"l'HI-i‘fi‘ ' LIBRARY. Michigan Sm; University J This is to certify that the thesis entitled Development of a Model For On—Line Control of The Cereal Leaf Beetle (Oulema Mglégopus (L.)) presented by Winston Cordell Fulton has been accepted towards fulfillment of the requirements for M— degree in Entomology ,/ @avwzlééci/M—p Major profeér Date May 4, 1978 0-7639 Ill!llllljlgllllllllfllllllllllllfllllll ,_ M. ; W DEVELOPMENT OF A MODEL FOR ON-LINE CONTROL OF THE CEREAL LEAF BEETLE (OULEMA MELANOPUS (L.)) By Winston Cordell Fulton A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Entomology 1978 G3/752C9é9d? ABSTRACT DEVELOPMENT OF A MODEL FOR ON-LINE CONTROL OF THE CEREAL LEAF BEETLE (OULEMA MELANOPUS (L.)) By Winston Cordell Fulton On-line control of insect pests requires models which are accurate for only short time spans into the future and which may be initialized using data easily gathered by a farmer or a pest manage— ment scout. Such a model is developed here by omitting certain parts of the cereal leaf beetle ecosystem which were considered unimportant in determining the amount of damage in the current crop. These factors included the parasites of the beetle, the evidence of density dependent mortalities in the first and fourth instars, and evidence of the oviposition rate being dependent on photoperiod. The model developed is a continuous time deterministic one, using time varying distributed delays of the Erlang type to repre— sent insect life stages. Much of the validation work was in terms of measuring the degree of synchrony between the model and field observations for several year's data. In order to get a high degree of synchrony, one parameter, that which was considered to move the adult beetles from wheat to oats in the spring had to be chosen arbitrarily for each year. This makes the use of the model in the on—line mode at Winston Cordell Fulton the moment impractical. However, under the assumption that this parameter will eventually be modeled or measured, sensitivity analysis of the model continued and showed that synchrony between the model and field was little affected by sampling bias against small instars, and was little affected by changes in larval develop- ment times. Synchrony is strongly affected by even small biases in the temperature data used to drive the model with biases of greater than 1% causing serious increases in the error. When synchrony is improved as much as possible by adjusting the rate of movement of adults from wheat to oats in the spring, field egg density estimates taken between 110 and 220 °D>9 may be used to estimate total incidence of larvae to between 1 and 4 times the actual number observed. Predicted density bounds of this order of magnitude could be acceptable in an on—line pest management mode, since bounds on the error are known. To maintain the error within these bounds following imple- mentation would require an accurate determination of the temperature to which the insects are exposed up to the time of the sample, and a method of measuring the rate at which adults are moving from wheat to cats when the sampling takes place. This movement rate might be determined either from the sample, or be modeled in terms of environmental factors. ACKNOWLEDGMENTS I wish to express my sincere thanks to Dr. Dean L. Haynes for his friendship and support throughout my tenure as a graduate student. His philosophy on pest management, expressed most strongly at the Friday afternoon seminar, will continue to affect me in my professional career. I also wish to thank my other guidance committee members for their invaluable input into my professional development: Dr. George Bird, Dr. William Cooper, Dr. Robert Ruppel, and Dr. Lal Tummala. Finally I want to express my great pleasure at having been associated with a very remarkable series of graduate students: Stuart Gage, Dick Casagrande, John Jackman, Emmett Lampert, Al Sawyer, and Kasumbogo Untung. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . LIST OF FIGURES . . . . . . . INTRODUCTION . . . . . . . . LITERATURE REVIEW . . . . PROBLEM DESCRIPTION . . . . . ANALYTICAL APPROACH . . . . . . The Model . . . . . . . . Model Parameterization . . Spring Adult Emergence . . . Adult Survival . . . . . Time Varying Delays . . . Oviposition . . . . . . Movement from Wheat to Oats . The Egg Stage . . . . . . The Larval Stage . . . . . FORTRAN Implementation . . Sampling to Initailize the Model MODEL VALIDATION . . . . . . . MODEL SENSITIVITY . . . . . Some Effects of Sampling Bias on Model and Field . . . . 0 O I Synchrony Sensitivity to Biases in Temperature Data Variation in Larval Development Times Egg and Larval Survival Functions . . THE ONFLINE MODE . . . . . . SUMMARY AND CONCLUSIONS . . . . iii Between Page vii 10 10 13 14 16 21 22 28 31 36 39 40 50 72 74 77 86 86 92 99 Page Appendices A. COMPUTING AN ESTIMATE OF K FOR THE ERLANG DISTRIBUTION FROM DATA . . . . . . . . . . 103 B. SIMULATION MODEL FOR CEREAL LEAF BEETLE . . . . 107 C. VALIDATION PROGRAM . . . . . . . . . . . 119 LITERATURE CITED . . . . . . . . . . . . . . . 126 iv Table LIST OF TABLES A Comparison of Population Estimates Made by Stem Counts and by Square Foot Counts in Three Fields at Niles, Michigan in 1976 . . . . . . . . . Values for Chi—Square from the Comparison of Model and Field Densities of Cereal Leaf Beetle Eggs and Larvae when Simulations were Run with Dif- ferent Sets of Parameters . . . . . Values for Chi-Square when Simulations Using Optimal Parameter Values for Years 1967—71 were Applied to New Data . . . . . . . . . Oviposition and Survival for the Simulation with YP Optimal and DELE = 1.25 * DELE . . . . . Chi-Square Values for the Correspondence Between Model and Field Data When the Number of First (L1) and Second (L2) Instar Larvae in the Model are Multiplied by the Factors Shown Before the Total Incidence was Adjusted and Compared . . . . Chi-Square Values for the Correspondence Between Model and Field Density Values when the Tempera— ture Affecting the Insect Differs from that Recorded at a Standard Weather Station by the Factor Given . . . . . . . . . . . . . Eggs per Female Laid in Oats and Egg Survival When the Temperature Affecting the Insect Differs from that Recorded by the Factor Shown . . . . . . Chi—Square Values for the Comparison of Field and Model when Larval Development Times were Changed by the Factor Shown . . . . . . . . . . . Total Incidence Ratio - Model/Field from Simula— tions with YP Optimal, DELE = 1.25 * DELE, and Survivals as Indicated . . . . . . . . . . Page 49 69 7O 73 75 80 87 88 91 Table 10. 11. Al. A2. Chi-Square Values for the Correspondence Between Model and Field Data When Three Different Temperature Regimens are Used as Input to the Model . . . . . . . . . . . . . . The Ratio of Model Values to Field Densities on the Sampling Day for Two Years . . . . . . . . Means and Variances for Cereal Leaf Beetle Larval Development Times . . . . . . . . K Values for the Erlang Distribution Computed from the Data in TABLE A1 vi Page 93 97 105 106 10. 11. 12. 13. LIST OF FIGURES Page Frequency Distributions of Ages of Individuals in the Population Being Sampled . . . . . . . . 6 Three Factors which Affect the Proportion of the Population Counted . . . . . . . . . . . 8 A Functional Block Diagram Model of the Cereal Leaf Beetle . . . . . . . . . . . . . . . 11 The Regression of the Probit of Cereal Leaf Beetle Adult Emergence on the Natural Logarithm of °D>9C . 15 Days from Adult Emergence from Overwintering Sites to Time of First Oviposition as a Function of Temperature . . . . . . . . . . . . . . 17 Instantaneous Survival Rate of Adult Cereal Leaf Beetles as a Function of Temperature . . . . . 19 Several Members of the Erlang Family of Curves Used in the Time Varying Delays in the Simulation Model . 23 Accumulated Cereal Leaf Beetle Egg Input as a Function of Accumulated °D>9C . . . . . . . . 25 Accumulated Cereal Leaf Beetle Egg Input into Wheat and Into Oats as a Function of the Natural Logarithm of °D>9C . . . ._ . . . . . . . 27 Cereal Leaf Beetle Oviposition Rate as a Function of Age in Accumulated °D>9C . . . . . . . . . 29 Development Times for Cereal Leaf Beetle Eggs and Pupae as a Function of Temperature . . . . . . 32 Survival of Eggs, Larvae and Pupae as a Function of Temperature . . . . . . . . . . . . . . 33 Instantaneous Survival Rates for Eggs and for Larvae and Pupae as a Function of Temperature . . . . . 34 vii Figure Page 14. Developmental Times for the 4 Instars of the Cereal Leaf Beetle as a Function of Temperature . . . . 37 15. The Variance-Mean Relationship for Single Oat Stem Samples of Cereal Leaf Beetle Eggs . . . . . . 42 16. The Variance-Mean Relationship for Single Oat Stem ’ Samples of Cereal Leaf Beetle Larvae . . . . . 44 17. The Variance—Mean Relationship for Single Oat Stem Samples of Eggs + Larvae of the Cereal Leaf Beetle . . . . . . . . . . . . . . . 46 18. Three Different Methods for Comparing Model Output to Field Observation . . . . . . . . . . . 52 19—22. Comparisons of Model Output and Several Years' Field Data . . . . . . . . . . . . . . 55 23. The Square Root of the Sum of the Squared Deviations Between Model and Field Values for Different Years (First 2 Digits) and Different Fields (3rd Digit) Plotted Over the Mean Value for YP, the Parameter which Moves Adults from Wheat to Oats in the Spring 0 O O I O O O O O O O O O O O 62 24. The Percent of Eggs Being Laid in Oats as a Function of °D>5.6C (42°F) . . . . . . . . . . . . 64 25. The Effects of Sampling Bias on Synchrony . . . . 76 26. The Effect of a 50% Bias Against First Instar Larvae and a 40% Bias Against Second Instar Larvae on the Fraction of the Whole Population that Would Have Been Sampled at the Sampling Times which Were Used in 1969 . . . . . . . . . . . . . . . 78 27. 1968. The Effect of Bias in the Temperature Recorded at a Weather Station in Comparison to the Temperature Affecting the Insect (TEMP) . '. . . 82 28. 1969. The Effect of a Bias in the Temperature Recorded at a Weather Station in Comparison to the Temperature Affecting the Insect (TEMP) . . . . 84 29. The Effects of Larval Development Times on Synchrony for Two Years, 1968 and 1969 . . . . . . . . 