AN ANALYSIS OF PATTERN AND INTERSPECIFIC ASSOCIATION ALONG A SOIL MOISTURE GRADIENT ON THE JACK PINE PLAINS OF NORTHERN LOWER MICHIGAN fluisforfhoboonM. S. MICHIGAN STATE UNIVERSITY Michael Daniél- Byor I960 ' HIIHHHIHINIIHI 3 5010 MW ‘ *v ’ .2. I _ a 1.11 Mid Udfiermy' This 1. to certify that the thesis entitled AN ASIALYSIS OF PATERN AND IEIT'ZRSPECIFIC ASSO— CIATION AL ONG A SOIL MOI STT'FE GN-UHEITT ON- THE JACK PINE PLAII‘ISO OF ‘TOR'I’HEFJI L01? R I-IICHI GATT presented by Michael Dani el Byer has been accepted towards fulfillment of the requirements for ___l"_u_$.._degree in__B_Q_tany_and Plant Path. <7{//M Major professor J. E. Cantlon Date 18 May 1960 AN ANALYSIS OF PATTERN AND INTERSRECIFIC ASSOCIATION ALONG A SOIL MOIsmURfi GRADIENT ON THE JACK PINE PLAINS OF NORTHfiRN LOWER MICHIGAN By Michael Daniel Byer AN ABSTRACT submitted to the College of Science and Arts Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE 1960 1. ABSTRACT This study deals with correlation and association between the frequent plant species occuring along a soil moisture and vegetation gradient ranging from Jack Pine to Leatherleaf Bog -in Crawford 00., Northern Lower Michigan.‘ This was done by first gathering quantitative presence and cover data, as well as environmental data, for 400 l X 1 meter quadrats located randomly in a study area of 100 X 100 meters. On the basis of examination of the soil profile in the center of each quadrat it was later assigned to one of seven segments correSponding to catenal soil types. For association and correlation analyses, the number of segments was reduced to five by combination of some soil types. Cole association coefficients, which give an estimate of the tendency of pairs of species to occur together, were calculated on each of five segments of the gradient for all possible pairs of species which occured above a given level of frequency on each segment. Of the 513 association coefficients 29 per cent are significant at the 5 % level, and 16 per cent at the l % level. Since far more coefficients were significant than one would expect by chance if none of the species were associated with each other, it seems evident that the species in question exhibit association Patterns within the segments of the gradient. Zero order correlation coefficients were calculated between each of these frequent vascular species and at least one other SPeciee. These coefficients show the tendency for high cover values.of species to occur or not to occur together. For these determinations, the frequent species were first divided into six EHWUps and correlation coefficients were then calculated for all possible pairs in each group. Of the 70 correlations, 21 per cent were significant at the 5 % level and 18 per cent at the l % level. The different groups were not randomly chosen for the correlation analyses, some were in fact picked because of the apparent ecological similarities of the species. Nevertheless there is a suggestion that high cover values of the species are also non-randomly distributed with respect to one another within the gradient segments. Zero-order correlation coefficients were also calculated for each frequent vascular species with at least one of the following environmental variables: depth of AOL soil layer, depth of AOH soil layer, per cent tree cover, per cent bryo— phyte cover, and depth of loose moss mat. These computations did not furnish convincing evidence that the variables chosen were particularly influential in determining the distribution patterns of the species. Partial correlation coefficients, which show the tendency for species to occur together or not to occur together when seve- ral other species and/or variables are mathematically held constant, were also calculated for all species-species and species-variable pairs in each group. In some cases discrepancies between the partial and the zero-order correlations for the same pairs, suggested that part of the correlation between species is due to interaction, or to similar reactions of the species to environ- mental variables. Differences between the association and correlation coeffic- ients for the same pairs of species, and changes in these coeffic- ients from one segment of the gradient to another, coupled with field observations, data for cover and frequency of species, uman values for environmental variables along the gradient, and general knowledge of the species were useful in formulating hypotheses concerning certain of the ecological relationships of and among the species studied. Ordinations were constructed of all frequent vascular species on each gradient segment, in which the coordinates of each species were plotted along two axes representing the correlations of the species with two environmental variables. These ordinations show a general ten- dency for species to keep about the same positions relative to each other on all gradient segments, which strongly suggests that the correlations are generally valid despite their low significance, for if the coefficients represented only random deviations there should be no similarity in species position between the segments. In general, the association and correlation coefficients agree with field observations of the visually evident associa- tion and pattern phenomena. They also agree with our general ecological knowledge of the plants concerned. These agreements, along with the high proportion of significant coefficients and the similarity of ordination figures for different gradient seg- ments, suggest that these coefficients are on the whole valid, though not exhaustive, estimates of the association phenomena which occur. Since some associations and correlations which appeared in the coefficients were not obvious in the field, these techniques would seem to be more than "an elaboration of the obvious" (Cole 1957, Graig-Smith 1957)- Though the techniques used here seem useful in detecting and describing species pattern and association, these are not to be considered ends in themselves. In the present study, the infor- nmtion gleaned therefrom was used in formulating logical hypotheses concerning the mechanism‘s responsible for the associations found. It would appear that interspecific interaction and differential tolerance to various past or present environmental conditions, are responsible in some degree for the various posi- tive and negative associations demonstrated. Certain of these association patterns appear to be related to various phases of microcyclic patterns (Watt l9h7). The hypotheses advanced are not intended as proofs for the underlying causes of community structure in the study area, but simply as possibilities which may be tested by experiment. The testing of some of the hypotteses presented here is the objective of work now in progress. AN ANALYSIS OF PATTERN AND INTERSESCIFIC ASSOCIATION ALONG A SOIL MOISTURE GRADIENT ON THE JACK PINE PLAINS OF NORTHSRN LONER MICHIGAN By Michael Daniel Byer A THESIS submitted to the College of Science and Arts Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Botany and Plant Pathology 1960 TASLE OF C lTIi‘TITTS List of Figures ............... List of Tables .... I-AKIIOITLEDG‘ENTS . II - INTRODUCTION AND BACKGROUND A—IIETRODUCTIOI B-P'T'EZRI‘ICOITCEPTS 1. Kinds of pattern ..... 2, Community patterns . 3. Patterns of single species ................. 4. Techniques useful in pattern study ......... III - I-ZETHODS A - FIELD AND LABORATCIRY TECETLTIQES ... . . . . . . . . . . . . . B-AIIALYSIS TECHNIQUES . C - BMW-TAHOE OF ASSOCIATI ON AID CCRFELATI ON Edam; ms USED 12: :24”? mass: STUDY Iv — RESULTS A“ DESCRIPTIOI: or 1.143 EILEA 0.0.0.0..0000-oooocooooo 1. vegetation 0.0.0.000......-00.00....00...... 2.1Jon_lin'ing val‘irgbles ......loooOODIODOIOOOOOO B - COLE COIL: f ICIETTS .‘IL‘LTD PDIIT.&TI (31:3 0 O O O O I O o n o a o o O C-CSTLPELATIAI: MT.UJYSES ..Oo-OcooooloonoooooInge...- ”A - scrunch. SOIL, mm 01m raj-mars or 77:3 AREA B - com: crmrzczazrrs 2...: omitrirzdts c — CORRELATION ALIALYCES, amass D - GROUP I 0......-0....0....OOOODIOIOIOOIOIOQOOOOO . C o .. \ 1. Gad (G8.ultflpl‘ia l)l.oc.'mbpilu3/ . g . o o a O o o o I o o o a o «meoox H k.) R) F) M) 1:.) \0 - . . . . . o . - . . . . . . . . . . . . . . . . . , . . . . . . . . c . . . . . . . . . A . t I a v - - , w - . U a u , o I c o v v . . . a - . . . , . ' a l t ‘ ' - > u I c e . . . . . . . v - a O a . r . o n . , . - ' l ' - u I a D r A v . , O a v a . c a o . - . 1 o o O O I a I I . a - n O - O I ’ e a ' ’ - . o 1 . u 0 Q - o . o v v c x c o o o o a u - a a 0 v c - . O O O C C l - . . o O r c C . ——. — s .— f o g” .. v 9 a.“ »L‘- _ I'Agvl A'N i(}‘;LbL“ AI Rel (Me ;_Jnvru 4_-:l. CE' Ll’|‘(;:.‘e) 0.... m lineare) 00...... £2 ‘ L:D,.fi:.. vaLL.J...-.:LA.5 (II. LAIL oi- ~JJ LL41? ., The two forms Correlations I -\J (“Vt 3*» N O E - ROD II .......... 7,. Of V’IILE . ‘u‘ 1 . Llitter derth .. . Multiple corral tion ........... ......l........-. C C) '1) '1 A O 3 ”J a 1d ) 3‘ pl: <2: :3 1. Ci :5 V a U . o 0 H10 0-th a B H A AC) 5': «a L~$<+ a) p :11 Pa (D ID \. O O O O O O O ‘1’. ”*1 (D ;..I O r H I F's ;. (L (A‘Jx Ch) (0 r4 a -’ 'ti _ I c ‘ I ”l A ’7' ct (1' H k. LA to E F - GROUP III ... ... .................. l. Anem (Anemone cuingfefolia) ..... 2. Dan (Danthsnln cliczta) . .. .. . 3. C333 (Cryzcu is puL.Lis) ........ w. Oras (O geopqie HQUtIIfDlia) .... ‘rciatjuhs VILH tree cover .... (MU! O C) k 0 G - GPOUP IV ......... l. Epig o I? H-GFaOI/PVQQIQO..QIO 1. Correlations w 1.. C )LI‘81QUAJ3A 3. H;Ztipl.e C0118 I':lj_1til:lle COI'I‘EICLIOI‘LS . o o o o o a o 0 o I calico-10.000000... .. ‘ l.(di~.ell*:"/ ..ooooocoov pines var. obeyslis '- “. \ (3 \_':'I'€ 8.1.13} ...-... :1 ltil t.’"C LOVE? 0... Va CL? -ltuii Iitvrbll. 3119‘ ., .L 11 S I" 01 litions 0.0.00.0... ‘L ....L'Z‘ tree (Ii-0.9.9.? .... v-‘iti humus depth ]-r]l1iKJILS ....oo-oooo GROUP VI .....,,..................... Clam (Chamaedaphne crlvculatc) .. W EU) to H Erio (Eriophcr‘ Kal (Kalmia 1313 Led (Le‘mt FFOE .n‘ .L‘H‘l COCO-'0... (1 \J‘\ 0 v9.11 g 178C! Jl'I I .1? n ari;istif nliiun) ., uuuuu erJe4r4r4+4 L‘K.) \A) \J) \l.‘ R) H\OC'\\n OCT) L4 I") “J \a) H C) \0 Co O'\\ u \ ‘ ~0 pcq' paeasaeJeJeJ ro L—J MO (‘0 Iv-J 1—4 H \s.) \L) \L) \ \J'l ‘J\ \. 1V. 1!) V o o C ‘ O U o C C 1:. Voxy (17900311311112 OXIrC-OCLH. 7. Kult3ple correlations .. ‘._ L _. 8.70.11!“~40?c:,C1e......IQOOOOOoClsOOOQpO..- J-G::.:::P~.L¢:J DISCUSSI 0:?.....OOOO-0.000.000.0000. VI - COITCLUEI C133 AI-“D SUI-THC VA - AMQA av ~ CU‘IV it: ...-0............oo-oop.u.o-...a L‘B - 5m 3", 3‘: Q 0 o O o O o I o o D g a O a O o I O o a I O Q C 0 o o O o o o o a g D VIII - BIBLE OFFLLEEIY . u g a o o I o o o o o o a o O o o o a o o o o I o a o 0 o o o APPENDICES A— STATISTICAL "“CIZ'TLV O C 0 c I o o o I w o 0 o Apl. Cole association coe¢ficient AFZ. Zero—order carrelntion coeff -3. b1~1€°t oruer pmrfiA] collelat-an csef ~u Multiple co 1e7213cn 001211630 Ls APE. Sfandurd pa roifi] rerre Siam carfficien B — CnITIQIA USED? SEPA;'TE SOTLT ES ....... 7' W mam-fl~’ V" hv-‘fiW-q 14V“ m—~--m C - v:—~_ICTI\,S S‘ ....D I: Mil—LL: :IVU 12:43, ‘hMCJ a-- 4‘.“ . . C‘lo 3146-03188 33431013 oonoo-aOoo..oOoo-o.o.. 0‘2. Parapleter S:VTI‘OO]. g . Q Q Q 0 0 D o o O O O o C a o o o o I 0-3. so]. 1 tz-IJC 837111013 Q C I o v o o I O I O o I O o o o o I u o {‘0 \A) Kn.) C" h” ‘\..J.) \J [4) N} \n \u ‘.n b) I —- 'V: R.) 10H.) (‘01) ‘ l ‘11 rd Ix N "\ if. \ IX) 1") \J\ ‘31 'xJ N} (i\ 4? N 10. 11. v _ 3 m ‘* a, 1 “_ ,, Location 0: fine st he! 912? ........ Photographs of the study area ..... Soil map of the study area . . . . . . . . Species—area curves ... .. ........ finnies—aree curves, continued .... .ection of the gradient .. SH no as 7, showing negative assooie ion coei ficlents ......... Same as 7. Wet Grayling—Croswell Send, association coefficients ...................... Same as 9, showing negative fimmzas 7. Au Gres~Saogmtu1V Send, association coeffi Sims #3 ll, shOWing netntive Ordination of vasculer species frequent on Devson-Greenwood Peat mih3te cover end tnickneqs of QrflJ‘V‘W~PUI ICYEhtS on br3 sho ing poeitive association coM Same as 13, Diagrams illustrating explanations Same as 15, continued ..........-. Same as 15, continued ............ Gl‘Pphs of Group I data . . . . . . . . . . . Gvfihs of Grogp I deta, continued A 'J 1‘ \flVpos of Group II data .....-...- frequent on showing :01 ents ................ associeti for disc association and correlation coeificients ' , oq .9 in GI“; 1. [$1.11 0 :7 shoxing coeff Y) J. ‘C Sflxd’ on itive UQSlu?Ve 0.000.000... ...-00...... 105 showing positive Cipllts 0.00.10.00.00.- his 00.... LT’ inhum not showing negative essociotinn coefficients ...... regencies betWeen \ ,) Kn ‘ N 1 71+ 80 81 Graphs Gr 9.}? 11 s Gragflls Hypothetical diagram of the bog cycle of o? GrOUp Groqp Groqp Groqp GrouP Group GrOQp II data, continued III data .......... IV data IV date, continued v 6.6.58. .0 00.- V1 1. LIST OF TESL“ I - Summary of per cent frequency across the gradient II - Summary of per cent cover across the gradient (vascular species) ........... ..... III - Keen velues of various variables on each soil type IV - Cole association coefficients ............. V - Zero-order correlation coefficients of specie with environmentsl parameters VI - Group I coefficients VII - Group II coefficients .. VIII - Group III coefficients IX - Group IV coefficients .. . X - Group V coefficients . .. . . XI - Group VI coefficients S _ . i ‘ . o , . . . . . . . 3 v n . . . . . e . i . . , , o . . - . s , . 4 - a . . . 4 . s . . . - » . . , - . , ~ » , A . q i . ~ . » , . , 3 I V . , . _ . , ‘ . . . v . < i A . . ACKNUJ LSDGflf-‘LESI‘ITS I wish to express my thanks and appreciation to all those who have helped and encouraged me in this work in various ways; particularly, I want to acknowledge the help of Dr. John E. Cantlon, who guided the problem and who provided material and intellectual help as well as personal encouragement during its completion. Also, I wish to thank Dr. Phillip J. Clarn, who provided statistical techniques used here an who patiently explained them to one not too well versed in mathematics. Drs. William B. Drew and John H. Beamsn, the other members of my committee, both provided many helpful suggestions concerning this manuscript. I am grateful to the Conservation Department of the State of Michigan for the use of State Forest land on which the study was made. II INTRODUCTION AND BACKGROUND 1. A - INTRODUCTIOI Interspecific association is the name of a now widely- recognized phenomenon describing the tendency for different species to occur together either more frequently or less fre- quently than one would expect if the species were randomly (independently) distributed with respect to each other. A profusion of techniques for describing and exploring interspecific association has come into the literature in recent years, and several are explored in this paper. The main purpose of this study is to advance our knowledge of order-producing phenomena in vegetation with the aid of these techniques. Hypotheses are advanced for explaining the associa- tions which are found. These are based upon comparison of the results of different techniques, and comparisons of the associa- tion of the same species in somewhat different habitats. In this way it is possible to obtain clues concerning the ecoloqy and physiology of local species populations and the phenomena producing community structure. These hypotheses must be tested experimentally at some future time, but the analysis presented here should suggest which, of the myriads of experiments possible with each species or species combination, might best help us to approach our ultimate goal of understanding pattern-producing phenomena. Interspecific association studies are one way of approach- ing the phenomenon of non-random distribution of species, or pattern, with the unique feature that here we consider non-random distribution of two or more species with respect to each other instead of considering each species by itself. But in reality this is a purely arbitrary distinction, for in studies of patterns 2. of single species one usually attempts to determine to what features of the environment the patterns are related. Since at the individual species level, other Species are as much a part of the environment as are various "abiotic" factors (cf. Odum and Odum 1959), we are merely concentrating on the biotic aspects of the environment in interspecific association studies. Although this study concentrates on interspecific association, and hence on the living portion of the ecosystem, we must con- sider the system as a whole if we desire information about the operation of the mechanisms which result in pattern. Consequent- ly, correlations of species with some non-living variables were also calculated. Most of the techniques used here have been used previously, in one form or another, to study interspecific association and other pattern phenomena. So far as the writer is aware, however, this is the first time that several such techniques have been combined in one study, although the problem of changes in interspecific association along a gradient has been touched Upon by several authors (e.g. Bray 1956, Hopkins 1957a). I feel that much more can be learned about the biology of particular species and the nature of community phenomena by using several different techniques, each designed to answer somewhat different questions, and comparing the results, than could be gained from the use of any one of the techniques by itself. The study of differences of association between the same species in different habitats along a gradient also yields more information than could analyses in each of the habitats separately. The study area was a soil moisture gradient in the Jack pine vegetation region in sandy outwash soils in Crawford Co., Northern Lower Michigan. The "dry end” of this gradient was in 3. open Jack pine forest, the "wet end" was an open Leatherleaf bog with scattered coniferous trees. Ring counts of the largest