I S-HHERT x R-HHERT 4 DOTS 260 400 000 000 1000 1200 1100 DEGREE-ORYS > 48 IF) 1 1600 Fig. 41.--Total regional adult population in each crop in 1977, and simulation results with host crops attractive and diffusion rates reduced in other habitats. 161 using the neutral model with a high diffusion rate (8000 inz/min) in the nonhost habitats. Environmental or temporal features other than those incor- porated into the model which increase a field's local uniqueness, or spatial variation in the density of overwintering beetles within habitats must be responsible for the great range in densities observed in the field. SIMULATIONS The Effect of Resistant Wheat One of the major objectives of the U.S.D.A. pubescent wheat pilot project conducted at Galien, MI is to determine what impact planting large acreages of resistant wheat will have on the number of cereal leaf beetles in oats. The proportion of the wheat acreage which was resistant was increased from 0% in 1975 to 13% in 1976, 63% in 1977 and nearly 100% in 1978. It was hoped that the effect of this change, if any, on the densities in oat and S-wheat fields could be assessed. The problem with this approach is that it is not a controlled experiment. Besides the proportion of wheat which was resistant, a number of other factors changed over the years. These include weather conditions, the regional CLB population level, the acreages and spatial patterns of crops, and even the variety of resistant wheat used. The advantage of simulation is that the wheat can be made susceptible or resistant while everything else is held constant: a controlled experiment can be achieved. The 1977 standard simulation was used to evaluate the effect of planting all S-wheat vs planting all R-wheat. Only the parameters (JVRED and DINCR were changed (from 1.0 to 0.68 and from 1.0 to 10.0, trespectively). The acreage of wheat was 1000 A, the acreage of oats was 80 A. 162 163 Comparing the two runs, the mean egg density in wheat was reduced from 9.69 to 5.03 eggs/ft2 by converting to R-wheat. The level of adult activity in wheat was reduced from 88.1 to 64.8 adult—°D/ft2. It might be expected that these displaced adults would end up in oats. Surprisingly, the density of adults and eggs in oats actually decreased when R-wheat was planted! The mean egg density went from 18.7 to 18.5. While this was not a statistically signifi- cant change (t = .325, 7 df), the direction of change was the oppo- site of what was expected. This remarkable result is actually easily explained in terms of spatial and temporal patterns. Most of the oat fields in 1977 were planted very near a wheat field (of one type or another). Beetles enter S-wheat and accumulate there before oats emerge from the ground. By the time the exodus of beetles from wheat occurs, however, oats are present. The dispersing adults readily move from the maturing wheat to the nearby oats, resulting in high densities in oats. If all wheat is resistant, however, there are fewer adults accumulating in the vvheat; they are more likely to disperse out of the R-wheat before (Dats emerge. By the time oats are present and the wheat matures, 'tliere is not a large, concentrated source of migrants near the oats. Irlstead, the beetles are spread throughout the environment, and the result is lower densities in oats. To test this hypothesis further, two pairs of oat fields were examined more closely in the simulation as the wheat was changed from susceptible to resistant. One member of each pair was located 164 directly between two wheat fields, while the other member, less than 1/2 mile away, had no wheat directly adjacent. (The field numbers are 136 and 235 for the between-wheat fields, and 711 and 612 for the away-from-wheat fields.) As the wheat was changed from S to R, the adult density in the two oat fields located between wheat fields decreased 2 to 3%, while in the other two oat fields the adult density increased 1 to 3%. The increase in density in oat fields not having wheat neighbors might be expected since the number of beetles dispersing in the environment would be greater when R-wheat is planted. As a further confirmation of the influence of wheat neighbors, actual adult densities in oats in 1977 were checked. Of eight oat fields, the three with the highest adult densities were located directly between two wheat fields. Four others, with significantly lower densities, had no wheat neighbors directly adjacent, while one field with one wheat neighbor was intermediate in density between the other two groups. Temporal Patterns QB Emergence Figures 42 and 43 show the effect of shifting emergence 50°D > 48 earlier or later on total regional densities in each crop. Early emergence results in higher adult and egg densities in S~wheat, lower adult density in R-wheat, and higher egg density in lW—wheat. Less activity is seen in oats. With later emergence, Opposite effects are seen. 165 ID 4 1977. EHERGENCE 50 0048 ERRLIER ‘0 .1 2 v 52 .J 4 :’ s-uncm Z . "d .1 CI 4 P I O F’ g I a; N R-HHERT Z 1 O 23 U c1 m C‘ ‘ oars c: I I I ”1* I I 1 I o 200 400 300 son 1000 1200 1400 1600 DEGREE DRYS > 48 (F) m- J 1977. EHERGENCE 50 0048 LHTER S-HHERT R-HHEHT REGIONAL TOTRL. MILLIONS Oj;§”,,.__s o I I 4T I I I I ‘fi 0 200 400 800 800 1000 1200 1400 1600 DEGREE-DRYS > 48 (F) Frig. 42-43.--CLB emergence shifted 50°D > 42 earlier and later. 166 These results are interpretable in light of the higher 0 value in R-wheat interacting with crop height. In S-wheat more adult activity is expected with earlier emergence, but in R-wheat the longer exposure to short wheat with a consequently higher dif- fusion rate drives proportionately more beetles out of this crop. The higher egg densities result from a higher mean eggs/female value for the season when emergence is earlier. The reason for this is not clear, but may be related to beetles aging less rapidly early in the season and therefore ovipositing at a higher rate. The inter- actions of temperature, sexual maturation, aging, oviposition rate and mortality are complex. Planting Date of Oats Earlier oats affects the population in wheat very little, but increases the population in oats. Therefore when oats are planted early a greater portion of the total beetle activity will take place in that crop. The small effect on wheat may be due to the very low acreage of oats in 1977 at Galien, and in the simulation. Late-planted oats has the opposite effect. Shifting the oats 100°D > 42 earlier increased the egg ciensity in oats 6%, while delaying the oats 100°D reduced the egg ciensity 21%. 100°D is about one week in mid May. The reason for the great reduction in egg density when planting was delayed is that cuat seedlings then emerged after the exodus from wheat (Figures 44, 45). IJelayed planting would appear to be a valuable management tool under the right conditions. Other interactions, such as reduced soil water 167 ”- 1977. ORTS PLRNTEO 100 0042 ERRLIER 03 z...q O .J :3 s-HHERT I: O n- .J C: .— O 5... .1 _’ N C: 2 O 5 R-HHEHT “J -I m “ firs °0 200 400 000 000 1000 1500 1:100 1000 DEGREE-DRYS > 48 (F) ”- 1977. ORTS PLRNTED 100 0042 LRTER m u 2 v E _.J 4 :1 S-HHEHT : .4 . m _J c: 4 g.— (:3 .— __1“d a: z: , S R-HHEHT (3) IL] -I c: "‘ 0975 lf”’————' " c, I I I T I T I I 0 200 400 800 000 1000 1200 1‘00 1300 DEGREE-UHYS > 48 (F) ‘Fig- 44-4S.--Oats planted 100°D > 42 earlier and later. 168 availability, and increased risk of pre-aestival feeding by adult beetles with very late—planted oats, must also be considered. Wheat Growth When the wheat growth curve is advanced 100°D > 42, the peak adult density in S-wheat and R-wheat is increased but the seasonal total activity is reduced (Figure 46). This is because the wheat matures and becomes unsuitable sooner after the beetles emerge from overwintering. The effect on the population in R-wheat is less because of the interaction of crop height and diffusion rate. The taller crop slows the rate of leaving the field, and higher densities are attained. This is relatively more important in R-wheat due to the higher diffusion rate in this crop. A delayed wheat growth curve (Figure 47) resulted in a higher adult density in S-wheat, but lower in R-wheat. Again, the inter- action of crop height and beetle diffusion rate led to a high emi- gration rate in the relatively shorter crop, and this was more :important in R-wheat. The effect on the population in oats was very similar for 130th early and late wheat: the density decreased. In the former cuase the beetles began to leave wheat before oats were available, udrile in the latter case beetles stayed in wheat longer instead of Inovntng to oats. This points out the delicate relationships involved herwe; and perhaps explains past difficulties in understanding the role of crop synchronies in determining the relative abundance of the CLB. The maximum CLB densities in oats can be expected when 169 1977. HHERT GROWTH RDVRNCEO 100 0042 S-HHERI REGIONRL TOTRL. HILLIONS N ‘ R-HHEAT _- o I T [I/Ifi I I I I I 0 200 400 000 000 1000 1200 1100 1000 DEGREE-DAYS > 48 (F) ‘0- . 1977. HHEAT GRDHTH DELAYED 100 0042 g n 0 fl 3 _l I: - s-unsnr . n _J c: . 0.. D p.- ..1 Nd C: 2 1 2 53 a: __- n-untnr cars 0 / 0 200 400 $10 000 1000 1500 1100 7000 DEGREE-DAYS > 48 (F1 Fig- 46-47.--Wheat growth advanced and delayed 100°D > 42. 