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Importance of coincidence in entomophagous insects with particular reference to certain parasites of… Griffiths, Kenneth John 1966

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THE IMPORTANCE OF COINCIDENCE I N ENTQMOPHAUOUS I 1 B E C T S WITH PARTICULAR REFERENCE TO C E R T A I N P A R A S I T E S OF NEODIPRION S E R T I F E R ( G E O F F . ) K e n n e t h J o h n G r i f f i t h s B . A . , U n i v e r s i t y o f T o r o n t o , 19& M . A . , U n i v e r s i t y o f T o r o n t o , 1953 A t h e s i s s u b m i t t e d i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r t h e d e g r e e o f P h . D . i n t h e D e p a r t m e n t o f Z o o l o g y We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY" OF B R I T I S H COLUMBIA S e p t e m b e r , 1966 In presenting this thesis i n p a r t i a l fulfilment of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of th i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Zoology  The University of B r i t i s h Columbia Vancouver 8, Canada Date August 8, I966 The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY KENNETH JOHN GRIFFITHS B,A0j, University of Toronto 1951 McA.g University of Toronto 1953 FRIDAY, OCTOBER lk9 1966 at 3; 30 P.M. i n Room 33329 B i o l o g i c a l Sciences Building of COMMITTEE III CHARGE Chairman% lo McT. Cowan D . I I . C h i t t y P o A. Larkin G. G. E. Scudder K„ Graham A. B. Acton J. H. G. Smith External Examiner: C. S. Holling Canada Department of Forestry Research. Supervisor: K. Graham THE IMPORTANCE OF COINCIDENCE IN ENTCMOPHAGOUS INSECTS WITH PARTICULAR REFERENCE TO CERTAIN PARASITES OF NEODIPRIQN SERTIFER (GEOFF,) ABSTRACT This stwdy represents the f i r s t of i t s kind to evaluate the importance o f . s p a t i a l and temporal co= incidence between p a r a s i t i c insects and t h e i r insect hosts. Extensive and intensive f i e l d observations here demonstrate that lack of coincidence i s possi= ble between the European pine sawflVj, Neodiprion s e r t i fer Geoff, and i t s three most important parasites« In the ichnemonids, Exenterus canadensis Proves, s p a t i a l coincidence i s nearly perfect^ while temporal coincidence may be poor's The bombyliid s V i l l a sinaosa (Wd.) shows imperfect s p a t i a l coincidence^ but good temporal coincidence.' In the ichneumonid Fieolophus basi&oraas (Grav„) both s p a t i a l and tem=> poral coincidence may be -imperfect.• The degress of coincidence are related to the physiology of develop~ ment and the behaviour of the parasites and t h e i r host i n t h e i r variable environmental contexts 0 The i n t e r r e l a t i o n s of host density^ parasite density^ time of contacts, number of eggs l a i d s and number of hosts attacked^ were studied experimentally with P. jpasigonuSo The resu l t s were more c l o s e l y described by the predictions of the R o l l i n g than of the Watt equation. The d i s t r i b u t i o n of eggs i n hosts was more often adequately described by the negative binomial than the Poisson equation for p r o b a b i l i t i e s . The effect of asynchrony i n the species studied cannot be considered without reference to super= parasitisms At low host densities superparasitism largely buffers effects of decreased synchrony, but i t s buffering diminishes to an asymptote as host density increases. In any given generation, imperfect spatial co= incidence has l i t t l e effect where attack i s asymptotic. Simulations of host=parasite interactions over 25 to 35 host generations showed that f o r P<> basizonvts and E„ canadensis 9 host and parasite populations would become stable a f t e r passing through one or more o s c i l l a t i o n s even when, temporal and. s p a t i a l coincidence are reduced., Pre° dictions" f o r V„ sinttosa indicate i t s i n a b i l i t y to r e s t r a i n host populations even a t perfect coincidence„ GRADUATE STUDIES Field of Study? Zoology Host=Parasite Relations Forest Insect Ecology Population Dynamics Forest Pathology Advanced SHvics Forestr" Seminar K, Graham IL Graham Do Co Buckland Po Go Haddock Po Go Haddock Go S. Allen PUBLICATIONS Griffiths, Griffiths, Ko Jo 1959- Observations on the European pine sawfly$ Neodipri'on sertifer (Geoff.)s and its parasites in southern Ontario. Canad. Ent. 91s 500.-512. K„ Jo I 9 6 0 . Oviposition of the red-headed pine sawfly9 Meodiprion lecontei (Fitch). Canad. Ent. 92; 4 3 0 - 4 3 5 „ Griffiths, K. J . 