trees, and examination for charcoal in the soil pro- file, suggested that the area was burned about 60 years before, near the turn of the century, but that it has remained rela- tively undisturbed since. Four-hundred randomly located 1 X 1 meter quadrats were studied in an area of 100 X 100 meters. For each quadrat, per cent cover of each vascular species, and presence of each bryophyte and lichen species, soil profile, and several other environmental variables were recorded, and pH determinations, soil moisture content determinations, and light intensity read- ings were recorded for sets of 100 quadrats each. For analysis, the gradient was divided into seven segments by soil type, and mean values of frequency and per cent cover of each species and mean values of each environmental variable were calculated for all the quadrats in each segment. The number of segments was then reduced to five, by combination. For each of these five segments, Cole association coefficients were calculated between all possible pairs of those species which occured above a pre- viously determined minimum level of frequency on the segment. The vascular species were then divided into six groups, and zero- order and highest order partial correlation coefficients were calculated for all possible pairs of species within each group. For some of the groups, correlations were run with certain environ- mental variables also. Multiple correlations of each species or variable in each of the groups with all other species and vari- ables in that group were calculated, and for one group standard partial regression coefficients were calculated. For supplementary 4. information, species-area curves were constructed for all five gradient segments, and ordinations of the species in relation to two environmental variables were calculated for all but one of the segments. A high proportion of significant coefficients suggested that association patterns were common among the Species in the study area. Correlations of the species with the particular environmental variables chosen for analysis, however, were not nearly so convincing. The validity of the techniques is suggested by the overall agreement of the coefficients with field observations. But in individual cases there were sur- prises, in that some associations were observed in the field only after the calculations had suggested their presence, and others were not visually evident, suggesting that the techniques are useful in detecting associations and do not merely elaborate the obvious. The various coefficients were useful in formulating hypo- treses concerning the roles of these species in the community and in advancing possible explanations of the mechanisms produc - ing each of the association found. Certain of the possible hypotheses appeared to be mutually exclusive, leaving a residuum of compatable ones some of which complemented one another. This also provides corroborative evidence for the validity and value of the techniques as used here. The species—area curves seem to indicate that sampling was adequate to characterize the area in all but one segment of the gradient. The ordinations show some possible trends in the correlations of species with environmental parameters, and shifts in these trends along the gradient. They seem to show also that the association between two species cannot be predicted on the 5. basis of their similarities or differences in tolerance ranges with respect to only one or two environmental variables. By way of background, a review and discussion of litera- ture pertaining to the whole field of pattern is presented below. In this way, the relative merits and peculiarities of the techniques used here will be more fully understood. B - PATTERN CONCEPTS The present state of our ecological knowledge makes it fairly clear that species in nature are not merely randomly dispersed within supposedly "homogeneous" communities and associations. Men have known at least since the dawn of history that plant species have definite habitat preferences, and that they therefore exhibit non-random distribution on a grand scale. Curiosity concerning these distributions and their causes, in fact, was a major factor leading to the beginnings of plant ecology. It was soon discovered that certain characteristic groupings of species tended to occur on sites with certain cli- matic and physical characteristics, and these observations, coupled with man's'hatural tendency to pigeonhole" (Gleason 1926), led to various attempts to classify large natural groupings of Species such as the Clementsian "community" (e.g. Weaver and Clements 1938) and the "association" of the zurich-Montpelier School (e.g. Braun-Blanquet 1951). Unfortunately, the Clementsian and Braun-Blanquet systems, as well as other similar systems, emphasized the larger units, 6. giving little attention to the smaller ones. Thus, by implica- tion, the vegetation within these large units was considered to be homogeneous and the plants within them were not examined for small-scale patterns. The "union" of Braun-Blanquet (1951) does recognize such patterns, but little effort is made to explain their causes and significance. However, the physical habitat contains many irregularities (e.g. small hummocks and hollows, boulders near the surface), as does the biotic habitat (e.g. sun- light patterns under a forest canopy, differential accumulation of litter), and these factors interact with each other and with the organisms in the ecosystem in various ways, to which must be added that the organisms themselves also interact directly or indirectly (Odum and Odum 1959). Thus, it is only reasonable that plant species should respond distributionally to the micro- environmental patterns which result, although the situation is further complicated by the non-randomness of dispersal and re- production. Within recent years, concepts and mathematical techniques connected with microdistribution patterns have been developed at a rapid rate. As Greig-Smith (1957) points out, however, the study of pattern is not an end in itself. Instead, such studies should provide clues to the biology of the plants studied and should serve as guideposts for future work of an experimental nature. 1. KINDS OF PATTERN. Odum and Odum (1959) Show that members of a.species population may theoretically be distributed in three basic ways within a community. These are: (l) randomness, where the individuals are distributed with no spatial relation- ship to one another, somewhat like hailstones which have fallen 7. from the sky upon a smooth surface without deflection by air currents or irregularities of the surface; (2) clumping ("superdispersion", "overdispersion", or "arrangement" (Hutchinson 1953), "contageous" distribution (Cole 1949 and other authors)), in which the average distance from one individual to its clos- est neighbor is less than would be expected in a random distri- bution, and variability in these distances is greater than expected in a random distribution, and (3) uniformity (infra- dispersion", "regularity", "order", or "underdispersion" (Hutchinson 1953)), where the organisms approach the arrangement of molecules in a crystal lattice, so that the distances between them show less variability than in a random distribution. Of the three, it is now generally agreed that randomness is probably the exception rather than the rule, if indeed it truly occurs in nature at all (e.g. Hutchinson 1953, Cantlon 1958-59). Clumping would occur if the species were reproductive groups, or drawn to- gether by social instincts or favorable interactions, or associated with patches of more favorable habitat. Uniformity might occur if the microhabitat variation was not critical, but the species in question required a minimum distance between individuals for optimum growth, efficient feeding, etc. (e.g. desert shrubs, territorial birds). According to Greig—Smith (1957) and Odum and Odum (1959): patterns may be either spatial, or temporal (i.e. cycles, succes- sion, etc.). However, the bulk of the existing work has been on two-dimensional (horizontal) spatial patterns, with some work on c301ic patterns (e.g. Watt 1945, l9h7. Kershaw 1958), and some on reproductive patterns which act in a time sequence (cf. Kershaw 1958, Kershaw and Tallis 1958, Phillips 1953. 1951+). In a way, 8. succession is also a pattern in a time sequence, but it differs from cyclic patterns described by Watt in that it is unidirection- al and not self-perpetuating. Studies of seasonal and long term fluctuations (cf. Elton 1949, Weaver and Albertson 1956) fall into the broad category of temporal pattern studies. Vertical layering as well as horizontal spatial patterns should be con- sidered (Hopkins 1957). Hutchinson (1953) has classified patterns into five types according to their causes. (1) Vectorial patterns are those re- flecting spatial gradients in particular environmental conditions; e.g. a pattern reflecting a "mosaic" of different physical micro- habitats in each of which a given species has a different probability of occurence. An example would be frost-fissured arctic tundra, but many vectorial patterns are less striking. (2) Reproductive patterns are determined by the manner in which organisms colonize an area. Thus, a plant which spreads by runners or stolons tends to form clumps or clones, whereas one which spreads by wind-borne seeds might tend towards randomness. (3) Social patterns are limited primarily to animals, and in- clude such things as the territorial patterns of birds (uniformity), and flock and herd patterns as well as colonies (clumping). In animals these patterns are effected frequently by signaling. (b) Coactive patterns are determined by interaction between species. Interspecific association (Cole l9#9, 1957, Goodall 1952, De Vries 1953, Graig—Smith 1957), which applies to patterns involving two or more species and with which this paper deals, is often brought about by coaction, (or interaction as it is called in this paper), between species. Thus, if A is a shade- requiring forest species and B is a root parasite on A, then the 9. two should occur together in patches of shade. Both of them thus show clumping and also positive association with each other. On the other hand, if A secretes an antibiotic substance inhibitory to B, then both might be independently clumped, but the clumps of the two species might be negatively associated with each other. (5) Stochastic patterns depend upon the association of species with certain microenvironmental factors which are in them- selves randomly distributed. An example might be the distribu- tion of plankton in relation to random water currents. Patterns may be thought of either in terms of the way in which individual species are distributed, or in terms of the ecological relationships of species to one another and the "associations" between species. The latter is the tendency of two or more species to occur together more or less frequently than one would predict on the basis of a theoretical random (inde- pendent) distribution, and is the way in which the problem of pattern is approached in this paper. 2. COMMUNITY PATTERNS. Krause (1952) suggests that phyto- sociological associations are arranged in a "mosaic" pattern over the surface of the earth. In this respect he seems to do little except to clarify what should already be evident from the work of the phytosociologists. Whittaker (1956) was able to show somewhat the same thing, with similarly large-sized units, on an altitudinal and slope-directional instead of a latitudinal basis. He perhaps admitted of more intergradation and transition be- tween the units than did Krause. Similar groupings occured in sites with similar moisture and edaphic conditions, within a broad range of altitudes and slope exposures. 10. But the present trend is towards the study of groupings on a smaller scale, which lends itself somewhat more to un— biased random sampling and statistical analysis. Rommell (1930) and Hopkins (1957a) have suggested that vegetation within a broad "homogeneous" stand consists of a mosaic of repeated elements that Hopkins has termed "basic units". The latter Hopkins defines as groupings of species, all of those within one grouping having mutually significant positive correlation coefficients. His procedure involves separating out all spe— cies which are negatively correlated with each other and, using these as centers, building up groups of species which are posi- tively associated with them. Earlier Goodall (1952, 1953) attempted to do somewhat the same thing. Basically, his tech- nique consists of eliminating quadrats containing a particular species or strongly associated species pair from a group, re— calculating correlation coefficients, and repeating the process until a group is left which shows no significant correlations among its species. The "residue" of eliminated quadrats is then repeatedly subjected to the same procedure until all quadrats are placed in some group. Goodall's method seems somewhat in- ferior to Hopkins' for both mathematical and biological reasons, since using the most frequent Species as a starting point as Goodall does seems to involve some bias. Also, one of the groups obtained may readily be a group of more or less "independent" species having broad tolerance ranges, which are not strongly associated with each other or with members of other groups. There is no doubt that patterns are occasionally quite dis_ tinct, and that "basic units" may be quite evident to the causal observer. This is certainly true of the patterns on polygonal ll. ground (Wiggins 1951), where sharp "breaks" in the habitat cause sharp breaks in the vegetation. Certain wetland vege- tation types, such as marshes (e.g. Miller and Egler 1950), and some tussock types (Watt 1947), exhibit fairly distinct "mosaics" of basic units", in which the species from one unit seldom overlap very far into another unit and where all the species of a unit exhibit a high degree of positive associa- tion. But probably by far the most widespread situation in nature, exhibited for example by the herbs of a forest floor, is one in which each species has a reasonably broad tolerance. range with respect to several or many microenvironmental fac- tors (here including the influence of other species). Thus, a species may potentially be able to occur over, say, 90 % of an area, but its probability of occurence will fluctuate rather widely from point to point, so that one could visualize the area in question as composed of "contour lines of probability" for each species. The individuals of each species will be con- centrated at the favorable "peaks" for that species, becoming sparser "downslope", but the species may still be represented by scattered individuals in some of the higher "valleys". Thus, a species may be positively associated with another whose "peaks" coincide fairly closely with its own, providing a deleterious interaction does not occur between them. Thus, various species pairs should exhibit all degrees of peak—coincidence and all degrees of positive and negative association, so that one could not simply classify them into separate groups of positively associated species such as "basic units". I do not mean to completely discredit the "basic unit” and 12. "mosaic" concepts. They can be useful in the classification and description of vegetation, or as a measure of heterogeneity, and in some cases they may be real entities. But perhaps there is too much effort to pigeonhole, or force every species in every situation into some basic unit or other. This may not only be undesirable but, if one is interested primarily in the actual interactive and environmental causes of pattern, unneces- sary. Therefore I would suggest that the continuum concept of Curtis and McIntosh (1951) is as applicable to small-scale as to large-scale patterns. De Vries (1953) found that in many cases two negatively associated species are tied together by one which is positively associated with both, and I have found this to be true in my own work. This is another argument against indiscriminate use of the "basic unit" concept. It is not difficult to see how such a phenomenon might occur, if we view the niche of a plant as multidimensional (Hutchinson 1953, Kohn 1959). Suppose for ex- ample that species A and B, herbs on a pine forest floor, both have a peak probability of occurrence on somewhat more acid patches where pine litter has accumulated in large quantities in the past. B, however, finds the small depressions in the topo- graphy more favorable, whereas A is more drought tolerant and peaks on old blowdown hummocks. For this reason the two might be negatively associated. But species C may have a broader tolerance than either A or B with respect to moisture, and so has a high probability of occurrence both on hummocks and in hollows. If A, B, and C are then all more apt to occur below openings in the canopy, C may "bridge the gap" between the two negatively associated species and show positive association with both. 13. Some work on grasslands (De Vries 1953, De Vries 33 al. 1954) illustrates one useful method of depicting pattern in vegetation without isolating discreet units. Symbols for the species are arranged in a "constellation" figure, with those species which show high positive association placed close together, insofar as possible, and those which show high negative association far apart. Since this constellation attempts to depict in two dimen- sions what is really a multidimensional phenomenon, and since two negatively associated species may both have a positive associa- tion with one or more other species in common, it is not always possible to represent the association pattern by distances alone. Therefore lines of different colors, or of different widths, are drawn between the symbols to indicate the degree of positive association. The positions of the species may be determined more objectively by using the correlations of each species