170 oats emerge just as nearby wheat fields become unsuitable. When the synchrony of the crops is altered in either direction (farther apart or closer together in time), the transfer from wheat to oats will be reduced. Spatial effects interact with this because it will be the oat fields nearest wheat fields which are affected most by changes in the temporal synchronies. As with the planting of all resistant wheat, oat fields not near wheat may have higher densities when wheat growth is advanced and that crop is less suitable. Spatial Patterns Simulations on the effect of spatial patterns included runs examining the effect of altering the absolute acreage planted to host crops, of altering the relative amount of winter and spring grains, of dividing a fixed acreage of wheat into fields of various sizes, of altering the shape of fields of a given acreage, and of altering the location of fields with respect to wood lots and other fields. Resistant wheat was not involved in any of these simulations. Each of the experiments was replicated two or three times by randomly selecting which cells would have their crop type changed in the acreage simulations, and the location of fields in the field-size .and shape simulations. Fields were deliberately located for the iiield-location simulation, but three fields of each location type were selected. Maps showing the spatial configuration of each experi- ment are found in Appendix I. 171 Absolute Acreages Under standard conditions, the acreage of wheat was 1000 a, and of oats 80a. Three simulations each of doubling and halving these acreages were carried out. The mean values of adult and egg total populations and densities in the 2x and 1/2x situations will be compared. When acreages were changed from l/2x to 2x standard (increased fourfold), the total adults and eggs in wheat increased 3.24x and 3.21x, respectively. In oats the increases were 3.28x and 3.3lx for total adults and total eggs. Densities were reduced by this change in acreage by factors of .81 for both adults and eggs in wheat, and .75 for both stages in oats. These results show that an increase in acreage is matched by an almost equal increase in the total population. There is a small effect of "dilution," however, as shown by the decreases in density. The results suggest that a large portion of the population is not found in the host crops at any one time, but is dispersing between :fields. When more host crop acreage is available, beetles are more likely to enter it, and a proportionately greater amount of their total activity takes place in the crop. These results are supported by the observation at Galien in 15976 and 1977 that only a fraction of the total number of beetles estimated to have emerged from overwintering can be accounted for if! the grain fields at the time of peak regional density. For eXé'unple, in 1977 the sum of the mean densities in five overwintering 172 habitats was 6.61. This sum was then distributed among the five habitats according to the frequency distribution developed above (Table 15), and the resulting estimates of density in each habitat were multiplied by the total acreage of that habitat in the region (given in section on Spatial Analyses, above). The resulting esti- mate of the total population emerging from 5 April to 12 May was 46 x 106 beetles. However, on 11 May the peak regional population total in small grains was only 7.6 x 106, about one sixth the number expected. The 1976 field data show a similar discrepancy. To be sure, there are sampling errors involved in both estimates, and a portion of the emerging population will have died over the interval involved, but the data support the above simulation result. Since the crop ratio remained unaltered while the acreages were changed, neither the ratios of totals nor densities in oats to wheat changed for either adults or eggs. Relative Acreages The crop ratio (wheat to oats) was changed in a series of simulations by increasing the oat acreage 2x, 4x and 8x from the .standard value of 80 acres while the wheat acreage was held constant at 1000 a. With each doubling of the oat acreage, the total population in (Lats just about doubled, but densities of both adults and eggs rEilnained quite constant, declining significantly only when the oat acreage was 8x the standard value and the population began to be "diluted" in this large acreage. 173 The total number and density of adults and eggs declined in wheat as the oat acreage increased, at first slightly but then increasingly so as the oat acreage became a significant portion of the total. The ratio To/Tw’ discussed earlier in the Analysis of Crop Preference, increased as the cr0p ratio declined, but the ratio EO/Bw remained relatively constant. These results are as expected for random dispersal, no fixed crop preference, and constant relative quality of the two crops. Field Size and Shape Only wheat fields (susceptible) were involved in the follow- ing simulations. Four experiments altering the size of square fields were carried out, with two random replications of each. The locations of fields were randomly selected from long lists of possible locations (there are more possible locations for lO-acre fields than for 160- acre fields due to the presence of wood lots, etc.). The numbers and sizes of fields used were six l60-acre fields (2 = 960 a), Ieleven 90-acre fields (2 = 990 a), twenty-four 40-acre fields (2 = 5960 a), and ninety-six lO-acre fields (2 = 960 a). In effect, a :Eixed acreage of wheat was increasingly partitioned and dispersed. The results can be simply stated: as the field size increased, ‘tlie density of adults and eggs decreased. The mean adult density in time l60-acre fields was 25% lower than in lO-acre fields; the egg density was 22% lower. Elongate 90-acre fields were compared to square 90-acre fields ‘by "planting" wheat in fields .125 mi wide and 1.125 mi long (1 x 9 174 cells). These absurdly impractical fields were located as nearly as possible in the same places as the square fields (see maps, Appendix I). The mean adult density was 11% higher in elongate fields, while the mean egg density was 9% higher. The field size and shape simulations suggest that high cereal leaf beetle densities are promoted by having fields with relatively more "edge." Conversely, lower densities might be maintained by adopting the practice of planting larger fields. The reason for the edge effect is two—fold. First, large fields reduce the amount of favored overwintering habitat in the area. Central portions of large fields will be more distant from overwintering habitats and the edge portions will have such sources of infestation on only one side. Second, since diffusion rates are higher in the noncrop environment surrounding a field, these habitats act as sources, while the host crops, in which beetles have lower diffusion rates, act as sinks. Nonhost habitats therefore convey dispersing beetles to the fields, but the central portions of large fields are buffered from this effect. Lecigne and Roehrich (1977) found that colonization of wheat fields by the CLB begins at the edges, but the insects are in the Iniddle of the field when they lay their eggs. Therefore the larval infestation was greater in the center. The results of the current simulation do not agree with Lecigne and Roehrich's findings in that :regard. For 90-acre and 160-acre fields, the inner cells had lower egg densities than the outer. 175 I would agree with their conclusion, however, that the popu— lation of the CLB is "promoted by the juxtaposition of cereal-fields and forests." Field Locations In an earlier section I indicated that wheat fields located near oat fields might have lower total seasonal populations, while wheat fields surrounded by woods might have higher densities. My reasoning was that an oat field would act as a sink, accepting more immigrants than it gave back. Dense woods around a field should act as a barrier to dispersal, holding the population in the area. In general it would be interesting to compare the effect of planting fields in several different types of locations. The field location simulation involved "planting" wheat fields in five different situations: (A) surrounded on two or more sides by sparse woods, (B) with sparse woods on one side only, (C) surrounded on two or more sides by dense woods, (D) with dense woods on one side only and (E) not near woods of any kind. Ten- acre wheat fields were placed in six examples of each of the above categories. Ten-acre oat fields were planted next to three of the wheat fields in each category, and three more were planted away from wheat. A total of 30 wheat and 18 oat fields were therefore systematically located within the habitat matrix of the Galien study area. An analysis of variance of the resulting adult densities in wheat gave the following results. There were significant (p < .02) effects of both the wood lot and oat factors, but there was no 176 interaction of these factors. Specifically, wheat fields with oat neighbors had lower seasonal adult densities. The ranking of the five location categories in order of increasing adult density was C, D, E, A, B. Wheat fields surrounded by dense woods (C) had significantly lower densities than those with sparse woods on one or more sides (A, B), and fields with dense woods on one side only (0) had lower densities than fields with sparse woods on one side only (B) (Duncan's new multiple