89 viii Figure Page 30. The Effects of Using Different Temperature Regimens after May 10 on the Synchrony Between Model and Field 0 O O I O l O O O O O O O I O O 94 ix INTRODUCTION The cereal leaf beetle, Oulema melanopus (L.) was once con- sidered to be a major threat to the small grain industry of North America (Webster, et a1., 1972). Since 1975, however, interest in the insect as a major threat has declined because the cereal leaf beetle has not, for unknown reasons, become a major economic prob— lem. This interest may again be kindled when the cereal leaf beetle invades the huge acreages of spring grains in the west, but its development as a pest there can not be predicted. The cereal leaf beetle is still an excellent experimental animal for research use because of the great deal of information which has been accumulated on its life history. It was with these points in mind that the procedure for developing a model for on-line control (Tummala and Haynes, 1977) of the cereal leaf beetle was investigated. Because of the amount of information available on the cereal leaf beetle, a number of models have been written concerning it, three of which have been published. Each of these models was dev- eloped for a different purpose from the present one. The model of Lee, et a1. (1976) was used to test the usefulness of partial dif- ferential equation models in an ecological setting and to find a closed form solution to the equations. The model of Tummala, et a1. (1975) was developed to study the between generations dynamics of l the cereal leaf beetle. The model of Gutierrez, et a1. (1974) is certainly the closest to the model developed here in design and intent, but it differs in being a discrete, physiological time based model as opposed to the continuous, chronological time type model developed here. The model developed here is for on-line control and that basically implies optimizing the use of pesticides. For long—term optimal control of the cereal leaf beetle (a model for which is currently being prepared by V. Varadarajan under the direction of Dr. R. L. Tummala at Michigan State University) it will be necessary to consider the effects of management strategies on parasites of the beetle. But for on—line control the larval parasites can be ignored, since they emerge after pupation, and thus do not greatly affect the damage caused by the larva which they infest. The egg parasite Anaphes flavipes (Foerster) Hymenoptera Mymaridae, would have to be included in the model were it not for the fact that it develops large populations only late in the season (Gage, 1974) after most damage has been done. To truly optimize the use of pesticides the model would have to predict the effects of beetle populations on yield, and determine the economic implications of that, but that is a study in itself. The approach here then is merely to predict population densities in a crop, the economic implications of which must await another work. LITERATURE REVIEW The natural history of the cereal leaf beetle in Michigan was described by Castro, et a1. (1965) who reviewed much of the European literature on the insect. Yun (1967) did most of the basic laboratory studies on the effects of various biological and environmental factors on the beetle. His data are used extensively in the model development and are discussed in the sections in which they are used. Yun (1967) had treated the larvae as a single life stage instead of breaking it down into its four instars. Helgesen (1967) for his work on the population dynamics of the beetle provided information on the developmental rates of the individual instars. Wilson and Shade (1966) provided some information on the survival and development of larvae on various species of Gramineae. Similar work was performed by Wellso (1973) who also investigated (1976) feeding and oviposition of the beetle on winter wheat and spring oats. Ruesink (1972) and then Casagrande (1975) provided informa— tion on the emergence of adults from overwintering sites and their subsequent mortality rate. The systems approach to pest management has been discussed often in the literature in the past few years, in. a published joint symposium of the Entomological Society of Canada and the 3 Entomological Society of Alberta (N. D. Holmes, ed., 1974) and by Giese, et a1. (1975) for example. Important aspects of the approach including environmental monitoring networks (Haynes, et a1., 1973) biological monitoring (Fulton and Haynes, 1977) and on-line pest management (Tummala and Haynes, 1977) have been discussed. There is certainly nothing new in using models in ecological systems (Pielou, 1969) but recently a wide variety of modeling techniques have been applied in ecology. For example, spectral analysis in general, reviewed by Platt and Denman (1975) and transfer function models in particular (Hacker, et a1., 1975). The use of flowgraph to model biological systems has recently been attempted (Wiitanen, 1976). Control theoretic approaches to control of insect and biological systems in general are now in vogue (Mitchiner, et a1” 1975; Vincent, 1975). The use of modeling and systems analysis in defining agricultural research needs has been evaluated by DeMichele (1975). As discussed in the introduction, 3 models written specif- ically for the cereal leaf beetle have already been published (Gutierrez, 1974; Tummala, et a1., 1975; and Lee, et a1., 1975) but again these purposes were different from that of the model developed here. The validation procedure is an integral part of modeling in the systems approach (Manetsch and Park, 1972; Shannon, 1975), but techniques and procedures for validation of complex ecological models are not well developed (Caswell, 1976; Miller, 1976). PROBLEM DESCRIPTION In the context of a sampling problem, any given population is composed of two types of individuals——those which can be observed with a given technique, and those which cannot be observed with this technique. The proportion which can be observed will depend on a number of factors, notably on the technique itself, the timing of the estimate in relation to population development, and intrinsic population parameters relating to the distribution of the individuals with respect to maturity (see Fulton and Haynes, 1977, for details of this development). Briefly, referring to Figure LA,the distribution of ages of the population at the initial value of maturity, f is shown. The dotted line indicates the position of the mean maturity, u. FigurelB shows the distribution of ages after some interval Af and so on to Figure 1E. The two vertical lines from ai and aj represent the limits of integration, i.e., the ages which are observable with the sampling method being used. The proportion counted, therefore, lies between a1 and aj. In the earlier work (Fulton and Haynes, 1977) it was assumed that 02, the variance of the age distribution, remains constant with changes in f. It was also assumed that changes in population level were negligible or constant in rate through all ages. These assump— tions were reasonable in the context of that work, but for pest 5 6 A Z(f) A a Z(f+A1f) /E\ >- 3 c uu :3 C, I “’ : E 2mg) /:\\ o 2(f+.;) / i \ E 2(f+A~f) Oi Oi AGE Figure l.--Frequency distributions of ages of individuals in the pOpulation being sampled. A is at an initial value of maturity f. B-E are at subsequent values of f as the population ages. management on an individual field basis, our interests are different. Here, a dynamic model capable of mimicking changes from field to field, and not just average conditions is essential. The static model points out three factors that affect the proportion of the total population which is counted in any type of population. These are indicated in Figure 2. The effect on the proportion counted of changes in the observable ages is shown in Figure 2A, where it is clear that if more extreme ages can be sampled, a higher proportion of the whole population will be sampled. The effect of the distance of the population mean age from the age class observed is shown in Figure 2B. Obviously a much higher proportion of the whole can be sampled when the mean age is in the sampling interval. The effects of different degrees of dis- persion in the population is shown in Figure 2C. A larger variance leads to a smaller proportion being counted. It is clear, then, that the maturity of the population can affect the proportion of that population which is counted at a specific point in time. Not only will it affect the counts of the primary organism, but in cases where parasitized individuals are concerned, it affects the estimates of seasonal parasitism. The effects of maturity on the population density estimate can be min— imized by choosing a sampling method which collects all age classes present or alternatively by sampling a life stage which is so long and stable that essentially all of the individuals in the population are in that life stage at one time. Slightly less effective is to attempt to take the population sample when the mean age of B C ’0’ // e a xvi/«’36.: m: \ 503.». 000000000000000000 \ V00000000... .0 00000000040000... u» lllll J u. 0 000000009. .000000000000000000 \\..o.0000000. 0.0»0>0>0..0»0>0»0 .I . «00.000... 0 .l o- o a a 2: N 5238:“. AGE - and a'i to a'c are observable fion age and o Is the standard ‘0. )l 0] Figure 2.—-Three factors which affect the proportion of the popula- to 3 ages, u is the mean popula deviation of ages. The 3 tion counted. individuals is near the midpoint of the observable age interval, so that the largest portion of the individuals can be observed. In on—line pest management peak damage is likely to occur at peak density of certain life stages. Sampling, therefore, must precede the occurrence of that peak. We have therefore to establish both population density and time synchrony to initialize a pest management model. Furthermore, sampling must be early enough so that control measures can be effectively applied after sampling and evaluating the management alternatives. That will constrain our choice of sampling techniques. Trade-offs exist between sampling early to get a longer time to implement a control procedure and the accuracy of model predictions over an increasingly future time. Models to predict the immediate future can be much simpler than those needed to predict the far future with the same degree of accuracy. ANALYTICAL APPROACH The Model Since the age structure of the population is important in interpreting population density, and field samples will be used to initialize a population model for the cereal leaf beetle, a pest model was constructed in which the age distribution of the popula— tion at any point in time is available as output (Figure 3). This model was constructed mainly from a structural rather than a black box point of view. System components are broken down to a level which shows their functioning in relation to physical factors. A black box approach would show the functioning of the components in relation to time only. The structural approach offers more insight into the workings of the natural system. Temperature (TEMP) has the most widely distributed effects in this model. It is used (directly or indirectly) to drive a num- ber of functions which affect adults leaving overwintering sites, survival, oviposition, and length of a life stage. Other inputs are the latitude and day of the year so that photoperiod can be deter- mined, the proportion of the population which is female, the propor— tion of the population which is in the crop being considered, and K values for the distributed delays (see below) used to represent life stages. 10 11 Figure 3.-—A functional block diagram model of the cereal leaf beetle. 12 (m! a 'Jm .1 » 3k 1151/...th— 5R 5% 5R 5...... 5% t“ w w l w w I + l + l + I + l + l + «4?. R :23»... k 129:» .R :29»... .R 25.35 91 - com :40... 2 .3505 m... 3 9...: mg n4 9.08». «a; N4 5...; a... .4 .058 m5. 338 0d. 333 3. «38 «a. 38 .d. ado 9. lo. 9. u. o. , o. o. u. '9. NM... VJ“ a \JV 1 I147 \ J_. 5 a a a a tin» - $82 5:528 35.8 :3 3:3 N 24 . 1! 3 9 23:9 I S I W , 58' 2.34: _ >JJSKUm .o. 1. a rl. 25» 3. 