with two environmental variables, as the x- and y-axes for the con- stellation. It is interesting that, in De Vries work, species with mutually high positive associations did tend to be grouped closely together when this method was used, so that there were a few groupings which were quite distinct and similar to Hopkinsian "basic units". But other species were "free-floaters" which were not very closely tied with anything else. An attempt has been made in the present study to arrange the species in "constellations". The ordination technique proposed by Bray and Curtis (1957) was devised to show graphically the relationship of stands to one another in two, three, or more dimensions. Stands are plac- ed.along one axis with two of the most dissimilar stands, as determined by an index of similarity, taken as the end points of 14. this axis. The stands are arranged a distance from these end points which is a function of their degree of similarity to each of the "reference" stands. For the ends of the second axis, two stands which are close together on the first axis, but which themselves have a low index of similarity, are chosen as endpoints. The process can be repeated several times to obtain a multidimensional arrangement. Now when the cover or frequency of particular spe- cies was plotted within the ordination figures, the authors found that most of them showed a peak at some point within the figure. There are drawbacks to the technique, however, in that it uses vegetation itself as a criterion for determining the ecological interrelationships of vegetation, and so is somewhat biased in favor of "proving" what it intends to prove. An "index of amplitudinal correspondence" was devised by Bray (1956) to show how much overlap existed between species fre- quency or cover curves along an environmental gradient. The same teChnique, however, could be applied to individual quadrats with- in an area selected for apparent large-scale homogeneity. The values obtained are similar to other kinds of association coeffic- ients, and Bray obtained good correspondence with Cole's (l9h9, 1957) association coefficients (discussed later). So far, only spatial patterns have been discussed. Tem- poral patterns may be of various sorts, including successional, seasonal, cliseral, and cyclic changes. Since cyclic changes may help to explain some of the association phenomena found in the present study, they deserve some comment. Watt (1947) gives several examples of cyclic patterns. Per- haps the one involving Calluna, Gaultheria, and lichens on wind- swept mountains is the most dramatic. Here, successive "waves" of Gaultheria, Calluna, lichens, and bare ground move across the 15. landscape driven by the wind, each phase being dependent upon the last, and distinct alternating bands of the four stages in that order are evident. In other areas where the same species are abundant, but the wind is not so strong, the same alterna— tion occurs. But here Calluna spreads outward from the centers of clumps and dies in the centers, the latter then being colon- ized by lichens, left bare, and finally reoccupied by Gaultheria and then Calluna. Watt gives examples in the same paper of a cyclic pattern governed by the buildup and decline of tufts of the grass Festuca, and also of a cyclic pattern caused by the rhizomaceous spread and eventual death of the bracken, Pteridium, where the litter of this fern is inhibitory to many other plants. Kershaw (1958) and Phillips (1954) describe similar patterns, but these studies concentrate on single species and so will be discussed in the next subsection. Goodall (1954) used a factor analysis technique to deten~ mine association between species. This method has not gained great popularity, judging from the literature, and perhaps with good reason. Clark (1958-59) says that it is mathematically un- sound, and points out that the method is biased in favor of show- ing whatever one sets out to prove. Bray and Curtis (1957) show that the results may be difficult to interpret biologically, and that their meaning may be interpreted in a number of different ways. For these reasons, factor analysis will not be discussed further. 3. PATTERNS OF SINGLE SPECIES. There is not always a sharp dis- tinction between studies of "community" pattern and studies of "species" pattern as they are delimited here. The studies of 16. Watt (1947), for example, which were discussed above, could be considered species pattern studies if the species involved in the cycles had been considered separately. As an example of this type of study concentrating on a sin- gle species, Kershaw (1958) has done a study of Avrostis patterns in pastures. He found that there were several "size units" of Agrostis patches in most pastures, and he attributed this to its pattern of reproduction, its interaction with other species, and its limitation by environmental variables. Kershaw and Tallis (1958) also showed similar patterns for Juncus tennis and Festuca, and Phillips (1955, 1954) found a similar pattern in Erigphorum. For three species of buttercups (Ranunculus £33.), Harper and Sager (1953) have shown a very striking pattern in pastures which is related to microtopography. One of these three species is associated with the tops of small ridges, another with the sides of these ridges, and a third species with the hollows be- tween the ridges. Experimental work showed that, while established individuals of all three species could survive under the moisture conditions present in all three microsites, seed germination sel- dom occured except under moisture conditions approximating those of their natural habitats. A word could be said concerning patterns in animal popula- tions, although a detailed discussion of them is beyond the scope of this paper. Elton (l9h9), who presents a comprehensive review of this problem, states that animal pattern studies must consider the problem of mobility which does not confront the vascular Plant ecologist. Consequently, it has proven impractical for Zoologists to study associations as intensively as have the plant ecologists. Elton points out, however, that associations are l7. definitely present among the animals, as well as between ani- mals and plants, and in fact Cole's (1949) association tech- niques used in this paper was originally developed for animal parasite-host relationships. "Clumped" and "uniform" distri- butions may indeed be quite marked in animals due to their social and territorial instincts, and the host specificity of some. Transitory variations (temperature changes, light vari- ations, precipitation, wind, etc.) shifting the distribution and the degree of clumping of motile organisms within short periods of time, make the problem of pattern analysis in animals more complex than in plants. 4. TECHNIQUES USEFUL IN PATTERN STUDY. The objective modern methods used in analyzing pattern all depend upon mathematical models and statistical techniques. It is not the purpose of this paper to delve deeply into the mathematical theories in- volved, although all the steps involved in the calculations used in this paper are presented in Appendix A. Rather, I hope to present a brief resume of the logic behind some of the most common techniques which have been used, and to give the reader a general acquaintance with them. Aids which may be used to advantage in studies of pattern are: (1) random sampling, (2) the use of a sample-unit size which will yield the most useful information, and (5) the use of some coding system whereby the data may be sorted rapidly and easily. (1) Random sampling makes the data amenable to statistical analysis and allows one to obtain valid significance tests (Clark 1958-59). Any regular or "grid" sampling pattern is in- clined to hit disproportionately small or large portions of certain elements in a vegetational mosaic, since there may be 18. some regularity in the patterns of species or "basic units", and if the grid is of a particular size it may be laid down so as to avoid or partially avoid a certain Species or vegeta— tion unit. (2) Quadrat size should be larger than the sizes of the smallest patterns present, but not larger than the scale of interaction of the species with one another or with habitat variables (Greig-Smith 1957). If quadrats are of the same order of size as individuals or smaller, negative association will appear simply because there is usually not room for indi— viduals of more than one species in the quadrats. If quadrats larger than the scale of interaction or habitat variability which cause positive or negative association are used associa— tion will not be demonstrated. Since the scale of pattern is not.often readily discernable, and since there may be associa- tion relationships of the same species on several scales, it is desirable where possible to use quadrats of several sizes. The type of community sampled will determine in part the size of the samples used; thus in a desert shrub vegetation the samples would be larger than those necessary to determine the associations of grasses and forbes in a pasture, since in the latter case the scale of pattern for vascular plants is much smaller. (3) Since the determination of association and other patterns involves a lot of sorting for various garaneters, it is often desirable to code the information on punched cards of some kind which may be sorted quickly for various species or species-microenvironmental combinations. One such techninue is described by Goodall (1953), another by Byer et al. (1959). 19. If one is interested primarily in the patterns of a single species, a technique proposed by Greig-Smith (1957), and used by Kershaw (1958), is effective. Cover is recorded in quadrats of various sizes, and the mean square of variability in cover is plotted against quadrat size. The peaks of this curve then indicate the average scales of pattern of the species or size of the clumps. There may be only one scale of clumping or several, with each larger clump itself composed of smaller clumps. The scale of pattern in environmental factors, or of other species, which are thought to be the causal mechanisms of the patterns in the species being studied, can be determined in the same fashion. If the sizes of the patterns of environ- mental factor and species correspond fairly closely, there is a good chance that the factor in question is indeed one of the causal agents of the pattern, as demonstrated by Kershaw (1958). The "distance to nearest neighbor" technique of Dice (1952), and further elaborated by Clark and Evans (1954), is useful in the determination of clumping or uniform distribution. Basi- cally, it involves a determination of the average distance one would expect between individuals if a population of this density were distributed randomly. The actual mean distance is then determined, and a comparison is made with the expected distances, along with a comparison of actual and theoretical variances. The technique can be adapted to measurements of interspecific association of one species with several others, also. In the present paper, we are concerned primarily not with individual species patterns, but with measurements of association between two or more species. There are two ways of approaching this problem, each of which answers a somewhat different ques- tion. These are: (1) simple association techniques, which 20. attempt to discover whether two or more species occur together in a given sized sample more frequently (positive association) or less frequently (negative association) than would be eXpected if the individuals of the species were randomly distributed with respect to each other, and (2) correlation,techniques in which we attempt to determine whether or not high cover values of two or more species are randomly distributed with respect to each other. III METHODS 21. A - FIELD AND LABORATORY TECHNIngS The study area is located on Michigan State Forest land in southern Crawford County, Twp. 25 N, Range 5 W, Sec. 50 S.E. It is in the northern part of the lower peninsula of Michigan, about one mile west of Route M 18-76 between the towns of Roscommon and Grayling, west of the point where this road runs north-south. It is also about one mile east of the northwest corner of Higgins Lake. Its location is shown in Figure l (p. 22). Crawford county is located in what is known as the "Jack pine area" of Michigan. It is characterized by extensive plains of sandy Pleistocene outwash, which have developed into very weakly Podzolized Grayling soils on the drier sites and into other, more heavily podzolized soils on moister sites. These outwash plains support, in the present day, a vegetation consisting predominantly of open forest of Pinus banksianai/and of open grassy Jack pine savannas. On the hilly sands of the moraines, a soil closely related to the Grayling soils is developed, which is called Roselawn sand. For some at present unknown reason, these moraines support a cover of oaks (particularly Quercus rubra, g. 3393, g. elipsoidalis complex), with fewer pines, but the understory vegetation on Rose- lawn and Grayling sands is quite similar. Both of these soils are submarginal for agricultural purposes, and consequently a great deal of Crawford and surrounding counties are in State Forest land. Smaller tongues and patches of more fertile soils, of the same age l/ All scientific names of vascular plants cited in this paper follow the eighth edition of Gray‘s Manual_g£ Botany (Fernald 1950). F‘ e If , CD . J-A LIGEND, Fig. 1c m Dawson—Greenwood Peat Grayling Sand Grayling Sand, gravelly Rifle Peat Rosconmon Loony sand Boselawn Send, gravelly Roselawn Sandy Loam, gravelly Saugatuck Send — Highways -— Secondary roads --‘~- Trails Section lines ‘ D Study area FIGURE 1. Location of the study area. A. Map of Michigan, with Crawford 00. and part of Roscommon Co. shaded, dot showing location of the study area. B. Portion of highway map showing the shaded area of ‘- dot showing the study area. c. Detail from a soil map, shaving four sections in Crawford 60.. Twp 25!. R 3'. (A from Veatch. Schoen- nann. and Moon 192b,, G fran Michigan Department of conservation 192?). 23. as Grayling and Roselawn or older, are present, and are often farmed. Also, several kinds of peats and mucks are present, which have developed in potholes in the Pleistocene drift or along streams. Almost all soils in the area are glacial in origin (Veatch 1953). The sampling universe was an area of 100 X 100 meters, situated so that it encompassed a fairly broad soil and mois- ture gradient. The northern side of the area consists of an open Jack pine forest on dry Grayling sand (Figure 2-a, p.2# ). The southern side is a bog dominated by a thick stand of Leather- leaf shrub (Chamaedaphne calyculata) vegetation on a mat of Sphagnum moss. The soils are Dawson and Greenwood Peats. In the study area, scattered individuals of Black spruce (Picea mariana), Tamarack (Larix laricina) and stunted Pinus banksiana occur on the bog mat (Figure 2-b, p. 24). In other places in this bog Picea and Larix form quite dense stands. The bog mar- gin (Figure 2-b) within the sample area is a dense stand of mature Picea, Larix, and Pinus banksiana. In some places the Legig and Eigga predominate, while in other spots Pinus banksiana forms the margin and gives way directly to open bog vegetation. This gradient, though fairly abrupt, included enough area on the soil types transitional between Grayling and Dawson-Greenwood Peat for statistical study. Ring counts on the largest Jack pines suggested that the tree vegetation had been relatively undisturbed for about 60 years. Charcoal in the soil profile both on the upland and in the bog indicated past fires. Since no fire scars were found on any of the living trees in the area, the last fires probably occured around 1900. The absence of recent stumps suggests that We a; "a ~51. 17.1 - FIGURE 2. A. Jack Pine forest near the study area. The transition from Carer-Danthonia understory in the foreground to Pteridium in the background corresponds approximately with the Grayling Sand to “Wet Grayling" transition. 3. Leatherleaf bog on Dawson-Greenwood Peat in the study area, showing bog margin vegetation at the left and in the background. 25. there has been no cutting since then either. A Jack pine-Leatherleaf bog transition was chosen for the study because the "dry" (Jack pine upland) end of such a grad- ient is on the poorest inorganic soil of the region, and the "wet” (Leatherleaf lowland) end is on the poorest organic soil, which is extremely acid and poorly drained. Consequently, the total flora of such a gradient is small, reducing the number of vari— ables which must be considered both in calculations and in inter— pretation of the results. Also, this gradient is ecologically broad enough so that only two species (Pinus banksiana and the Low sweet blueberry, Vaccinium augustifolium) bridge the entire gradient from the driest to the wettest soil type. This means that broad-ranging species must of necessity have different associates along the gradient and must exist under different en- vironmental conditions. Furthermore, the study of species associa- tions along an environmental gradient is desirable, since species do not have precisely the same tolerance ranges, and changes in the association of a pair of species, or changes in the associations and correlations of given species with other species and environ- mental variables along the gradient, can tell us more about their ecology than could such analyses in a relatively homogeneous area. After a reconaisance of the study area, the sampling universe was so located that a strip about 20 meters wide occured in the peat, giving a relatively equitable distribution of soil types. Accordingly, along what was to be the east side of the area, a base point was located on the bog margin by a stick thrown over the shoulder. A string was then laid out from the base point along a magnetic north-south compass line, extending 80 meters to the north (towards the "upland") and 20 meters to the south (into the bog). The other three sides of the area were then marked off with 1-.