range test, % level, Steele and Torrie 1960). Among the oat fields, there were no significant differences in adult density related to location, although fields not planted near wheat had the lowest mean density. DISCUSSION Two distinct types of information which an operational pest management (PM) program requires for management decisions to be made are the time at which a relevant biological event will occur, and the magnitude of the event. For example, the necessary information might be the peak larval density of a pest and the time at which peak density occurs. While models of the pest system under consideration may ultimately provide estimates of these, such models will usually depend on other, earlier information for initialization. Initial field observations put a model "on track," in both timing and mag- nitude, with events in the field. Fulton (1978) discussed the role of egg and larval sampling in initializing his within generation model of the cereal leaf beetle for pest management decision-making. Biological monitoring is one of the more costly and time consuming components of an implemented PM system. The spatiotemporal model developed here, if totally successful, would have contributed to this need by providing the .information necessary to initialize a within-generation model such £15 Fulton‘s, or at least by reducing the cost of biological monitor- :ing. It was hoped that the adult model would help to identify the :influence of specific spatial and temporal structures of the environ- Inent on the distribution and abundance of the adult beetle. A 177 178 knowledge, then, of such features as the relative acreage and devel- opmental synchrony of different host crops for a large region, and each field's crop variety, relative maturity, acreage and proximity to beetle overwintering habitats and other fields, might have enabled predictions to be made of potential pest populations through space and time. The model would thus have served to at least identify those fields with a potential pest problem. Sampling by scouts to initialize a detailed within-generation model could be restricted to these fields, or the growers responsible for the specific fields could be alerted to monitor the pest population level. In effect, a realistic model of adult distribution and abundance might reduce the sampling effort required for the pest management program and buy time for decision making by providing earlier predictions of pest density. While the model developed here failed to predict densities in specific fields, or even to broadly classify the fields into high and low density groups, based on simulation results general statements about the role of certain spatial structures of the environment in determining the density of beetles in a field might be made. These generalizations are unlikely to be of much help in deciding where sampling to monitor pest populations should be done, but might serve as recommendations for designing a regional crop system that would minimize the probability of seeing damaging numbers of cereal leaf beetles. The simulations carried out suggest that large fields, of a shape which minimizes the "edge development" index, will have lower densities of beetles. Winter grain fields should not be located near 179 prime overwintering habitats, such as sparse woods, but should take advantage of the low source populations and barrier to dispersal offered by dense woods. Lower densities might be achieved by locating fields where dense woods occupies as many borders of the field as possible. Oat fields should not be planted immediately adjacent to wheat, unless the wheat is of a resistant variety, in which case it seems some advantage might be gained by planting the oats right next to the wheat. The density of CLBs in oats appears to be little affected by changes in the absolute or relative acreage of oats in the region. This is in large part due to the large reserve population of beetles in the nonhost crop environment. The existence of this reservoir, predicted by the model, needs to be confirmed. Support for the idea comes from calculations showing that in 1976 and 1977 at Galien most of the overwintering population was not accounted for by beetles in the grain fields at any one time, although Ruesink (1972) and Casagrande (1975) did not find this to be the case from 1971 to 1974 at Gull Lake. The experiment of Wells (1967), in which spraying all the wheat fields in a township did not reduce the population later found in oats as compared to controls, also supports the argu- ment for a large population of inter-field transients. The existence of this extra—field population is not merely a result of there being acceptable nongrain host plants in the environment; it is a result of the spatial separation of fields and the nature of a diffusion process. Time lags involved in inter-field dispersal result in fewer beetles being found in the fields at any one time. Further studies 180 on the role of the nonhost environment in the population dynamics of the cereal leaf beetle seem warranted. The successful prediction of densities in specific fields might be improved by a better understanding of the factors involved in defining the local uniqueness of a field. The role of variations in relative crop maturity, microclimate, wind patterns, and initial source populations all need to be better defined, and may improve the predictability of field densities. "Hot spots" of high density in overwintering sites may be a result of patterns of summer adult dispersal in the previous year, but almost nothing is known about this portion of the beetles' life cycle. The influence of environ- mental conditions, the physical structure of the crop, and the host plant's physiological state on the diffusion rate of adults is an area of research that also demands attention. With regard to the timing of events, the other type of infor- mation needed to initialize pest management models, the spatiotemporal model developed here makes a more substantial contribution. Fulton (1978) discovered that in order for his cereal leaf beetle model to be correctly synchronized with field events it was necessary to know when the adults moved from wheat to oats. In the context of the hypothesis of random dispersal set forth above, the problem may be restated as determining when the rate of emigration from wheat increases dramatically. This may be related to maturation of the crops, and needs to be investigated further. Many explanations have been suggested for the relative numbers of beetles found in winter and spring grains in particular years. 181 Ruesink (1972, p. 65) proposed a fixed preference of individuals for one grain or the other, but then said that the portion of the population entering winter grains depends on the size of the plant as it comes through the winter. Gage (1972, p. 78) noted that very low densities of CLBs in wheat may occur when wheat is planted early. Casagrande (1975, p. 51) suggested planting both winter wheat and spring oats late to increase the portion of the population infesting wheat. Contrary to Ruesink's statement, Casagrande (1975, p. 41) found no relationship between the early height of wheat and the relative densities in winter and spring grains, and no relationship between relative beetle densities and the acreage of oats. Casagrande (1975, p. 46) then proposed a model relating the proportion of the population in winter grains to the regional beetle density, but as was shown above, 11 years of data from Gull Lake fail to support this idea. The spatiotemporal model developed here relates the observed proportion of beetles in each crop, and the apparent move- ment from wheat to oats, very simply to the relative synchronies of CLB emergence, winter grain development, and oat planting date. Although the underlying model is simple, variations in the timing of these events, the diffusion rate of the beetle and the spatial configuration of the crop system result in a complex array of patterns of distribution and abundance. Initial observations to synchronize a pest management model with field events should be aimed at identify- ing the temporal positioning of beetle emergence, wheat growth in particular fields, and the expected planting date of oats. 182 As shown above by simulation, densities in oats might be minimized by either increasing g£_decreasing the temporal separation of wheat and oat growth. The synchronies might also be manipulated by selecting varieties with long or short growing seasons: for example, late-maturing wheat and early-maturing oats. These possibili- ties for managing temporal patterns, as well as the impact such manipulations might have on other components of the crop system, such as the Hessian fly, parasite species, grain yield, etc. need to be investigated further. SUMMARY AND CONCLUSIONS Population dynamics as a science deals with the distribution and abundance of organisms, yet too often the emphasis is on "abundance." Whenever dispersal plays a part in a species' life history, the contribution of the dispersal process to the population's dynamics may be major and must be considered. Only a spatiotemporal approach will lead to an understanding of both the population's spatial distribution and changes, through time, in its abundance at a particular place. Preliminary analyses showed that survival and redistribution