0 50:. I is , . :43 n a .33 \J _m 38 28.53. on n 28.! all T Eco 4 tutu a» 13 Model outputs are the number of individuals in each life stage at any time. The usual temperature data available from the National Weather Service are daily maximums and minimums. Assuming that temperature changes within a day are sinusoidal with maximum and the minimum 12 hours apart, degree-day accumulations with errors on the order of 5% over a growing season can be computed (Baskerville and Emin, 1969). Equation 1 is used in the model for temperature at any time of day (HTIME). TEMP = TAMA§_§_AHIE1 + (AMAX - AMIN)* (1) {Sin (HTIME - 9)* (Zn/24)} Where AMAX is the maximum temperature and AMIN the minimum for that day. The factor 9 causes AMIN to occur at 3 a.m. and AMAX to occur at 3 p.m. Since development is not linearly related to temperature (Fulton, 1975) the use of degree—day values to determine develop- mental times is not, strictly speaking, valid. Despite this, degree-days were used as a predictor of spring movement of adults from their overwintering sites and the oviposition rate of females. Model Parameterization In this section of this thesis the parameterization of the various components of the model will be developed, beginning with 14 the emergence of adults in the spring and ending with the emergence of summer adults from the pupae. Spring Adult Emergence Referring to the upper left—hand corner of Figure 3, the base temperature of 9°C for CLB aging is subtracted from the instantaneous temperature TEMP to give the temperature EFTEMP which is effective in CLB aging. This value is integrated over time to give the °Day accumulation (DDAY) which is transformed to natural logs (ALDDAY). ALDDAY determines the rate (SE) at which adults move from their overwintering sites. Data on the spring movement of adults from their over- wintering sites for 1971, 1972 (Ruesink, 1972), and 1973 (Casagrande, 1975) at Gull Lake were the basis for a probit—regression model for this movement. The relation between the probit for emergence of adults and the natural logarithm of accumulated degree—days > 9 for these three years is linear (Figure 4). The regression line for the pooled data is: Pr = -2.90974 + 1.98964 1n A (2) where Pr is the probit of spring emergence and A is the accumulated degree-days > 9. A probit is defined by Finney (1971) as Y in 3: Y-5 P =-—-— J exp {—fiuzl du (3) 15 0 6.0 . .Jrliiiil l I l 1 L 1 lg l l l l j l l l PROBIT OF EMERGENCE PR:-2.910+1.990(LN[DD>9)) U U U l V V V V l U V Y Y] 7 T V T I V I V 1'1 Tfj—l .0 3.5 4.0 4.5 5.0 5.5 6.0 LN DD>9 Figure 4.--The regression of the probit of cereal leaf beetle adult emergence on the natural logarith of °D>9C. The line above the data was used in later model runs. Data from Ruesink (1972) and Casagrande (1975). 16 that is, it is 5 more than the abscissa corresponding to a probability P in a normal distribution with mean 0 and variance 1. Emergence data were transformed to cumulative percent and then to probit values. The last observation was assumed to represent 99A9percent emergence rather than 100 percent emergence, since the probit of 100 percent is + w. Solving equation 2 for A when Pr = 5 gives 50% spring emer— gence at 53 °D > 9. The standard deviation of the normal distribution is given by the reciprocal of the slope in equation 2: _l _.___1___._ S ’ b ' 1.98964 ‘ 05026 (4) The other line in Figure 4, with its defining equation, is used in the model development and will be discussed in a later sec- tion. Having moved from their overwintering sites, spring adults undergo a maturation process the length of which, DELM, is tempera- ture dependent (Figure 5). Adults leaving this delay at a rate DM, enter the sexually mature adult stage then die at a rate AD. Adult Survival Yun (1967) showed that at the extreme temperatures of -l8° and 43°C spring adult mortality reached 100% in well under 1 hour. Unfortunately this is the extent of the information from controlled environments on the survival of adult CLBs as a function of tempera- ture. Adult mortality in the field over various finite time periods were presented by Casagrande (1975). Those data are confounded by the fact that temperatures fluctuated over the period when mortal- ities were being measured, and the possibility of seasonal changes 17 32 24 28 All—111 AL4LIALL 20 DRYS T0 FIRST EGG r V C8 T"ié"Tié' é6"‘éi"'éé"'éé"‘ésIT'Ab TEMPERRTURE . CELSIUS Figure 5.--Days from adult emergence from overwintering sites to time of first oviposition as a function of temperature. Data from Yun (1967). 18 in the mortality rate of adults which was not determined by tempera— ture. The model is a continuous as opposed to a discrete one, and the assumption was made that temperature dependent mortalities operated continuously. This implies that: at P = P e t 0 where; t = time Pt = population at time t. P0 = initial population. and a = instantaneous survival rate. A more thorough treatment of this subject will be undertaken in the section of egg and larval survival, below. Instaneous survival rates for adults were computed from Casagrande's data and are plotted over temperature in Figure 6. Excluding the aberrant point (19.4, ~12.2) made little difference in the position of the regression line, so the line is for all of the data. The survival rate is used to compute the half—life of adults under the existing temperature regimen; at = P Pt 0 e P 19 Figure 6.-—Instantaneous survival rate of adult cereal leaf beetles as a function of temperature. (Data derived from Casagrande, 1975, Table 9.) O O INSTHNTRNEOUS SURVIVRL RRTE ‘—" .122 TEMPERRTURE CELSIUS 21 setting this equal to a; _P_t=eat 15 P O t = -1n 2 a This half—life, t, while it is a median and not a mean, is used as an estimate of the mean survival time, DELA, and fed into the sexually mature adultstagerepresented by a time varying delay. Time Varying Delays A basic element of this model is the use of time varying delays to represent the life stages of the CLB. Manetsch and Park (1972) show that these delays represent an aggregative approximation to the response of individuals in a population undergoing a pure time lag in the input variable. The time lag of individuals in the population are assumed to be random variates from a probability density function, f(T). In this case, f(T) is assumed to be the Erlang function: (K—l) e—Kar m) = (odoK (n (5) (K—l)! The mean for this distribution is: €[I] = 1/oc (6) 22 its variance is given by: Var['r] = EST (7) The strictly positive integer valued parameter K determines the member of the Erlang family of density functions desired. When K = l, the density function is the exponential (Figure 7). When K increases without bound, the Erlang distribution approaches the nor- mal distribution with mean l/a and zero variance. The Erlang function was selected because different values for K allow the same function to be used as an approximation for many different density functions. Manetsch and Park (1972) have shown that the aggregative delay characterized by a Kth order Erland function are represented by a Kth order linear differential equation. The output from such a delay is easily simulated by delay routines presented by these authors. Computing an estimate of K from the data is shown in Appendix A. The number of individuals in any life stage is now computed in the delay routine itself and passed back to the main program (see Appendix B). Oviposition Unpublished data from S. G. Wellso on the oviposition by CLB in oats and wheat in 1972 at East Lansing indicated that the oviposition rate on Genesee wheat and Clintland oats are essentially the same during the initial period of oviposition. Figure 8 shows the pooled wheat and oat data for the first 222 °D>9 after 23 Figure 7.-—Several members of the Erlang family of curves used in the time varying delays in the simulation model. 24 .fio .3. .53 Lu; . . Hub . town I] Own: man: a. ._u. m. ._. D P b MW» .. bun mu m N x E 25 .owHHmB .0 .m .uo Eouw mumv vmnmfiansmcs .mumo mam poms: you dump wwHoom .ovoo wouMHSEDUUw mo coauuasw m mm usacfi wwm mauoon mama wauoo wwumaaeauu¢D mmmomo OOH we on mN n—bth>—>->>_>>>>—>>>\ 0mm www com mhfi owfi mNH —->>>—->bP—bthPPL>>—pphb—pbu cu lfldNI 003 OEIUIONOJJU 26 subtracting the degree—day value at the beginning of the experiment from each data set. The equation for the line is: E = -5.855 + .9296 D, r2 = .996 (8) where E is the accumulated number of eggs per female and D is the accumulated °Daysi>9 value from the start of the experiment. Figure 9 shows the oviposition data for wheat (lower curve) and oats after 222 °D>9 had been accumulated. The relationship is nearly linear on a log scale, but clearly the slopes of the lines for wheat and for oats are different. The equations for the lines are: Wheat: E = —630.79 + 153.606 1n D, r2 = .998 (9) Oats: E = -820.05 + 189.253 1n D, r2 = .996 (10) In the model, it is the oviposition rate which is needed; hence, the derivatives of equations 8, 9, and 10 were used. dE/dD = .9296 (11) for pooled linear part. dE/dD = 153.606/D (12) for wheat when D is more than 165 °D>9. dE/dD = 189.253/D (13) 27 .omHHmz .o .m .Ho acne mums ememaflnsaaa .umAn. mo aeuaummoa m Housuma mau mo coauucom m mm mumo cam omega ouafi Danae wmo maummn mama ammumo cmumaaanoo9. Although equation 8 is based on pooled data from 0 to 222 °D>9, and equation 9 and 10 on data from 222 °D>9 and greater, the rate equations 11, 12, and 13 are used over a slightly different range. This was necessary in order to have a single valued function for oviposition in each case. For, solving for the point at which the pooled data rate equals the curvilinear rate on oats, one has: 189.253/D = .9297 £> D = 203.6 (14) and for wheat: 153.606/D = .9297 £> D = 165.2 (15) Figure 10 shows the oviposition rate functions as used in the models. The vertical axis is eggs/female/°D>9; the horizontal axis is ”age" of the female in °D>9. Yun (1967, pp. 47, 48) showed that the CLB oviposition rate is strongly related to photoperiod. This function is present in the model, however, its output is set to one because the degree of refinement of the model does not permit its use. Movement from Wheat to Oats Of the eggs laid some will go into the crop of concern, e.g., cats or wheat, and only those are considered in each simula— tion. An initial estimate of the rate at which adults moved from wheat to oats was computed as follows: .ovoo woumasssoom ca mwm mo coauoonm m mm Dump coaufimoafi>o oaummn mama ammumuul.oa unawam m A m»¢o mmmomo 00». 0mm Dom 0mm oom 0mg OOH om - Th F P — b b P P P P b b P b b b P b h b b h P h h b h h h P b P P P b b h b 29 99- 99' '99-“ 99-0 1.7111 I 91. 