- 26. the aid of a compass and tapes. The area was divided by strings into 20 X 20 meter squares, in order to facilitate location of the quadrats. Four hundred 1 X 1 meter quadrats were located randomly with- in the study area. In order to locate them, the east and west sides of the study area were numbered in one—meter increments from O to 100, starting at the south end of the area. The north and south sides were similarly divided and numbered, starting with zero at the east end. Thus the east and south borders of the area corresponded to two axes, and any numbered point could be located by measurement from these axes. Four hundred four-digit numbers had been chosen from the random number table in Dixon and Massey (1957), before the study area was staked out, and each of these was then considered as two two-digit numbers. Thus "4537" would be "#5, 37", the location of the southeast corner of a quadrat along the ”east" and "south" baselines respectively. A metal frame was used to delimit each quadrat, the south- east corner of the frame being placed at the "base point" (i.e. the point "45-37" mentioned above) and the sides being placed parallel to the sides of the study area with the aid of tapes. Where trees were encountered in a quadrat, the bolts holding the frame were disconnected and the frame then reconstituted around the tree, and where trees lay in the path of one or more sides of the quadrat it was sometimes necessary to lay out the quadrat with tapes and strings. Data for four hundred random quadrats, located in the manner described above, were recorded between early June and late September, 1958. The quadrats were run in four "series" 27. of 100 each, with the first hundred random numbers chosen corres- ponding to the first series, the second hundred to the second series, etc. This was done because certain species (for example Bracken, Pteridium aquilinum, and Wood anemone, Anemone quinque- 32132) are seasonal, and the size of the vegetative parts may vary during this study period. In this way it was possible to sample completely across the gradient in each part of the area at approximately the same time. Each "series" was run systematic- ally by starting at the NE corner of the study area. The NS 20- meter-wide bands, conveniently marked off with the strings, were run one at a time, by working from north to south within each band, and by starting with the eastern-most band and working west- ward. In this way it was usually possible to run quadrats on the driest part of the gradient, in the bog, and on all the inter- mediate soil types on the same day. Admittedly, however, some of the associations, and especially the correlations, such as those involving the two species mentioned above, could still be markedly influenced by the long time span for the sampling as a whole. Thus a negative correlation between two species might mean that they were in their full foliage at different times of year, while a positive correlation could reflect the tendency for the cover of the two species involved to be highest at the same time of year. One might well ask why it is necessary to take so many sam- ples. Species-area curves, which are explained later in this section, show that according to Vestal's (1949) technique, sufficient samples were taken to characterize the segment in at least four of the five gradient segments. However, in a statisti- cal analysis of association, far more samples are necessary than 28. for a mere characterization of the area, and the more samples one has, the more critical are the significance tests and the easier it is to demonstrate those associations that exist. In each quadrat, general character of the vegetation, per cent cover estimates of each vascular plant Species, and presence of each bryophyte and lichen species which occured in the quadrat were recorded. Green soil algae and moss protonemata which were visible were lumped as "Protococcus", and included with the bryophytes, since it was not possible to distinguish between them in the field. Total moss cover, lichen cover, and tree cover were recorded for each quadrat; total shrub and herb cover were calculated later by adding the cover values for all the individual species in each quadrat. For one of the four quadrat series, chosen randomly, light readings were made with a Weston Model 756 sunlight illumination meter,in the center of each quadrat at breast height, on a cloud- less day between 11 AM and 2 PM. A series of five light readings was made in full sunlight, in an open area in the bog, at the beginning of the study, another after 50 quadrats had been done, and a third after values for all 100 quadrats had been recorded. A curve of the values of full sunlight was drawn on graph paper, and values for the quadrats plotted against this curve in order to calculate "percentage of full sunlight" for each quadrat. This was done later by allowing 50 spaces between each of the mean "full sunlight” readings on the graph, and plotting the light readings for the quadrats in these spaces in the order in which they were recorded. The estimated full sunlight value at that point could then be divided into the value of that parti- cular quadrat, to obtain an estimate of "percentage of full sunlight". Of course, this technique assumes that an equal amount 29. of time elapsed between the light readings for each quadrat and the next one, which is not strictly true, but since the quadrats were done systematically without interruption the error is probably not serious. Also, full sunlight showed a variation of only about 7 % during the whole period. A soil profile was taken for each of the #00 quadrats, after the vegetation data had been recorded on all quadrats. A rectangular block of soil was cut from the center of each quadrat with a spade, except in those few cases where trees or large roots interfered. In the latter, the block was cut as near the center as possible. The soil data were all taken at the same time, because it was felt that variation in judgment of the demarcation between the different layers of the profile would thus be kept to a minimum. The depth of each of the following layers was recorded in miflimeters: A0 (loose leaf and other litter), A0 (leaf mold, leaves and twigs which are readily identifiable mas such but which are tightly packed and mixed with humic materials), A0 (humus), Al (mixed decomposed organic and mineral materials),H A2 (leached zone), Bl (zone of heavy deposition of iron and organic materials, Orterde), and 82 (zone of lighter iron deposition, unconsolidated) (modified from Robinson 1936, except for the subdivisions of the A0 which are modified from various sources). Depth to glei was recorded, if glei was present within approximately 75 cm. of the surface, as well as the coloration of the B layer. For the peats, only the first three layers (the A0 corresponding to the peat proper), and for the Saugatuck and H Roscommon soils, only the layers through the A2 were recorded. Depth of the peats was recorded with a heavy wire used as a sounding device. All data were quantitative except for the coloration of the B1 and B2, which r . 4v. 30. were more or less subjectively called reddish, reddish-brown, or coffee-brown, in lieu of the Munsel color code designations. On one of the four series of quadrats, the series having been chosen at random, soil samples for moisture, volume-weight, and pH determinations were taken on one day at the end of the study period. All of the loose litter at a point north of the center of each quadrat, just far enough away (10 cm.) from the soil block which had been removed so that the portion disturbed by the soil profile work was not encountered, was brushed aside. A washed soup can 66 mm. in diameter and 100 mm. in height, with both ends cut out with a circular can opener, was driven down verti- cally until its upper lip was flush with the soil surface. The can was then dug out and the surfaces leveled off. Each sample was then pushed into a separate plastic refrigerator bag, as nearly intact as possible, and labeled with the number of the quadrat on a slip of paper placed inside the bag. Each bag was then secured with a rubber band at the top so that moisture could not escape except by slow diffusion through the plastic. The wet weights were determined in the laboratory over a week later, but several bags which were weighed right after they had been broujht back from the field and again just before drying was begun showed no measurable change in weight. Wet weights were obtained by weighing the samples in the plastic bags. It was previously found that the weight of several unused bags, with labels and rubber bands, had a maximum varia- tion of less than 0.02 grams, so an average value for the weight of the bag, label, and band was considered a constant, and sub- tracted from each raw weight in order to obtain the wet weight of the soil sample. For dry weight determinations, the samples 31. were emptied from the bags into 800 ml. beakers, and the beakers of soil were dried in an oven at 105° for four days. The bags, with rubber bands, labels, and all remaining soil and moisture, were also dried for the same period at the same time, but in another oven at #00 C. Both bags and beakers were removed from their respective ovens after drying, and placed in dessicator jars to cool. The soil samples were each placed back in the proper bags and immediately weighed, and constants for bag weight, etc., weretnbtracted as before. The volume of the soup can used to take the samples was later calculated in order to obtain dry weight of each soil sample per cubic centimeter. The per cent moisture of the samples was calculated simply by dividing wet weight into wet minus dry weight, and multiplying by 100. In the peat soils, pH and moisture vary so much between one portion of a quadrat and another, because of the hummocky micro- topography, that it was hardly worthwhile to determine values for the individual quadrats for use in the association and correla- tion analyses. Accordingly, five of the quadrats were chosen at random, so that a rough average could be determined which would be useful in describing the peat area. PH values were determined for each sample in the laboratory with a Beckman pH meter. For this purpose, a level Spatula of soil, from one inch below the top of each sample, was diluted with 10 cc of distilled water. The pH meter was calibrated periodically against Beckman buffer solution. B - ANALYSIS TECHNIQUES The data for each quadrat were punched into an "MSU-Bot" modified Royal—MacBee keysort punch card of the type described by Byer gtngi. (1959). These cards may be easily and quickly 320 sorted with a special sorting needle for values of environmental variables, or over a template if one wishes to determine cover values of species, co—occurence of species, or the cover values in each quadrat of two or more species for use in calculating correlation and regression coefficients. The quadrats were separated into seven groups by soil type. The descriptions of the various soil types were taken from McKenzie and Whiteside (1956). Unfortunately, there is usually no single criterion for separating a given soil type from other soil types along the gradient, and soil scientists, like vege- tation scientists, seldom seem to set exact limits to their types. In order to make the separations as objective as possible, two or more criteria were used for each separation, except where a single criterion was given in the reference. The criteria used for separation are listed in appendix B. These criteria are based upon the descriptions, and insofar as possible an attempt is made to strike an average between the descriptions of two ad- jacent soil types in the separation. Hence the soils here de- limited correspond as closely as possible to my interpretation of McKenzie's and Whiteside's classification. This technique was sufficient to place all but about 20 of the #00 quadrats into one of the seven soil types. The remainder were referred back to the published description, then placed as objectively as possible by scoring them "1" or "2" for each characteristic according to whether they were closer to the "drier" or "wetter" of two possible soil types, respectively. Those with more "1"s than "2"s were assigned to the "drier" soil type, those with more "2"s to the "wetter". Sometimes it was necessary to use discretion in the assignment of quadrats to a soil type; 55. i.e. since many of the types are delimited on the basis of the depth of various horizons in the profile, and since the profile depth is dependent upon the age of the profile at a particular spot as much as upon the moisture regimen, recent blowdowns with profiles shallower than normal must be treated individually. In no case did a soil profile show characteristics of more than two soil types, so it was never necessary to decide be- tween three or more. The attempted objectivity in the assignment of quadrats to certain soil types may have certain drawbacks. One is that a few of the quadrats may not correspond, from a Pedologist‘s viewpoint, to the soil type to which they are assigned, des- pite all efforts to take age, etc., into consideration. Slight inaccuracies in soil classification, however, may be the cost of statistical objectivity. Furthermore, it is not necessary in this study that all quadrats be assigned to a correct soil type, only that they be placed in relatively homogeneous groups. 0f the 400 quadrats, the original breakdown found 166 in the Grayling sand and only 101 in the Dawson-Greenwood Peat, showing that a slight misjudgment had been made in laying out the sample universe, giving more area on the dry end. There were not enough quadrats for statistically critical association analysis in some of the intermediate soil types. There was enough vegetational variation within the Grayling, however, so that a further separation seemed justifiable; accordingly #6 Grayling quadrats which had a deeper A2 than the rest and gener- ally better profile development were selected out as an inter- mediate soil type and called "wet Grayling". This does not 54. correspond to any soil type in the pedologists' classification. Also, after the initial separation, 15 of the quadrats in the Saugatuck soil type having characteristics close to Roscommon soil were removed and placed with this adjacent soil type. This was done so that the Roscommon quadrats could be included in the association analyses, for the sample of this soil type was not sufficient. These "wet Saugatuck" quadrats were always consider— ed part of the Roscommon soil and were analyzed with it. The criteria used in this paper for the separation of soil types are listed in Appendix B. Because of vegetational similarity and because there were so few quadrats in Greenwood Peat, the Dawson and Greenwood Peats were lumped into a single type. Thus the #00 quadrats were placed in a total of seven different soil types. A map of the study area, showing a distribution of the soil types, is presented in Figure 3 (p- 55). This map was made by first locating the quadrats on graph paper and marking them in with symbols indicating the soil type to which they belonged. Lines were then drawn separating groups of similar symbols, and these lines were then traced on a plain piece of paper. In the species-area curves, the horizontal axis of each curve represents the cumulative total number of quadrats, or total area in square meters, the vertical axis represents the cumulative number of species encountered. With the punch cards, it was possible to run the cards for each soil type over a template in a random order and to blacken in spaces on the template for species encountered as the cards were run over it one by one. Thus only new species showed up as unblachened spaces. Any new species encountered in each quadrat were recorded by moving the points for that quadrat a number of units up from the point for n 0‘..— .HO g Hflou .M gaHh Jone .33 “dom vein—0090 “duh «Balsa I van 8§oonofl v.3» no.5 3 5555 can» 3259.6 ' ..wdflhdna so}. /////I can manage D .. ’1a11;z ....;a44 . I I II I I I I Illplltoal I If I: ..... 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Ill IIIIII/I III/I lI/I/I/l/II/II/I/I/II/IIIIIIII/I/ a I/lI/II/l/IIII/l/IIII/I/l/l/IIIII/ I/II/I/II/IIII I III/I’ll I‘I I/I/l/I/ III/I III/III/I/I/II/I/l/I/I/I/I/I/I/l/ NU o II/IIIIII/II/IIIIIIIIIIIIIIIIII III/III!!! II/IIIIIJVIT II III/III] 111/! ///II//////////////////////////// . ////////l/II/////////////////I III/I I II I/ II if II III/III! I/II/ ll/I/III/Il/II/l/IlI/II//IIIIIIII V III/ll/IIIIIII/IIIII/I/IIIII . I III/III II .I III/III! III/I Il/l/l/l/lI/lIII/III/IIIIII I . III/II/IIIII III/I b: . III/I’ll?) I? .I II III]! IIIIIII/IIIIII/JIIIIIIIIII . . IIIIIII IIIII.ll .. , u Ill/IIIII’III/IIIIIII ‘ ’. . III/IIIIIIIIIIII 4yuunauuu,uJ,. ,lrll \ 33 in ....