during the adult stage was the factor most associated with year to year fluctuations in the density of cereal leaf beetle larval popu- lations in research plots at Gull Lake. Efforts to understand this situation led to the identification of broad classes of influences-- general (regional) and unique (site—specific)--producing temporal and spatial variations in density. Dispersal interacts with this array of factors, increasing the effects of some and reducing the effects of others. It has been suggested by one worker (Ruesink 1972) that individual cereal leaf beetles have a preference for either winter wheat or spring oats, and that movement between these crops is minimal. A more common assumption has been that beetles move 183 184 sequentially from wild grasses to winter wheat and then to spring oats. A new model was proposed, here, of beetles moving at random between fields, entering them as they are encountered. The number of beetles in a field at any particular time is a net result of immi- gration and emigration rates. The rate of entering a field is a function of the spatial distribution and nature of overwintering sites and other fields nearby, and the relative length of the field's boundary. The rate of leaving the field depends on the suitability of conditions within the field. The spatial distribution of beetles among fields is related to general features of the region such as the relative acreages and developmental synchronies of the different host crops. This hypothesis was examined by analyzing existing data and by conducting new field investigations, and, in general, was supported by these findings. The precise relationships between environmental features and density in individual fields are difficult to define; the factors leading to high density may be many and complexly inter- related, and are likely to vary from one year to the next as temporal and spatial patterns change. A simulation model of cereal leaf beetle spatiotemporal dynamics was developed, and was found to perform fairly well in vali- dation runs comparing its output to observations made near Galien, MI in 1976 and 1977. Alternatives to the assumption of random inter- field dispersal were evaluated and did not increase the validity of the model. The major shortcoming of the model is that it fails to generate sufficient between-field variation in densities. This is 185 thought to be due to not having incorporated enough features defining the local uniqueness of each field. Interesting simulation results were that the conversion of all wheat acreage to a resistant variety need not increase the density of beetles in oats; that advanced, as well as delayed, growth of wheat may reduce the density of beetles in oats, depending on the planting date of oats and the timing of the emergence of beetles from over- wintering; that an increase in total acres planted may lead to an increase in the total number of beetles observed in small grains, with little reduction in density; that small or elongate fields might be expected to have higher beetle densities than large, square fields; and that wheat fields surrounded by dense woods and having oat neigh- bors will have lower densities than wheat fields near sparse woods without adjacent oats. The model, in its present form, will be of little use in an operational mode for pest management purposes, but has been quite successful as a research tool. 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Ph.D. Thesis, Michigan State University. 153 pp. APPENDIX A OPTIMIZATION PROGRAM FOR 1977 COMPARTMENTAL ANALYSIS 194 PROGRAM OPT(OUTPUT,TAPE1,INPUT) REAL M DIMENSION DEG(36),X1088(36),XZOBS(36),XBOBS(36) DATA DEG/A96.,507.,52A.,539.,562.,587.,613.,636.,660..688., +715.,7A5..772.,798.,823.,8A6.,865.,889.,913.,939.,959.,973., +977.,987.,1011.,1033.,10A2.,1OA8.,1056.,1061.,1070.,1086., +1095.,1107.,1123.,11AO./ DATA XTOBS/A.316,3.A52,3.021,2.833,2.545,2.232,1.888,1.U6,1.087, +.863,.759,.6AA,.5u,.A38,.381,.338,.302,.296,.289, +.282,.28,.151,.108,.029,0.,O.,0.,O.,O.,O.,O.,O.,O.,O.,O.,O./ DATA XZOBS/3.16A,2.826,2.911,2.79.2.605,2.HOA,2.312, +2.288,2.353,2.36A,2.12u,1.88,1.282,.771,.627,.521,.A32 +.378,.323,.26“,.25,.162,.O8u,.023,0.,O.,O.,O.,O.,O.,O.,O.,O.,O.,O. +,O./ DATA X3OBS/.O73,.151,.ZON,.278,.392,.515,.590,.7A, +.712,.603,.597,.ABA,.928,.369,.223,.2A8,.269,.229, +.190,.1A6,.119,.055,.OA1,.038,.ON9,.058,.063,.055, +.031,.017,.015,.016,.017,.018,.02A,.O17/ C MEAN VALUES OF X1 (S-WHEAT),X2 (R—WHEAT) AND X3 (OATS) C OVER 37 DAYS IN 1977 FROM “88 TO 1140 DD > “8 (F) XlBAR=O.886 X25AR=1.0NO XBBAR=O.218 DT:O.2 I T=u88. N=652 ND=1 U=O. REWIND 1 READ',M,A12,A13,A21,A23,A31,A32 IF(M.EQ.9.D)STOP IT=FIOAT(N)/DT+1. C INITIALIZE STATES AND RATES X1=u.239 X2=3.257 X3=0.032 C READ*,X2 WRITE(1,102)T,X1,X2,X3,X1,X2,X3 RT=-(M+A31+A21)‘X1+A12'X2+A13*X3 R2:A21*X1-(M+A12+A32)*X2+A23*X3 R3=A31*X1+A32*X2-(M+A13+A23)*X3 C LOOP OVER DEGREE-DAYS DO 10 I:1,IT T=T+DT DD=IFIX(T+.005) C UPDATE STATES C PREDICTOR (EULER) XTP:X1+DT*R1 XZP:X2+DT*R2 X3P=X3+DT'R3 195 R1P=-(M+A31+A21)‘X1P+A12*X2P+A13'X3P R2P=A21*x1P-(M+A12+A32)*X2P+A23*X3P R3P=A31*x1P+A32*x2P-(M+A13+A23)*X3P c CORRECTOR (TRAPEZOIDAL RULE) x1=x1+DT/2.*(R1+R1P) x2=x2+DT/2.*(R2+R2P) X3=X3+DT/2.'(R3+R3P) c UPDATE RATES R1=-(M+A31+A21)ix1+A12*x2+A13Ix3 R2:A21'X1—(M+A12+A32)*X2+A23*X3 R3:A31*X1+A32*X2-(M+A13+A23)'X3 0 UPDATE OPTIMIZATION CRITERION ON SAMPLING DATES IF(DD.NE.DEG(ND))GO TO 10 U=U+((X1-XTOBS(ND))'*2)/XTBAR+((X2-X20BS(ND))**2)/X2BAR+ +((x3-x3OBS(ND))'*2)/XBEAR WRITE(1,102)DEG(ND),XTOBS(ND),XZOBS(ND),X3OBS(ND),X1,X2,X3 102 FORMAT(7ETO.4) ND=ND+1 10 CONTINUE PRINT 101,0 GO TO 1 C STOP 101 FORMAT(* U=‘F15.N) END APPENDIX B DATA FOR FIELDS AT GALIEN IN 1976 AND 1977 196 Table B1. Adult and egg densities in small grain fields at Galien in 1976, with field acreages, cell assignments in spatial analysis, and hierarchical cluster membership based on environmental features. Field Acres Cellsa Adult-ODb Eggsb Cluster S-Wheat 133 18 5-6,5 10.20 1.82 4 136 18 7-8,5 29.71 5.15 4 145 5 5,4 24.99 2.76 4 214 21 1—2,9 5.71 1.33 5 217 5 2,12 28.55 4.16 2 222 10 4,13 28.25 2.62 2 225 60 1,15 2,15-16 13.93 1.99 4 3,15-16 4,16 231 33 5,16 6,15-16 47.20 4.69 4 241 10 7,12 115.21 6.42 2 311 19 l-2,18 24.83 2.97 4 313 70 2,17 3,17-19 19.06 2.56 4 4,17-19 333 8 5,23 29.43 2.62 5 334 14 7,23 82.33 8.85 5 336 7 6,23 21.17 2.73 5 343 14 6,17 11.94 1.56 4 345 10 7,17 23.60 3.62 4 415 12 2,25 36.25 2.25 2 421 10 2,29 106.20 11.94 2 431 34 6-8,32 203.24 28.35 3 432 11 7,30 186.75 36.44 3 525 5 12,30 53.57 3.35 5 637 17 13,21-22 48.42 2.98 5 644 5 16,17 25.44 2.92 3 713 15 10,9-10 43.29 4.66 2 729 7 11,16 70.39 18.43 2 747 11 13,9 73.10 6.16 2 811 18 9,3-4 19.76 2.95 4 812 15 10,3-4 11.32 1.31 4 813 15 11-12,4 42.84 3.14 5 821 20 9-10,5 36.49 2.75 4 822 5 12,5 53.25 6.30 5 843 10 13,2 20.85 3.40 5 911 14 17,3 13.52 1.55 2 924 5 17,8 18.17 2.50 2 933 10 23,8 65.53 6.81 3 1017 5 17,12 33.08 3.83 3 1115 55 17,19-20 33.79 2.64 4 18,19-20 19,19-20 1144 22 24,17-18 12.74 1.12 2 197 Table Bl. Continued. a o b b Field Acres Cells Adult— D Eggs Cluster 1214 30 17,28 18,27-28 27.03 2.13 5 1222 7 19,31 10.94 11.00 1 1224 20 17-18,30 21.69 2.25 5 1227 6 20,31 8.65 0.69 l 1311 30 27,27 28,26-27 19.10 2.13 5 1410 16 7-8,l 25.54 2.49 4 1411 25 26,18 27,18-19 14.95 1.82 3 1511 20 28,10-11 65.57 13.21 5 1514 12 25,9 53.97 5.32 5 1542 7 30,11 44.25 12.06 5 1548 15 32,8—9 116.37 14.04 5 1625 12 26,7 93.51 17.28 5 R—Wheat 611 20 10,19-20 26.70 1.68 2 625 20 10,21-22 46.51 3.51 2 632 20 15,21-22 63.03 3.66 2 726 12 9,13 60.50 5.06 1 1014 15 19—20,11 62.39 4.12 1 1023 10 17,14 33.72 3.59 1 1122 18 17,21-22 23.45 1.94 2 1124 20 19,21—22 21.97 2.49 2 Oats 136 12 8,6 58.17 21.00 — 149 12 8,2 27.29 8.08 - 236 15 7-8,16 57.77 16.67 - 246 12 8,12 57.63 31.37 - 337 8 6,23 52.74 33.19 - 346 20 7,18—19 17.71 8.08 - 524 8 12,32 140.09 44.80 - 612 20 9-10,18 11.02 2.64 - 1024 18 17-18,14 22.60 8.36 - 1135 5 23,22 0.96 1.16 — 1228 7 20,31 50.13 7.16 - 1547 8 30,11 119.90 28.68 - arows,columns bseasonal total per ft 2 198 Table B2. Adult and egg densities in small grain fields at Galien in 1977, with field acreages, cell assignments in spatial analysis, and hierarchical cluster membership based on environmental features. a ob 1) Field Acres Cells Adult- D Eggs Cluster S-Wheat 125 28 3,7-8 4,8 97.73 4.32 2 149 12 8,1 44.58 6.54 - 218 16 3,10—11 57.52 6.83 2 225 56 1,15 2,15-16 54.84 4.50 4 3,15-16 4,16 227 4 1,10 48.65 5.45 4 322 25 3,22 4,21-22 61.13 10.47 4 427 6 1,16 57.19 5.62 l 513 8 10,26 47.86 4.43 2 615 4 9,21 52.12 6.87 4 626 2 9,22 131.83 26.56 4 731 7 16,13 50.08 4.78 3 735 6 16,15 57.25 4.24 3 747 11 13,9 245.67 22.74 2 833 12 16,5 77.79 7.55 3 933 6 24,9 115.66 10.61 3 1022 17 17-18,15 139.18 7.69 3 1042 21 22-23,ll 84.22 10.33 3 1223 14 20,29 44.02 3.72 1 1511 16 29,10-11 149.25 15.20 4 1514 8 25,9 91.98 10.34 3 1524 2 28,12 92.88 7.10 3 1525 9 27,12 106.67 5.82 3 1533 14 31,15 51.02 7.15 3 1612 6 26,3 170.22 42.09 4 1636 22 32,6-7 84.79 7.68 4 RrWheat 136 11 8,6 43.74 5.96 3 137 34 6,5 7,5-6 89.83 5.92 3 141 14 8,3 30.29 2.29 2 226 10 2,13 24.45 2.48 4 233 15 6,13-14 115.13 5.62 4 236 14 8,16 42.10 3.06 4 241 8 7,10 78.32 7.91 4 311 24 1-2,l8 28.69 1.42 4 312 16 1—2,20 31.67 1.28 4 322 11 3,21 32.87 1.56 3 323 18 3,23-24 36.51 3.56 3 346 9 7,18 54.69 1.33 2 199 Table B2. Continued. a o b b Field Acres Cells Adult- D Eggs Cluster 348 15 