548 (Gage, 1974, pp. 77, 78; Fulton, 1975, p. 60). Assuming that on the average these were half developed when found, then they were laid at about 580 °D>48, or = 840 °D>42. Assuming adults start to move as soon as oats emerge, first eggs in oats are found at about 193 °D>48 (Gage, 1974) and would have been slightly developed, say they were laid at 145 °D>48 (2 240 °D>42). Assume all adults move from wheat, etc., to oats, etc., (or die) during that 600 °D>42. Peak eggs in cats occur at about 485 °D>48 (467, Gage, 1974; 503, Fulton, 1975) 2 710 °D>42, again assume they were half developed when found, they were then laid at about 365 °D>48 = 540 °D>42, that is about halfway between time of first egg in oats and last egg in wheat. If it is further assumed that the movement between crops follows a normal distribution, and that at the first observation of an egg in oats, about 1% are there, then the proportion of the adult population which is in oats is given by the equation; Y = .8625 + .00766 °D>42F (16) (.01379 °D>5.6C) where Y is the probit of the proportion of adults in oats at any value of °D>42 (in Fahrenheit) or °D>5.6 (in Celsius). Total egg input (ATEGG) is computed as the integral of net oviposition rate (E). This value is the "egg input" used to estimate density-dependent survival in the first and fourth instars by Helgesen and Haynes (1972). Density-dependent survival is not incorporated 31 into this model, but it would be very easily added (Figure 3). It is not currently there because the evidence for density-dependent mortality is sketchy, and certain of the scaling procedures devel— oped during model validation can not be used if density dependent functions are used in the model. The Egg Stagg Eggs enter the egg stage or delay at a rate E and remain there for a length of time (DELE) which is dependent on temperature (Figure 11) and survival, which is a function of temperature (Figure 12). Survival as a function of temperature can be represented in a number of ways. In Figure 12 we have survival over the whole stage, but since the time spent in the stage is also a function of temperature, there is an interaction there. That interaction can be removed using the instantaneous survival rate for eggs (Figure 13). In the model, the equation used for egg survival is: -.0423 -.002975 TEMP P = P e t+Dt t (17) where, t = time Dt = the simulation time increment P = population TEMP = temperature, in Celsius. The form of the exponent has been assumed linear throughout this work. A longer series of experiments on survival and development 32 A.somfl .csw aoum mumav .musumudeou mo coauucsw m no woman mam mwww mauoon mood Hmmumo you moEHu uuoEQOHm>oall. wsznmu mmaeqmmmzme em mm om mm mm «N «N mom. 2 2 Eu PkbbPbbLPFbFFPPbPFPFbePh bhl—bbrLbbhb ././././ 9 lNBWdOWEABO EIHWdWOU 01 8160 moon T8 [)8 98 madam HH «Human 33 O— 00. EGGS 0-. [\J . '2 1 CD« a UD~ LRRVRE : 9ND . DIPUPRE _J _ CI: 4 :> F—i >0- ll 01v- :> . It 09 j n O- (7). 0-4 N4 Du F“ d ‘1-.fir'vv I'VYYYI'V IrrijY1IVVVUI' '1] C8 12 '16 20 ‘61.“ 28 32 38 4o TEMPERRTURE . CELSIUS Figure 12.--Survival of eggs, larvae and pupae as a function of temperature. (Data from Yun, 1967.) 34 Figure l3.-—Instantaneous survival rates for eggs and for larvae and pupae as a function of temperature. (Derived from data presented by Yun, 1967, and Table 12.) 35 v 16 .3 ... i o T \. . .\“ I2 4 .3 18 II .2 m \ * v 00 T m . x -4 \ v2 T [0 m . .2 004 r e 1 .o 16 00 .1 D 4 r Y 12 v1 T ....a-. . ..a.a-. . -w..a-. . .Dl.a-. . .Nl.... mecm 4¢>H>m3w msowzqezchmzH CELSIUS TEMPERRTURE 36 as a function of temperature would be necessary to determine the exact relation. The aberrant points (near -0.04) in the data were excluded from determining the function used in the model since they affect the position of the line considerably, yet the slope of the line is essentially the same for both lines. In the block diagram model, mortality of the various immature stages is shown as taking place between the stages. That is for eggs at the time of eclosion, and for larvae at the time of the moult. This is a reasonable approach under the assumption of discrete periods of mortality, but under the assumption of continu- ous mortality used herein, mortality must take place within the growth stage, that is within the delay. When the change was made to this type of mortality, it was found that the delay function with attrition provided by Manetsch and Park (1972) was in error. A modification to another of these routines (VDEL) was made in order to implement the continuous mortality function. The modified routine is included in Appendix B. The Larval Stage Eggs hatch and enter the first larval stage at a rate LlS. Survival as a function of temperature for larvae and pupae was shown in Figures 12 and 13. Development times as a function of temperature were given for pupae in Figure 11. They are given in Figure 14 for the individual larval instars. The approach used for egg development and survival is con- tinued through each of the larval instars and the pupa, ending with 37 Figure l4.——Developmental times for the 4 instars of the cereal leaf beetle as a function of temperature (after Helgesen and Haynes, 1972). 38 II v r r" T 21 TENPERRTURE T r T T 1 T T T fl T T T T 1 T T T T I T T lNBNdOWBABO 3131AN03 01 SAUO 19 15 CELSIUS 39 the rate at which summer adults are being produced (SADS) and the number of summer adults (NSA). New survival functions could easily be added as multipliers if the survivals are multiplicative, or by modification of existing survival functions when two or more of these are additive (Morris, 1965). Pupae which survive to become summer adults are accumulated and stored since there is no diapause function in the model. FORTRAN Implementation Table look—up functions TABLIE and TABLI from Llewellyn (1965) are used in the FORTRAN version of this model (Appendix B). These routines use linear interpolation between data points on each entry, and both restrict the value of the function returned to certain limits. Values for arguments below the minimum are set to the functional value for the minimum, and values for argu- ments above the maximum are set to the functional value for the maximums. TABLIE requires that the functional values be given for equally spaced arguments, and is, therefore, efficient for smooth, regular functions. TABLI does not require equally spaced argu- ments, and is, therefore, more efficient for irregular func- tions. These function subroutines are used extensively in this model since they allow one to emphasize the structure of the model rather than curve fitting. Also, frequently the quality of the data does not warrant extensive curve fitting efforts. 40 Function VDEL returns the output rate when the input rate is XVIN. The distribution of the delay is Erlang with mean 5%: and variance related to K (equation 7). The time-varying aspect of the function is reflected in the parameter DELP, which is the previous value of DEL. Function DAY computes the length of the photoperiod on day I at latitude PHI. The accuracy of this function is related to the latitude and the time of year. In the worst case tested (PHI = 54°N), the average error was about one minute, while the worst was about 15 minutes in September. The logic was developed by R. Brandenburg. Function NDTR is from the IBM Scientific Subroutine Package Version III (anonymous, 1968). It computes the normal probability density (D) and distribution (P). This function is used to estimate the rate at which spring adults move from their overwintering sites. As was mentioned earlier, the effects of photoperiod on oviposition are not yet included in the model. The mechanism for doing this is included in function DAY and function PEG. PEG uses TABLI to find the percent of maximum response which can be expected under the current photoperiod and reflects the data presented in Yun (1967). Sampling to Initialize the Model Extensive use was made of the sampling data in Helgesen (1969, square yard and square foot samples for larvae); Ruesink (1970, sweepnet sampling for adults and larvae); Gage (1972, 1974, 41 square foot samples, planting date, number of stems per square foot); Jackman (1976 and unpublished, planting date, square foot samples, number of larvae per stem, number of stems per foot through the season); Fulton (1975, sweepnet sampling of larvae through the season); Sawyer (1976, square foot samples, stem densities, relation of mean and variance in square foot samples); Logan (1977 and unpublished, sweepnet samples and square foot samples). If the information to initialize the model is to be provided by the farmer or scout from individual fields, it would be desirable, if indeed not essential, that the data provided be gathered cheaply and with little technology. Data of this type include: (a) plant— ing data, (b) plant height at sampling time, (c) number of eggs per stem and number of larvae per stem, (d) number of stems per foot. The sampling for this dissertation was primarily the number of eggs and larvae per stem. Data were taken from three fields at Niles, Michigan from the area studied by Sawyer to determine the effect of pubescent wheat on cereal leaf beetle populations. Several times through the season one hundred single stem samples were collected from randomly chosen locations within each of three fields and the numbers of eggs and of larvae on each stem were recorded. The variance plotted over the mean for those three fields (designated 10-2-4, 1—3-6, 3-3-3 by Sawyer) is shown in Figure 15 for eggs (r2 = .86), and in Figure 16 for larvae (r2 = .96), and in Figure 17 for combined eggs and larvae (r2 = .96). These relation- ships can be used to determine the sample size required to achieve a given degree of precision in the estimate of the mean density. 42 Figure 15.-—The variance-mean relationship for single oat stem samples of cereal leaf beetle eggs. VHRIHNCE 2.0 43 CERERL LERF BEETLE EGGS 5.0 4.0 3.0 T 0.0 I 110 I 220 310 NEHN NUMBER PER STEM 44 Figure l6.--The variance-mean relationship for single oat stem samples of cereal leaf beetle larvae. VHRIHNCE 45 CERERL LERF BEETLE LRRVRE T I T r r I 0-0 1.0 2.0 3.0 HERN NUMBER PER STEM 46 Figure l7.-—The variance—mean relationship for single oat stem samples of eggs + larvae of the cereal leaf beetle. VHRIHNCE 47 CERERL LERF BEETLE EGGS + LRRVHE T l 1 1 4-0 6-0 :3 ' I 0.0 2.0 HEHN NUMBER PER STEM 48 The mean number of eggs and of larvae per stem, and the mean number per square foot (from Sawyer) are listed in Table 1. Square foot samples were not always collected on the same date as stem samples, but data from the nearest such sampling date was used. Also given are the ratios of the two observations. These ratios are quite variable and tend to be higher at times of higher population densities. In the regressions of number per square foot on number per stem for eggs, the regression line was Y = 2.276 + 3.154X, r2 = .48. This poor fit was due in large part to one point (1.2, 15.5) the deletion.efwhich yielded the equation Y = 1.910 + 2.886X, r2 = .71. A log-log transformation of the data gave a much poorer fit (r2 = .35) than did the straight regression. In the regression of number per square foot on number per stem for larvae, the regression line was Y = .3937 + 11.13X, r2 = .59. Here a log-log transformation gave marginal improvement in the fit (r2 = .65), but it is not sufficient to justify the additional complexity of interpretation, in view of the fact that the trans- formation does poorly for eggs. Even a casual glance shows that there are huge discrepancies between the number per square foot in Table 1 and the number per stem multiplied by the number of stems per square foot. That will be considered later. 49 5.5 5. 55. 5.5 5.5 55. 5.5 o. 51. 5551 555 1515 5.5 5.5 55. 1.1 1.1 55. 5.51 5.1 51. 5511 515 5115 5.55 5.55 55. 5.5 1.5 55. 5.55 5.5 55. 5111 551 n1\o 5.51 5.55 55.1 5.51 1.55 15.5 5.55 5.5 55. 555 one 11\5 1.51 5.55 55.5 5.11 5.11 55.1 5.5 5.5 55. 515 155 515 in u- u- 5.51 1.5 15. 5.5 5.1 55. 551 555 ~15 1.5 5.5 55.5 .n I- u- u- u- u- 515 555 115 u<>5<1 55 5.5 5. N1. 55 5.15 5.5 51. 55 in 5.5 no. 5551 555 1515 5.5 1.5 55. 5.5 5.5 55. 5.51 5.1 51. 5511 515 51\5 5.5 1.5 55. 5.1 5. 55. 5.55 5.5 so. 5111 555 51\5 5.51 5.51 55.1 5.5 5.5 55. 5.51 5.5 55. 555 555 1115 55 5.5 5.1 55.1 55 1.5 5.5 15.1 55 5.5 1.5 55. 