é+ 2...;252???? . . v v : a 36. the last quadrat, along the vertical axis of the graph, corrGSpond- ing to the number of new species in the quadrat. The per cent frequency and the average per cent cover of each species were calculated for each of the seven soil types. The average values for the following variables were also calcu— lated: thickness of the AOL, Aom, AOH, Al, A2, B1’ B2, total B layers of the soil profile, depth to glei, per cent of quadrats with glei evident, per cent cover of lichen, bryophyte, herb, shrub, and tree layers, per cent of full sunlight, soil pH, per— cent of moisture in the soil, and dry weight of the soil per cc. Next, the second and third soil types along the gradient (starting with Grayling, at the "dry" end, as the first and work- ing "down—gradient"), were combined into one group, as were the fourth and fifth, so that there would be enough in each group to warrant statistical treatment. With this rearrangement, there were five groups of quadrats, the smallest of which contained 28 quadrats. I Cole association coefficients were then calculated for each of the five gradient segments, for all possible combinations of those taxa (32 in all) which occurred frequently enough to warrant such analysis. The Cole coefficients for each segment were then arranged in a matrix with that pair of species having the highest positive coefficient taken as a point of reference. The most fre- quent species of this pair was designated the "reference” species, and all other species were arranged relative to it in the order of their decreasing positive and increasing negative Cole coefficients with it. Thus the species having the highest positive Cole coefficient with the ”reference" species was placed adjacent to it in the table, that having the second highest 37. positive coefficient with it next, etc., until the species ex- hibiting the highest negative association with it was placed the greatest distance from it. The original plan was to include in the analysis only those species which occured in 20 or more quadrats in each gradient segment. However, since some of the types included only a small number of quadrats, it was necessary to reduce this figure in some cases. The gradient segments, with the corresponding mini- mum numbers of quadrats in which a species had to be present in order to be included in the Cole analyses, are listed below, starting at the "dry" end of the gradient: Grayling..................... 20 Wet Grayling-Croswell........ 20 Au Gres-Saugatuck............ 15 Roscommon (with "wet Saugatuck")....... l2 Dawson-Greenwood............. 20. If a species occurs in most or all of the quadrats, the Cole co- efficients will be just as invalid as will coefficients involving a too-infrequent species. Accordingly, the median cover value for such species was calculated, and the species were counted as absent if their cover value in a quadrat was below the median value. Zero-order correlation coefficients with tree cover, and with depth of the A0 layer, were calculated for each vascular species for which H Cole coefficients had been calculated on Grayling, Wet Grayling-Croswell, and Au Gres-Saugatuck. The same was done for the vascular Species on Dawson-Greenwood, ex- cept that per cent of moss cover and depth of the unconsolidated organic mat were used as the environmental parameters. The number of quadrats in Roscommon was considered too small to warrant this type of analysis. 38. These correlations of the vascular species on four of the soil types with two environmental parameters were used in con— structing combined "ordination" and "constellation" figures, the two environmental parameters being used as X and Y axes. The species were placed in the figures according to their coordinants on these axes, and lines were drawn between those pairs with high positive and high negative Cole coefficients. The magni- tude of the Cole coefficients is indicated by the breadth of the lines connecting the species symbols. The vascular species for which Cole coefficients had been calculated were broken down into six groups for further analysis, and particular environmental variables were included with some groups. The information obtained for each of these groups was: (1) Zero-order correlation coefficients for all possible species- species and species-variable combinations, (2) highest order par- tial correlation coefficients for all such combinations, and (3) multiple correlation coefficients of each species or variable with all of the others in the matrix. In addition, standard par- tial regression coefficients were calculated for all possible 'combinations in Group I, but they were not calculated for the other groups because of the time involved, and because those obtained for Group I were all very similar to the corresponding partial correlation coefficients. The matrices of the various coefficients were studied for each group, taking into consideration also the association and correlation coefficients of the species and variables in each group with other species and variables not included in the group. Possible postulates for explaining the results were listed. 39- Certain postulates were mutually exclusive, and others were in direct contradiction with field observations, thus leaving a set of hypotheses for future experimental testing. C - EXPLANATTCN OF ASSOCIATION AND CLRRELATION TJCEHIQUES 2F USED IN ”n3 'Rhsewr STUDY- (1) Cole association coefficients are a widely used method for determining association. These coefficients, which are al- ways between minus and plus-one, can be calculated by any of several formulas (i.e. De Vries_g£_al. 1954, Goodall 1952), but perhaps the best known are those proposed by Cole (1949, 1957). The latter is used here. The calculations of this coefficient and of the chi-square test of significance for it, are given in Appendix A-l. (2) Zero-order correlation coefficients. The calculation tech- nique for these is given in Appendix A-2. They are comparable to the Cole Association Coefficients, except that they are based upon cover (in some other studies density), and they thus show whether or not high cover values of the species tend to occur together, not merely whether or not the species tend to be present together. g/ Except for the equations for the Cole Coefficient, Dr. Phillip J. Clark of the Department of Zoology, Michifian State University, devised the techniques presented here and in Appendix A. Many of the ideas for analysis are his also. #0. Quantifiable environmental variables as well as species cover values may be included, and thus species-microhabitat correla- tions may be obtained. Like the Cole Coefficients, these vary between minus and plus one. (3) Partial correlation coefficients. The technique for obtaining highest-order partial correlation coefficients is given in Appendix A-B. They differ from the zero-order correlation coefficients in that they show not the situation in nature, but what the tendency for high cover of two species to occur together or not to occur together would be if a number of other variables were held con- stant (partialled out). This is in a sense like a consideration of the two species only in those parts of the area where they occur. Thus, it is somewhat analogous to removing from considera- tion that part of the area where two species are not abundant, or where their probability of occurence is low. If one wishes to pin down exactly the particular variables which influence the association between two species, it is poss- ible to partial out only one variable or any combination of variables at one time. But only the highest order partial corre- lations were calculated for this study, due to shortage of time. These are the correlation coefficients between two variables when all other variables in the matrix have been partialed out. (4) Multiple correlation coefficients. The formulas used in finding and testing these coefficients are given in Appendix A-#. Multiple correlation coefficients are simply the correlation of one species or variable with several other species and/or variables at once. In this study, they are run for each species 41. and variable in each correlation matrix against all of the other species and variables in that matrix. Because they are less specific than the other coefficients mentioned here, they are perhaps not as useful. But they do give a clue as to whether a species is a "dependent" or a fairly "independent" one within a community, e.g. whether or not it is greatly influenced by microenvironmental variation and/or association with other spe- cies. Unlike all the other coefficients mentioned here, multiple correlation coefficients vary between zero and plus one, making no distinction between positive and negative association. (5) Partial regression coefficients may be found by the for- mulas given in Appendix A-S. The regression coefficients are more critical than partial correlation coefficients in that they show the association of each member of a variable pair with the other. Because the standard partial regression coefficients require several times as much calculation as the highest order partial correlation coefficients when both are found by the matrix method, it is probably best to use the latter if time is in short supply, and if an electronic computer is not available. IV RESULTS A - DESCRIPEICU CF Tin AREA 1. VBGJTATION.-The general character of the area has been treated in the introduction and methods sections. The total flora of the study area is shall. The 400 1 X 1 meter quadrats were found to contain a total of only 8% vascular species, 24+ bryophytes, and 6+ lichen speciesfé not including mosses and lichens on the upright branches of trees and shrubs which were not recorded. Thus 114+ embryophyte and lichen Spe- cies in all were found in the quadrats. A thorough reconnaisance of the area showed only three other vascular species to be present, as listed at the end of Table 1. It is possible that an additional small number of species, present in very low abundance, was not encountered. .2/ Species of Sphagnum and cup-shaped species of Cladonia (pyxidata-group) were lumped in the analysis, since they were not identified in time, hence the "plus" signs after the figures for bryophytes and lichens. Proper identifications would raise these figures by 5 or 6 species, at most. Voucher specimens of most of these species are on file in the Michigan State University Herbarium. This includes all taxa studied in the association and correlation analyses. 43. The species-area curves (Figures A, 5, p. 44—45) rise to a height which is a function of the richness of the flora. The rapidity with which the curve rises is also dependent upon the richness of the flora (Hopkins 1957). It is thus evident that the flora of Roscommon is the richest, that of Dawson— Greenwood the poorest. Grayling is intermediate between the two, and the total flora seems to increase slightly from Grayling through Au Gres-Saugatuck, going from the "dry" end of the gra- dient towards the bog margin. A quantitative description of the vegetation of each seg- ment of the area is presented in Tables I (p. 46-53) and II (p. 54- 59). Grayling sand (G)fl/ is characterized by Pinus banksiana as the only dominant in the tree layer, the pine forming a semi- closed canopy. Prunus serotina (Black cherry) is of sporadic occurence as a large shrub. Vaccinium angustifolium (Low sweet blueberry) dominates the shrub layer and is nearly ubiquitous, and Comptonia pgregrina (Sweet-fern) occurs sporadically but is fairly frequent in the quadrats. Among the herbs and ground shrubs, Carex pensylvanica (Pennsylvania sedge) is definitely dominant with high average cover, and occurence in nearly every quadrat. More or less in order of importance, other common mem— bers of this layer are Pteridium gquilinum (Bracken), Melampyrum lineare (Cow-wheat), Gaultheria procumbens (Teaberry), n E/ Appendix C-3 lists these symbols, and the soil types to which they correspond. .0093 Son xodacwsamtuoue 54 can .Haoxmouolwazmoko no: .maaahouw no.“ .uobhso dean-0303 on 1+4. avenge mo hop—Ba Haven. a he! Modagmnuouc 3 .3235... "Houuaorwuzhauc so: IIIIIII Meghan at ..: amps: 60.305028 .0 «com. 1009 _ #5. .393 ion vooruoonoaaouxun and 55833“ .3.“ :53 00.27.3303 .m HMDGHH conga. mo hoe-"8 Haven. up is vacanoouounoatdn llllll a. noguuom echoes—«80L too #6. TABLE I SUMMARY OF PER CENT FREQUENCY ACROSS THE GRADIENT* Species Soil Type # VASCULAR G ‘WG 0 AG Acer rubrum. (h) - - 1.52 - Amelanchier humilis (s) - 2.17 9.09 - (h) 0.83 - 1.52 7.1a Amelanchier "large toothed" (t) - - - - (3) " " - 3057 (n) - - - - Amelanchier oblongifolia(t) - 2.17 1.52 - (s) 4.17 2.17 4.55 7.14 (h)10.00 8.70 15.15 lh.29 Amelanchier sanguinea (t) - - - 3.57 (s) - - 3.03 3.57 (h) "" "' 1052 7011‘ Anemone quinquefolia 20.00 15.22 9.09 - Antennaria neodioica 3.33 - - - Apocynum androsaemifolium 3.33 2.17 - - Arctostaphylos uva—ursi 6.67 10.87 - - Aster "hairy ovate" 8.33 6.52 7.58 3.57 Aster laevis 13.33 10.87 6.06 - Aster "lanceolate" 0.83 - 1.52 - Aster macrophylla - 2.17 1.52 - Bromme ciliatus 0.83 - - - Campanula rotundifolia 2.50 - 1.52 - * See page 53 Species Carex "fine" Carex pedunculata Carex pensylvanica Chamsedaphne calyculata Connemara umbellata "Composite small narrow" Comptonia peregrine Coptis groenlandica Cornus canadensis Cypripedium ac aule Danthonia spicata "dead bush" Epigaea repens Eriophorum spissum F‘ragaria vesca Gaultheria procumbens "grass big hairy" "grass smooth" "grass smooth broad" * See page 53 1+7. TABLE I continued G 3.33 2.17 10.83 6052 9009 10071 " WG Soil Type # C AG 3 R - - - 3.45 3 .45 DC 98033 97083 9309‘} 82.14 190000 30‘55 '- 0.83 - 3057 20.00 58.62 100.00 1.52 3057 -' " 16.67 21.74 48.48 50.00 30.00 3.45 10.61 35.71 50.00 10.34 2.17 7.58 39.29 60.00 17.24 6.06 7.14 - - 19.1710.87 4.55 - - .. 1.52 3057 - - 4.17 8.70 31.82 57.14 10.00 13.79 1.67 - 3057 '- 37.93 48.51 32.50 60.87 87.88 96.43 100.00 $.62 0.99 1.67 2.17 0.83 0.83 Q8. TABLE I continued * Species Soil Type # G HO O AG 8 R DG Hieracium venosum 2.50 - 9.09 - - - - Ilex verticillata (s) - - 7.58 17.46 20.00 24.14 2.97 (h) - - 6.06 21.13 10.00 3.65 - Kalmia angustifolia - - 1.52 - 10.00 6.90 6.93 Kama ”111.0118 " " - " - 20069 550165 Krigia biflora - -. 1,, 55 - - - - Krigia virginica 0.83 - .. - - - .. Lari; laricina (t) - - - - 30.00 17.24 11.88 (s) - - - - - — 0.99 (h) - ' 1052 - " 3045 1098 1:de groenlandicum - - - - 10.71 30.00 79.31 31.68 Liatris sp. 2. 50 - - _ .. - .. Lycopodium obscurum - - 12.12 14.29 10.00 - - Maiarrthemum canadense 25.83 34.78 74.24 82.11. 60.00 10.34 - Melampyrm lineare 36.67 30.43 53.03 67.86 40.00 3.65 - Nemoparrthus mucronata (s) - - - 3.57 10.00 13.79 1.98 (h) - - - - 10.00 6.90 - Oryzopsis asperifolia 19.17 15.22 21.12 14.29 0172013818 pungens 16.67 10.87 4.55 - - - - Panicum "basal inflor." 0.83 - - - - - - 'Panicum "broad leaved" 0.83 2.17 - - - - - Panicum "narrow leaved" 0.83 - - - - - - Panicum sp. 0.83 2.17 - - - - - * 300 page 53 49. TABLE I continued* Species Soil Type’glg G WG C AG S R DG Picea maflana (t) 0.83 - 1. 52 7.14 50. 00 41.38 14.85 (s) - - - 10. 00 10. 34 3.96 Pinus banksiana (t) 97.50 95. 65 87. 88 92. 86 1.0. 00 21.11. 6.93 (s) 1.67 1. 52 3.45 1.98 (h) 0.83 2 .17 - - - - 1.98 P211115 resmosa (to) 0.83 " - - " 6090 0099 (s) 0.83 - - - - - - (h) - - 1.52 - - - - Pinus strobus (t) - - - - - 6.90 0.99 (S) "' - - " " " 2097 Polygonum sp. - 2.17 - - - - - Populus grandidentata (t) - — 1.52 - - - - Populus tremuloides (t) - 2.17 - 3.57 10.00 3.45 - s) — - 3.03 - - - - Prunus serotina. (t) 1.67 - 6.06 17.86 10.00 - - (S) 7.50 1 .22 12.12 21.43 - " " (h) 10.80 8.70 18.18 35.71 40.00 - - Prunus virginiana (t) - - - 3.5 - - - (S) 0.83 - - - 10000 3014-5 - (h) 0.83 - - - ' ‘ ' Pteridiun.aquilinum. 61.67 76.09 65.15 53 57 10.00 - - Quercus rubra (s) 5.00 4.35 - - - ’ ‘ (h) 2.50 - - - - - - Ribes (3) 0,33 - - - - - - "dull" (h) 0.83 - - - - - - Ribes "seedling" (h) 0.33 - - - - - - Ribes ”shim" (h) - - 1.52 3.57 - - - * See page 53 Species Rubus canadensis Rubus hispidus var. obovalis Rubus idaeus "snag unidentified" Solidage "lanceolate long petiole" 10.00 13.04 Solidago IMarrow" Solidago rugosa Solidago "sessile" Solidago ."8harp teeth" Solidago -"white bloom" Trientalis borealis Vaccinium angustifolium Var. nigrum Vaccinium.angustif01ium (typical) Vaccinium.mwrtilloides Vaccinium.0xycoccus Viburnum cassinoides Viola adunca * See page 53 500 TABLE I continued* Soil Type)? G WC 0 AG S R DG 9.16 6.52 6.07 14.29 - 3.45 0.83 4.35 43.94 64.29 50.00 13.79 - - 3.03 - - - - - ‘ ' ’ ' 30h5 0.83 0.83 0.83 - — - - - - 0.83 - - - - - - — - — - - ' 0099 1067 6052 150091 71.43 60000 10034 "' 69.17 82.61 93341000010100 75.86 13.86 60.00 71.74 96.97 96.43 100.00 79.31 20.79 0.83 4.35 37.88 50.00 70.00 37.83 1.98 - - - - - 13.79 91.09 (S) - - #055 1‘029 50000 31003 0099 (h) - - - 10.71 10.00 - - 14017 A035 3003 - - - - . . . . I . . . . . o . I . u . . . o . ‘ . . ' 0 - , ‘ v - . 0 ‘ _ . . ‘ 0 O _ . . . O 0 . o . I . . . O 0 ' O 0 h————_— N» I. a a Species Viola "larger" MOSSES Amblystegium varium Aulocomium.pa1ustre Brachythecium.salebrosum Calliergonella schreberi Campylium hispidulum Ceratodon purpurascens "delicate tiny bristle leeved“ Dicranum.undu11atum. "ferny:moss" "ferny big moss" Geocalyx graveolens ? Lsphocolea Piagiothecium sp. Pohlia nutans Polytrichum.commune POIytrichum "little" * See page 53 51. TABLE I continued* Soil Type# G ‘WG C AG S R " 2017 - - " '- - 2.17 — - - - "' "' " "’ - Boll-5 9.17 21.74 18.18 32.14 30.00 13.79 42.50 28.26 28.79 39.29 80.00 48.28 - - - - - 3.45 12.50 2.17 4.55 - - - 43.33 26.09 21.21 14.29 20.00 24.14 - - 3003 - " 30195 1067 - 3003 3057 100% 30105 0.83 - - - - - - - - - 20.00 6.90 0.83 - - — - - 13033 [+035 6006 10071 "’ 6090 - ' - .. - 10.00 6.90 0.99 2.97 6.93 0.99 3.96 1.98 0.99 0.99 Species Polytrichum.strictum "Protococcus" ? Ptilidium Rhyncostegium.serru1atum Sphagnum "big" # Sphagnum "compact" # Sphagnum.p1umosum Sphagnum spp. Tetraphis pellucida ? Tortella "twisted orange stalk" LICHENS "chalky thallus" Cladonia coccifera Cladonia cristatella Cladonia p yxid eta-group Cladonia mitis Cladonia,rangiferina * See Page 53 520 TABLE I continuedit N\O 28.33 23.91 12.12 - 40.83 30.43 22.73 11.67 4.35 1.52 29.17 8.70 9.09 - - WG Soil Type# C AG S R DG 1.52 25.00 70.00 44.83 81.19 .17 10.70 4.55 - - - - .50 .83 2.17 1052 - 6090 "‘ 1.52 - 10.34 5.94 - 12.50 33.33 1CD.00 95.83 33-33 70.83 7.14 40.00 89.66 98.02 - 7.14 30.00 79.31 98.02 20.00 6.90 1.98 3.57 20.00 20.69 5.94 10.00 - - 3045 - 0.99 20.00 24.14 6.93 7.14 30.00 37.93 16.83 0.99 6.90 1.98 55. TABLE I continue d* SPECIES SEEN, BUT NOT FOUND IN QUADRA_T§ Cirsium hillii I Poe pratensis S piranthes lacera * Frequency is based upon presence in randomly located 1 X 1 meter quadrats. # These two Sphagnum "species" are the components of "Sphagnum spp.," two lines down. . Emlanation of soil type symbols is given in Appendix C-3. The symbols in parentheses indicate: (h), herb size class (under 1 foot tall); (3), shrub size class (1 ft-6 ft tall); (t) tree size class (over 6 ft tall). q ‘0. ECL‘ vb. 826. .F A. 01 .» 