5,17-18 102.44 7.55 2 413 7 3,27 26.54 0.94 1 416 2 4,26 33.92 1.08 l 421 12 2,29 29.71 2.24 l 425 21 1—2,31 51.01 2.58 1 441 17 5,27-28 31.72 1.79 l 522 15 9-10,30 86.64 5.34 4 535 38 13,30 14,29 45.79 1.35 4 15,29-30 536 22 14-15,3l 27.34 0.87 4 625 12 12,22 24.73 2.32 4 722 13 9,14 74.00 6.04 4 742 19 13-14,12 62.60 6.66 4 744 10 16,12 72.59 3.69 4 818 13 9,1 40.87 4.82 4 1024 13 17,14 75.24 5.64 4 1131 19 20-21,21 46.42 2.20 4 1144 6 24,19 50.47 2.28 l 1212 7 17,26 25.00 2.37 3 1213 16 18-19,25 60.73 3.95 3 1216 5 17,25 45.02 2.89 3 1228 18 19-20,31 36.56 1.39 1 1312 24 26-27,26 61.56 3.03 4 1341 9 30,27 42.38 2.26 4 1412 27 26-28,21 49.09 2.52 4 1626 20 28,7—8 69.82 10.56 4 Oats 235 6 8,15 111.45 42.99 - 426 4 3,31 187.48 18.93 - 537 7 14,30 149.30 7.50 - 541 13 16,26 83.13 8.02 - 612 7 9,17 12.67 1.65 - 613 4 9,17 16.47 2.66 - 711 10 9,9 42.79 10.10 - arows,co1umns bseasonal total per ft2 APPENDIX C REMOTE SENSING DATA (Available on computer) KEY BD SW DW CL FR Buildings (no. of .4 a subcells) water " Sparse woods " Dense woods Cropland Fencerows (ft) Edge of woods (ft) 200 Row Col BD WT SW DW CL FR EW 1 1 0 0 O 0 25 1340 O 1 2 0 0 O 0 25 650 0 1 3 0 0 0 O 25 650 O 1 4 O 0 0 0 25 1320 0 1 5 0 0 0 O 25 1320 0 1 6 0 0 O 9 16 400 1653 1 7 0 0 0 0 25 650 0 1 8 2 0 0 0 23 1005 0 1 9 0 0 0 O 25 1980 0 1 1O 6 O 0 6 13 720 1450 1 11 5 0 O 2 18 260 555 1 12 0 0 5 4 16 1420 1095 1 13 0 0 0 12 13 924 1320 1 14 2 O O 0 23 870 O 1 15 O 0 0 0 25 660 0 1 16 2 0 O 0 23 640 O 1 17 2 0 2 0 21 520 530 1 18 0 O 0 0 25 520 O 1 19 O 0 0 O 25 660 0 1 20 2 0 0 O 23 1120 0 1 21 2 0 0 O 23 1320 0 1 22 9 0 0 0 16 790 0 1 23 2 0 8 1 14 1915 0 1 24 0 0 3 0 22 1190 0 1 25 O O 10 0 15 1755 0 1 26 0 0 10 0 15 650 O 1 27 0 1 O O 24 790 O 1 28 3 0 6 4 12 650 1715 1 29 0 0 0 7 18 660 600 1 3O 0 0 0 0 25 660 O 1 31 2 O O 0 23 640 0 1 32 0 2 5 1 17 530 565 2 1 O O 0 0 25 675 0 2 2 O 0 0 0 25 O 0 2 3 0 0 0 0 25 660 0 2 4 O O 0 0 25 1320 O 2 5 0 0 0 0 25 660 O 2 6 0 0 0 O 25 660 0 2 7 0 0 0 0 25 1320 0 2 8 O O 0 0 25 1270 O 2 9 0 0 0 0 25 660 O 2 10 0 0 0 0 25 1320 O 2 11 0 0 O 0 25 1320 0 2 12 0 0 7 0 18 1340 725 2 13 20 O 3 1 1 330 660 2 14 0 0 2 0 23 325 640 2 15 O 0 0 0 25 O 0 2 16 0 0 0 0 25 660 0 2 17 3 0 O O 22 660 0 2 18 O O O 0 25 660 O 1:4:-zzwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwmmmmmmmmmmmmmm COCO-AGOOOOOOOOAOOOOO—loONOOOOOOOOOOOOOOOOOOOOO—IEOOO OOOOOOOOCON}LTOOOOOOOOOU'!OOOOOOOOOOOOOONOOOOO:NOOOOOO 201 NMOOOOO —-§ .4 4.4 01.00 OOOO-lr-ANO‘O‘OO‘NWNOOdOOOOOOOOWLDOOOOOOOOO-K‘JOO OOOOOOWOKOOOU'INOOOOOOOOOOOOOOOOO—AOOOOOOOO—IO‘OOOUUOOOOO 25 25 25 21 24 20 21 1O 15 14 25 25 14 25 25 25 25 25 24 25 25 25 22 22 25 23 25 1O 24 25 25 25 24 25 24 23 10 25 10 24 1O 25 25 25 25 0030 O 1040 645 1070 1570 1255 1065 U1 N OOOU’IOOOOOOOO ~10" \Ofl 00 U) N OODOOOOOOOO CID—s our) 00 730 r.- 0 CO 975 1230 250 670 0000 mmmmmmmmmmmmmwmmwmmmmmsnazzzszzzzzzzzzzzzzautumn-arc: OOOOOOOOdO—‘OOOOOOOOOOOOOOOOOOOO—IAOOOOOdOOOONOOOOO-A OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO\OJ=OOOOOOOOO 202 OOOOOONAWOOOU'INOOOOOOOO-‘rO'OOOAOOOOWOOOOOOOOOJINOOOOOO N N (DO—IU'IU'IOOOZOOOOOOOOQU'IONO—IO A NM NM WWW QINOOOOOO‘O‘WWO‘OOWJOOOWOON 2A 211 18 25 13 21 25 11 16 24 25 25 25 11 25 21 24 20 24 17 22 19 25 25 25 25 25 24 18 10 12 15 23 25 25 25 25 22 18 '4-4~P<-4~®Q-QChOHmChO\OMhONUNIChOH$ChOHwChOHIChONhC‘OMBO‘OMhO50WhChmkflUTWKDUkanUHm OOOOOOOOOOOOOOOCDOd—IOOOOOOOOAOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 203 ants-1| och OOOOOOOOOOOU‘I—IOONWOOOOOOOOOOMOt-AUJOOOOOU’IOOOOOOOOOGJOO NNNN—t OUTU'IU'IU'l—IOO‘NWO A \OOU‘IGDU'lO-AOOOOOOO:NOOC’QOOOOOOO NM -—I_L 3:0 A =OOOOOOO-4N1 25 22 25 25 25 25 25 25 25 21 J:- O" 1590 oooooooooooooooooooooooooooooooooooooooooooooooooooo-I«I-q-q-q-Iq-q-Isi-JQQQQQ-QQ-q-q-IQ-q-q ONOGOONw-sd-AONONB—I—IOOO—AO—tU‘lNOOOOOOOOAdOOOOOO—‘OOOOOOO ooooooodoooooooooooooooooooooooooooooooooooooooooo 204 8 4 13 265 1260 8 o 17 0 755 1 o 24 o 0 o 0 25 660 0 1 0 24 0 0 o 13 12 0 1365 6 10 9 o 1451 0 0 24 0 0 0 0 25 660 o o 0 25 330 0 0 0 25 1980 0 0 0 25 660 o 0 O 25 325 o 0 0 25 950 0 0 0 24 1500 0 o 11 13 650 830 0 21 4 O 650 5 20 0 0 660 8 0 17 660 1310 12 0 13 0 845 25 0 0 0 0 11 0 14 0 1395 2 19 4 0 475 0 0 25 660 0 0 0 23 1320 0 0 0 20 1060 0 0 0 24 1300 0 0 0 25 1890 o 0 o 24 1120 o 0 o 25 660 0 0 o 25 980 o 10 11 4 1000 635 8 8 8 330 1630 0 0 24 1095 0 0 0 21 2095 o 0 0 23 660 0 0 0 25 1320 0 0 0 23 1055 0 0 o 25 660 0 0 0 24 720 o 0 0 24 1320 0 0 0 24 1095 O 3 13 5 660 1980 0 o 23 660 o 0 o 25 1320 O 0 0 25 1320 0 0 0 19 800 o 2 0 23 1960 790 4 0 19 1490 980 O 25 o 0 0 \O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\O\D\O\O\O\D(DCDCDCDCDCI) d-Ad—I—A—i—A—Ad-Ja—h OOOOOOOOOOO OOOO—IOOOOOOOO-PJO-ANOO—INOAAAOOONOOOOOAONONOOLAOOOOOO—tl‘: d O OOOOOOOOOOOOOOOO—SONOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 205 19 2615 O 17 655 1360 14 660 885 18 500 1230 A 4500000OOONOOOOOdflm'fiO—IUJWOOOOOO—BNAOKOEOOOOOO-P—‘ONONANIN 2 2 0 1650 23 1190 530 25 1200 0 1 6 660 1970 22 926 0 25 1320 0 25 660 0 23 400 0 25 660 O ——| 10 400 2090 21 1135 980 15 240 1305 15 660 790 24 1320 330 23 645 585 23 1005 400 25 660 0 23 1190 0 25 1980 0 25 1980 0 0 0 —| 25 1385 24 2440 21 1005 660 21 1584 685 24 1320 530 22 160 500 17 1425 1000 14 1015 1055 14 660 2110 21 1770 370 23 925 265 25 845 O 21 1120 O 25 1160 0 25 1320 0 1 8 360 1715 25 1315 0 25 660 0 25 0 0 25 0 0 19 495 950 18 1585 730 25 1310 0 25 460 0 8 265 1255 OUOOOO‘GOOOOWOOOO—‘OS’OO~30OOOOOOOO—IOOOOOWOOOOOU’IOOUJOOOO A... 14 360 1870 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 13 14 15 16 17 13 19 20 21 22 23 24 25 26 27 28 29 30 31 \oooqoxmzwm... 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 OOOOOOOOAOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOd—AOOOOOOOO—I OOOOOOOOOJOOOOOOOOOOOOzOOOOOOOOOOOOOOOOOO—‘U'IOOOOOOO 206 4 Ad ad a ooomooso—soooo—soooxwoooowowoooooooooooommowooooodooomz N..; «I. moooodwdzooomooo-amoooooooooooooooootwooom—soooowoowwmz —.I A a... 16 22 25 24 22 20 24 24 24 15 23 23 20 25 12 21 25 25 25 25 25 25 25 25 25 25 12 25 17 15 24 25 16 23 25 24 24 2O 24 14 13 25 17 10 1780 1320 1585 675 275 1170 650 1595 790 130 660 620 1190 155 1905 1350 660 660 1320 1320 600 660 660 660 1190 460 745 1520 395 670 660 395 O 460 1315 1875 405 120 171 200 1320 (D O .11 N w .4 U1 OOOOOOOOOOOO 2245 31 \ooo-qoxmzwm—n 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 \OCDNIO‘U'l-ELAJN-i 10 12 13 14 15 16 AOOOOOOO-AOOOOOO—IOOOOOOOOONOOOOOAAOOO—hOO-IWOOOOOONOO OOOOOOOOOOOOONOOOOOOOOOOO—JOOONOOOOOOOOOOOOOOOOOOOO 207 —I -—I “)4 NOOOOWNOWU‘INWOOO—S—‘U'IOOOOO:OOONIOOOOWODO‘OOOOOWONOOOWOOO .6 NtOOJr-‘OO‘OOU'IOOOCDNO‘NNCDAOOUJO«AWOOOOCDOSO‘zOCDN—DO-JOOOOOOOO 24 25 23 22 25 25 25 23 15 18 24 24 23 16 25 15 17 24 17 23 25 18 25 19 24 21 22 25 25 24 17 18 22 17 18 25 22 13 15 11 25 17 21 25 25 11 0 0 4505 1200 1120 660 1980 1320 1370 130 1188 1530 1980 690 1980 530 645 265 530 1320 1055 460 1160 660 660 1320 1070 380 130 3795 660 130 660 660 1310 1255 530 844 660 775 660 O—I—‘OOOOOOOOONOOOOWOOO5000—:AOOOU’OO—AOOOOOOOOONOOOOO-—I OOOOOOOOOOOOO—IOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 208 14 0 1670 23 0 1115 18 660 705 20 660 1120 12 290 720 19 685 1320 23 1120 0 25 1020 0 22 660 1055 25 660 0 25 0 0 N..; WNOOOONWO-tOOOO‘ItWOOOOQ5000000000dfiOOO-AJTOOUOOON-C'U'IGOO 0" O ‘1 \O O 22 660 485 25 885 0 25 1716 0 14 530 1980 ——I_I 17 145 1005 22 400 370 12 725 970 thfiOU‘iO‘OOW-‘WOOOOObOO-‘NO 25 0 0 0 24 0 660 265 10 14 260 640 9 1 5 2 O 0 330 0 21 1320 785 6 6 0 2105 11 14 500 1980 3 22 640 800 25 0 0 1585 2 20 462 400 3 19 1255 1265 0 21 965 1930 0 18 145 765 0 24 1715 0 0 23 925 0 0 25 660 0 0 25 0 0 1 20 650 930 0 19 845 1385 0 1 10 0 725 0 23 765 790 0 25 0 0 0 25 660 0 O 25 660 O 0 24 1255 0 3 19 270 700 11 1 1 0 O 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 000 OOOOOO-‘OOO ON—I—IOOOON—sOOOOOOOOOONOOOOON “wvoow—de OOO OOOOOOOOOOO OOOOOOOOOOOOO—AOOOOOOOOOOOOOOO NOOOOOO 209 ‘4 N —I ONU’I OtOONOOOOO oooooomzoooooouooooooooquom U.) OOOOOOCDOO—I -—3 N ad .4 17 25 23 22 18 18 15 25 25 23 25 25 25 25 14 19 25 25 25 20 16 18 20 25 25 12 24 19 22 22 24 12 15 12 25 22 22 130 620 710 660 1410 1110 1470 680 790 1120 990 1330 1635 0000000 1225 830 1400 1980 890 710 910 1320 500 1450 460 1335 860 1320 2000 16 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 O AOOOOO—s—IOOON O WO—IONOOL‘d-AAANOOOOO—ItNOOOO—‘OO 000000 .44 000 OOOOOOOOOO OOOOOOOOOOOOOOOOOOO—iOOLUU'lOOOOOO 0000000 210 A -—I 000 OOOOOOOOOO OOOOOOOONOOK—AOOOOONOkmO‘OJNOOO KI'ICDNNOOU'IOO A 0 00000001300 OOOOOOOOU)AOOOOOOOOO-INNOOO-AO \OCDU'IOOOO out ——l—.| .6“) ONI—‘mm 25 23 25 21 25 24 24 25 25 25 25 25 23 25 25 24 15 18 15 16 21 17 24 25 25 25 25 21 24 24 22 21 25 25 23 25 24 25 22 24 19 16 1140 0 525 0 1315 0 1320 845 660 0 0 0 395 0 1320 o 0 0 o 0 1120 o 1255 0 1320 430 1320 0 660 O 925 O 265 1715 790 700 1500 1625 1140 1055 1300 1255 1520 o 1065 2110 1585 0 1320 0 1320 0 660 o 990 O 1405 395 1030 2375 1200 0 1440 0 355 865 0 0 1320 0 1470 o 910 0 660 0 515 o 1320 o 595 o 540 0 1045 665 0 1585 435 1310 0 260 0 905 740 1710 o 1320 o 660 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 OO OOMOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOO‘UOOOOOOOOOOOOOO OOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 211 d—A at»: .3 OOOOOOCXJO‘OOOO—AO—SONCDOOWNAO‘J'IAOOOOONOOONOOzOOOOO—IU'IU'I c—I OOU'INOOOOOS’O.E—AOOOOOOOOOOOO:OOOO-AU'IOOOOO 2 12 24 20 10 19 24 25 25 25 25 25 25 23 22 19 25 23 25 25 25 25 25 23 15 20 22 25 25 11 10 24 25 12 11 19 25 25 25 23 25 25 0 1460 1610 420 530 540 660 680 1120 687 1320 660 1095 1650 1565 1225 140 660 660 1320 660 320 1050 100 660 1320 410 2075 660 235 0 805 390 530 1690 1320 820 1755 1470 425 1400 550 660 1290 2415 380 1545 1345 660 1425 1377 645 1573 000000 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 .u-A d O—IOUTGOOOOOWOOONOOOOOOOOOCDUOOOO-fiOO-AO‘NUUOOOOWOOOOOOOOO N MN somzflooowcoozmwmzooooooo .34 0‘30 A .s «AOOOOOOOQOOOOOOOO OQOOOOOOOOOO-‘NWOOOOOOOQOOOOOOOOOOOOOOOOOOOOOOEQOOO d OOONOOOON—IOOOOOOOOOONOOOOOOOOONO—l—bOONOOOONOOOOOOOO OOCD'QO‘U'IKWN.