515 15m 515 u: u- u- 5.5 1.5 15.5 5.5 5.1 55. 555 555. «\5 5.5 5.51 15.5 i- :1 1- in n: In 511 555 1\5 5555 .15.55 6115“ .15.55 amum .15.55 6115» .um.5m 5615 .um.55 61161 .u5.5m amum 55.5. 55A5. mama \maoum \mEmum \mEmum 5 u 5 u 5 5 u 5 a N u 51 "51555 .5151 :1 c551155= .55112 .5 moaoau mouzu cfi muasou uoow mumavm an vow wucsoo swam 5n Dome mmumefiumo cowuofisaoa mo comauwaaoo <:I.H mqm .6), but with poor fits it distorts the shape of the curve. Even with a good fit, the right end of the curve tends to be too high (Figure 18). When the slope alone is used to make the adjustment, the shape is closer to that of the field, but it is still very difficult to compare model output to field observation. When the model output is adjusted by a factor equal to the ratio of the total incidences of the two sets of data, a visual determination of the goodness of fit can be made (Figure 18). This method was adopted for most of the validation procedure. This method of adjusting the model output for comparison to the field data was very effective for making visual comparisons, but 52 .coeum>ummno macaw ou uoauso Mecca wawummaou MOM moonuwa uconMMfic mousHI|.wH ouswam m A m>¢o mmmOmo 0mm cow 0mm Dow 09. oov 0mm oom owN ooMu bbhbblb-bbPLDLDLbb>>bbb>bbRPhb>bbhnbbbbK> 940—5! 02 09 08 ...-,....,....VH-.,....T 0? AlISNBO 001 V I T 1 021 V I 'fi—T T 0?! 091 53 a quantitative measure of the degree of similarity was needed in order to objectively compare different simulation runs. The first measure used for this was the squared differences between field observation and adjusted model output, summed over the season. While this statistic worked well for comparing the effects of dif- ferent values of a parameter on the match between field and model for any one year, it did not work well for evaluating the effects of parameter changes across all field-year changes since it is data-dependent. That is, the possible size of the error is related to the observed density. This led to the result that one or two years with high densities were determining the optimum value for the parameter. Two methods were used to overcome this problem. The first was to choose as the optimum value for a parameter that value which gave the best fit to the largest number of field-year combinations. The second procedure, used only in later simulations, was to compute a chi—square-like statistic as: 8 2 = (Adjusted model density - field density)2 Adjusted model density (18) X This statistic is relatively stable over all values of density, except very small ones (<1). Because of the way in which this statistic was calculated, it was deemed inappropriate to use the value in a significance test. Instead it is the magnitude of this statistic and its rate of change under manipulation of the model parameters which should be considered. 54 In Figures 19 through 22 a comparison is made of the match between model output and field data for several different year— field combinations with optimum values of several parameters (vertical axis). The topmost comparisons in each figure are from the initial simulation with all parameter values set at the best estimate possible from field and laboratory data, as described earlier. In all of these figures the points represented by squares are for eggs, model; triangles are eggs, field; X is for larvae, model; + is for larvae, field. First consider the graphs for the initial base run in Figures 19 - 22. The correspondence between larvae for 1967 was very good, but that for eggs was poor. In this case, however, the problem may be with the field data, since judging from that data, peak eggs apparently occurred after peak larvae, a very unlikely possibility. For 1968, correspondence between larvae was again excellent, but that between eggs was not good. The general shape of the model egg curve seems all right, but it occurs later in the season than the actual egg curve. For 1969 we have good correspondence between the egg curve, except that the tail end of the distribution drOps off too quickly. The larvae match but poorly for 1969. For 1970, two different fields were used, with an excellent match of both eggs and larvae in each field. There was a slight tendency for the model values to be more peaked than the field data. 55 Figures 19 — 22.—-Comparisons of model output and several years' field data. The digits in the corner of the figure indicate the year (first 2 digits) and different fields within the same year (third digit) eg. 713 indicates data are from field 3 of 1971. Squares — eggs, model; triangles — eggs, field; X - larvae, model; + - larvae, field. Top series of graphs are for the basic parameter set of the model. The second series is with the optimum value for the mean of YP. The third set has optimum YP and egg development time increases by 25%. The bottom set of graphs has YP the same as the top series, egg development as the third series, but the optimum value for adult emergence. See the text for details. 56 N 67 8. 55 3. .. In mammals. .. 0 500351110 :' "’ ' x LnnvaemooEL g= 2‘ I + LnnvaE.nELn D o 2‘ ” ‘0 8 / \\ M 2. ,/ [I :5:- 2 MJ D :_. I32 2 Lu D Sq 53‘ 2 m D ctoo 360 «in 560 560 760 060 960 1630 lioo _|200 ‘tuo 360 «'10 560 660 760 060 960 1600 U00 1500 Figure 19, DEGREE Davsne m GULL LnKE DENSITY DENSITY DENSITY DENSITY 69 80 90 I20 150 00 210 30 60 90 I20 150 180 210 240 0 30 120 150 180 2l0 240 0 90 30 00 90 IZO ISO I00 210 2‘0 0 30 360 060 560 ‘500 Figure 20. 660 760 060 950 1100 1200 57 80 90 120 I50 l00 ZIO 30 El EOOSJIODEL A EOOBJ’IELD X LRRVREJTDDEL 1+ LflRVflE.FIELD 60 90 |20 ISO 100 2l0 240 0 30 60 90 120 150 100 210 2’0 0 3O 60 90 120 160 [00 210 2’0 0 39 ‘Eho 300 000 560 560 760 060 960 1600 iioo 1560 DEGREE DRYS>48 RT GULL LRKE 2. 702 2‘ 711 g‘ 8 m £008.000EL E- 3- A 1500351110 X LRRVHE .HOOEL + LRRVHE.FIELO f ‘0 60 20 30 0 '9 1 190 0 09 I40 70 I20 60 DENSITY .9 \’ 3 40 29 20 .9 00 100 ‘0 50 O o O @< °_ T. O O C. O ‘ F O N- O. "‘ D O O- O- "' ID )1 .— _ (D O o. 2 ° ' U D O- o. D n O- O- ‘ a o- c- N — O " O D ID- o. "' D O 1 C o. ‘ F O N- o "' O O O- o "‘ \D DENSITY 00 30 40 A O Q. ‘ N O- a N .- :200 300 400 500 000 700 000 900 1000 Tina 1230 900 300 000 500 000 100 000 900 woo uoo 1200 DEGREE ORY$>4B RT GULL LRKE Figure 21. 160 DENSITY DENSITY 09 I00 I20 [’0 190 O 20 ‘0 69 09 100 1¥0 1,0 V 80 1. 0 I) 59 100 120 1’0 I60 0 DENSITY 00 ‘9 20 DENSITY ‘0 00 00 :00 igo :90 100 0 =9 / \ ‘1 300 400 500 $00 700 000 900 Figure 22. O O 1000 1100 3500 00 70 00 59 00 30 29 10 ET EOOSoHODEL b.5008oFIELO X LHRVREMODEL +'LflRVflE.F1ELD 00 70 50 £0 39 20 IO 29 30 40 50 00 70 00 30 .0 50 00 70 00 ‘too 300 400 500 000 700 000 000 1000 1100 1500 DEGREE ORYS>48 RT GULL LRKE 60 For 1971, three different fields were used. Development in those fields seemed to be unusually early in that year, and that is reflected in the fact that for both eggs and larvae, simulated values occur later than the observed values, although larvae match more closely than do eggs. While it is ultimately the larvae which one is interested in for pest management purposes, good correspondence between the curves for both eggs and larvae ought to be sought for the model. Since the distribution of larvae depends to a great extent on the distri- bution of eggs, it seemed reasonable to first try to bring the curves for eggs from the field and the model into close correspondence for all years. From a consideration of the model structure, it is clear that two features would have the most influence on the time rela- tionships of the egg curve. They are the emergence from over— wintering sites and the rate of movement of adults from wheat to oats in the spring. Because the latter is a more immediate influ— ence, it was the first factor considered. As was previously stated, adults were assumed to move from wheat to oats at a rate such that the probit of the proportion of eggs going into oats at any value of °D>5.6 was given by: YP = Probit of Proportion = .8625 + .01379 * °D>5.6C (19) This represents a normal distribution with mean equal to 300 °D>5.6 and standard deviation equal t0'% = 72.5 °D>5.6. 61 Therefore there are two parameters involved here which might affect the distribution of eggs. Several preliminary simulations indicated a greater sensi— tivity of the error between model and field to changes in the mean than to changes in the standard deviation, so the mean was varied. Since the synchronization of eggs was good for the 1969 data, but poor for 1967 (model too early) and 1968 and 1971 (model too late) it was anticipated that no single value of YP would be optimal for all fields. In Figure 23 the square root of the sum of the squared differences between model and field for several fields are plotted over the YP (the mean). For three fields true optima do exist, that is a point of minimum error. Those fields are 69, 701, and 702, each with a minimum error near 350 °D>5.6. For the other fields, with the exception of 1967, the best value of YP is a very low one, unrealistically low when it is remembered that YP is the time (°D>5.6) when half of the eggs being laid are going into oats. Data for the year 1967 were peculiar in the distribution of eggs being later than larvae, and this is reflected in a large value of YP being best for that year. As anticipated, no one value of mean YP gave best results for all fields. The optimal curve for each year is shown in Figure 24. A comparison of field with model, with the best value of YP used for each year (all fields for one year used the same value of YP) are shown as the second row of graphs in Figures 19 — 22. 62 Figure 23.-—The square root of the sum of the squared deviations between model and field values for different years (first 2 digits) and different fields (3rd digit) plotted over the mean value for YP, the parameter which moves adults from wheat to oats in the spring. 63 m» mmemzcmcm mom m:1¢> zcwz Dom omv 005 com com owN Dow om1 001 om _ b F i b 55: 2:. mm NZ. I D F D h b p p b b F P F D I P F F b (P Ll P PL PP _ P D b b P ’L D b b bhlbyllpb D l“ NI \’ ‘0 I T V l T T I V V 1 T T T T I j j T I ' T 1 I I l T r f T T DVZ 1m 091 021 06 09 08 (Z**(808831NDSJIBDS‘SOOB 012 081 64 Figure 24.