0° “ nu 51+. TABLE II SUI-MARY OF PER CENT COVER ACROSS THE GRADIENT (VASCULAR SPECIES)* Species 3611 Type# G 'WG C AG S R DG Acer rubrum - - '1' .. .. _ - Amelanchier humilis (s) - 0.01 0.03 - - 0.02 - (h) T - 'r 0.01 - .. - Amelanchier "large toothed" (s) - - - 0,01 - - - Amelanchier oblongifolia(t) - 0.11 0.05 - - - - 0.06 0.15 0.02 0.04 - 0.04 - 0001 0003 0003 000‘]. 0001 - " Amelanchier sanguinea (t) - - - 0.07 - - - "' - 0001 0001 0012 0001 - - "' 0001 0003 0010 0001 - Anemone quinquefolia 0.09 0,05 0.02 - - - - Antennaria neodioica 0.04 - - - - - - Apocynum androsaemifolium 0.02 0.01 - - - .. - Arctostaphyles uva-ursi 0.21 0.10 - - - - - Aster "hairy ovate" 0003 0002 0002 0001 " -' " Aster laevis 0.03 0.03 0.03 - - - - Aster “lanceolate" T .. T - .. - .. Aster macrophylla - T 0.01 - - - - Bromus ciliatus 0.06 - - - - - - Campanula rotundifolia T - T - - - - Carex "fine" 0.02 0.02 - - - 0.07 - Carex.pedunculata 0.45 0.05 0.07 0.25 - 0.02 - * See page 59 Species Carex pensylvanica Chamaedaphne calyculata Commandra umbellata "composite sma11.narrow" Comptonia peregrine Coptis groenlandica Cornus canadensis Cypripedium acaule Danthonia spicata "dead bush" Epigaea repens Eriophorum.spissum Fragaria vesca Gaultheria procumbens "grass big hairy" "grass smooth" "grass smooth broad" Hieracium venosum Ilex.verticillata (s) (h) Kalmia angustifolia Kalmia polifolia Krigia biflora * see page 59 55. 9.75 0.28 0.04 0.01 0.52 0.01 WG 8.85 0.63 0.03 0.03 0.09 TABLE II continued* Soil Type# 4.55 1.25 0.07 0.31 0.02 0.01 0.99 0.03 0.08 0.01 0.09 0.02 AG 3.48 0.01 0.05 0.99 0.39 1.63 0.09 0.01 0.95 S 1.02 4.03 0.27 0.28 0.57 0.05 0.02 0.80 R 0.02 5.99 0.05 0.03 0.18 0.16 0.20 1.93 0.20 0.02 0.37 0.10 DG 23.58 0.66 0.01 0.05 0.31 0.55 Species Krigia.virginica Lari: laricina (t) (s) (h) Ledumlgroenlandicum Liatris sp. Lycopodium.obscurum Maianthemnm.canadense Melampyrum.lineare Nemopanthus mncronata (s) (h) Oryzopsis asperifolia Oryzopsis pungens Panicum "basal inflor". Panicum "broad leased" Panimmn "narrow leaved" Panicwm spp. Picea.mariana Pinus banksiana * See page 59 56. 0.01 0.12 0.09 0.30 0.06 T T 0.33 0.03 T 0.17 0.08 0.05 0.03 T T TABLE II continued* Soil Type; 0.04 1.24 0.25 0.08 0.01 0.68 25.97 27.52 21.15 2 T AG 1.06 0.06 1.04 0.35 0.03 0.31 0.39 S 0.02 0.88 0.16 0.20 0.30 5.03 5.34 0.03 0.37 0016 7.70 10.80 1.20 5.82 14.80 0.11 4.66 0.17 1.58 0.01 1.98 3.21 0.21 0.32 0.06 Species Pinus resinosa (t) (8) (h) Pinus strobus gt; Polygonum.sp. Populus grandidentata (t) Populus tremuloides(t) (e) Prunus serotina (t) (e) (h) Prunus Virginians. gt; 3 (h) Pteridium aquiJinum Quercus rubra (s) (h) Ribes (s) "dull" (h) Ribes (h) "seedling" Ribes (h) "SM" Rubus canadensis Rubus hispidus var. obovalis Rubus idaeus - * See page 59 0.37 0.19 0.03 6.15 6.31. 0.22 0.01 til-38 0.03 57. 0.04 0.09 TABLE II continued* Soil Type # 0.04 0092 AG 0.12 1.59 S 0.19 Species "snag unidentified" Solidago "lanceolate long petiole" Solidago "narrow" Solidago rugosa Solidago "sessile" Solidago "sharp teeth" Solidago "white bloom" Trientalis borealis Vaccinium.angustifolium (typical) Vaccinium angustifolium var. nigrun Vaccinium.myrtilloides Vaccinium.oxycoccus * See page 59 58. 0.03 0.01 1.67 2.86 0.01 1%} 0.03 0.04 2.08 5.02 0.17 TABLE II continued* Soil Type# 0.20 3.78 4.25 0.55 AG 00% 4.36 5.39 1.61 S 0.29 2.61 2.99 3.27 0.03 0.27 4.09 4.48 2.07 0.08 0.01 1.20 0.89 0.01 1.65 59. TABLE II cont inued* Species Soil Type# G WG C AG S R DG Viburnum cassinoides (s) 0.12 0.49 2.22 1.24 (h) " " - 0003 0003 ‘- 0'3 Viola admca ' 0 .03 T '1‘ .. .. .. _ Viola — '1‘ .. .. - .. .. ”larger" * Explanation of soil type symbols is given in Appendix 0-3. The symbols in parentheses indicate: (h) herb size class (under 1 foot tall); (3) shrub size class (1 ft. - 6 ft. tall); (t) tree size class (over 6 ft. tall). 60. Maianthemum canadense (False lily-of-the-valley), Orzzopsis asperifolia (Harsh-leaved mountain-rice), Q. Dunrens (Sharp- pointed mountain-rice), Danthonia spicata (Poverty-grass, which is very lush in a few patches but which has a relatively low frequency), Anemone_guinquefolia (Wood anemone), Aster laevis (Smooth aster), and Viola adunca (Hooked violet). Important 5/ mosses on the dry end are Dicranum undulatum— , Calliergonella schreberi, and Polxtrichum commune; important lichens are 5/ Cladonia pyxidata-group— , ("cup" Cladonias), g. rangiferina, .9. cristatella, and g, mitis. 0n Wet Grayling Sand (HG) and Croswell Sand (0), the cover of Pinus banksiana remains about the same as on Grayling. Some of the other characteristic dry end species, however, begin to drop out here, notably Anemone quinquefolia, Aster laevis, Danthonia spicatai Oryqusis pungens, Viola adunca, (nearly disappearing), Dicranum undulatum, Polytrichum commune, Cladonia cristatella, g, pyxidata-group, g, mitis, and 9, rangiferina (the last two nearly disappearing). Comptonia peregrina, Gaultheria procumbens, Iaianthemum canadense, VaCCinium angusti- folium increase in importance on this soil type. Species import- ant farther down the gradient, appearing for the first time in the samples here, are Coptis groenlandiga_(Goldthread Canker-root), Cornus canadensis (Bunchberry), Ilex verticillata (Black alder), 2/ Bryophyte nomenclature follows Grout and Evans (l9H0). é/ Lichen nomenclature follows Hale and Culberson (1956). 61. Rubus hispidus var. obovalis (Obovate bristly blackberry, which increases rapidly on Croswell), Viburnum cassinoides (Nitherod) and Sphaanum spp. In addition certain species which are very rare on Grayling, such as Epigaea repens (Trailing aroutus,May- flower), Trientalis borealis (Star-flower) and Vaccinium myrtilloides (Sour-top-blueberry), become fairly common here, though not ubiquitous. On AE_Gres-Saugatuck Sand, most of the "dry end" species, which began to decrease in importance on Wet-Grayling-Croswell, drop out completely in the samples. Such are Anemone quinque- folia, Aster laevis, Danthonia spicata, Oryzopsis asperifolia, _Q. pungens, Polytrichum commune, and Cladonia rangiferina. While they do not drop out completely, Carex peusylvanica, Pteridium aquilinum, and Dicranum undulatum, decrease rapidly and become relatively unimportant. The cover of the character- istic "dry end" tree, Pinus banksiana, is fairly uniform over the first two segments of the gradient already described and on Au Gres, but it drops rapidly on Saugatuck and is largely replaced here by Larix laricina (Tamarack) and Picea mariana (Black spruce), giving Saugatuck a "bog margin" aspect. Some species, notably Melampyrum lineare and Prunus serotina, have about the same importance throughout the first three segments of the gradient on the "upland" side of the bog margin. Some characteristic species, which extend farther up the gradient and even into Gray- ling, reach a sharp maximum here, particularly Epigaea repens, Coptis groenlandica, Cornus canadensis, Gaultheria procumbens, Ilex verticillata, Maianthemum canadense, Rubus hispidus var. obovalis, Trientalis borealis, and Vaccinium myrtilloides. Vaccinium angustifolium, which is quite extensive on the drier soils of the gradient and a dominant in the shrub layer on Grayling, none- 62. theless reaches a maximum on Au Gres-Saugatuck. "Bog" species which appear for the first time on Au Gres-Saugatuck, mainly on the latter, are Chamaedaphne calyculata (Leatherleaf), Eriophorum spissum (Here's-tail), Ledum groenlandicum (Labrador tea), Nemopanthus mucronata (Mountain-holly), and Polytrichum strictum (large haircap moss), besides the two trees already mentioned, Larix laricina and Picea mariana. Roscommon soil (R), together with Saugatuck, is coincident with the hingeline of the bog. The transitions between the three non-organic or "dry" segments of the gradient, elaborated above, are gradual and almost imperceptable. Here, however, there is an abrupt change in the character of the vegetation, and in fact the quadrats classified as Roscommon contain two quite different associations. Some of them have characteristic "bog margin" vegetation, with a dense overstory of Larix laricina and Picea mariana and some Pinus banksiana. Others appear to be in the bog proper, except that the organic soil layer is not deep enough to be classified as a peat (see Appendix B), and they have a somewhat richer flora than does the peat itself. Upland species which "stick it out" on Roscommon, though their per cents cover drop to a fraction of what they are on Au Gres-Saugatuck, are Amelanchier spp. (Shadbush), Melampyrum lineare, and even Carex pensylvanica and Comptonia peregrina. Pinus banksiana and Vaccinium augusti- folium are present here, and sporadically even on the peat itself. Characteristic Au Gres-Saugatuck species which begin to drop out here are Cornus canadensis, Epigaea repens, Gaultheria procumbens, Maianthemum canadense, Trientalis borealis, Vaccinium myrtilloides, the mosses Brachythecium salebrosum and Calliergonella schreberi. Other species seem to reach their maxima here: Coptis_g£oenlandica, Ilex verticillata, Ledum groenlandicum, Nemopanthus mucronata, and the mosses Tetraphis pellucida and ? Tortella 52, All of the common bog species are present on Roscommon also, though some in lesser quantities than in the bog prOper. In general, this segment of the gradient seems to be dominated either by an overstory of Picea and Larix, with a discontinuous Suhawnum mat underneath, or else by an almost treeless, dense shrubbly vege- tation dominated by Chamaedaphne and to a lesser extent Ledum, below which is a nearly continuous Sohagnum mat. The latter type has a distinct "boggy" aspect. Dawson and Greenwood Peat (D0) are similar to the "shrubby" phase of Roscommon in their vegetation, except that there is less admixture of upland and bog-margin species and the Sphagnum mat is essentially unbroken. Chamaedaphne calyculata is the un- disputed dominant here, forming a nearly continuous cover above the Sphagnum mat, making the bog look superficially, from a dis- tance, like a broad green pasture with scattered stunted Picea, Larix, and Pinus (Figure 2b, p. 2h). The more open places on the mat are occupied by Erigphorum spissum, Kalmia bolifolia (Bog-laurel), Ledum groenlandicum, and Vaccinium angustifolium, the last two particularly on the shallower peats adjacent to the bog margin. Vaccinium oxycoccus, the Small cranberry, thrives on the abrupt and high hummocks of the Sphagnum mat where Chamae- danhne is present, but not too dense. Unimportant constituents are several species which reach their peaks on the upland and bog margin, notably Gaultheria procumbens, Ilex verticillata (occuring here only near larger trees), Nemopanthus mucronata (near trees only), stunted Pinus banksiana, and the mosses BEachythecium salebrosum, Calliergonella schreberi, and Dicranum undullatum. Polytrichum strictum reaches a maximum here, and is 64. a codominant with Sphagnum on the highest hammocks. Perhaps because of the great profusion of dead Chamaedaphne branches here, the upland lichens become somewhat more important on Roscommon and Dawson-Greenwood than they were on Au Gres- Saugatuck. The Chamaedaphne branches seem to serve as a suit- able substrate particularly for Cladonia cristatella and Cladonia pyxidata-group. Looking at the cover of the various layers or synusia in the vegetation (Table III, p. 65-66), lichen cover appears to have a peak on Grayling and another on Roscommon, with the low- est cover on the Croswell and Au Gres soil types. The mosses have a slight peak on Grayling, drop on Wet Grayling and Cros— well, and understandably begin to rise again on the wetter soil types, reaching a maximum on Dawson-Greenwood. Herb cover falls steadily from the dry to the wet end of the gradient as shrub cover steadily rises, the former perhaps being at least parti- ally due to the latter. The curve for tree cover rises gradually from Grayling to Roscommon, then drOps precipitously on Dawson- Greenwood. A general graphic picture of the vegetation and soil profile across the gradient is shown in Figure 6 (p. 67). 2. HON—LIVING VARIABLES.-From Table III and Figure 5, it is evident that on the whole, the soil profile becomes deeper from the "dry" to the "wet" end of the gradient. The study area just falls within the limits of the podzol region in Michigan (Veatch 1953), and the deepening of the profile is due to (l) the increase in podzolization from the dry to the wet end of the gradient (note the increased depth of the A2 horizon in Figure 6 as one approaches the middle of the gradient), and (2) the 65. TABLE III MEAN VALUES OF VARIOUS VARIABLES ON EACH SOIL TYPE* Variables Soil Type G WG C AG S R DG SOIL PROFILE Thickness AOL, mm 13.6 14.1 13.3 14.1 13.2 12.3 12.2 Thickness AQm; mm 14.3 13.1 11.6 14.9 29.1 42.8 62.0 Thickness AoH, mm 28.7 35.2 37.2 57.1 60.0 139.3 579.2 Thickness A1, mm. 26.1 34.9 30.5 37.3 36.0 27.0 - Thickness A2, mm. 9.7 27.0 62.4 86.9 183.8 216.7 - Thickness 31’ mm. 35.4 38.5 32.9 72.5 14.5 103.8 - Thickness 32’ mm 103.2 109.2 110.1 112.5 168.8 89.0 - Thickness B, mm. 138.6 147.7 143.0 185.0 183.3 192.8 - Depth to Glei, mm. 86.1 107.0 123.7 134.8 152.5 92.9 - Percent of quadrats with 15.0 50.0 83.3 96.4 100.0 10030 - Glei evident COVER OF VEGETATI ON IAIERS Percent Lichen 0.69 0.38 0.10 0.01 0.15 0.69 0.17 Percent'Moss 2.95 1.96 0.99 8.42 24.36 55.91 74.47 Percent Herb 18.17 17.20 19.58 21.35 7.71 3.38 2.29 Percent Shrub 5.82 8.66 11.18 15.34 18.25 24.76 29.39 Percent Tree 26.03 26.58 20.80 29.45 37.70 21.72 5.12 PERCENT 01“ FULL SUNLIGIT 12.6 16.7 22.5 33.4 9.33 76.25 84.5 * See page 66 66. TABLE III continued* Variables Soil Type G WG C AG S R DG SOIL pH 4.57 4.25 4.04 4.13 3.45 3.51 3.34 SOILIMDISTUREAWEIGHT Percent moisture in soil 12.6 16.3 19.1. 25.1. 45.5 35.9 65.8 by'weight Gms. dry wgt./cc 1.16 .99 .95 .83 .42 .60 .14 * Explanation of soil type symbols is given in Appendix C-3. .nfio OH I lo n 58.3%. canon segues gen .3 a I Be H oases Haunouauomw .mao Huesonafi aw 80523.3 0.3 03.8”” on» )3 n a Fan , on .08» on mode a“ £33 neuron omenebe son: 6023 a“ 03m?“ flmon a «on wuwawwpawmwon uww Wouuuao ewwmsHSonn .osefieeew the mo seapoon fideuaneb seawaeaesom 4 0 Hannah ones «nae. some H .. p' HEQW apnea o documnflw usnamnmw neouw message 8 68. increased accumulation of organic material (note the increase in the depths of the Ao horizons from the "dry" to the "wet" end of the gradient, Figure 6). The El horizon, where the humus and sesqueoxides leached out of the A2 horizons have been deposited, also tends to increase in thickness from the dry to the wet end, but then to decrease in thickness again, and if the A2 layer were followed far enough into the organic soils it would be found to decrease in thickness and disappear. It is also darker in color, and there is generally a sharper distinction between the B1 and B2 horizons near the wet end. The El shows an increasing tendency towards cemetation from Grayling to Saugatuck (the latter is in fact distinguished from Au Gres by this character), and then cementation tends again to diminish as the bog margin gives way to the bog. The A2 also varies in color, being a light grayish brown on the Grayling, and becomming almost pure white in some of the Saugatuck and Roscommon quadrats, indicating that podzolization may be more thorough on the latter soil types. Per cent of total sunlight at breast height is greatest in the bog proper, with a secondary peak on Au Gres. The lowest light intensity seems to be on the Saugatuck, where tree cover is greatest, and in general light intensity is inversely prop- ortional to tree cover. Though even the dry end of the gradient is fairly acid (mean pH of Grayling, 4.57), acidity increases steadily from the dry to the wet end, until in the bog mean pH is only slightly above 3.0. Soil moisture increases about four- fold from Grayling through Saugatuck, as might be expected, and is highest on Dawson-Greenwood. However, there is a slight drop in soil moisture on Roscommon. Soil dry weight is essentially a 69. reciprocal function of organic matter, which also is reflected in the soil moisture. Volume weights drop from relatively high values on Grayling to low values on Saugatuck. They increase again on Roscommon before finally reaching their lowest value on Dawson-Greenwood. Possible reasons for the ”discontinuity" on Roscommon will be brought forth in the discussion. The peat contains at least two discontinuous lenses of sand, with charcoal below the sand. These are probably the re- sult of fires, which burned over the peat surface, followed by deposition of sand eroded from the denuded upland. The top lens of sand may be connected with the fire of about 60 years ago, following which the present individuals of_Einu§ became establish- ed. If so, the rate of peat accumulation has been about O.l-O.2 inches per year since the turn of the century, which agrees with the generally accepted rate of accumulation (Dachnowski 1921). B - COLE COEFFICIENTS AND CRDINATIONS The Cole coefficients are presented in matrix form for each soil type in Table IV (p.70-73). Ordination constellation diagrams are shown in Figures 7-14 (p.74-8l). Certain generalizations can be made concerning the Cole association coefficients, and the ordination figures which are based upon them. These are listed in the ensuing paragraphs. 1. Positive associations are far more prevalent than nega- tive associations. \\nvZ.—rih>a.uv.~u~ lm‘..a.~L.;.\.~ ~ NV ~1v~r.~...~. «NJ w‘~n~nvn.v II <|> h u:.--QL\ 70. 9.6 gave. 350 #35. Re. can _ 30. So. «8. 38 ..KR.isS. oma. mm. 5.8 .... a. m. .8. a. Q on“. «mm. .5”. 8H. 9:. ma. ~33 a a. pm pfioaficmam . r. :25 ..NN. MN. mfl. meld *mmm. mmm. «3. H23 a m em sausages u .. 55 630.38 0.8 as? .850 cages Nd. awargdm. mm. mm. mwflrams. NH. :93 :33 Emma... 3 e358 38QO not shaman 2.. 38.8338 8.538: So. 80. fl.$nfl.$mos. 43. 