1960* Parasites of Ngodiprion pratti banksianae Rohwer in northern Ontarioo Canad, Ent. 92: 653=6580 Griffiths, K. Jo I 9 6 I . The l i f e history of Aptesis basizona (Grav.) on Meodiprion sertifer Geoff.) in southern Ontario. Canad. Ent. 93: 1005=1010. Lyons,, Lo A„ and K. J . Griffiths 1962, Observations on the development of Heodiprion sertifer (Geoff.) within the cocoon (Hymenoptera: Diprionidae). Canad, Ento §4: 994=1001. - i -ABSTRACT Chairman: Professor K. Graham Previous investigations of the interactions between hosts and parasites did not take into account temporal or spatial barriers separating the parasites from their hosts. Different rates of develop-ment, or different reactions of parasite adult and attacked host stage to environmental factors may introduce par t ia l disjunctions or lack of coincidence i n time and space between host and parasite . The intention i n this study was to demonstrate the nature of lack of coincidence between the European pine sawfly, Neodlprion ser t i fer (Geoff.) and three of i t s parasites, and to develop a descriptively accurate mathematical model to handle the interactions between parasite and host density and coincidence. Demonstration of lack of coincidence i n the f i e l d was accomplished largely by observation or from routine collections and rearings of hosts over a number of years. The basic material for the mathematical model was obtained by a series of laboratory experiments with N. sert ifer and a multi-voltine ichneumonid cocoon parasite Pleolophus basizonus (Grav.) . Exenterus canadensis Prov. , an ichneumonid attacking late-stage larvae, had good spatial coincidence, while at least some members of each generation showed imperfect temporal coincidence, or asynchrony. V i l l a sinuosa (Wd.), a bombyliid cocoon parasite, was well synchronized, but showed imperfect spatial coincidence. The third parasite, P . - i i -basizonus, could be imperfectly synchronized i n the f i r s t generation and could show lack of spat ial coincidence i n a l l generations. The basic equation for the submodel expressing the relat ion between number of eggs l a i d and host density was that developed by Holling (1959b), which gave a better description of the data than that of Watt (1959) • A second equation, the handling time submodel, was developed to describe and explain observed changes i n oviposition behaviour with time, and a th i rd , the suporparasitism submodel, permitted the prediction of number of hosts attacked given the number of eggs l a i d . This submodel was based on the observation that the presence of supernumerary parasite larvae did not decrease the probability of one parasite developing from a host, nor affect the sex ratio or size of the surviving parasites . Thus the only facts needed to determine the number of hosts attacked was the number of hosts offered and the number not attacked. The exact mathematical form of the submodel depends on the distr ibution of eggs among hosts . In the present case they neve better described by the negative binomial dis t r ibution than by the Poisson. The effect of asynchrony i n these species cannot be considered with-out the influence cf superparasitism being taken into account. At low host densities , superparasitism largely buffers the effects of decreased synchrony, i t s effect as a buffer decreases as host density increases u n t i l , when the attack level i s asymptotic on the functional response equation, i t s further effect i s almost eliminated. Obviously specific differences i n amount of superparasitism exist , which affect this general conclusion. - i i i -In any given generation, lack of spatial coincidence has l i t t l e effect where attack i s asymptotic, and at lower host densities i t s effect i s shown by the functional response curve. A number of simulations of host-parasite interactions over periods of 25 to 35 host generations were made, using i n i t i a l conditions resembling those ensuing when small numbers of both host and parasite invade a previously unattacked plantation. With P. basizonus and E . canadensis parameters, host and parasite populations became stable after passing through one or more osc i l la t ions , even when temporal and spatial co-incidence were reduced to nearly h a l f . However, i n the simulations usinj V . sinuosa parameters, this species was unable to prevent increase i n host populations even at perfect coincidence. I t i s d i f f i c u l t to generalize on the effects of lack of coincidence on host-parasite interactions. In the two species where osci l lat ions were produced i n simulations, increasing lack of temporal and spatial coincidence increased host and parasite density at the i n i t i a l peaks and increased the ultimate steady density of host and parasite . Other differences i n results were highly specific ones. - iv -TABLE OF CONTENTS 1. Introduction 1 2. Biology of Neodiprion sertifer 4 3. Demonstration of coincidence in N. sertifer parasites . . . . 