-—The percent of eggs being laid in oats as a function of °D>5.6C (42°F). The different curves are those that minimize the error in the comparison of field and model incidence curves for eggs in the year indicated. PERCENT IN ODTS 65 1967 Initial Estimate 100 'ébb"960"100*'660"ééb"660"060"906'7i000 DEGREE DRYS > 5.6 66 Clearly adjusting this one parameter allows a remarkably good correspondence between egg curves from the field and from the model. Even in the case where the data are questionable (1967), the fit is remarkable. For 1970 the slight change in mean YP to get the best fit does not disturb the good fit for larvae in that year. The fits for larvae appear to be improved for fields in 1969 and 1971, however results are poor for 1968 and much worse for 1967. With the fits for eggs established, it appeared that the length of time from peak eggs to peak larvae was lower in the model than was observed in the field. There are a number of possible causes for this, two of which were considered likely and were investigated with the model. The first of these is that eggs on the surface of leaves are experiencing temperatures different from those at the standard weather station from which data were obtained, and were therefore deve10ping at a rate different from.what the model would predict. The second possibility is that the development rates are different in the field than those determined in the laboratory (Figure 11). The first possibility was investigated by multiplying the temperature input to the egg time delay function by a constant for a number of simulations. The second possibility was investigated by multiplying the output from the egg time delay function by a con— stant. Of the two methods, the second, which is equivalent to changing the actual developmental time curve, gave the best results, with an optimal value for the development time of 1.25 times the 67 values suggested by Figure 11. (While it is possible for the average developmental time of a population to change from year to year (Morris and Fulton, 1970) that possibility was not admitted here.) The third series of graphs in Figures 19 - 22 show the com- parison of model and field when this adjustment to DELE, the time spent in the egg stage, is applied to distributions with their optimal value for mean YP. While this adjustment causes slightly poorer fits in 1970 and for field 711, the overall effect is an improvement in the larval fit, particularly for 1968 and 1969. By adjusting two parameters then, mean YP and egg develop- ment time, DELE, it is possible with the model to mimic well the time sychrony of the cereal leaf beetle in the field. The adjust— ment to DELE constituted no great difficulty to the further develop- ment of this work along the lines which were originally intended, but if a parameter must be determined anew each year, then it does constitute a problem. The value for the parameter must be observed in the field, or the factors causing the change in the parameter must be determined, and the changes themselves modeled from a mea- surement of those causal factors. The first solution is undesirable in the context of a pest management scheme if it involves sampling more than once, a high possibility when a rate is involved as here with YP. The second solution--modeling the process, could not be attempted here because of a lack of data. Because of these difficulties with using the optimal value of mean YP the possibility of a single value for adult emergence which would give improved fits for all fields was investigated. Here 68 the intercept of the probit regression line was kept constant while the lepe was changed. The value for YP was set to its original value, but development time of eggs, DELE, was left at 1.25 times the original DELE value. The emergence line which gave best overall fit is shown in Figure 4, and the comparison of the simulation out- put with field data is shown as the bottom set of graphs in Figures 19 - 22. While the overall effect is an improvement on the original parameter values, the results for 1969 and 1970 were slightly worse than they were for the original parameter sets. In any case, this single alteration to emergence rate is not as effective in reducing the error as is the yearly adjustment of YP. These conclusions are shown more objectively in Table 2 where the chi-square statistic discussed earlier is tabulated for the different fields under the different parameter sets. The values for 1967 are included for reference, but were not used in computing the mean or the standard deviation. Reference to the means and standard deviations shows very clearly the tremendous superiority of adjusting YP and changing DELE over the other approaches, but again that approach requires a different value for YP for each year. It was thought necessary therefore to test the alterations to spring emergence rate and to egg development rate on data which were not used in the optimization procedure. That was done using data from 7 fields from the years 1972 to 1977 provided by E. Lampert and A. Sawyer. Table 3, which is similar in structure to Table 2, contains the computed chi—square values for these fields for the 69 .>mm 0mm own Nam wwm cm on Hm 50H m5H mmq .mum 511 555 $1 555 55 51 55 55 551 555 285 mH5lwo mm moH HH 50H 5 ma ma ma OH 5NH ma5 mom 5wqa 5N 5am mm mm 5H me on «MNH ~H5 5mm H55 w5 5mH mm m5 ma «0 0mm mmm HH5 5H ca «ma mo 5m H5 om om mm mm N05 ma 5 5mH mma 5m me «m cm 5m om H05 55H cam oaqa o5om mm mmH mmm mom «on qu mo 5m 5mm mm 55H 05 5m em 05 a 5mm we ma mmm 055 wmmm 5cm om moH mm mm mmma 5o mm>umm wwwm mm>umm wwwm mm>umm wwwm mm>wmm mwmm mm>pmm wwwm mama mmma + mmmm + mm mm umm mmmm poem monowuwem .mumumEmumm mo mumm ucmwmmm5v mafia can ouo3 macaumanefim owns mm>umH com wwwm oauoon mama ammuoo mo mmwufimaov macaw was Hmwoe mo somfiummaoo onu scum mumsumlflnu pom mosam>ll.~ mmmumm 54 mm NA Hm wwwm oamfimm\wwwm Hmow musumsEH m<>H>mmm .mgmm 5 mm.m u mqmo 5cm HmeHuao m5 £553 :Ofiumasefim was now Hm>5>u=m 5cm aOHuflmoaH>onl.5 mgmuma “mums“ vacuum mo nomads on» van Now an vmmmmuoov Hopes any ca om>uma “mumcfl umufim mo “moan: :uwa umm wumvamum I 3ou vacuum .Auwm wumvcmumv mmmn « mm.H u mmmm mam HwEHuao mm Bow moy .maounoa5m :0 mafia mafiaaamm mo muommmo 055:1.mm ounwfim wxqm Dnso 5c m5kw>qo ummomo 8: 2:: 8m 08 2: 8m 8m 8. 8m 8m. 8w. 8: 02.: 8m 2.; 85 com 2.5 2.: 8m 8m. b b D I h h 1 \\\V \ x \‘ 1 . 4 . 6c 6: 09 69 as / 06 / 021 I DZ! Us! 05! 091 09! 012 0'2 9 69 69 06 69 06 021 05.1 / \ / // aqw~u.uc>¢¢4 + // amour. uc>¢¢._. X 9.5— m. 80w Q 423:. gen 8 091 0%! 091 051 012 012 _05 mm mm 0L 092 0‘2 5 AllSNEO AllSNBO 77 The effect of this degree of bias on the number that would be counted at each of the sampling times for 1969 is shown in Figure 26 where the ratio of the total number in the biased model sample over the total number in the unbiased model sample is plotted over the appropriate °D value. Here the bias has an obviously serious effect, and worse, its effect changes with the season. Sensitivity to Biases in Temperature Data Previous work (Fulton and Haynes, 1976) had indicated that relatively small differences between the temperature measured near an experimental plot and the temperature to which the insect is exposed have profound effects on the interpretation of experimental results. Therefore temperature within the model was multiplied by a series of constants and the generated density curves were compared to the field data, ignoring these temperature biases. The chi2 values for the correspondence between model and field for the egg and larval curves when the temperature affecting the insect ranged from 80% to 120% of that observed are given in Table 6. Anything beyond a l - 5% bias causes a rapid rise in the chi2 value but this translates into only about 1°C! That kind of accuracy is extremely difficult to attain in field work and yet the effects are quite striking (Figures 27 and 28). Section A of Figure 27 and 28 is with unbiased temperature data. Section B has a bias of .95, for Section C it is 1.01, and for Section D it is 1.05. Again, a 5% bias might be too great to tolerate for pest management! 78 Figure 26.——The effect of a 50% bias against first instar larvae and a 40% bias against second instar larvae on the fraction of the whole population that would have been sampled at the sampling times which were used in 1969. 79 mxoo wuzmp czmqmncm mmm~ one com on» com Lr } b b b > r bk 0&5 » 90¢ can con emu DON ’0 SL’O 01.0 ss'o os-o 99'0 09 Sanoa UBSUIBNn/UBSBIQ 09'0 99‘0 06’0 80 mmM5 000 M5 «N «M cm 05m HMMH 0HONN N05 5005 050 05 0m 5m MMH 0N0 000M mammq H05 HMNmN H5HN mom 00 mm mm HNH 00m HONOH m0 MomM 050 qu mm 00 0M H0 mMH now 00 m<>m¢A qoMmN MMOM 000 M00 MHM 0N0 HMmH NON5 mmNNHH 5:0 000 NHH 0N NH Mm 5H mm 05H 0mHH MH5 00¢ 0m 0m 05 mm mNH mHM H00 05mm NH5 000 50m mm 00 M5 00 NOH 00M 000m HH5 mama qu MM 0N H5 H0 MqN 0NOH wqwmm N05 mmNN N5N 5M «N me 05 05M mem 0005N ~05 HM50H wawm 005 mmm mmm 00H 000 Mwmm finamq m0 000 05 «N M0 50 m5 «Hm M50 0000 00 000m N.H H.H 00.H H0.H 0.H mm. mm. m. w. Hmmw .cw>ww HOuomm map 50 coaumum “maummz mumwcmum m um mammoowp umsu Eoum mnmwmam uommcw mnu wafiuoommm mnaumumaamu mzu c0£3 mmsfim> mufimcmw UHmHm 0cm Hmpoa ammBumn muam0aoawmuuoo msu How monam> mumsvmlfi£0|l.0 mmm<5 81 50H0q N05M mqw 05m <5N mNM wqmm mm00 M0500 5:0 000 00 5N 0 5 0 Mm 0M HOH MH5 N00 00 5H NH 0m ON 50 Mmm HNO. NH5 M0 0 0 0m 0M 00 mam NHM 50mm HH5 N.H H.H 00.H H0.H 0.H 00. m0. 0. w. Ham» .0msafludooll0 mummfi 82 Figure 27.—-l968. The effect of a bias in the temperature recorded at a weather station in comparison to the temperature affecting the insect temperature. A. TEMP = tempera- ture. B. TEMP = .95 * temperature. C. TEMP = 1.01 * temperature. D. TEMP = 1.05 * temperature. 83 00N~ IF 00__ 000— 000 000 005 1" II! 043 m. u¢>¢¢4 + queer. mc>¢¢4 X 043 .0. 80m 4 June... gen 8 0x04 4420 m0 05Aw>¢0 mmmowo 000 00v 00M 000 000 AlISNBU AlXSNBG 84 Figure 28.-—l969. The effect of a bias in the temperature recorded at a weather station in comparison to the temperature affecting the insect TEMP. A. TEMP = temperature. B. TEMP = .95 * temperature. C. TEMP = 1.01 * temperature. D. TEMP = 1.05 * temperature. 85 0x00 00:0 00 05Aw>qo wmemo 000 000 005 000 000 00v 00M 00AU 005— 00—. 000— 000 000 005 000 00m 00v 00M COAU » L .. . . r. .. L » i > L»... I . >:. . ..... r r > >>>>> 00m. 00__ 000— 091 021 081 012 0?? / / Sutficzs + .w 68:655.. x 1 321.58.”. c m g—lg a KM m 000 092 921 AIISNBU .081 v tvvv 081 05 v‘vvvvvvvy v vvvvv AlISNBO 86 There are other factors which might be affected by a dif— ference between the recorded temperature and the temperature affect- ing the insect. For example, fecundity, egg survival, and larval survival. Fecundity and egg survival in the model with several values for the temperature bias are listed in Table 7 for the years 1968-71. Clearly these factors are little affected by the tempera— ture bias. A similar conclusion holds for larval survival. Variation in Larval Development Times The developmental time of a species can be difficult to determine. For instance cereal leaf beetle larval development time was found to be about 1.7 times faster by Helgesen ahd Haynes (1972) than the value found by Yun (1967). The effects of such great dif— ferences were not investigated, but development rates from 0.8 to 1.2 times those reported by Helgesen and Haynes (1972) were tested (Table 8). Within these bounds the effects are certainly not serious. Extreme cases existed in 1968 and 1969 (Figure 29). The top sections, labeled "A" were generated with the larval development times decreased by 20% compared to the standard, sections "B." Sections "C" had the development times increased by 20%. Note that development times in sections C are 1.5 times longer than those in sections "A" without serious disruption of the synchrony between model and field. Egg and Larval Survival Functions The automatic scaling factor was always greater for the eggs than for the larvae. That indicated either that egg survival is 87 TABLE 7.--Eggs per female laid in oats when the temperature affecting the insect differs from that recorded by the factor shown. EGGS/FEMALE FACTOR Year .8 .9 .99 1.0 1.01 1.1 1.2 1968 106 105 108 109 110 118 125 1969 43 44 43 43 43 42 44 1970 55 56 55 54 54 51 49 1971 117 117 121 122 123 128 130 EGG SURVIVAL 1968 .307 .340 .342 .341 .340 .339 .358 1969 .298 .315 .336 .339 .341 .363 .377 1970 .315 .344 .363 .366 .369 .400 .425 1971 .340 .358 .367 .367 .368 .379 .399 88 TABLE 8.