30. Na. Na. To washed. .3 Sages 93 3823 u \w 25 sadism“. ma. .5. mm. mm. .5. .28. gm. 3. 3.5 gram. mfi. Hm. Nam. Mm. m3. $8. an... Rates. as. @5013. MN. an. www. Nd. mam. ..omm. Rm. mediating. Q: a. HR. QM. 48. mm. Hfl. wsmfmam. Nod. 3a. 3a. 8a. 3a. Ho: Hm. NM. a. a. «.8. Naming. mariana. «8. m3. fidfimmm. .28. a8 helm. mm. mm. flm. fl. So. flm. 5. ending. 03. tom. .aom. has. .amm. d8 ...mmdfmfl. “Hm. «mum. .mwm. mud. Nam. $4.35. ea. 53m. epitaxis. $3.35. 9 3%.ionww. abudm. Nd. a. a. mud. mam. #mom. Mmm. $4.8. *Hmm.*#qmb.*uoaw.**o$.#n.m3.iooo.a ® Edwiflw. a. gm. .5: flu. s8. «8. a. sou. an. 3. $3.523. sagging $804 9 990 3.5 :3 800 5.5 Q EEO gum hcpm 3.5 mayo 305. and: do: 360 duo 9 g 6 Eggs .mszfioflamoo n38 .. «:3 Eng .2. - '1‘ ‘1— r..- \N.u. h n.\_(— F h> ‘(V-unfl ‘ futonhr— u~n_ ~u.— P a \ F nonlvh.vnfl \0\ .‘1 h.- \i I: in oo gags moo. 48. a. EH. NS. 8N. mm. :2... .38 20QO mm 8058 880% Q .0>30m0c 0.3 0.503338 02393:: MN. mm. *mm. $4. "0%.. wwm. flu. mod .Huo fiooooae 5. 8stch oh... 383% ..Q Q flu. mm. QM. an. .onom. mam. giants? 3 gm. *wm. fid.§§. ham. 3. Now. to. «ma. ..oom. Ho: rod. a. Nam. so. on". mm. mm. assassination. 5 www. a. NM. Nolo: #30. ma. 9:. tan. $§.im3.imsm. ..Ss. a2o mm. *3. mm. a. mo. Mmm. *wwm. mom. son. mom. §m.**sos. rams. as, .mw 5%. $9.. Nam. mom. mmd.¥a|aum. mam. do». 48.....Nom. sow. «Angina. was mm mm? No.4. *flm. *fim. 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H. :04. «um. mew. mass .H0>oa a H a. sumoacaomam n ** .H0>0H R m #0 acmowwflCMfim I # .U0Houflo 0A0 0dam> A0>oo assume 9H0np 30H0p 920030 00 o0»:500 00H00am .mbfipmm0: 0am mpd0wofimm0oo v0CfiHn0ch .Hlo_xaos0aa< aw U0CH0HQx0 0A0 macashm I\w 0mm. mom. moa. Ham. mom. ape *NMm. mwm. 40m. mmm. H00 *bmm. 404.**woo. #qu. *mmm. **OOO.H cam .ENP choc goo u0pm Boo H02 two :00 ”as am a 9 manm ape ado com a¢> ch00 goo 73. TABLE IV-D - COLE COEFFI 0111-713, 11030014110109! Vig Vang Gan 0.11 Spa? Vyp Led Vig .828“ .628* .265 .163 .091. .0_9zi .gg Vang .396** .Ohl. .112 .6286 .245 .og Can .93; .991. .195 .125 ._45 Cal .108 .m .252 .103 Spha .265 .070 .021. Vyp .799W .265 ...2 Led TABLE IV-E - COLE COEFFICIEJTS, DAWSON-GREE\F¢’JOOD# Vyp Vang Led Eric Kz-fl. Voxy Vyp 1.000% .257 .223 .025 .m .322 .Lw-x Vang .1290 328* ..Aé .112 ._56 .1140 Led .176 .165 ._82 .42 .3632“ Eric .110 .176 .1_22 ._2_81** Kal .291 .072 .121 .2h8 .933 Voxy .211 W‘ Symbols are explained in Appendix C-l. Underlined coeffi- cients are negative. Species counted as absent below their median cover value are circled. * - Significant at. 5 % level ** - Significant at 1 % level. 114131135 Idemadrokwpl novooamw .nofiwa v defiance CEIK Saw) .4 M0 5300: 08303 95:21 no.2; .m .E. ..H .0H 0.3%: 23..., 93mm; 50.? 035 33303.38 oaou 03:000.. mamaaonuuQVu noaua Ava: .ecxm waaazccw no mowooan academy» Mo ouswmm noaaafiaoannoOIaoaoucucuo .4 .n amacnh \ nan0d mo< new; new Houpoo mo m unavammooo .. 0:. ...»1 i :0“ N.» a o u A - . .. - _ u - . .— Ho: .0. < ac 'I-:6 " 74- 3 (b 8‘ o ---- W". 0080 00.3 A»? noapmaoupoo mo canmaouumooo 23 L4 75. .Adno Nudconmq an VOHHGHAHHO MEOflvflflgkfiPU “CHOOADV ahF 0% .OH 03%“ 3&3 UGDUOH Jada} Dada oIOQOHOHNMOOO OHOO O>fl&$.fl unaccoaouguu nonua nu“: .aaum mnuflhuue no .oaoonu anonuouu mo onsmfim coauaaaounnuouaouawuweao .0 ampeam named mo< n»«> nouacaouuoo mo mucouowmmooo : 0.x m.* .x m.‘ me "ax - _ _ . _ q . - _ a o hoboo 00a neuadH0huoo no «one My ..- m _ «6w out hhoou .Aauo Mug—0&1 cu void-HES 303033550 03933 62.3 .mN coma-Ha. nod-lb .8..- ..u now: .4 no 330: doflooap mat—one «.33: .n .R. .A .OH 0.3»: new) $5on as: .53 ...a'uoumuooo 0.70 03:23 vague-cumin 00:: Ana: .dflam HHotuouonmnuahduu 00> no undo-An 0:03.93 no 0.3m: advises-3050310520 .4 .a gar— npgue mod no“: nonpua.ueoo co nuqoaoauuooo Sn - LO 0? 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LIV 6 \IV I‘ rhth viixl 79. .Aalo Nag-0&9 5 confining; 0.: 3336“ Ibupppd nwfioomwv .mu .m .0H ousmuh new: cuomua new“; o-fin oI0fl0HOflH Imooo ouoo abuadmou 9:20.930.” 3:: no“: .v-dm xosudmsdm .95 3 do 330%» uaoduuum no 0.3m: soundflouuuoounogunguo .NH gnu namru mo< nu“) aofiuuaouuoo no .unoaoaugooo n I u . . . u Hm! /m.h\ ~.- mm- . . 0.---- :o «udaouuow omwonumuwowwwnoo IIJ'H. 80. A710 «manopow :* ccczwcko o...- nnomodmbouppa nouovmmv {..b .n .oa madman nun: gnawed not“... 0:3 .nuaofiocmooo oaoo ozawnom magnum team: «on: new: .3!“ agacouuoufiomiwn no noaoocm psosvouu mo 93mg nowuaaaoanaoucnogaqsuo .9 Eng no 0 3390.?9 n»; :ofiuwouuoo mo naqofioamooo \Mc‘ NP HI 0 .r-I d u 1 field W : . a ll mOol II 00.. 1.. no... QOP o I---‘ 'I'II"'LI o .. no.» owns “ ‘ .i .8 . . a «afloafiuwmuw wasnnnuwowwwuoo . . .. ul ‘. .Ill[l|l.[[[[[ll\[[[lll’ « .210 52.284 5 353%» Chi: Jami anon-u A033 2.3 .nauououwooo 0.30 :31»: Minus: . inn Fifi? . 4 mounta- vlofidouh Mo Puswnm goualHHOa-IoOIlogduuvuo 1: gr— . ‘ a ‘ - . .. . fin. dwa: dowflMWouuou mo manuaow‘muooo m.M a? F 9 1h J- 4 q d . . - . o no «a «no... Ioauuumwuow we 3930 wwuou IAJI IJ' - 82. 2. There are certain species on each soil type with which most of the other species are negatively associated. In general, these are species having very high cover values in this soil seg- ment. 3. If two species are highly positively associated on seg— ments where both are relatively rare, they are usually less posi- tively or even negatively associated where both are more abundant. 4. The large majority of vascular species exhibit a positive association with mosses and a negative association with terre— strial lichens, especially on the dry end of the gradient. 5. The degree of positive or negative association of pairs of species does not seem to be a function of their distance apart on the axes of the ordination figures. 6. On Grayling soil, there is a fair variation with respect to correlation of species with tree cover. On Wet Grayling-Cros- well, however, there is a slight tendency towards negative correlation with tree cover, and on Au Gres—Saugatuck, there is a stronger tendency in this direction though the majority of these negative correlations are slight. Nevertheless, this general ten- dency of the bulk of the species is noteworthy (see also Table V, p. 83-8e). 7. On Grayling, with four notable exceptions, all of the species exhibit near-neutral correlation with A0 depth. This also seems to be true on wet grayling-Croswell, gut on Au Gres- Saugatuck the tendency of most species to be negatively correlated with A0 is striking, particularly for wide-ranging species which are notH restricted or nearly restricted to the bog margin. 83. TABLE V ZERO-ORDER CORRELATIONS OF SPEEIES WITH ENVIRONMENTAL PARAMETERS # I - Correlations with per cent tree cover (tre) and depth of the AOLSOj-l layer (hum) on G, W00, and A03 G WGC AGS M r tre hum tre hum tre hum Anem .037 .586We Car .147 .03}; .159 .013 .057 .3§_é Com .001 ._§2 .922 .921. ~92 $32 Cop .052 .021. Corn .037 .1110 Dan .131 .132 Epig .Qfl .051 .123 .923 Gau .015 .201* .08 .128 .32 .1133 Mai ._'{_Q .007 .931 .019 .260 .99; Mel .3213“ .933 .332 .087 . 033 422* Opun .159 .043 Oras .047 .013 Prun .126 .092 .015 .116 .055 Pter .998 .071. .141 .096 09.1.2 3.5.2 Rho gig .9_0_§_ .022 .323 Tri .018 .118 .29_6_ .922 Van .179 .182 .322 .372 Vang .981 .015 . .032 .017 .9_8_§ .393 * See page 81.. 84. TABLE V continued # §pecies mat moss Chem. .064 .12g Erie .047 .019 Kal .979 .182 Led . 001 . 139 Vang .333 .027 Voxy .9_1_J_, . 286W # The high positive correlation of Prun with tree cover on AGS (circled) may be due to the cover contributed by Prun trees themselves. Blank spaces indicate that the category is not appli- cable 0 Explanations of species, parameter, and soil type symbols are found in Appendices C-1, C-2, and 0-3 respectively. Underlined coefficients are negative. * Significant at 5 % level. ** Significant at 1 % level. 85. 8. Species tend to retain about the same relative posi- tions with respect to each other on the ordination axes. This tendency is strongest between Grayling and wet Grayling—Cros- well, but is not very evident between Wet Grayling-Croswell and Au Gres-Saugatuck. Since different variables were used on the peat and since there are few species in common, there is no basis for comparison of peat and non-organic soils. 9. On peat, there is a general tendency for the vascular species to exhibit positive or neutral correlation with depth of the loose Sphagnum-Polytrichum mat. 10. Again on peat, most species exhibit fairly highly posi- tive though usually non-significant— correlations with bryophyte cover. 11. A total of 150 of the 513 Cole coefficients calculated, or 29 per cent of them, are significant at the S % level, and 84 of these (16 per cent of the total) are significant at the 1 % level. This indicates that interspecific association is extensive in the study area. Possible reasons for these trends are suggested in the dis- cussion. .Z/ The term "non-significant", as used in this paper, means not significant at the 5 % level. 86. C - CORRELATION ANALYSES In the assignment of species and variables to groups for these analyses, in which an attempt was made to place species together in such a way as to yield most useful information, the following groups resulted.— Group I. Gaultheria procumbens (Gau), Maianthemum canadense (hai), Nelampyrum lineare Thel), Vaccinium angustifolium (Vang), along with depth of the litter or A0 layer (lit). This group was chosen for its mutually high Cole co- efficients on the Grayling segment of the gradient, and because all of its members continued from the Grayling through the Saugatuck soil types in suffi- cient abundance to warrant analysis. It was analysed separately on the three "dry end" segments of the gradient; Grayling, Net Grayling-Croswell, and Au Gres-Saugatuck. Grouo II. Carex pensylvanica (Car), Comptonia pereggina (Com), PTUHUL serotina (Prun), and Pteri- dium aquilinum (Pter) were selected as the only spe- cies remaining after Group I had been designated, for which Cole coefficients had been calculated on all three of the "dry end" gradient segments. As with Group I, these species were analysed on each of the three segments separately. Depth of the Ao lay- er (hum) was included as an environmental parameter. Group III. This is a group of primarily "dry end" species; Anemone quinquefolia (Anem), Danthonia spicata (Dan), Oryzopsis asperifolia (Oras), and g. pungens (Opun), which were run with tree cover (tre). They were abundant enough for analysis only on the "driest" segment of the gradient, Grayling. ,9/ The symbols listed after each species or variable in paren- theses are used in some of the tables and figures to indicate the species or variables named. They are explained in Appendices C-1 and C-2. 87. Group IV. On both Net Grayling-Croswell and on Au Gres-Saugatuck (the second and third segments of the gradient-respectively starting from the ”dry" end) four species which peak on the "upland” side of the bog margin, but which tend to be most abundant on the wetter non-organic soil types, were analysed with tree cover (tre). The species are Epigaea repens (Epig), Rubus hispidus var. obovalis (Rho), Trientalis borealis (Tri), and Vaccinium myrtilloides (Vam). Group . The two remaining vascular species occur- ing abundantly enough in the samples on the ”dry” side of the bog margin to warrant calculation of Cole coeffi- cients were analysed on the Au Gres—Saugatuck, the only segment on which these species were sufficiently fre- quent. They are Coptis groenlandica (Cop) and Cornus canadensis (Corn), which were analysed with the two vari- ables tree cover (tre) and depth of the AOH soil layer (hum). Group VI. The six vascular species which character- ize the bog proper were analysed on the "bog" segment of the gradient (Dawson-Greenwood). Chamaedaphne calyculata (Cham), Eriophorum spissum (Erio), Kalmia pplifelia (Kali, Ledum ggoenlandicum_(Led), Vaccinium angtstifolium (Vang), and V._ggygoccus (Voxy) were run through the correlation analysis. No environmental variables were included in the matrix, although zero-order correlation coefficients were calculated for each species with depth of mat (mat) and per cent moss cover (moss) in the ordination studies. Thus, all of the common vascular species except trees on each of four segments of the gradient were run through one correlation mat- rix, and correlation coefficients were calculated for each species with several others. The Roscommon segment, it was felt, did not contain enough samples to warrant correlation analysis. Where poss- ible, each species was analysed with the same group on more than one gradient segment. The results of these studies are found in Tables VI-XI (p. 88- 95) and Figures 15-28. The figures are included 88. .Hn>oa a a pm neeoaoanmam . ** .m.m .Uenflampfigmo posv mHonsmm pmpmfimaem .HIo Kflecoam< ca emsflmagxo “He: who. mwm. mmo. H00. pad N”. 3.0.. wqqm. wsm> QM. osm. dNN. msd> mam. mmo. A02 mom. mmo. Hes mom. Hes moo. dam emu sew l M0294UD 00H. II mHH. *wqqm. II Hex. Hem 5mm Adda om. mna. fiNm. 0N0. mod. pad Hopes a m an unmoananmam I * *Hom. moa. zoom. msm> mpemwowmmmoo coapmamuuoo younOIoumN I HH awmmm. spam. waned. mcm> anon. II *wmqm . $83. I .32 .82 new mpsowowmmmoo soapmfioommd oHoo I H AAMBmomoIUZquwmw amz «Ban H gnome a H>.samaa *aoao. *aqmv. niOso. .muo waecmana ea Apaa o «voswdwpfiamOV mHonahm uoaoonm Hoe. I. mmo. *mmm. am: fine mma. II 53.13q Hem fimm OZHAwdmo .0>Hummoc one musoaoflwmooo coedahouus I % pad mzw> H02 .32 use mcm> Hes new “came Hwom JrJIII-I.I.‘l-blvnIl .l.> «.9. N. —H\IHI 89. .ESU mSHBHoo 2.3 30.“ 5.855 93 :0 mmflomam sumo mo scammmhmwn on» you @ .mw omwm mom m. m~o. «an. aua mad» I- mac. mac. In nae. mmm. gm. .Hm. goo. *mom. nag may» ac. .. NHO. fl. wad. mm. omc. *aem. pad may» 2H. .5. .32 am: So. ma. MIR—”I. mm... .... wmm. WNW. II :8. ma. do: «a: me. .... go. mum. ac: fix M033 avg Dd mam. mug .mnw. Eda. inn. Ha: Ha: NNN. «30 p: 353338 aofiaaohoo «£392 .. > mm. Im-«Mmo who. 03. mag *flwflo WNW. go II mam. m8. o3. SH. .... «NH. «mo. mm. «3. .... an. my. hmo. $3M. I dun. do: «a: :8 an @nuaofiOHHHooo cognac.» 65355 I PH «.3. cum. 25 3." Re. .. goon. mm 80. .wwm. :3. male. I. mm. 3 a: mum. *NWM... mm. In New. :8 3a ~40. m3. m3”. mag :3. I Now. 3a. .... mwm. amo. imam. II 2.". Ho: «a: :8 ...: E866 zago 9M3 % gfidpcoo HP age can *mom. «a. £53. $63. was» N3. #8.... 3.0. :3. wag *HHN. So. .3. wag 3.8.3qu0 €338.30 393 ”who «magma I H an: .3: :8 ~an male. «3. 3: tum. m8. man. was I db. mm. flux .30. II imam. «at wmm. $3. I. ago an: «a: :8 mag I. an: 2.0. I. an: walo. imam. .I :8 an: do: :3 mg 3.5 20m 90. www. oma. 0mm. 909m 050. moo. 004. umpm omo. u- opo. In 04a. moo. I- mam. moo. I: amm. **mww. ova. I- moo. «mm. mma. .. mmm. www. mam. aoa. I. amm. odpm 800 you as: uopm cohm 500 you .85: mpcofioammooo coapmamhaoo umUHOIOMmN I HH I- mam. I- m0m. nu wmw. mma. In aoo. mom. I: Noa. 5mm. mom. I. Guam .800 you popm £59m Sou moo mpsmaoammmoo coapwaoommd oHoo I H mosewwaqmlmmmw D< AqmzmoonUZquwmo em; ¢B.mama omo. oma. “mg. a. as: Mma. *kmmw. NINA—HI. popm *Hmm. moo. capm 0J0. Eco poo Mod. gag 00H. popm mac. a. Nd. pmpm mpcoacammoco :cflpoaoppco Hoflppom poopo pmonMflm I HHH MODH _ {ad - bc‘ neeetive association) . ever is smaller \\ N ) ~ For our example, we use the first formula, obtaining C = ,1 .724. U) II - CHI SQ’ARE TEST OF IGHIFICAICB. For a 2 X 2 table, Chi- square may be approximated by a short—cut formula (Greig—Smith 1957): 3. >(‘ 2 _ (ad - bc)2 N \ Iar0)(b1[€:1(<=¥d)(a1(b7. which is an approximation to the exact chi-square for a 2 X 2 table: N2 X’\Z_ (ad-bc-Z 1: la f we ,I we .1 cuca I b). . o . , For our example, using; the {Approximate formula, )4: = 0.659, Wnicn for one degree of freedom (in 2 X 2 tables (If is elwzgs 1) is Sli’lliflC'5nt at the 1 % level. 235. EPEITDIX Ar-Z ZERO—ORDER CORRELATION COEFFICIEHTS The zero-order correlation coefficients are found in the conven- tional fashion, as suggested for example by Snedecor (1956). However, they are arranged in a matrix so that they can be used later in finding highest order partial and multiple correlation coefficients, as well as standard partial regression coefficients, by the shortcut method devised by Clark (1958-59), which is presented in parts 3, h, and 5 of Appendix A. First, find Exp 2X3, and 5315‘; for each pair of species or other variables where: fiix, is the sum of values for the first variable, 2X3 is the sum of values for the second variable, ‘3. xix is the sum of the products of the Values of the two “ variables in each quadrat. The values of -X are then ar'renred in a matrix: 3 z. x1 x2 x3 x, xi ”a? as as w; 1:, {X22 2x275 £11219, X3 1152 21% b» in}, ° For example, we have the values for Group I, consisting of Gaultheria grocumbens (Gan), Maianthemum canadense (Mai), lielezpyrun lineare (Mel), Vaccinium angustifolium (Vang), and depth of leaf litter (lit): to \ A) C\ Gau Mai Eviel Vang l i t Gau 200.56,; 27.06 6.31 1166.16 082600' Mai 16.07 1.95 92.93 201.20 Mel 11.79 76.26 135.50 V8115 7633.75 8053.140 11:; “H“. ‘ 25190.00 , 1. Next, find xixJ for each pair, by the formula: 2x113 - EXiXJ - (ixifigngl ’ where N is the number of quadrats in the sample. The values of /xix J are then arranged in a matrix as were the values of £11113, as follows. Note that the symbol "x" (small "11") differs from "X" (large "X")). : 2 I ' 7 ( WV J‘1 £31 1 2x112 ! {X135 < x114 J‘2 ’2: J‘22 / 1:sz 5&1:sz . a 2 (r 3::3 ; 2.3{3 (: 13X“, ‘ 2 z.i__ .leb - From our example, using; the values of 2X for the five variables (Gau = 61.8, Mai = 114.4, Mel = 10.6, Vang I Sul.0, lit 3 1626.0), we have: Gan Mai Riel Vang 11 t L. " 1 Gau 168.73 19.64 0.85 187.55 105.01! Mai 11». 30 0.68 28.01 6.C8 1:61 3 . 8 5% 28A? -8. 13 Vang ' 5191+. 75 722.85 lit 3161.70 237. Now the zero-order correlation coefficients are calculated by the formula: / {an 2 2 Vixi ixj o It is desirable to save the denominators, \/§in2§:sz, in a separate matrix, since they will be used later in calculating the standard partial 2. r133 regression coefficients. The zero-order correlation coefficients are now arranged in a matrix: 1‘ r11 r12 _r13 18 1‘22 1‘23 ’20 ’44 For the example, the zero-order correlation coefficients are: Gau Mai Mel vang lit Gen 1 .3993** .0333 .2003* .1991* Mai 1 .0910 .1026 .0286 Mel 1 .2013 -.0737 Vang l .178“ lit 1 . o 1 V The above matrix is symmetrical (i. e. riJ : r31), so that the lower left portion may be c0pied from the upper right portion. It is convenient to do this when the matrix is to be used to calculate highest order partial correlation coefficients. 