8 3.1 Methods 8 3.2 Results 9 3.2 .1 Exenterus canadensis Prov 9 3.2.1.1 Biology 9 3.2.1.2 Temporal coincidence . . . . 18 3.2.1.3 Spatial coincidence 21 3.2.2 Pleolophus basizonus (Gray.) 24 3.2.2.1 Biology 2iU 3.2.2.2 Temporal coincidence 32 3.2.2.3 Spatial coincidence 33 3-2.3 V i l l a sinuosa (Wd.) 35 3.2.3.1 Biology 35 3.2 .3.2 Temporal coincidence 39 3.2.3.3 Spatial coincidence 39 4. Simulation of coincidence . . . . . . Ill 4«1 Introduction 41 4.2 Methods 42 4.3 Results f?l 4.4 Simulation of the effects of lack of coincidence . . . . 75 4'4«1 Pleolophus basizonus 83 4.4 »2 Exenterus canadensis 90 4.4*3 V i l l a sinuosa 93 - V -Table of Contents (cont'd.) k<& Simulation of host-parasite interactions 99 $. Discussion 116 6. References . . . . . . . . . . . . 138 « - V I -LIST OF TABLES Table I - Summary of sex ratios of adult Exenterus canadensis in various areas and years 11 Table II - Summary of experiments to show the concentration of ovipositions by Exenterus canadensis on prespinning larvae • • 12 Table III - Time spent by Exenterus canadensis adults in contact with two types of potential hosts 13 Table IV - Comparison of effect of host alarm reactions on oviposition and rejection by Exenterus canadensis . . lf> Table V - Distribution of Exenterus canadensis eggs on Neodiprion sertifer prespinning larvae 16 Table VI - Spring development of Exenterus canadensis at l5°C and 2 0 °C 19 Table VII - Average temperatures at five possible cocoon-spinning sites 2 0 Table VIII - Tests to determine the reaction of Pleolophus basizonus to the various developmental phases found, in the host cocoon . . . . . . . . . 2 8 o Table IX - Chi values obtained vihen observed distributions of Pleolophus basizonus eggs per cocoon are compared to Poisson and negative binomial distributions 2 9 • v i i -L i s t of Tables (cont'd.) Table X - Post-larval development of Pleolophus basizonus after three months at 0°C 31 Table XI - Conversion of parasite and host densities to numbers per square meter U7 Table XII - Number of replicates at each host and parasite density 4 8 Table XIII - Relation between number of attacks par parasite and parasite density i n Pleolophus basizonus slopes of lines of best f i t and " t " values obtained when slope compared to zero slope . . . . . . . . . . 55 Table XIV - Comparison of equations developed 1$r Holling (1959b) and Watt (1959) i n describing the functional response of Pleolophus basizonus to host density 63 Table XV - Comparisons of observed daily ovipositions of Pleolophus basizonus and that predicted by the b submodel . 67 Table XVI - Test of Holling (1959b) model using b submodel and a from data . . . . . . . . . . . . 68 Table XVII - Relation between daily oviposition rates of normal and deprived females of Pleolophus basizonus . . . . . 70 - v i i i -List of Tables (cont'd.) *m m i i i i Table XVIII - Comparison between observed zero categories and those calculated by the Poisson and negative binomial distributions 73 Table XIX - Parameter values used i n simulation studies . . . 8£ Table XX - Effect of varying degrees of asynchrony on attack by three species of parasites 86 Table XXI - Number of eggs l a i d and number of hosts attacked by Pleolophus basizonus at three host densities, two parasite densities and four indices of synchrony, with handling time constant . 88 Table XXII - Number of eggs l a i d and number of hosts attacked by Pleolophus basizonus at five host densities and two parasite densities by late and early emerging parasites, using handling time submodel . . . . 8? Table XXIII - Number of eggs l a i d and number of hosts attacked by Exenterus canadensis at three host densities, two parasite densities and four indices of synchrony 9k Table XXIV - Number of eggs l a i d and number of hosts attacked by V i l l a sinuosa at three host densities, two para-site densities and four indices of synchrony . . 