‘ .LN .LN dNU'INIQU'I d 25 25 25 18 21 25 25 21 18 19 21 25 23 18 23 25 16 25 21 12 25 18 25 23 25 25 25 25 25 23 24 25 12 24 23 25 24 two-SOC 0000000 0 1715 1450 790 1275 1505 420 1635 1320 1345 790 1505 0‘ 0" 0000000000 .5 \O O O 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 OOOOOO400«AND-JOOO—AOOO—A£000OOOOOOOOOOOOONOOO—JNOOO—IOO OOOOOOOOOOOOOOOOOOONOUOOOO«If-'OOOOOOOOOOOOOO—AWMOOOOOOO 213 .5 d—‘OOOOOOOWO£OZOOOONWOOOOOOO OOOWNNOO-fiO-‘OOOJOOOO N..—5 o~1mmooowmomoz~omo¢=o=aoo NNNN-J U'lan'IONd 1740 2072 510 920 565 650 800 550 1180 1115 .5 .5 U100 5N U) moo KO OOOOOOU‘OOOOOO CO 1225 1290 1200 660 1280 1045 1335 1320 1450 790 1460 1525 1375 1110 00000 0000000 1295 1490 1320 590 310 925 2400 3J5 1480 660 660 790 390 890 410 1610 680 700 795 745 925 660 700 580 210 660 790 1135 1445 937 765 330 120 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 24 24 24 24 24 24 24 24 24 24 24 24 24 24 .5 .5.5 UTO"\OU1 -I-_b mzwaoooomooooszooxlmoo-tmzomooow dd u—I :WNOO-‘OOWOOOOOt’mWNOWOONOWONOONOZNNWOOOO‘U‘IOGWOOO1:000 A OOOOOOAOOOOOOOOOOOOOOOOOOOOOOOOOOOAOOOOOOOOOOOOOOO OONOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO‘OOOOOOOOOAOOOOOO dmtm—OUIOOQU'IOOCDON N- 895 160 1912 1680 000000000 660 660 1085 890 2175 435 345 1450 1290 0 0 775 980 1390 485 980 540 1005 1465 725 240 630 585 1300 830 1720 370 1670 1573 1260 890 2165 1040 130 260 565 995 2112 1115 750 1485 995 685 660 580 O 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 \OCDNChU'I-PJUUN-d 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 OOOOOOOOOOOCOOOOOOOO—IOOO—AOOOONO—AOOOOOOOOOOOOWO—AOOO d .5 O—ICDO‘UJ—tONOOOOOOOOOOOOOOOOOOOOOt‘OOOO-‘WOOOOOOOOOOOOOO 215 A d .5 omzmo-4=ooo—1omwmouoowoooowoxomooooozmmooomoooooooooom N OOWO‘NONWU‘IO‘U‘I-«JN-IOOOOOOOOOUU—iw N .5I\).5 OOOtNUUO 0 9 24 24 20 21 21 25 25 25 .5 N (DOOOOO-BO 23 22 19 25 25 23 25 18 13 25 23 N OGJBOOKDUU 20 18 18 22 25 18 WCWOOO N.. 0 925 555 705 696 620 1530 1015 732 365 0 855 180 1200 440 930 1490 2220 645 395 805 530 1355 930 660 710 752 700 970 725 855 695 875 855 540 O 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 \OCDNO‘U‘II—‘WNJ OOOOOOOOOWNOOOOOOOUIOOOOOOOOOOO—IOOOOOOOOOOOOOOOOWNO OOOUUNOOOdOOOO-‘OOOOOOOO(1330400000OAOOONROOOOOOOAOOOO 216 A .5.5[’\) moo—-omm—soodoooomoomwoooo—aw—aommwm-ooomoozoooooooow A cub—J A)- CDU'IN A .115 OOOO‘NWOtOOOOO‘ N..—5.5 302mm 4 “3.5 NOGJOOWOOOOU'IZOOOO-JWOOOOOOU)AO—‘CDCDer m- 660 1320 1685 1320 1320 1320 1300 800 625 305 660 2245 1140 000000 1145 620 790 1245 705 775 820 1410 1170 1250 460 1950 2110 2000 1300 1175 1320 1940 1170 00000 27 27 27 27 27 27 27 27 27 27 27 27 27 27 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 29 29 29 29 19 20 21 22 23 24 25 26 27 28 29 30 31 \OQNO‘U‘IZWN—A zWN—b ooooooowmzomoooodooooooooooooooooooooo:moooooooomo OOOOOOO00003000000dO-AOOOOO-A'JOU'IOOOOOOOOOOOOOOOOOOOOO 217 null-ual mNOOO‘OOOOOOOO-fiOOOOOOOOOOOOO«t OOOOOOOOOOOOOOOOJ: —-|-—l dd .4 id CIA N OOU'INOOOOOOOOOOOOONGOOU‘IWOOOWW-‘dflOOOOWOOOOOOOOOOG—IOO MN 590 300 1710 0000000000 1665 1340 1055 1205 .5 W N 00 O‘U'l O‘C‘ 000000000000 00 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 kON—IU'I—AOCOO—4000AOOOOOOOOOOOO—SU'IU'I—JOOCOCOAONOO-AOOOOOOO OOOOO—IOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 218 OOOOOOOOOOOOOCDQCD—INb’NOOOGDOOOO [v.5 -I\O cub OOONQNNOOOOO-‘OOOOOOO OOOUJUJ—ICDNOOOOOOOOOOOOBO‘OOOOOOOOOONOOdO‘OKON-D’OOOOOONGDO 25 17 18 25 17 25 25 24 23 19 15 16 16 25 25 13 24 20 20 24 25 25 25 25 25 25 25 25 25 24 25 24 25 24 25 25 23 20 10 14 23 25 21 O 265 130 1305 975 885 660 1520 410 530 2295 675 135 1545 315 1610 575 660 1320 660 660 120 1320 660 795 805 670 720 1780 1320 2495 1320 1690 1110 1425 410 805 1305 700 750 O 860 655 1320 820 2390 665 1200 1275 645 920 .5 w N 000 105 0‘ \D OOOOO‘OOOOOOU‘IOOOOOOOOOOOO A) 0‘ U1 2350 610 540 1320 30 30 30 30 30 30 30 30 30 30 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 32 32 32 32 32 32 32 32 N00 ooooooooooooooo-Ammmmmmmmmzooomooooooooooooooomm O oooooozoooooooooooooooooooooooooooooooooooooooooo 219 OOOOW—IOEWO N U'l an)- OONJ:OU1\O\OOOOOON-AO‘O‘NOOOOWU‘DOOOOOOOOOOO(»U1831 ——I—8 CONNAOO‘NOOOOOONOQOOWONNUI‘OOOOOOOOOOOBWOOOOOOOOOt—AOU'I 15 10 21 24 22 25 25 25 25 17 18 25 25 23 25 25 25 21 20 20 20 11 10 15 18 10 17 24 14 22 23 25 25 25 25 25 14 14 21 25 23 0000000000 1315 670 895 370 780 1085 925 460 755 1005 00000000 1355 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 condemns-0010a 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 OOOOOOOOOOOOOON—bONU'IOOOOOOOOOOOOOOOOOOOOdOOOOOOWU'IU'Iw OOOOOOOOONOOOO-AOOOOOOOOOGOOOOOOOOOOOOOO3:0-300000000 OOOth’ONOQ‘QOdNO‘OOO‘OAAQOONOOOOOOOOOONOZOO-‘m—IOOOOOOO 220 dd MN 12000OOOU‘INOOOOEOOOKOO-AOU'IO‘OOOOOOOWKTIQOWOWNGDNOOOOOU'IU'I 17 15 20 22 25 25 15 22 17 16 25 16 25 25 25 25 25 25 25 25 14 17 15 24 20 16 0 1060 395 925 1360 1650 135 875 0000 O 460 765 1095 855 1235 910 995 0‘ O‘ 00 0000000000 27 28 29 30 31 32 COCO—to 000000 221 OOOOWO" OOOOU'IU'I 14 16 25 25 25 25 0 690 1440 0 0 0 750 1625 0 0 0 0 APPENDIX D FIELD MAPS Fig. D1.--The Galien study 222 HEN —1—_—— ——— 1 mil. area (from Logan 1977, p. A4-1). -—1»= P) . 121 M, g 214 145 my 133 1410 K, . —149 223 GILIEN .._/ g 136 as 136 = 5 ‘=MII ‘4'; “pass“ 713 812 ,2 may % w; 713 813 WI]; 822 8 . 43 747 .1 E. 734 m * 1017 s 3 g 735 5 . 1 1227. ‘ 911 $3 y- m 121,, . 924 1014 '— 1024 1115 35".)1222 1023 .' . .. g ‘ ‘ ’ ‘ $5131“? z... 1 2 2 5 _ . - 5 § 1228 \ MICHIGAN 112‘ 1215 1227 933 INDIA!“ :- mm 1146 1135 £51 s-wum % n-umcn E on: .L 1 1m: Fig. D2.--Small grain fields in 1976. 224 llilllllllll 1223 51mm 1‘ . ,3: 1mm I-um E 1111 r 1 Ill! 7 Hum Fig. D3.--Sma11 grain fields in 1977. 225 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X 1 1 1 X X 1 1 1111 1 1 X X 1 11111 1 X X 1 1111 X X 11 1 1 X X 1 111 3 1X X1 1 1 3133 1 1 1X x13 13 3 3 1x X 111 2 3 X X 111 11 32222 X X 1 1 1 X X 11 1 3X X 1 1 11 X X X X 22 X X 1 1 1 X X 1 1 1 3 1122 1 1 X X 3 11 11 1 X X 2 1122 11 X X 2 1 13 X X X X X X 1 3 X X 11 X X 1 X X 1 X X 11 X X 11 11 X x 33 x X 3 X X X X 11 X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. D4.--Digitized field map for 1976. Each numeral is a lO-acre cell. 1 = S-wheat, 2 - Rrwheat, 3 8 cats. 226 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X ‘11 2 2 2 X X 2 ‘11 2 22 Z? 2 X X 11 11 11 2122 2 3 X X 1 1 11 2 1 X X 22 22 X X 2 23 X X 22 2 2 X X1 2 23 32 X X2 3 2 3 11 2 X X 1 2 X X 2 X X 2 X X 1 2 2 X X 2 232 X X 222 X X 1 21 1 3 X X 21 2 22 X X 1 2 X X 2 2 X X 2 1 2 X X 2 X X 1 X X 1 X X 1 2 X X 1 X X 1 2 2 X X 1 2 2 X X 22 1 2 X X 11 X X 2 X X 1 X X 11 1 X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. D5.--Digitized field map for 1977. Each numeral is a 10-acre cell. 1 = S-wheat, 2 = R-wheat, 3 = oats. 227 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X 5 5 X X 56 65 5X X 6 6 7 6 6 66 X X 5 6 5 6 55 6666X X 65 566 666 X X 66 5 6 X X 6 6 6 5 X X 5 X X 6 5 66 X X 7 55 5 6 X X 6 X X 7 5 6 5 66 X X 66 55 66 6 5 6 X X 66 55 55 6 6 X X 55 5 5 X X 6 5 6X X 66 6555 5 5X X 6 5 6666 5 X X 6 56 66 6 6 X X 66566 666 56 56666X X 65555 6 6666666 6X X 56 66 6 666666 X X 5 6666 666666 X X 6 666556 6757 X X 6 666555 7 X X6 6 5655 X X6 6 6 655556 6 X X66 6 5 X X555 6 66 X X555 66 X X655 6 6 66 X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. D6.--Digitized map of woodlots and water at Galien. 5 = sparse woods, 6 = dense woods, 7 = water. APPENDIX E PROGRAM SEARCH OOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOQOOOO 228 PROGRAM SEARCH(TAPE1,TAPE2,TAPE3,TAPE4,0UTPUT) PROGRAM SEARCH SEARCHES AROUND FIELDS IN A CIRCULAR PATTERN AT 4 FIXED RADII AND REPORTS THE ACRES OF EACH OF 8 CATEGORIES 0F HABITAT FOR EACH OUADRANT OF THESE CIRCLES. TAPE1 CONTAINS THE ROW BY COLUMN GRID-CODED ACREAGES FOR 5 HABITATS (GRID CELLS ARE 10 ACRES TOTAL) OBTAINED FROM INTERPRETTING AN AERIAL PHOTO OF THE 4.125 (N-S) BY 4 (E-W) MILE PUBESCENT WHEAT STUDY AREA IN BERRIEN COUNTY SOUTH OF GALIEN. TAPE2 CONTAINS INFO IDENTIFYING THE SHAPE, SIZE AND LOCATION OF FIELDS TO BE SEARCHED AROUND. TAPE3 CONTAINS ACRES OF SMALL GRAINS IN CELLS WITH GRAIN FIELDS SMALL GRAIN ACREAGE MAY EXCEED 10 ACRES PER CELL, SINCE GRAIN FIELDS WERE ASSIGNED EVENLY TO N/10 CELLS, WHERE N IS THE FIELD ACREAGE ROUNDED TO THE NEAREST 10 ACRES. THUS A 14 ACRE FIELD WOULD BE ASSIGNED TO ONE 10-ACRE CELL, AND THAT CELL WOULD HAVE 14 ACRES 0F GRAIN RECORDED FOR IT. TAPE4 IS OUTPUT, GIVING THE ACREAGE OF EACH HABITAT IN EACH OUADRANT OF 4 "CIRCLES" OF RADII .125, .250, .375 AND .500 MILE FROM FIELD BOUNDARY. CATEGORY (HABITAT) CODES: 1: EDGE OF WOODS (20 FT INTO WOODS) 2: SPARSE WOODS (75 PCT OR LESS CANOPY CLOSURE), SHRUBBY AREAS 3: TREE LINES, FENCE ROWS 4: CROPLAND (INCLUDING SMALL GRAINS) 5: DENSE WOODS 6: SUSCEPTIBLE WHEAT 7: RESISTANT WHEAT 8: OATS DIMENSION A(33.32,8),FACTOR(5,4),CAT(9).IXL(4),IXU(4),IYL(4), +IYU(4) INTEGER