238. It is usually sufficient to round these coefficients off to two or three decimal places, but if they are to be used in order to find the highest order partial correlation coefficients, then at least four places are necessary. The significance of these coefficients is read directly from the usual correlation tables, such as that on p. 17% of Snedecor (1956), with H - 2 degrees of freedOu (E = number of quadrats). The significance of the figures above is indicated by a single asterisk (*) after the \ 1" fl . ‘ 3 “r figure for significance at tr 5 p level, and a dounle asterlsa (**) '— ’U for sirnificance at the l p level. 239. APPEKDIX APB HI GHEST ORDER PARTIAL CORRELATION COEFFICISKT The matrix of zero-order correlation coefficients (r13), which we have obtained (Appendix Ap2), is now placed in the upper left- hand corner of a larger matrix, with the identity matrix in the upper right (see below). The combined correlation and identity mrtrix is now "reduced" by the square root method (Dwyer 1951) as follows: r11 r12 r13 rlb l O 0 0 r21 r,,2 r23 r24 0 1 0 0 r31' r32 r33 rqu' 0 0 l 0 r41 11LL2 r43 run C C 0 1 S11 S12 813 91o 315 ‘16 S17 q18 S22.1 s23.1 S211.1 S25.1 26.1 ‘27.1 28.1 333.2 S3M2 S35.2 836.2 37.2 S38.2 51.1.3 555.3 $116.3 $117.3 SL633 ' The various values of Sij and SiJ.h are found as follows. (1) The values of sij are identical with the corresponding values of rid' Thus the top row of the s-matrices may be copied directly from the top row of the r- and identity matrices: lo 513 2 r139 for example: 912:1‘12, 516:0. (2) The iagonals in the 10 er left s—matrix (sii.h) are found by § ‘ L ‘ . . P.- subtracting the squares of all tue terms which are above this dlag 2&0, O :3 TD ....J Cf I) 3 Ho 1‘ Q . in r. 1 ‘ n the s-matiix, namely s1, h’ from tne corresponding 0.. ' V ' a the square root of this quantitv; U 2. .. _ _ _ 2 1 _ 2 2 2 911.h - \V/gli S (i—l)1.h~1 S (1-2)i.h—2 ' "' ‘ S 21.1 ‘ S for example: - 00 2 2 Snu.3" \V/;b4 ' s 35.2 ' 8 2n.1 " 3210 ' M - 2— S22.1 - )V/}22 ‘ 9 12 ° (3) Each of the other s-values (s.. h) is obtained by first multip— lying each value in the colgmn aiove it in the s—matrix (s .. , s(i-2)j.h—2’ etc.) by the term in the same row as the latter value, but in the column containing the ultbOE91 (311 h) of the row in which *— ‘- . the value we are trying to find lies (3(i-l)i.h-1’ 9(i-Z)i.h—2’ etc.). "Diagonal" in this case refers to the lower left matrix only. These products are summed, and the sum is subtracted from the r—value (rij) corresponding to the value we wish to find. The difference is then divided by the diago;al of the row in Vthh the unknown lies, namely s . .. Thus: 1.n }Jo rid ”(5(1-1)j.n-1)(9(1-1)1.h-1) ' (9(1—2)j.h-2)(3(i-g)1,. ... ‘(32J.1)(sgi.1) “ (slj)(sli) Q 9.. 11.0 f or example: 0 ' s35.293113 ‘ s25.192b.1 ' s159111 “w.3 9 ’u 9 = 27'1 822.1 Now, we obtain the inverse of the correlation matrix (c. 13 mat- rix) from the reduced identity matrix (the matrix in the lower right in the table at the beginning of Appen‘ix Ap3). For a particular value of Cij’ each value in column "i { l" is multipliei by the cor- responding value in column "3 ¥ 1" (n being eoual to the number of columns in the left-hand matrices), and the products are summed; 1+. 01.1 = (91(i*n))(81(3{ 11)) 1‘ (32(i¥n).l)(92(37{n).1) * no # (sn(i{n).nél)(sn(jfn).n-l) ’ for example: 023 = 816817 * 526.1927.l * 536.2337.2 % su6.3847.3 ' Arranging these values in matrix form, we have:. chl chZ Ce} chfi , the matrix being symmetrical (Cid 3 631). As a check, we can multiply the ciJ matrix by the rij (zero- oroer correlation coefficient) matrix, which should yiela the iden- tity matrix. To get the Value in the 1th row, Jth column of the identity matrix, multiply each of the values in the ith column of the cij matrix by the corresponding value in the Jth column of the rij matrix, and sum these products. For example: r12“13 " r22°23 ’1 r32°33 " 52°93 = 0 ' I19619 7‘ r29°21+ " r39°39 7‘ rwcub, a 1 ' For our example of Appendix APE, we 0 292. btein the following.matrices. Negative values are underlined in order to save space. r13 Gau Mai Mel Vang lit Gen 1 .3993 .0333 .2003 .1991 1 o o 0 0 Mai ..3993 1 .0919 .1026 .0286 o 1 0 0 0 Mel .0333 .0919 1 .2013 .9991, 0 o 1 c 0 Vans .2003 .1026 .2013 1 .1789 0 0 0 1 0 lit .1991 .0286 .9991 .1789 1 0 0 0 0 1 siJ 1 .3993 .0333 .1003 .1991 1 o 0““ o 0 .9168 .0852 .0297 .9555, .9955, 1.0908 0 0 0 .9958 .1933 .0759 .0038 .9999, 1.0092 0 0 .9602 .1610 .9999, .9999, .9999, 1.0919 0 .9621 l .9995, .0571 .1129 .9299, 1.0399 cij 1.2689 .9999, .0215 .9199 .2069 .9999 1.2019 .9959, .9999, .0593 .0215 .99399 1.0620 .9999, .1173 .9739 .9999 .2999 1.1195 .1801 .9999, .0593 .1173 .9999, 1.0809 .293. Identity matrix (cij matrix tines r11 matrix) .9999 .0001 .0000 .9999 .0002 1.0001 .0000 .0000 .0001 .9999 .0000 .0001 1.0000 .0001 1.0002 This "check" identity matrix suggests that there have been no errors in the calculations save those caused by rounding Off to four places, or that if there are other errors they are very slight. All the highest order partial correlation coefficients, rij.h’ are now obtained by the formula; 5° rij.h = ___ “011 \/911CJJ . for example: -c 1.12.34 a 12 \( 11:22 ’ ~c r29.13 " 2“ Wan— . As with the zero—order correlation coefficients, significance of the highest order partial correlation coefficients is ascertained directly frOn tables such as those on p. 179 of Snedecor (1956), with N'- (h¥2) degrees of freedom, with N sets of observations (quadrats) and h variables partialled out. For our example we obtain: Gan Mai Eel Vang lit Gau - .393** -.019 .195 .176 Mai - .076 - .017 -.052 Yel - .211* —.109 Vang - .16“ lit - , where significance at the 5 % level is indicated by a single aster- isk (*) after the figure, and sign fiCance at the l % level by a double asterisk (**). 295. 31:32me 1.4.9 ""1 ”II-"7 cor ~ ELATCJII cannon?" Tiese coefficients show the correla ion be weeii a.particular var- iable, which we shall call “y”, and several others. In the present study, multiple correlations are calculated between each variable in a matrix and all of the others. The matrix of zero-order cori elat ion coefficients (M endix A~2) must be arranged so that the zero-order correlation coefficients of "3“ each other variable are in the right—hand colinn. This 0011“] tion Po Cf' ...) ratrix must then be reduced by the technique given in.Aggendix Ap3, except that svy h need not be found. The multiple correlation coeffic- ~ 0 ient between variable y and all the others (Ry h) is then found by taking 0 the sguare root of the sum of squares of all 3;" h valies in one liah 4J0; “ hand column of the rednced corielat on matrix (tLP 10 or left matrix on p. 239) except va h‘ Using the matrix on p. 239, we 2 2 ’2 R9.123 = \\/é 19 # S 24.1 % S 39.2 ' This formula may 8180 be applied in a stepwise fashion, 3' 1 = V 9219 . R9.12 “ \[5219 7‘ 52211.1 . etc. reduced correlation metrix have ale tinis: If a correlation matrix and ready been obtained, one can save time by keeping rows and columns of the or1 e'r 81 order, as each multiple cor- on“ H H ’“* pa this correlation matr“ relation coefficient is c lcule ted, except for the row and column rep- resenting ve Mi ble "y” which are placed to the bot tom and r5“.t. If n original correlation matrix, then the first r0ws in the reduced correlation matrix may be copied directly from the orii~inal Sij h«matrix, ta lin: care to 21160 matrix. .L o~ _“. .1 11“. 111'“? r LI. rearronve columns to correspond to the rearrangenen i ?e reduced correlation ma rix must be completely 1. th k variables, V L]. T11 us W recalculated for x1 3 y, bit for Ek-B = y we need only recalculate five s—velues, for xk_1 = y only two, and for xk a y none. The significance of Ri-h may be conveniently tested by the F—test: 1. F : gz/P 1-12. /N—P—l , where degrees of freedom are P and N - P - l for the numerator and de— nominator, resgectively. N is equal to the number of sets of observa— tions (qiedrats), and P is the number of indegendent variables or "pre- dictors" (the number of variables in the matrix minus one). For our example from Aypendices A»2 and APB, we have: SPECIES cr VARLATLE Gau . R1.23h5'= .u60**, F = 7.719 Mai 32,13h5 = .310**, F g 5.800 Mel R3.1245 . .242 , F a 1.786 Vang R; 1235 = .308"I , F a 3.006 lit 35.1231, . .272 , F 1. 2.298 , where one asterisk after the figure (*) indicates significence at the 5 % level, and two asterisks (**) indicate significance at the l % level. L—1- Zhv, APPENDIX.A~5 STANDARD PARTIAL REGRESSI 0H COEFFI CIELTTS The first steps in the calculation of these regression coef- ficients is the same as the f’rst steps in the calculation of cor— relation coefficients, and the reader is refered to Appendices APZ and APB for formulas and.procedures. Recapitulating these steps briefly, with the necessary moaifications: (1) obtain all the sums of squares and products of deviations from the mean (in: 2, ixixj), andrarrange in a matrix; (2) compute all the zero-order correlation coefficients, retaining the denominators (Vixizész) in a matrix for later use; (3) construct the correlation matrix, as 53101-311 on p. 239, but leave out the value of xi which is to be the dependent variable, y; (1+) obtain the matrix of the inverses of the zero- order correlation coefficients rij’ namely cm, as explained in Appendix A-B; (5) check the latter, as before, by multiplying by the r matrix in appmpriate fashion. 13 till using our example from Apbendices L—Z and A—3, if we wish to let x2, Mai, be equal to y, we obtain: i 1113 Gan-x1 Mel-1:3 Vang-.59, 11 t-xS Mai-y! x1 168.73 0.85 187.55 ' 1L»5.z+1 'fl 19.61» 3:3 9.85 3.85 28A? —8.13 0.69 x” ‘l87.55 28.#7 5194.75 722.85 28.01‘ x5 1453a -8.13 ¥2£5 31235: 6.08 y 19. 64 0.68 28.01 i 6.08 ,J 11ml; l‘1 (By coaparing the above with the matrix on the can see t representing x2 in the latter are labeled "y", bottom and right, resyectively). 2&8. hat the two are ilentical exceyt that bottom of p. 236, one the row and column and are placed to the \/gx12Ex22 ‘ X1 3“3 Xu J“ Y 11 ll:0.73 25.h9 ?36.22 735.3 :1 “9.19- x3 3,25 1&1.02 110.33 7.03i‘ In 5190,75 #052.68 .13331331. ‘5 3131-70 2129 y j—-- ‘ 1h.34 (Negative values are uhuerlined in the following matrices). rid 11 X3 Xu X5 x1 1 .0333 .2003 .1991 1 0 0 0 x3 .0333 1 .2013 .9131 o 1 0 0 x44 .2003 .2013 1 .1784 0 0 1 0 x5 .1991 .9131 .1780 1 0 0 0 1 Bid 1 .0333 .2003 .1991 1 0 o 0 .999“ .l9h7 .rs0u .033 1.0006 0 0 .9002 .1606 .3913 .202 1.0;1u 0 ..SBM ] .1152 .1173 .1133 1.030 C” 1.0727 .9119 £22: -l<‘3»£i .9130 1.0561 .3311 .1218 .1123, .3311 1.11b7 .1393 9: .1910. ._1_3_g_2_ 1.077“ Identity matrix (ciJ matrix times rij matrix) 1.0000 .0000 .0003 .0000 1.0000 .0000 .0000 1.0000 .0000 .9999 . It is well to note here that the fiixixj, riJ’ and identity mat- rices are identical to the corresponding matrices for the correlation coefficients, but with the row and column for values of y omitted or (in the‘fixixj matrix) changed in position. 50 if the correlation coefficients have already been calculated these need not be redone. The "lower" matrices (813 h matrices), on the other hand, may be cop- ,_ ied, keeping all values in the same order as in the correlation mat- rices with the y column omitted, onlr‘gg far down flfi the omitted row, and from this point on must be recalculated. The inverse of the cor- relation matrix (011) must be completely redone, as must the check. We now obtain the inverse of the matrix of sums of squares and products, dij’ by the formula; . cij \[2‘123’12 ' using the values from the inverse of the correlation matrix and from 1. did I the matrix of denominators used in calculating the zero-order cor- relation coefficients. For example: d 23 . C23 ; WXZZzfid . 250. The various partial regression coefficients (bi? h) are now ob- .0 tained from the formula; 2' biy.h = dilzxr’”t ‘1223‘23’ " ’l dinixny a $61.1 ixjy) ’ where i is constant and J is variable. For example: .. < ~ The error, as, is obtained from: q. S = 72 - ’ - A ' - u- “ S 3 bly. 11 ley b4y. hi 1‘2y ’ ' ' bny. h ixny ’ with N'- p - 1 degrees of freedom, N observations (quadrats), and p independent variables. Consequently, we obtain the variance from the formula; b, 2 ss 3 y.h= N'- p - 1 , and the standard deviation is found in the usual fashion by taking the square root of the above. We also have the formula for the variance of the individual regression coefficients; 5. Sb." h : vii—{($37.10) lg. The t-test is used to test the significance of each of these coef— ficients, as follows; b 6. 15,,i h . Jim—h . . s y biy.h - It is convenient to arrange the various values in a particular form in a table, as demonstrated by using the figures from our example. Negative values are underlined in this table. [ii I? (ueu/ (Mel; (Va.g/ (lit) .6033/‘5 .0004101 .0001916 .000 #99 .0797}: .000<101 .2733117 .ooiseefiiu .oeii0ib_u Wh.ééjvbe‘q d. " ' "' "' ' IJ “(‘1 n ~>~-~—-———_—_-——~_ r -_~_—-_—' *"""—' "“‘ " v- "'-H .000i016, .031630' .ooozlbé .Cnoouug .0146u9 ‘ L .0002u99 .oollobo .ooooaug .oooghoa .018u61 1 , J biy h .118 .137 .001 .001 3'2 = Mai ... 11+.31+ 9N, .-. “10361826 - 0.321%“5 5b mh .026 .169 .005 .006 tb 1y.h u.r38*- .811 .200 . 00 If now the standardized regression coefficients, caiV'h (which are .0 pure numbers comparable to the highest order partial correlation coeffic- ients) are vented, they may be computed from: 7' (31y.h = biy.h\/€X12/€y2 - For our emqmle, we have: (d12.3a5 = .u05** £332.145 = 071 (342.135 = '019 stmsh '5 ’ where two asterisks (**) after the figure indicate 1 % level. significance at the H**.*m GRAXL HG "'13,? GPJLVLII’G u CROSNILL 99 Acme-1a AU \J’-.4b SAUGATU * See p. 2530 ' p AP.ETB X B GRIT MI U373 TO SEPARAIL SOIL TYPES LIMITS “F Tl“E A3 37“ 7 D?FIV3D* A9 depth O-lL mm., 4 " " A2 centu13-l9 mm., B color 1 to 2 on an ar- bitrary scale, th ZO-ZL mm., B color 1. depth 15-19 mm., B color 235 to 3, or A depth sac-2'4 m... B color Z-to 3, 23 A9 dep h 25- L9 mm., B color l-to 3. A? depth Ej—LQ mm., “B color 3.5 to 5, £3; under 50 mm., and or depth 50 mm. B texture ”unconsol- or over. idated". B texture "chunky" or B texture "crumhlv", A i A % Ab denth over s 0L 0m w .4. 80 mm. “ B texture "cement d" A0" depth under 90 mm. H B textur "crumbly", or B texture—”unconsol- idated" or "chunky", A1 depth over 50 mm., .23 B t 1"=re "cemented", Ap_ 6.9 ioth over 90 mm. B color 5, A0, depth under 12 inches. 253. Cr; ‘ "‘fif‘flh "V'T‘ “ ’“"“ ‘ ....In .....‘L I: __. _ (L IpTIT: OF Tim: AS TERI] :‘E’TTTTED" "mM NH (”1 ~~ DAnsoJ :F::‘\\ ‘OH depth l2_L2 inches. 0 \ x~DG :aamLC 0D PERT A depth over LB inches. '35. * Soae of the soil "tyines“ used here, for the kae of convenience, are not t;rpes recognized b; (McKenzie and Whiteside, 1*; ), and the descriptions of the tyne are not to be re :srded as "official" designations. B color, on a scale from 1 to 5, refers to the €_e e;ree of ClJWH fe“‘o“r—cro color 'n t.e horir son, with 1 de sigxat ing the least and 5 the H 1 woloration. . F": 'h“. “' Y" “ ON he 4'£.1.L.'&lg:a.& #epc'Lu Mment of Agriculture ost SYNFQL' Anem Bra Corn 1 "d Ho (‘1. H *1 Ho 0 Gen Kal Led APPEHZIX O-l . ."1-1 ya “'3 9 A}. ‘Du’I Inn-1L l‘o‘io'E* m... Anemone gginquefolia A 0“. 0’ I ‘d ,I‘acl‘gtl e 'iiurl sale]. I") SKIL- m) Celier;0rella schreterl Carex pensy venica I‘_1J r. .". n - _ —— 1- CUuuC (€1.0uleta _L a "'.V‘-’~_\_' CALMCet IJ. Comptonia Derir' Pa ! Coptis‘groenlendice (3 ornus canedonsis (L) Cladonia re? Tferinn (L) Cladonia cristetella (L) Cladonia pixydata—group ("cup“ Cladonias) Danthonia snicata (K) Dicranum undulietgm ggigeea repens Erigphorum sgissum Geultheria trocumbens Kfilmia Qpiifolia Ledum_groen endicnm fiaienthemum cannaenee * See p. 255. -\ -. r—n I LHJ \ .. 25 SPEC YES I“; " 3* q Melrmpgrum linesre OIL :r O‘HG.‘ 8 1311158;— I S Orgzqgsis esferifolia Prwnus serotina r Pteflwiw‘m ggtilimgg Rubxs Linidus var. obavrlig mfrtilJOidcs Vscci nium enrustifo Vig “cccinium anrustifolium ver. Vex" Vccc i - u CI”CGCCJS '71 ' . . o I. Vacc:rium en:vstw 011 m ”typlce 5. ,1" ium (ootL ve rieti es) * Moss es are desirneted by an (I4) prece 0y an (L). Lames without prefixes de 401‘ ulr sig 1g the species name, lichens nete vascular species. SYI-"V‘OL hum 256. EPEZTDI X C- 2 PAKVIETER S 34301.! U 3.43 IN T253333 , FI (7‘33 3 , A173 TEE-IT 3T1 RO‘TI-Ti V7-1 PA? i'-.'.':'I'_“"IR 31' SI G1"!- "'71) .-.... deg‘th of the A0? horizon or” the soil profile. 1 depth of loose leaf litter (AOL horizon of the soil profile). depth of the loose mat of dead 119mm?" 5nd Polztri C‘ztom moss in the bog Q percent cover of mosses (mostly Spncrnwm and Polrtrichum) in the bog (Zlilfil‘ats percent cover of the tree canopy atove the quadrats 257 . lemma 0.3 r‘ “W I - Am ‘v a. n-u :OIL m II SWBCLS 173:7: Tu tenants, 3:31-33, A172) “512:1“ G j? GPJLYLIIIT} SHTD if G “XE? GRAYLI‘ITG" SA‘ITD C ‘ CROSNELL SAND AG AU GP: S S.’II*D S , S'VGATUCK SAID R 303001.240: sofa (including Hirer SATJG TUCK") DAWSON PE'T DG GREm’i-IOOD FEAT b — combined soil types (gradient segyents) G GRAYLI ZTG S .131) WG—C or WGC NET GRAYLIXm—CR S?ELL SAKD AG—S or £435 AU GRE S- SAUGATU K SA‘IID R ROSCOI-fl-IGH SAL DG D111! SGET-GFEEZYFOOD PE. '1‘ * The soil types named here are based upon types designated by the I-Eichigen Department of Agriculture (McKenzie end 'A’hiteside,1956), but their primary use here is as reference points for the division of the gredient into convenient "homogeneous" segments. The names and delimiting; characters of these types do not correspond exactly to stendard definitions. M JF:/JJ‘1 r'snéi l i. I OCT 31. ‘963 E W 7’ .,_ rv‘“ -. ‘43:”: 5M k» F£819 f” “,v OCT 1" .52 1" W1? 1' CHIGGN STATE UNI I.V 111111311131131111131131111331111 1311131111311131131111