98 - i x -~ L i s t of Tables (cont'd.) Table XXV - Effect of changing synchrony and coincidence on times to reach peaks and their height with Pleolophus basiz onus, b constant one generation per year 10k Table XXVI - Effect of changing synchrony and coincidence on times to reach peaks and their height with Pleolophus basizonus, b constant two generations per year I l l Table XXVII - Effect of changing synchrony and coincidence on times to reach peaks and their height with Pleolophus basizonus, b submodel two generations per year 112 Table XXVIII - Effect of changing synchrony on time to reach peaks and their heights with Exenterus canadensis. 115 Table XXIX - Slopes of l ines obtained when number of eggs l a i d i s plotted against synchrony 123 Table XXX - Effect of changing synchrony on steady host and parasite densities using constant host and parasite factors of l e 8 7 5 and 0 . 1 2 5 respectively 1 2 8 Table XXXI - Effec t of changing spatial coincidence on steady host and parasite densities using constant host and parasite factors of 1.875 and 0.125 respectively « 130 LIST OF FIGURES Figure 1 - N. sertifer prespinning larval population, as indicated by collections of larvae from trays under trees at two plots in southwestern Ontario, 1953; Bothwell, daily data; Grand Bend, two-day averages • 7 Figure 2 - The presence of N. sertifer larvae and of E . canadensis adults i n the f i e l d , Chatsworth, Ontario, 1959 . . . . 22 Figure 3 - Schematic presentation of coincidence between N. sertifer and E. canadensis. A. Temporal coincidence, solid line indicates host density, broken line para-site adult density. B and C. Spatial coincidence, distribution of prespinning larvae beneath and be-yond the crown projection of an open grown tree (B) and those of two adjacent trees in a plantation (C). Cross-hatched areas indicate where attack by E . canadensis can occur 23 Figure Ij. - Daily egg production of P. basizonus when offered a surplus of host cocoons. After day 13, when the number of females dropped below 10, a 2-day average was used. Vertical lines through each point re-present ± 2 S.E 26 Figure 5 - Schematic presentation of coincidence between N . sertifer and P. basizonus. A. Temporal coincidence, solid line indicates host density, broken line para-L i s t of Figures (cont'd.) s i te adult density. B and C Spatial coincidence. The frequency distributions indicate the dis t r ibution of host cocoons beneath the surface, the cross-hatched area the number of host cocoons available f o r attack i n B, an area of shallow l i t t e r , and C, an area of deep l i t t e r 3k Figure 6 - A b i l i t y of P. basizonus adults to attack N . ser t i fer cocoons buried i n various depths of whole and crushed needles. The figures at the bottom of each column are the dai ly number of eggs l a i d per female. The figures within the ovals i n the columns are the per cent of the to ta l attack that occurred at that l e v e l . 100 cocoons and six females were used i n each experiment.. . . . . 36 Figure 7 - Schematic presentation of coincidence between N . ser t i fer and V . sinuosa. A . Temporal coincidence, s o l i d l ine indicates host density, broken l i n e para-si te adult density. B and C . Spatial coincidence, dis t r ibution of host cocoons beneath and beyond the crown projection of an open grown tree (B) and those of two adjacent trees i n a plantation (C) . Cross-hatched areas indicate where attack by V . sinuosa adults can occur • kO - X i i -L i s t of Figures (cont'd.) Figure 8 - Experimental cages i n place on the rack. A . Diffusion screen between l i g h t source and cage. . . kk Figure 9 - Detai l of side of an experimental cage showing a closed introduction port and a closed capture p o r t . . . . . . k$ Figure 10 - The mechanical arm used to capture parasite females when cocoons were about to be changed. I t has been put i n the cage through a capture port • h $ Figure 11 - Relation between number of attacks per female and density of female P . basizonusj experimental data and l ine of best f i t calculated by the method of least squares. A . Open c i rc les and s o l i d l ine - Day 1, hosts 3»17 M^j closed squares and broken l i n e - Day 2, hosts 6.35 M 2 . B . Open c i rc les and s o l i d l ine -Day k, hosts 2$.k0 M j closed squares and broken l ine - Day 5, hosts hk»hk M 2 54 Figure 12 - The relat ion between number of attacks per parasite and host density i n