XMIN,XMAX,YMIN,YMAX,CODE LOGICAL IPART NOTES WHETHER OR NOT QUASDRANT IS ONLY PARTIALLY WITHIN GRID BOUNDARIES. DATA FACTOR/1.0,.938,.950,.917,.920, + 1.0.0938,09u790909509339 + 1.0,.967,.971,.947,.961, + 1.0,.966,.969,.944,.963/ FACTOR TO CORRECT TOTAL. ACREAGE FOR ODD CORNERS WHICH MUST BE 'REMOVEL T0 ACCOUNT FOR FIELD SHAPE (WITHOUT REGARD TO SPECIFIC LOCATION OF THESE CELLS). FACTOR(CODE,IR) IS REDUCTION FACTOR FOR FIELD WITH SHAPE GIVEN BY CODE AND SEARCH RADIUS IR. CODESd 1:RECTANGULAR (ANY NO. CELLS) 2:L-SHAPED, 3 CELLS 3:SHAPE OF FIELD 5-3-5 IN 1977 4:SHAPE OF FIELD 2-2-5 IN 1977 5:SHAPE OF FIELD 3-1-3 IN 1976 SHAPES 2,3,4 REQUIRE DROPPING ADDITIONAL CELLS FROM SEARCH PATTERN READ(1,101)(((A(I,J,K),K=1,5),J=1,32),I:1,33) C 60 61 62 63 (3.5 O 229 STORE GRID DO 60 I=1,33 DO 60 J=1,32 DO 60 K=6,8 A(I,J,K)=0.0 NGC=O READ(3,105)ICROP,IROW,ICOL,ACRES IF(EDF(3))63.62 ICAT=ICROP+5 NGC=NGC+1 A(IROW,ICOL,ICAT)=ACRES GO TO 61 PRINT 106,NGC NR:O READ(2,102)IC,IF,ACRES,CODE,XMIN,XMAX,YMIN,YMAX READ DATA FOR ONE FIELD TO BE SEARCHED AROUND IF(EOF(2))50,2 IF(CODE.NE.O)GO TO 3 CODE:1 YMIN=XMAX YMAX:XMAX XMAX=XMIN FOR SINGLE-CELLED FIELD, READ ONLY X,Y CFACT=1 NR=NR+1 XMID=FLOAT(XMIN+XMAX)/2. YMID=FLOAT(YMIN+YMAX)/2. LOCATE MIDDLE OF FIELD EXTREMES IXU(1)=XMID IXU(3)=XMID IXL(2)=XMID+.5001 IXL(4)=XMID+.5001 IYU(1):YMID IYU(2)=YMID IYL(3)=YMID+.SOO1 IYL(4)=YMID+.5001 FIND INNER EXTREMES FOR EACH QUAD OF SEARCH PATTERN DO 4 IR=1,4 LOOP OVER RADII IXU(2)=XMAX+IR IXU(4)=XMAX+IR IXL(1):XMIN-IR IXL(3)=XMIN-IR IYU(3)=YMAX+IR IYU(4)=YMAX+IR IYL(1)=YMIN-IR IYL(2)=YMIN-IR FIND OUTER EXTREMES FOR EACH QUAD OF SEARCH PATTERN DO 45 IQ=1,4 LOOP OVER QUADRANTS 1=NW, 2:NE, 3:SW, 4:SE 230 UHOLE=PLOAT((XMAx-XMIN+1+2*IR)*(YNAx-YMIN+1+2*IR)*1O)/4. C CALCULATE ACREAGE OF WHOLE QUAD (INCLUDING CORNERs) IPART=.F. IF(IXL(IQ).GE.1)GO TO 5 IXL(IQ):1 IPART=.T. C PREVENT SEARCH FROM FALLING OUTSIDE GRID, AND NOTE PARTIAL QUAD 5 IF(IXU(IO).LE.32)GO TO 6 IXU(IQ)=32 IPART:.T. 6 IF(IYL(IQ).GE.1)GO TO 7 IYL(IQ)=1 IPART=.T. 7 IP(IYU(IQ).LE.33)GO TO 8 IYU(IQ)=33 IPART:.T. DO 9 ICAT=199 CAT(ICAT):0.0 ZERO TOTAL ACREAGE IRL=IYL(IQ) IRU=IYU(IQ) ICL:IXL(IQ) ICU=IXU(IQ) C SET DO-LOOP PARAM FOR QUAD SEARCH DO 10 IROW:IRL,IRU R=1.0 IF(ABS((FLOAT(IROW)-YMID)).LT.0.001)R=0.5 C IF CELL LIES ON MID-LINE, COUNT HALF IN EACH QUAD DO 11 ICOL=ICL,ICU C=1.0 IF(ABS((FLOAT(ICOL)-XMID)).LT.0.001)C=O.5 CAT(9)=CAT(9)+10.*R*C C SUM UP TOTAL ACRES IN SEARCHED QUAD DO 12 ICAT:1,8 05000 12 CAT(ICAT):CAT(ICAT)+A(IROW,ICOL,ICAT)'R*C C SUM UP CATEGORY TOTALS IN QUAD 11 CONTINUE 1O CONTINUE PART=1. IP(IPART)13,15 13 PART=CAT(9)/WHOLE C CALCULATE PROPORTION OF QUAD LYING WITHIN GRID BOUNDARIES DO 14 ICAT=1,8 14 CAT(ICAT)=CAT(ICAT)/PART C UPWARDLY ADJUST CAT TOTALS FOR PART OUSIDE GRID (ASSUME SAME C HABITAT PROPORTIONS OUTSIDE AS IN). 15 GO TO (40,16,16,27)IR C DIFFERENT RADII REQUIRE DIFFERENT CORNER ADJUSTMENTS 16 IF(IPART)22,17 17 CFACT:1.0 231 GO TO (18,19,20,21)IQ 18 IYO=IYL(IQ) IXO=IXL(IQ) C LOCATE 1 CORNER CELL TO BE REMOVED (FOR .250 AND .375 C MILE RADII) TO CREATE ROUND (CIRCULAR) PATTERN GO TO 23 19 IYO=IYL(IQ) IXO=IXU(IQ) GO TO 23 20 IYO=IYU(IQ) IXO:IXL(IQ) GO TO 23 21 IYO=IYU(IQ) IXO=IXU(IQ) GO TO 23 22 CFACT:(WHOLE-10.)/WHOLE C CFACT WILL REDUCE ACREAGE BY 1 CELL FOR QUAD WHOSE CORNER C FALLS OUTSIDE GRID AND CANNOT THEREFORE BY SUETRACTED DIRECTLY 23 WHOLEzWHOLE-10. IF(IPART)40,24 24 DO 25 ICAT=1,8 25 CAT(ICAT)=CAT(ICAT)-A(IYO,IXO,ICAT) C REMOVE CORNER GO TO 40 27 IF(IPART)33128 28 CFACT=1.0 GO TO (29,30,31,32)IQ 29 IYO1=IYL(IQ) IYO2=IYL(Io) IYO3=IYL(IQ)+1 IXO1:IXL(IQ) IX02=IXL(IQ)+1 IXO3=IXL(IO) C FIND 3 CORNER CELLS TO REMOVE FOR .500 MILE RADIUS Go TO 34 3O IY01:IYL(IQ) IY02=IYL(IQ) IY03=IYL(IQ)+1 IXO1:IXU(IQ) IX02=IXU(IQ)-1 IX03=IXU(IQ) GO TO 34 31 IYO1=IYU(IQ) 1Y02=IYU(IQ)-1 IYO3=IYU(IQ) IXO1=IXL(IQ) 1x02=IXL(IQ) IX03=IXL(IQ)+1 GO TO 34 32 IYO1=IYU(IQ) 232 IY02=IYU(IQ) IYO3=IYU(IQ)-1 IXO1:IXU(IQ) IX02=IXU(IQ)-1 1X03=IXU(IQ) GO TO 34 33 CFACT=(WHOLE-30.)/WHOLE C CFACT WILL REDUCE ACREAGE BY 3 CELLS FOR QUAD WHOSE CORNER C FALLS OUTSIDE GRID 34 WHOLE:WHOLE-30. IF(IPART)40,37 37 DO 35 ICAT=1,8 35 CAT(ICAT)=CAT(ICAT)-A(IYO1,Ixo1,ICAT)-A(IY02,Ix02,ICAT) +-A(IY03,IXO3,ICAT) c REMOVE CORNER 40 SCAT=0.0 DO 36 ICAT=1,8 CAT(ICAT):CAT(ICAT)*CFACT'FACTOR(CODE,IR) C REDUCE ACREAGE BY CFACT FOR CORNER REMOVED (TO CREATE ROUND C PATTERN) FOR THOSE QUADS WHOSE CORNERS WERE OUTSIDE GRID EDGES C AND BY FACTOR FOR ODD—SHAPE OF SOME FIELDS WHICH C REQUIRES DROPPING ADDITIONAL ACREAGE FROM SEARCH. IF(ICAT.GT.5)GO To 36 SCAT:SCAT+CAT(ICAT) C SUM OF 5 CATEGORIES 36 CONTINUE AREA:WHOLE'FACTOR(CODE,IR) C CALCULATE EXPECTED TOTAL ACREAGE TO COMPARE WITH SCAT WRITE(4,103)IC,IF,CODE,ACRES,IR,IQ,PART,(CAT(JJ),JJ:1,8), +SCAT,AREA 45 CONTINUE 4 CONTINUE GO TO 1 50 PRINT 1O4,NR STOP 101 FORMAT(9X,5F7.3) 102 FORMAT(2I5,F5.1,5I3) 103 FORMAT(12,IS,IZ,F5.1,212,F6.3,10F8.3) 104 FORMAT(I6* LINES READ FROM TAPE2') 105 FORMAT(15,5X,2I5,F7.3) 106 FORMAT(I6' LINES READ FROM TAPE3*) END APPENDIX F CONTOUR PLOTS Adult densities at Galien plotted daily from 11 April 1977 233 234 235 @606 236 237 238 0 2% «:4 9 2% CF <84 > O‘@ &. @ 9©© 1‘; 9&7)” OE. ©© . G ©© . G O ° O 8 (O O O o 69 © ’3 Q @ ® 41 ® ‘2 240 166 Q @O O 6 .1 Q .@ Oo . @ § O O 5 4 . u « WOO... O 0 $26 6 DO O@O QC A OOO Q .@ Q ©® 0 © 9% I © QQ WM © 21 A 5 A A HOMO Q ©O . 0 O 06 9 < O .0 co 6 00 O 0 I O . Mo 9 @ -OOO Q Q O, APPENDIX C STICKY BOARD TRAP DATA 241 Table Gl. Catch by date of incoming and outgoing cereal leaf beetles on sticky board traps placed along each border of six fields at Galien in 1977 (each entry is sum for 4 traps). North East South West Date In Out In Out In Out In Out S-wheat 1022 4/20 0 0 0 0 0 0 0 0 4/21 11 9 0 0 0 0 0 0 4/22 3 9 0 0 0 0 0 0 4/26 2 l 0 0 0 O 0 0 4/27 2 l 0 O O 0 0 0 4/29 0 O 0 0 0 0 0 0 5/03 1 1 1 0 0 O O 0 5/05 1 1 0 3 0 0 0 0 5/09 4 14 ll 3 0 0 0 1 5/12 3 21 3 8 13 13 0 0 5/18 197 127 59 37 31 39 7 15 5/20 19 77 19 40 21 34 0 1 5/24 23 20 20 16 3 15 9 24 5/27 15 8 l O 0 0 0 0 6/01 9 l 3 0 4 8 0 0 6/08 5 6 3 3 l 4 0 1 6/13 9 1 0 5 0 2 0 0 6/14 0 3 0 1 O l 0 0 6/16 101 323 10 52 10 38 6 41 6/21 302 485 9 29 56 129 6 27 6/24 243 365 5 44 101 165 62 122 7/01 60 43 2 7 31 54 26 73 S-wheat 322 4/26 0 0 0 0 0 0 O 0 4/29 0 0 0 0 0 0 0 0 5/03 0 0 0 0 0 0 0 0 5/05 0 O 0 l 0 0 5 1 5/10 0 2 0 0 2 0 0 12 5/13 0 2 0 l 0 0 2 6 5/16 6 1 l 2 2 6 13 11 5/19 15 8 3 4 10 9 5 5 5/23 3 12 2 l 8 28 3 12 5/27 1 l 0 l 2 6 0 2 6/02 1 l O l 0 0 0 0 Table 01. Continued. 242 North East South West Date In Out In Out In Out In Out vaheat 1024 4/20 0 l l 0 0 1 0 0 4/21 0 0 0 0 0 0 0 0 4/22 0 0 0 0 0 0 0 0 4/26 0 0 0 0 0 2 0 0 4/27 0 0 0 0 0 0 0 0 4/29 1 l 0 0 0 0 0 0 5/03 1 2 0 0 0 0 4 0 5/05 0 0 0 1 0 l 0 1 5/09 0 0 0 0 0 0 7 2 5/12 1 l 2 0 O 0 ll 14 5/18 11 12 52 82 ll 19 375 130 5/20 5 5 62 101 50 182 256 118 5/24 25 12 23 90 38 122 93 65 5/27 1 5 8 l4 7 21 20 15 6/01 0 4 5 ll 5 21 9 6 6/08 0 0 2 4 5 9 0 3 6/13 0 0 0 l 0 l 0 0 6/14 1 2 0 0 0 l 0 0 6/16 1 l 4 10 3 3 5 2 6/21 2 6 19 20 6 13 1 3 6/24 6 3 55 33 18 57 4 5 7/01 4 3 64 43 77 94 7 9 Rrwheat 323 4/29 0 0 0 0 0 0 l 0 5/03 0 0 0 0 0 0 0 3 5/05 0 0 0 0 0 0 0 2 5/10 0 O 0 1 l 0 0 12 5/13 0 0 0 0 4 1 0 1 5/16 2 0 2 3 7 2 0 0 5/19 3 3 3 0 9 3 l 1 5/23 0 3 4 2 l 8 0 1 5/27 0 3 0 2 0 0 0 1 6/02 3 5 0 3 l 6 2 l West Out In 243 East South Out In Out Oats 541 In North Out Continued. In Table 61. Date 0334749n5620102460 5.171203011145321 ll... 043478834231001700 221220000033511 143611 122 1 6 S a 001379482250120122 0 131/410200030021 12 02055823706103.0400 322240100043400 111111 11 593691728034624735 369472834624735 001112200111122011 111220011122011 ////////////////// /////////////// 555555566666666777 555556666666777 APPENDIX H SPATIAL DYNAMICS SIMULATION MODEL C**** Ci!!! Ciao: Ci!!! Ci!!! Cl!!! on!!! 059.! CC!!! CDDQO Ci!!! Cl!!! 051.. CONDO Cali! Cocno Cin! Coos! CGDOM cfifiii Cass! CG!!! CI!!! 101 244 PROGRAM SPATIAL(OUTPUT=129,TAPE1=129,TAPE2:129,TAPE3:129, +TAREu=129,TAPE61=OUTPUT) DIMENSION P(3u,3u),PL(7),ow(3u,3u),DEGu8(22),DEGu2(22),DOT(22), +A(7).D(7),EGGINR(3).CADDR(3),TAD(3),XMAT(u),YMAT(u),RMAT(15), +RP(3n,3u),AE(3u,3u),OVR(3u,3u),EGGIN(3u,3u),CADD(3u,3u),HT(3) INTEGER R(3u,3u),VARYA,VARTD REAL NE(3u,3u),MATuR LOGICAL ALTERD DATA XMAT/10.,15.6,21.1,26.7/ DATA IMAT/32.,16.,1O.,u./ DATA DOY/91.,95.,100.,105.,110.,115.,120.,125.,130., +135.,1uo.,1u5.,1so.,156.,161.,166.,171.,176.,181.,186. +191.,196./ DATA DEGu2/59.,88.,121.,160.,202.,2u6.,3o1.,366.,u3u., +508.,6OO.,7OA.,825.,962.,1098.,12u6.,1388.,15AO.,1682., +1836.,1988.,2152./ DATA DEGu8/27.,u2.,58.,79.,1O3.,129.,16O.,198.,2u2., +286.,3u8.,u16.,510.,620.,720.,832.,950.,1072.,1196., +1320.,1AA8.,1576./ 9 P = POPULATION IN CELL(I,J) PL = PROBABILITY OF LEAVING A CELL OF HABITAT TYPE H(I,J) H : HABITAT TYPE OF CELL(I,J) HABITATS ARE: 1 SUSCEPTIBLE WHEAT 2. RESISTANT WHEAT 3. OATS u. NON-HOST CROPLAND 5. SPARSE WOODS 6. DENSE WOODS 7. BORDER CELLS (1 TIER DEEP, ALL AROUND AREA) NB = NON-BARRIER PROPORTION OF CELL"S BOUNDARY (SUM OF A/A FOR A NEIGHBORS) OW : WEIGHTED AMOUNT OF OVERWINTERING HABITAT IN CELL(I,J)/SO. YD. (RANGES FROM 0.0 T0 0.2) ALTERD:.F. SET FLAG INDICATING THAT ALTERATION IN WHEAT DIFFUSION RATE HAS NOT YET OCCURED. SEXR=O.5 PROPORTION FEMALE, ADULTS IPRINT:1 KM=15. ORDER OF DISTRIBUTED DELAY FOR MATURATION PROCESS READ PARAMETERS READ(1,101)ISIZE,NDAYS,DT,NPRINT,IPF,(A(I),I=1,7), +(D(I),I=1,7),TOW,IOW,VARYA,VARYD,CHW,AWNEW,DWNEW,OVRED,DINCR, +DEM,Dwx,DOX