--Chi-square values for the comparison of field and model when larval development times were changed by the factors shown. FACTOR Year .8 .9 1.0 1.1 1.2 68 61 46 40 37 35 69 107 75 52 37 27 701 63 74 87 101 117 702 29 30 34 39 46 711 49 32 38 44 50 712 11 13 16 18 21 713 9 8 7 7 6 Sum 328 277 274 283 301 DENSITY DENSITY UENSITY HQ 596 70 89 210 210 I! EBOBoRODEL A EoosoflELD X LHRVRE .HODEL \ + LHRVRE .FIELD 80 39 50 90 \ \ // 150 120 60 90 l20 150 I80 2l0 2‘0 30 80 60 7O 0 \ IO 90 120 150 180 210 240 60 30 700 800 900 1000 1100 1203 $00 300 400 500 =00 700 800 960 150': 110.: 7230 DEGREE DQYS>4B HY GULL LRKE Figure 29.--The effects of larval development times on synchrony for two ‘5 _. :B .— (:._ years, 1968 and 1969. development times decreased by 20% standard development times development times increased by 20% 90 higher in the field than in the model, which has been indicated; or the sampling for eggs in the field is less efficient than is the sampling for larvae; or both of these effects may be operating. Those effects can not be sorted out here, but the effects of changes in survival on these ratios can be considered. In Table 9 are listed the total incidence ratio for eggs and for larvae with 5 different sets of survival functions, A - E, and the ratio of those values for eggs over those for larvae. The general trend is for increases in the survival rate to cause the ratio of eggs over larvae to decrease, with the value being near 1.0 for some years (1971) when average egg survival is about .65 to .70 (column B). For other years however, this ratio is near 1 only when both egg and larval survival are set to 1. Reference to the chi2 values in Table 9, which are again for the correspondence between field and model, show that these kinds of changes in survival have little effect on synchrony. JWH—t -&.*E 9]. .0.. I H¢>0>h=o 51>una .0.. I .->0>u:o 000 I u 5.. I .2533. 00m I .— .Uomzmh c 050500.150. I I ..¢>«>h=o usoocaucuuacq 00m 1 o .Uomzwh c 050500.I.0. I n ..n>0>u:u oaoocuucaun=« 000 I 0 .oco.uw:vv .a>.>u:o vuavcoum n < m5n 5N5 ~_n 5N5 con 6.. 505 .85 55~ 5.0 «x 0.. 0.. 00.0 0.. 00.0 00.0 00.0 .5.0 00.0 05.0 .q>.>u=m can: 00. 5... 05.. 55.. 05.. coo: 00. 5.00. 5.00 00. 0.50 5.00 50. 5.05 5..0 50. ..50 0.50 55.. 0.55 0.05 5.5 50. 5.05 0.05 05. 5.05 0.05 50. 0.55 5.55 00. 0.05 0.05 55.. 0.5. 5.0. 5.5 00. 0.55. 0.55. 00.. 5.5.. 0.55. 0... 5.50 5.00. .~.. 0.50 0.50. 00.. 5.55 0..5 ..5 5... 5.0. 0.05 05.. 0.5. 0.05 50.. 5... 0.0. 50.. 5.0. 0.0. 5~.N 0.0 «.5. ~05 00. 5.5. 0.0. 00.. 0.0. 0.0. 55.. 0.5 0.0 05.. 0.0 0.0 05.. 5.5 5.0 .05 50. 5.0 ..0 5... ..5 ..0 05.. 5.0 5.5 .0.. 5.5 5.0 00.. 5.5 0.5 00 5... 0.00 ..50 05.. ..05 ..50 50.. 5.05 5.00 50.. 5.55 0.00 55.5 5.0. 0.05 00 on>qu un>uma 0000 00>»mq ou>ueq awum oa>umA oa>uqa uwuw on>uqm oa>hu4 uwuu ow>uaq oa>uwa .000 any» 50005.. 5000”. 5000.. 50000. 5000mm 0 0 u 0 < .560a655c. on m.a>.>t=u 5:6 .ugua . 05.. - mama ..«a«uao 5> 005: acoauu.:a.. eon“ 5.0.0..»56a 1 6.8a“ oucov.uc. .a»o~--.0 nan48 should be compared to the ratios of the two areas under the density curves (Table 11). 97 TABLE 11.--The ratio of model values to field densities on the sampling day for two years. Model egg and larval survivals set to 1.0. 1968 Density Ratio 1969 Density Ratio 6D;48—- Eggs Larvae 30:48—- Eggs Larvae 218 18 -- 378 3.6 76 296 35 97 392 4.9 5.5 347 53 266 420 6.2 -- 370 45 120 479 6.8 13 384 50 67 548 11.2 7.2 419 68 103 568 10.2 8.1 443 63 94 615 10.3 9.5 476 77 111 677 10.8 11 519 59 76 595 137 74 686 397 43 Area ratio 67 59 8.1 8.7 98 The 1968 density ratios for samples between 600 and 700 °D>48 become very large (Table 11). This is very apparent in the values for the other years not contained in Table 11. Assuming we restrict the sampling to the interval 200 to 600 °D>48, the number of eggs appears to be a better estimator of the ratio between total populations (model/field) than does the number of larvae or the total of the number of eggs and the number of larvae. This would give estimates from 0.31 to 2.32 times the actual values that do occur (Table 11). For all of the standard data set, 67 - 713 the range is 0.24 to 2.32. In fact for that data with the egg samples taken below 400 °D>48 the range is 0.24 to 1.0. That means that from egg samples taken in the range 200 to 400 °D>48 the seasonal larval population can be estimated to between 1 and 4 times its actual value. Using several samples does not seem to provide any additional information in the range 200 - 400 °D>48 and therefore need not be done. SUMMARY AND CONCLUSIONS A continuous time dynamic simulation model for the cereal leaf beetle was constructed. Initial adult densities were not available for the validation data, therefore a number of procedures were tested for equating field and model populations. The method which was finally accepted was to equate the egg and larval total incidence curves of the model to those of the field. It became obvious during validation studies that either through sampling or through the development of a sub—model, the rate at which adult beetles moved from wheat to oats in the spring had to be determined. That is because synchrony between model and field depends to a very great degree on this rate. The rate of adult emergence in the spring also affects synchrony, but it is not nearly as effective in decreasing the error in synchrony between the model and field, as measured by a chi2 like statistic computed from adjusted densities. Although the rate at which adults move from wheat to oats could not be determined from the existing data, it was possible to establish an empirical relationship for each year. Oviposition rates into wheat and into oats under these empirical relationships were sufficient to explain the observed year-to-year differences in the percent of the beetle larvae found in oats as compared to wheat, 99 100 even though the relationships were developed by considering synchrony only. Sampling bias against the first and second instar larvae of as much as 50% and 40%, respectively, had little effect on the synchrony but continued to have a strong effect on the pOpulation estimate, which was still only about .66 of the true value at peak density. The model was very sensitive to biases in the temperature used to establish the synchrony. Biases greater than 1% caused serious errors. Oviposition rates and egg and larval survival are not greatly affected by temperature. Changes in larval development times of as much as i 20% had little effect on synchrony, but a 25% increase in the development time for eggs gave an overall improvement. Egg and larval survival values had to be increased in order to have model values correspond more closely with field values, especially for use of the model to predict populations for manage- ment purposes. When estimated temperatures instead of actual temperatures are used in the model, synchrony is disrupted far less if actual temperatures up until May 10 are used and then long-term monthly extrema are used rather than by using the daily temperature extrema from a previous year for the whole growing season. The conclusion is that very accurate temperature information up to the time of the density sample accurately establishes the synchrony which is not then easily distorted. 101 Egg population density estimates taken between 200 and 400 °D>48 make it possible to estimate the total incidence of larvae to follow to between 1 and 4 times the actual value. These large error bounds are due largely to problems in establishing the synchrony between model and field. The solution to this problem would involve a more accurate determination of the temperature affecting the insect, and an accurate estimate of the rate at which beetles move from wheat to oats. Work currently being done at MSU to develop satellite oriented environmental monitoring systems may increase the precision of temperature estimates. Research currently being done by Alan J. Sawyer (MSU Ph.D. proposed date 1978) on the between field movement of beetles may lead to methods for modeling the spring move- ment from wheat to oats. Neither of these efforts would be necessary if the synchrony could be determined from the sample; however, two previous efforts to do this have failed (Fulton, 1975; Logan, 1977), and that must await future investigations. APPENDICES 102 APPENDIX A COMPUTING AN ESTIMATE OF K FOR THE ERLANG DISTRIBUTION FROM DATA 103 These estimates are based on mean development times and the relations for the Erlang distribution: E(T) = 1/01 Al and V(T) = l/K * :5- A2 k (k—l) -kaT f(1) = (“'9 (:1 9 A3 (k—l)! Table A1 lists the means and variances for the development times of larvae at different temperatures. The variances were unpublished in Helgesen and Haynes (1972). Table A2 presents K values computed by solving equation A2 for K for each treatment. The overall mean, computed as the mean of the individual K values is also presented in Table A2. No attempt was made to determine if this procedure is an unbiased estimator of K. In practice the value of 5 turned out to be too small and an empirically determined value of 15 was used in the model. 104 105 TABLE A1.-"Means and variances for CLB larval development times. (Unpublished variances from Helgesen's work.) Temperature, °F 60° 70° 80° Instar mean var mean var mean var 1 3.81 2.66 2.55 .83 1.86 .93 2 5.33 3.06 2.12 .86 1.71 .71 3 3.00 3.63 1.87 .84 1.44 .40 4 3.59 3.26 2.00 .71 1.36 .26 106 TABLE A2:-K values for the Erlang distribution computed from the data in TABLE A1. Temperature, °F Instar 60° 70° 80° 1 5 8 4 2 9 5 4 3 3 4 5 4 4 6 7 Mean 5.25 5.75 5.00 Grand Mean 5.00 APPENDIX B SIMULATION MODEL FOR CEREAL LEAF BEETLE 107 0000000000COOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 108 PROGRAM POPDIs(OUTPUT=129,TAPE6=129,TAPE63=129,INPUT=129,TAPE60=IN +PUT, +TAPE61=OUTPUT,TAPE6A=129,TAPE65=129,TAPE66=129,TAPE67=129,TAPE62=1 +29,TAPE87:129) NMM=NUMBER OF REPRODUCING ADULTS. ATEGG=NUMBER OF EGGS LAID TO DATE. NEGG=NUMBER OF EGGS NOW PRESENT. NL1=NUMBER OF FIRST INSTAR LARVAE. NL2=NUMBER OF SECOND INSTAR LARVAE. NL3=NUMBER OF THIRD INSTAR LARVAE. NLA=NUMBER 0F FOURTH INSTAR LARVAE. NPP=NUMBER OF PUPAE NIA:NUMBER OF SEXUALLY IMMATURE ADULTS. ATN=TOTAL NUMBER OF LARVAE PRODUCED TO DATE. TL=TOTAL NUMBER OF LARVAE PRESENT. NA=TOTAL NUMBER OF MATURE AND IMMATURE ADULTS PRESENT. ATA=TOTAL NUMBER OF MATURE AND IMMATURE ADULTS PRODUCED TO DATE. E=EGG PRODUCTION RATE FOR THE POPULATION. L13: NUMBER OF EGGS SURVIVING TO ENTER THE 1ST INSTAR DELAY. L25=NUMBER OF L1"S SURVIVING TO ENTER THE 2ND INSTAR. L3S=NUMBER OF L2"S SURVIVING TO ENTER THE 3RD INSTAR. LuS=NUMBER OF L3"S SURVIVING TO ENTER THE ATH INSTAR. NPS:NUMBER OF Lu"s SURVIVING TO ENTER THE PUPAL STAGE. HOUR=NUMBER OF RADIANS REPRESENTED BY 1 HOUR ON A 2A HOUR CLOCK. Q1=NUMBER OF HOURS REPRESENTED BY A TIME CHANGE OF 1 DT. AMAx=MAXIMUM TEMPERATURE FOR THE DAY. AMIN=MINIMUM TEMPERATURE FOR THE DAY. DAILY TEMPERATURES ARE ASSUMED T0 FLUCTUATE IN A SINUSOIDAL MANNER WITH MINIMUM=AMIN AND MAXIMUMzAMAX. HTIME IS 2n HOUR CLOCK TIME. MAXIMUM AND MINIMUM TEMPERATURES ARE ASSUMED TO BE 12 HOURS APART, WITH MINIMUM OCCURING AT 3 AM AND MAXIMUM AT 3 PM. DELLVF IS A TIME VARYING DELAY FUNCTION MODIFIED SLIGHTLY FROM MANETSCH, T.J. AND G.L. PARK 1973. SYSTEM ANALYSIS AND SIMULATION WITH APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS. PART II PRELIMINARY. MICHIGAN STATE UNIVERSITY. THESE ARE TIME VARYING DELAY VALUES USED AS INPUTS TO FUNCTION DELLVF THE MATURATION DELAY FOR EACH STAGE IS A FUNCTION OF TEMPERATURE WHICH IS IN THIS CASE A FUNCTION OF TIME. M=THE RATE(NO./DAY)AT WHICH SEXUALLY MATURE LOCAL ADULTS ARE ENTERING THE POPULATION. RATE(NO./DAY)AT WHICH PUPAE ARE BECOMING ADULTS. NP =RATE (NO./DAY) AT WHICH 4TH INSTAR LARVAE ARE BECOMING PUPAE. OOOOOOOOOOOOOOOO0000000000000 109 Lu=RATE AT WHICH 3RD INSTAR LARVAE ARE BECOMING uTH INSTAR LARVAE. L3=RATE AT WHICH 2ND INSTAR LARVAE ARE BECOMING 3RD INSTAR LARVAE. L2=RATE AT WHICH 1ST INSTAR LARVAE ARE BECOMING 2ND INSTAR LARVAE. L1=RATE OF EGG HATCH. AD=SEXUALLY MATURE ADULT MORTALITY RATE, WHICH IS TEMPERATURE DEPENDENT. TABLIE IS A TABLE LOOK UP FUNCTION FROM FORDYN. BY R.W.LLEWELLYN, 1965. RALEIGH , NORTH CAROLINA. TABLI IS A TABLE LOOK UP FUNCTION FROM FORDYN. BY R.W LLEWELLYN, 1965. RALEIGH, NORTH CAROLINA. SET THE ARRAYS FOR INTERMEDIATE RATES FOR THE DELLVF DELAY ROUTINE TO THEIR INITIAL VALUES. THESE K VALUES ARE THE ORDER OF THE DELAY USED TO REPRESENT VARIOUS STAGES THEY ARE RELATED TO THE VARIANCE OF DELAY (DEVELOPMENT, LIFETIME) TIMES OF INDIVIDUALS IN THE POPULATION. KA=ADULT LONGEVITY. KM=ADULT PREMATING PERIOD. KE=EGG DEVELOPMENT PERIOD. KL1=L1 DEVELOPMENT PERIOD. KL2=L2 DEVELOPMENT PERIOD. KL3=L3 DEVELOPMENT PERIOD. KLu=Lu DEVELOPMENT PERIOD. KP=PUPAL DEVELOPMENT PERIOD DIMENSION AYE(10) DIMENSION DEGG(7),DL1(5),DL2(5),DL3(5),DLu(5),DP(7) DIMENSION MATT(u) DIMENSION RL1(15),RL2(15),RL3(15),RL4(15),RSA(15) DIMENSION RE(15) DIMENSION RA(15),RM(15) DIMENSION YEAR67(20),YEAR68(20),YEAR69(20),YEAR70(20),YEAR71(20) DIMENSION YEAR(20) DIMENSION YEAR72(20),YEAR73(2O),YEAR7u(2O),YEAR75(20) DIMENSION YEAR76(20),YEAR77(2O) LOGICAL WHEAT REAL NL1,NL2,NL3,NLu,NPP,NEGG REAL NIA REAL L1,L2,L3,Lu,NP REAL NA,NSA REAL MATT REAL NMA,NMM DATA AYE/-3.27u,3.966,.10u6,.1ou6,3.966,5*.1ou6/ DATA YEAR71/3u.,u1.,u2.,u8.,55.,62.,70.,76.,83.,90.,1O*O./ DATA YEAR70/31.,n3.,u8.,52.,58.,65.,71.,78.,85.,91.,10*O./ DATA YEAR67/27.,38.,u6.,63.,73..82.,89.,97.,12*O./ DATA YEAR68/26.,29.,37.,uu.,u7.,52.,5u.,57.,6O.,63.,66.,69.,72., +75..78.,81..85.,89.,93.,0./ - DATA YEAR69/50.,53.,56.,59.,63.,66.,70.,73.,77.,80.,8u.,87.,93., +98.,6*0./ 3H7 “711 C IKO 110 DATA MATT/32., 16 DATA DECO/16.5, 1 DATA DL1/3. 8, 3. 2, DATA DL2/5. 3 3 7. DATA DL3/3. 2. u,1. 9 DATA DLu/3. 62 28,2 DATA DP/u2.,30. ,22.5,17.5,12.5,10.5,10./ DATA YEAR72/u7.,52.,55.,63.,69.,75.,82.,89.,96.,11*O./ DATA YEAR73/u6..53.,61.,68..73..79.,82.,88.,96.,11'O./ DATA YEAR +7u/u7.,51.,55.,59.,6u.,68.,73.,78.,82.,86.,89.,93.,96.,7*O./ DATA YEAR75/50.,53.,59.,6u.,67.,71.,7u.,78.,81.,85.,88.,9*O./ DATA YEAR . +76/33.,u7.,51.,5u.,58.,61.,65.,68.,72.,79.,82.,86.,89.,92., +6’O./ DATA YEAR77/u7.,50.,5u.,57.,61.,6u.,68.,71.,75.,78., +82.,85.,89.,92.,6*O./ REWIND 6 DO 3M7 IU=60,67 REWIND IU CONTINUE CONTINUE TITX=TIME(ZZ) TITY=DATE(JO) FACTOR=1.05 DDAY2=O. WHEAT=.F. DT=.1 HALFDT=DT/2. DETERMINES THE PRINT FREQUENCY IKO=5 1 2. 5 .5, 5. 0, A. 5/ NM C PROPFEM IS THE PROPORTION OF FEMALES IN THE MATURE ADULT POPULATION 12 PROPFEM=O.5 IRLLGT=110 TIMEX=O. IDTR=1./DT+1. Q1=DT*2u. PIE=3.1H15926 TOPIE=2.'PIE HOUR=TOPIE/24. AMAX=0. AMIN=O. D012 J=1,15 RA(J)=0. RM(J)=O. RE(J)=O. RL1(J)=O. RL2(J)=O. RL3(J)=O. RLH(J)=0. RSA(J)=O. CONTINUE C0=1. EGSUR=1. 111 DDAY:O. DD5=0. PROB=O. PROB1:O. TPOP:100. DM=O. DELPA=1. DELPM:1. DELPEz1. DELPL1=1. DELPL2=1. DELPL3=1. DELPL4=1. DELPAS=1. NSA=O. TL=O. NEGG=O. NL1=O. NL2=0. NL3=O. NLuzo. NPP=O. E=O. ATEGG:O. NIA=O. NP=O. L1=O. L2=0. L3=0. L4=0. SE=0. NMA=O. NMM=O. KA=15 KM=15 KE=15 KL1=15 KL2=15 KL3=15 KL4=15 KAS:3 ATL1=0. ATL2=0. ATL3=0. ATL4=O. ATP=0. SKIP=10. EFTEMP=O. SKP=10. READ(6,21)ISTATE,INDEXNO,IDIV,IYEAR IF(EOF(6))1111,1101 1101 CONTINUE 110A 1105 1106 1107 1108 1112 1113 1114 1115 1116 1117 1109 1102 21 555 556 22 6 66 112 IV=1 JP=IYEAR-66 IF(IYEAR.LT.67.OR.IYEAR.GT.77)JP=12 DO 1102 IM:1,20 GO TO (11ou,1105,1106,1107,1108,1112,1113,111u,1115,1116,1117 +,1109)JP YEAR(IM)=YEAR67(IM) GO TO 1102 YEAR(IM):YEAR68(IM) GO TO 1102 YEAR(IM)=YEAR69(IM) GO TO 1102 YEAR(IM)=YEAR70(IM) GO TO 1102 YEAR(IM)=YEAR71(IM) GO TO 1102 YEAR(IM)=YEAR72(IM) GO TO 1102 YEAR(IM)=YEAR73(IM) GO TO 1102 YEAR(IM)=YEAR7A(IM) GO TO 1102 YEAR(IM)=YEAR75(IM) GO TO 1102 YEAR(IM)=YEAR76(IM) GO TO 1102 YEAR(IM)=YEAR77(IM) GO TO 1102 YEAR(IM)=O. CONTINUE FORMAT(12,Iu,I1,12) WRITE(62,22)ISTATE,INDEXNO,IDIV,IYEAR,TITx,TITY,WHEAT WRITE(61,22)ISTATE,INDEXNO,IDIV,IYEAR,TITX,TITY,WHEAT WRITE(63,22)ISTATE,INDEXNO,IDIV,IYEAR,TITx,TITY,WHEAT WRITE(66,22)ISTATE,INDEXNO,IDIV,IYEAR,TITX,TITY,WHEAT WRITE(67,22)ISTATE,INDEXNO,IDIV,IYEAR,TITX,TITY,WHEAT WRITE(6u,22)ISTATE,INDEXNO,IDIV,IYEAR,TITX,TITY,WHEAT WRITE(6u,555) WRITE(66, 555) FORMAT(* 1OAE123uLPS*) WRITE(65, 22)ISTATE, INDEXNO, IDIV, IYEAR, TITx, TITY, WHEAT WRITE(65, 556) WRITE(67,556) FORMAT(* 9AE123uPS*) FORMAT(*1WEATHER ,STATE ’I3'STA.NO.*IS +* DIV. *12* YEAR=19*I2,* TIME *A10* DATE *A10' WHEAT: *L1) WRITE(61,6) FORMAT(* DAY',2X,‘DD>A8*2X*EMER'1X,‘IM.AD.*,1X,‘MAT.AD*, +3x,*EGGS*,ux,*EGG INPUT*1x,*T.LARVAE*1X,*N.PUPAE*,1x,* DD A2 WRITE(63,66) FORMAT(5X* DAY'ZX'DD>48'2X'DD>9'3X'F I E'BX' ONE*3X*TWO’1X*THREE* +2X'FOUR'1X'S.ADULTS') 113 DO1 I=1,IRLLGT HTIME=O. READ(6,29)AMAX,AMIN 29 FORMAT(2F3.0) AMAX=.555555555'(AMAX-32.) AMIN=.555555555*(AMIN-32.) C AMAX=18.5 C AMIN=12.5 HRANG=(AMAx-AMIN)/2. TMEAN=(AMAX+AMIN)/2. DO 3 J:1,IDTR HTIME:HTIME+Q1 THETA=(HTIME-9.)*HOUR TEMP=TMEAN+HRANG*SIN(THETA) TEMP:TEMP*FACTOR TIMEX=TIMEX+DT DELM=TABLIE(MATT,1O.,5.56,3,TEMP) CERN=.OO16u-.002u2*TEMP DELA=-.6931S/AMIN1(-.OOOO69315,CERN) C COMPUTED AS LN(2)/INSTANTANEOUS SURVIVAL RATE DELE=TABLIE(DEGG,15.5,2.75,6,TEMP) C DELE=DELE*1.2 DELE=1.25*DELE C DELE:DELE*1.3 C DELE=DELE*.8 C DELE=DELE*.9 DELL1:TABLIE(DL1,15.5,2.75,H,TEMP) DELL2=TABLIE(DL2,15.5,2.75,H,TEMP) DELL3=TABLIE(DL3,15.5,2.75,N,TEMP) DELLA:TABLIE(DLA,15.5,2.75,u,TEMP) DELNP=TABLIE(DP,15.5,2.75,6,TEMP) 50 FORMAT(* *7G10.3,/* *7G1O.3) SAD=DELLVF(NP,RSA,NPP,CO,DELNP,DELPAS,DT,KAS) NP=DELLVF(Lu,RLu,NLu,CO,DELLu,DELPLu,DT,KLu) LA=DELLVF(L3,RL3,NL3,CO,DELL3,DELPL3,DT,KL3) L3=DELLVF(L2,RL2,NL2,CO,DELL2,DELPL2,DT,KL2) L2=DELLVF9 RDT IS THE INTEGRAL OVER ONE DT AND IS THEREFORE THE CHANGE 115 NMAzNMA+RDT E=EFTEMP*PROPFEM*NMA*FEC(DDAY,WHEAT) IF(WHEAT)Y1=1.-Y1 E=E*Y1 C USE Y1=1.-Y1 TO GENERATE THE WHEAT CURVES EGSUR=AM1N1(EXP(DT*(-.Ou23-.002075*TEMP)).1.) C0=AMIN1(EXP((.00775-.002569'TEMP)'DT),1.) FA=1.8'DDAY2 DD”2=DD5'1.8 IF(FA.LT.SKIP)GO TO 3 IF(FA.GT.500.)SKP=50. IF(FA.GT.1OOO.)SKP=1OO. IF(FA.GE.1500.)SKP=1OOO. IF(NEGG.GT.1.)ELRAT=TL/NEGG WRITE(87,70A)FA,ELRAT 7OA FORMAT(* *F5.1,*,*F16.8) SKIP=SKIP+SKP WRITE(6A,666)FA,NA,NEGG,NL1,NL2,NL3,NLA,TL,NPP,NSA WRITE(65,666)FA,AAE,ATEGG,ATL1,ATL2,ATL3,ATLA,ATP,NSA 666 FORMAT(* *10F7.0) 3 CONTINUE WRITE(66,666)TIMEX,NA,NEGG,NL1,NL2,NL3,NLA,TL,NPP,NSA WRITE(67,666)TIMEX,AAE,ATEGG,ATL1,ATL2,ATL3,ATLA,ATP,NSA XTIME=TIMEX+HALFDT IF(IFIX(XTIME).NE.IFIX(YEAR(IV)))GO TO 8n IV=IV+1 WRITE(62,87)TIMEX,FA,IYEAR,WHEAT,NEGG,NL1,NL2,NL3,NLA,TL 87 ~FORMAT(* *F5.1,F5.0 ,12,L2,6(F6.1,1X)) 8A CONTINUE IT=I/IKO IT=IKO*IT IF(IT.NE.I)GO TO 1 WRITE(61,u)TIMEX,FA,PROB,NIA,NMM,NEGG,ATEGG,TL,NPP,DDA2 WRITE(63,5)TIMEX,FA,DDAY,FIE,NL1,NL2,NL3,NLA,NSA 5 FORMAT(* *9(1x,F6.0)) u FORMAT(* *Fu.O,F6.O,1X,F5.3,F6.0.3(3X,F6.O),uX,F6.O,3X,F6.O,uX,F5. +0) 1 CONTINUE EPF=ATEGG/(TPOP'PROPFEM) WRITE(61,u57)EPF u57 FORMAT(' EGGS / FEMALE =¢F5.1) SURE=ATL1/ATEGG SURL1=ATL2/ATL1 SURL2=ATL3/ATL2 SURL3=ATLu/ATL3 SURLu=ATP/ATLn WRITE(61,3u9)SURE,SURL1,SURL2,SURL3,SURLA 3N9 FORMAT(* SURVIVAL ,EGG=*F5.3,1X*L1=*F5.3,1X*L2=*F5.3,1X*L3=*F5.3,1 +X*Lu=*F5.3,1X) ATL=ATL1+ATL2+ATL3+ATLA ENDFILE 62 ENDFILE 6n 116 ENDFILE 65 ENDFILE 66 ENDFILE 67 ENDFILE 87 GO TO 4711 1111 CONTINUE CALL EXIT END FUNCTION DELLVF(RIN,R,STRG,SURVR,DEL,DELP,DT,K) DIMENSION R(1) C SURVR MUST BE COMPUTED ON A PER DT BASIS VINzRIN FK:FLOAT(K) B=1.+(DEL-DELP)/(FK*DT) A=FK*DT/DEL DELP=DEL DO 10 I:1,K DR=R(I) R(I)=DR+A*(VIN-DR*B) VIN:DR 1O CONTINUE STRG=0. DO 30 I:1,K R(I)=R(I)*SURVR STRG=STRG+R(I)*DEL/FK 30 CONTINUE DELLVF=R(K) RETURN END 117 FUNCTION TABLIE(VAL,SMALL,DIFF,K,DUMMY) DIMENSION VAL(1) DUM=AMIN1(AMAX1(DUMMY-SMALL,O.),FLOAT(K)*DIFF) I=1.+DUM/DIFF IF(I.EQ.K+1)I=K TABLIE=(VAL(I+1)-VAL(I))*(DUM-FLOAT(I-1)‘DIFF)/DIFF+VAL(I) RETURN END FUNCTION TABLI(VAL,ARG,DUMMY,K) DIMENSION VAL(1),ARG(1) DUM=AMAX1(AMIN1(DUMMY,ARG(K)),ARG(1)) DO 1 I=2,K IF (DUM.GT ARG(I))GO TO 1 TABLI=(DUM-ARG(I—1))*(VAL(I)-VAL(I-1))/(ARG(I)-ARG(I-1))+VAL(I-1) RETURN CONTINUE RETURN END FUNCTION FEC(RNDT,WHEAT) LOGICAL WHEAT FEC=.9297 IF(WHEAT)2,1 IF (RNDT.LT.2OM.)RETURN FEC=189.25/RNDT RETURN CONTINUE IF(RNDT.LT.166.)RETURN FEC=153.606/RNDT RETURN END 118 FUNCTION DAY(I,PHI) C THIS FUNCTION COMPUTES THE LENGTH OF DAY (SUNRISE TO SUNSET) C FOR ANY LATITUDE .THE LOGIC WAS DEVELOPED BY R. BRANDENBURG C AND PROGRAMMED BY W. C. FULTON C "TO" IS MARCH 21 , 197” C SEE MY FILE "FPHOTOPERIOD" —3 DATA TO/127./,Y/.O172020236/,X/.39795/,2/-.O1u5u39/,R/7.639AU/ T=I+u8 XL=Y'(T-T0) SD=X*SIN(XL) D:ASIN(SD) CT:(-.O1u5u39-SIN(PHI)'SD)/(COS(PHI)*COS(D)) ACT=ACOS(CT) DAY:R*ACT RETURN END SUBROUTINE NDTR(X,P,D) AX=ABs(x) T=1./(1.+.2316u19*AX) D=.3989u23*EXP(-x*X/2.) P=1.-D'T'(((1.33027H*T-1.821256)'T+1.781A78*T- +.3565638)'T+.3193815) IF(X)1.2.2 P=1.—P RETURN END FUNCTION PEG(T) DIMENSION PHO(8),PHE(8) DATA PHO/O.,9.,13.5,1u.5,15.5,16.5,2o.,23.5/ DATA PHE/.02,.005,.02,.36,1.,1.,.65,.O6/ PEG=TABLI(PHE,PHO,T,8) RETURN END APPENDIX C VALIDATION PROGRAM 119 A5 1 7 3 u 10 55 3H7 13 23 22 25 24 120 PROGRAM COMPARE (OUTPUT,TAPE61=OUTPUT,TAPE62,TAPE80,TAPE81) DIMENSION IDAY(20,2),EGG(20,2),AL1(20,2),AL2(20,2) +,AL3(20,2),ALN(20,2) DIMENSION ATL(2O,2),IYEAR(11),JYEAR(11) DIMENSION KDAY(7) DIMENSION X(2O,11),Y(2O,11),IIYER(20) DIMENSION IDDAY(2O) DIMENSION CHI(2O,2) INTEGER TIMEX,DATEX REWIND 62 REWIND 80 REWIND 81 REWIND 61 DATA KDAY/O,O,O,O,3O,61,91/ DATA IYEAR/8,19,1u,1O,1O,9,9,13,11,1u,1u/ DATA JYEAR/1,1,1,2,3,1,2,1,1,1,1/ IIYER(19)=AHMEAN IIYER(2O)=AHS.D. KY=O READ(62,1)IYER,TIMEX,DATEX FORMATA8 MODEL FIELD EXPECTED DEV MODEL.B DEV * +*MODEL.TIR DEV CHI SQ“) 29:0. 85:0. 25:0. 26:0. 51:0. 32:0. 33:0. XMD:B(N1) XFD:A(N1) DO 107 KX:N1,J VAL:YINTER+SLOPEB*B(KX) Z=VAL-A(KX) z1:B(KX)*ABS(SLOPEB) ZZ=B(KX)'RATIO Z3:Z1-A(KX) zu:22-A(KX) ZS=ZS+Z3 Z6=Z6+Zu s1:s1+z**2 $2:S2+23**2 zu2:zu!*2 S3:S3+ZH2 IF(22.NE.O.)GO TO 930 29:0. 930 927 925 926 91111 900 107 19 23 125 GO TO 927 CONTINUE 29:2u2/zz SS=SS+29 CONTINUE IF(B(KX).LT.XMD)GO TO 925 XMDD:JDDAY(Kx) XMD:B(KX) CONTINUE IF(A(KX).LT.XFD)GO TO 926 XFDD:JDDAY(KX) XFD:A(KX) CONTINUE WRITE(61,9uu)JDDAY(KX),B(KX),A(KX),VAL,z,z1,23,22,zu,z9 FORMAT(* I*Il1,F8.1,3F8.1,5F8.1) IF(IWR.EQ.1)WRITE(81,9OO)JDDAY(KX),22 FORMAT<1X,Iu,',',F8.1) CONTINUE WRITE(61,19)25,Z6 FORMAT(38X,'TOTAL= *F8.1,8X,F8.1) WRITE(61,23)S1,32,S3,SS FORMAT(* SUM OF SQUARED DEVIATIONS : '2(F8.0,8X),2F8.0) IF(IWR.NE.1)RETURN ENDFILE 81 WRITE(81,9OO)(JDDAY(IQ),A(IQ),IQ=N1,J) ENDFILE 81 RETURN END LITERATURE CITED 126 LITERATURE CITED Anonymous, 1968. System/360 Scientific Subroutine Package (360AeCM— 03X) Version III programmer's manual. 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"Effects of Some Physical and Biological Factors on the Reproduction, Development, Survival, and Behavior of the Cereal Leaf Beetle, Oulema melanopus (Linnaeus), under Laboratory Conditions." Ph.D. thesis, Michigan State University, 153 pp. r .... IIIIIIIIIIIIIIIIIIIIIIIII 11131111111111111111131111111111111311113111111111111113113111111