FORMAT(IZ/ CG!!! CG!!! csuuu CGONO cl!!! CGDOI CO!!! CI!!! cl!!! Ci!!! Ciil! Cl!!! CQOO§ C§a§§ CO!!! 0!!!! Casi: CiQGG CI!!! CO!!! cl!!! Cliii cuss! cuss: Ci!!! Clifli Ci!!! canon Ci!!! 245 +I3/ +F10.A/ +13/ +A1/ +7F3.0/ +7F10.0/ +F5.0/ +A1/ +A1/ +A1/ +F3.0/ +F3.0/ +F10.0/ +F3.0/ +FN.O/ +F5.0/ +F5.0/ +F5.0) ISIZE INCLUDING BORDER CELLS NDAYS NO. ROW AND COL IN GRID, DAYS TO SIMULATE DT TIME STEP, FRACTION OF DAY NPRINT DAYS BETWEEN PRINTING REGIONAL POPULATION TOTAL IPF (Y OR N) PRINT INDIVIDUAL FIELD POPS EVERY NPRINT DAYS? A ABSORPTIVITY CONSTANT FOR HABITAT(I) (0 TO 1) 0 IS PERFECT BARRIER (O.LT.A.LT.1) IS PARTIAL BARRIER 1 IS NEUTRAL (A.GT.1) IS ATTRACTIVE D = DIFFUSION RATE FOR HABITAT(I) (1,2 AND 3 WILL LATER VARY) (INFIN/MIN) TOW = SUM OF MEAN OVERWINTERING DENS (/SQ.YD.) IN 5 CW HABITATS IOW (Y OR N) WANT TO READ IN INDIVIDUAL OW FOR EACH CELL? (IF N, WILL READ FOR EACH HABITAT) VARYA (Y OR N) WANT TO ALTER ABSORPT OF WHEAT AFTER CHW? VARYD (Y 0R N) WANT TO ALTER DIFFUSION IN WHEAT AFTER CHW? CHW = CRITICAL HEIGHT OF WHEAT (IN.) AT ALTERATION OF A OR D AWNEW = NEW A VALUE FOR WHEAT AFTER CHW DWNEW = NEW D VALUE FOR WHEAT AFTER CHW OVRED = FACTOR TO REDUCE OVIPOSITION IN RESISTANT WHEAT DINCR = FACTOR TO INCREASE DIFFUSION RATE IN RESISTANT WHEAT DEM = SHIFT MEDIAN EMERGENCE BY DEM DDAS DWX = SHIFT WHEAT GROWTH CURVE BY DWX DD42 DOX : SHIFT OAT GROWTH CURVE BY DOX DDAZ AOAT:A(3) A(3)=A(A) ABSORPTIVITY OF OATS WILL BE SAME AS NON-HOST CROPLAND UNTIL OATS EMERGE ISM1:ISIZE-1 102 C*"* 103 C§§i§ cliui 355*: cl!!! Cfiiii ciiii ciiii cl!!! 10 11 Ciifli Clii! Ci!!! CONN. Ci!!! CI!!! ca!!! 0911* COOS; Ca!!! 246 READ(2,102)((H(I,J),J=1,ISIZE),I=1,ISIZE) FORMAT<3uI1) READ IN SPATIAL PATTERN IF(IOW.EO.1HY)GO TO 3 READ(2,103)(OW(I),I=1,7) GO TO A READ(2,103)((0W(I,J),J=1,3u),I=1,3u) FORMAT(17Fu.2) READ IN ON DISTRIBUTION INITIALIZE CELL VARIABLES CONTINUE DO 10 I=2,ISM1 DO 10 J=2,ISM1 LOOP OVER CELLS (I : P(I,J)=O. RP(I,J)=O. POP LEVELS AND RATES FOR INNER CELLS CADD(I,J)=O. EGGIN(I,J)=O. ROWS J : COLS) CUMULATIVE ADULT DEGREE—DAYS (AREA UNDER CURVE) AND EGGS OVR(I,J):O. OVIPOSITION RATE NB(I,J):(A(H(I,J+1))+A(H(I,J-1))+A(H(I+1,J))+A(H(I-1,J)))/U. DO 11 I:2,ISM1 P(1,I)=O. P(ISIZE,I)=O. P(I,1)=O. P(I,ISIZE)=O. FIX BOUNDARY CELLS AT ZERO POP. LEVEL INITIALIZE STATE VARIABLES T=91. TIME (DAYS) DAY 91 : CDDA2=59. CDDA8:27. CUMULATIVE DEG-DAYS (FAHRENHEIT) FOR EAU CLAIRE CEMERG=O. CMATUR=O. PMATUR=O. APRIL 1 CUMULATIVE PROPORTION EMERGED AND SEXUALLY MATURE, OF EMERGED FEMALES WHICH ARE MATURE HTW:O. HTO:O. CROP HEIGHT (INCHES) ZAGW=27. ZAGO=27. BASE LINE (DDAO) FOR AGE OF OVIPOSITING FEMALES AND PROPORTION 247 D0 12 1:1,3 CADDR(I)=O. 12 EGGINR(I)=O. C**'* REGIONAL CUMULATIVE TOTALS FOR HOST CROPS Cu!!! CFFFF INITIALIZE RATE VARIABLES CNS'I' DDA2:O. DD“8=O. C**** DEGREE-DAYS ACCUMULATED/DAY EMERG:0. MATUR=O. CF... PROPORTION EMERGING AND MATURING PER DAY DELMP:32. DO 13 I=1,KM 13 RMAT(I)=O. C**'* DELAY TIME AND INTERNAL RATES FOR MATURATION PROCESS NPRINTzFLOAT(NPRINT)/DT+.5 NIT:FLOAT(NDAYS)/DT+.5 CFFEP TOTAL NO. OF ITERATIONS, AND ITERATIONS BETWEEN PRINTING C‘H‘H‘I" DO 20 IT=1,NIT Cans! C*'** LOOP OVER TIME Cults CFFFF UPDATE STATES CHGH‘W T=T+DT CDDA2=CDDA2+DDN2FDT CDDA8=CDDA8+DDU8'DT CEMERG=CEMERG+EMERGFDT CMATUR=CMATUR+MATURFDT IF(CEMERG.LE.O.)GO TO 21 PMATUR=CMATUR/CEMERG 21 WX:CDDA2+DWX OX=(CDDAZ-ZOO.)+DOX HTW=AMAX1(HTW,('3.9A8+0.0ZAB'WX+0.0000QOB'WX'WX—0.0000000U81 +*WX*'3)/2.5A) HTO=AMIN1(HTW,AMAX1(0.0,-21.21+0.0563'OX-0.0000ZBZ‘OX‘OX+ +0.818E-8'OX"3)) C"** LET MAX OAT HT = MAX WHEAT HT HT(1)=HTW HT(2)=HTW HT(3)=HTO IF(PMATUR.LT.0.05)ZAGW=CDDA8 OVAGW=(CDDAB—ZAGW)*.55555 IF(HTO.LE.O.)ZAGO=CDDA8 OVAGO:(CDDAS-ZAGO)'.55555 C“... EFFECTIVE AGES (DD9 (C)) FOR OVIP BEETLE IN WHEAT AND OATS TAD(1):O. COGS! Ci!!! Ci!!! CNN!» 22 A0 Cain: CNN»: C}!!! Ci!!! Ciiifl Ci!!! Ci!!! Cans! 09:5: C§§§§ Ci!!! CONDO 248 TAD(2):O. TAD(3)=O. DO no I:2,ISM1 DO no J:2, ISM1 LOOP OVER CELLS P(I,J)=P(I,J)+RP(I,J)*DT UPDATE POPUL. LEVELS GO TO(22,22,22,AO,AO,AO,AO)R(I,J) FOR HOST CROP CELLS, CALCULATE CUMULATIVE TOTALS (IF CROP HT GT 0.0) IP(HT(R(I,J)).LE.0.0)GO TO no CADD(I,J)=CADD(I,J)+P(I,J)*DDA8*DT EGGIN(I,J)=EGGIN(I,J)+OVR(I,J)*DT CADDR(R(I,J))=CADDR(H(I,J))+P(I,J)*DDA8*DT EGGINR(H(I,J))=EGGINR(H(I,J))+OVR(I,J)'DT TAD(H(I,J))=TAD(H(I,J))+P(I,J) CONTINUE UPDATE RATES TP1:T+1. D1:TAELI(DEGA8,DOY,T,22) D2=TABLI(DEGA8,DOY,TP1.22) DDA8=D2-D1 DD9:DDu8*.55555 CDLA8=ALOG1O(CDDu8) ACCUMULATION OF LOG1O DEGREE-DAYS (us F) DLA8=ALOG10(D2)-ALOGIO(D1) DDA2=TABLI<><><><><><><><><><>< XXXXXNNNXXXXXXXNNNN Eleven 90-acre wheat fields. 271 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X WW X X WW WW X X WW X X WW X X WW WW X X WW X X X X WW X X WW WW X X WW X X X X WW WW X X WW WW X X X X WWX X WW WWWWX X WW WW X X X X WWWW X X WWWW X X X X X X WW WW X X WW WW X X WW X X WW WW X X WW WWX X WW WWX X WW WW WW X X WW WW WW X X WW WW WW X X WW WW X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. 120.-—Run 51: Twenty-four 40-acre wheat fields. 272 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X WW X X WWWW X X WW X X X X WW X X WW X X WW X X WW WW X X WW WW WWX X WW WWX X WW WW X X WW WW WW X X WWWW X X WW X X WW X X WW WW X X WW WW X X WW X X WW X X WW X X WW X X WW WW X X WW X X WW X X WW WW X X WW WW X X WW WW X X WW X X WW X X WW WW X X WW WW X X WW X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. 121.--Run 52: Twenty-four 40—acre wheat fields. 273 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X W W X X 11 W W W X X W WW X X 19 WW X X W X X W 11 X X WWW X X WW' 11 X XW 11 W W X X W WW W 11 X X WW X XW W X XW W WW W W 11 X X W W X X W X X W W W X X W W W X XW W X X W W W 11 X X W W 11 X X W W W X X W W X X WW 14 WW X X W W WW X X WW X X W W W X X W W WW 11 X X W W W X X 11 W W X X WW W X X WW W X X W X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. 122.-Run 53: Ninety-six lO-acre wheat fields. 274 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X W WWW WX X W VH1 WW W X X W V! X X W W WX X W W X X W W W X X W W W X X W W X X W W WW W X X W W X XW W W X X W X X W W W X X W W X X W W W X X W W X X W WW W X X W W X X W W W X XW WW W W WX X W W X X W W X X W W W X X W W WX X W W W X X W WWWW W X X W W W X X W W W X X W W W X X W X X W X X W ‘W W W X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. 123.--Run 54: Ninety-six lO-acre wheat fields. 275 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X W X W X X W WWWWWWWWW X X W W X X W W X X W W X X W W X X W W X X W W X X W X X W W X XWWWWWWWWW W W W X X W W X X WWWWWWWWWW W X X W W X X W W X X W W X X W W X X W W X X W W X X W X X W X X W W X X W W X X W W X XWWWWWWWWW W W X X W WWWWWWWWWWX X W W X X W X X W X X W X X X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. IZ4.--Run 55: Eleven elongate 90—acre wheat fields. 276 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX WWWWWWWWW WX WWWWWWWWW ZSS‘EtZSfJZ :zzzzzzzz zzzzzzzzzz: £££££££€£I WWWWWWWWW >4><><><><><><><><><><><><>< WWWWWWWWWX X WWWWWWWWW X X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX SEIZZSZSSZ X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Fig. 125.--Run 56: Eleven elongate 90-acre wheat fields. 277 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X 3 3 X 13 1 X X 3 31 1 X X 1 X X X X X X 3 1 1 X X X X 1 X X X X 1 X X 3 31 X X 3 1 X X 1 X X 1 3X X 1 1 1X X 3 3 X X 1 1 13 3 X X 1 X X 1 X X 3 X X 1 X X 1 X X X X X X X X 13 13 X X 1 1 X X X X 3 1 X X 1 1 X X X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Fig. I26.-Rnn 57: Configuration for simulating the effect of specific field locations. APPENDIX J DEGREE-DAY ACCUMULATIONS NEAR GALIEN 278 Table J1. Degree-days > 48 (F) accumulated at Glendora, Michigan (Berrien County) during 1976 and 1977. Source: PMEX DEGREEDAYS . Day April May June July 1976 1 998 309 573 1172 2 100 309 586 1187 3 109 309 598 1201 4 109 315 615 1217 5 112 335 636 1236 6 115 335 652 1256 7 117 335 669 1278 8 117 338 690 1299 9 117 349 714 1321 10 123 361 739 1356 11 123 363 765 1389 12 123 367 797 1404 13 129 381 826 1417 14 142 394 855 1446 15 167 409 885 1473 16 191 424 897 1491 17 215 426 914 1505 18 236 429 937 1524 19 244 437 950 1548 20 255 453 962 1579 21 268 461 978 1606 22 279 465 994 1626 23 285 468 1013 1655 24 294 473 1030 1683 25 294 479 1049 1704 26 294 486 1072 1730 27 294 498 1100 1756 28 295 512 1124 1780 29 298 525 1143 1802 30 304 542 1156 1824 31 558 1843 Table J1. Continued. 279 Day April May June July 1977 b 1 112 401 973 1478 2 124 414 977 1495 3 125 426 987 1518 4 126 437 1011 1553 5 126 458 1033 1587 6 126 474 1042 1621 7 128 481 1048 1652 8 128 485 1056 1675 9 130 486 1061 1698 10 145 488 1070 1722 11 166 496 1086 1747 12 185 507 1095 1776 13 205 524 1107 1797 14 214 539 1123 1826 15 230 562 1140 1861 16 249 587 1163 1888 17 272 613 1190 1917 18 297 636 1215 1946 19 315 660 1234 1980 20 337 688 1252 2012 21 353 715 1264 2041 22 356 745 1281 2064 23 364 772 1299 2082 24 364 798 1327 2102 25 364 823 1349 2125 26 365 846 1369 2137 27 . 377 865 1393 2150 28 378 889 1419 2168 29 381 913 1441 2190 30 388 939 1459 2213 31 959 2241 a99 °D > 48 accumulated during March 1976 at Eau Claire, Michigan (Berrien County) (Michigan Climatological Data, NOAA). b110 0D > 48 accumulated during March 1977 at Dowagiac, Michigan (Cass County) (Michigan Climatological Data, NOAA). M71113111111111[11111111111111111I1I1"5