P. basizonus on the f i r s t and second days of experiments. The sol id l ine i s that predicted by the equation of Holling (1959b), the broken l ine that predicted by the equation of Watt (1959) , 57 - x l i i -List of Figures (cont'd*) Figure 13 - The relation between number of attacks per parasite and host density in P. basizonus on the third and fourth days of experiments. The solid line is that predicted by the equation of Holling (1959b), the broken line that predicted by the equation of Watt (1959) 58 Figure Ik - The relation between number of attacks per parasite and host density in P. basizonus on the fifth day of experiments. The solid line i s that predicted by the equation of Holling (1959b), the broken line that predicted by the equation of Watt (1959) 59 Figure 15 - The relation between observed number of hosts attacked on f i r s t day of experiments and that predicted by the combined basic functional response* handling time and superparasitism submodels. Line of best f i t calculated by least squares method, r « •930; "t" obtained when slope of line of best f i t compared to that for perfect prediction - .618» . • 76 Figure 16 - The relation between observed number of hosts attacked on second day of experiments and that predicted by the combined basic functional response, handling time and superparasitism submodels* Line of best f i t calculated by least squares method, r » - xiv -L i s t of Figures (cont'd.) ,967J " t " obtained when slope of line of best f i t compared to that for perfect prediction .301 77 The relation between observed number of hosts attacked on third day of experiments and that predicted by the combined basic functional response, handling time and superparasitism submodels. Line of best f i t calculated by least squares method, r •= .961; " t " obtained when slope of line of best f i t compared to that for perfect prediction .778 « • * • » • « » » • « • • * • » • • * # • 78 The relation between observed number of hosts attacked on fourth day of experiments and that predicted by the combined basic functional response, handling time and superparasitism submodels. Line of best f i t calcula-ted by least square method, r = .971; n t n obtained when slope of line of best f i t compared to that for perfect prediction .7920. . . . . . . . . 79 Figure 19 - The relation between observed number of hosts attacked on f i f t h day of experiments and that predicted try the combined basic functional response, handling time and superparasitism submodels* Line of best f i t calcula-ted by least squares method, r « .967; n t " obtained when slope of line of best f i t compared to that for perfect prediction 80 Figure 17 Figure 18 *-L i s t of Figures (cont'd.) Figure 20 - Schematic representation of synchrony between a host (cross-hatched block) that i s vulnerable to attack for 13> days and a parasite (open blocks) whose female adults l i v e 15 days. The changes i n handling time based on the b submodel are shown within each para-s i te block . 82 Figure 21 - Simulations of number of hosts attacked at various host densities and with four indices of synchrony, using P . basizonus parameters, b constant, parasite density 1 per square meter Figure 22 - Simulations of number of hosts attacked at various host densities and with k indices of synchrony using E . canadensis parameters. Parasite density 1 per square meter 92 Figure 23 - Simulations of number of hosts attacked at various host densities and with 4 indices of synchrony, using V . sinuosa parameters. Parasite density 1 per square meter , 97 Figure 24 - Fluctuations of host populations over 35 generations with simulated attack by P . basizonus, 1 generation per year, b constant, at 4 indices of synchrony. Original host population 0.5, parasite female popula-t ion 0.005 per square meter 103 List of Figures (cont'd.) Figure 25 - Fluctuations of host populations over 35 generations with simulated attack by P. basizonus, 1 generation per year, b constant, at 5 indices of coincidence* Original host population 0.5, parasite female popula-tion 0.005 per square meter. . . . . . . 107 Figure 26 - Fluctuations of overwintering host populations over 25 generations with simulated attack by P_. basiz onusp 2 generations per year, b constant, with k combina-tions of lack of temporal and spatial coincidence. Original host population 0.5, parasite female popula-tion 0.005 per square meter 110 Figure 27 - Fluctuations of host populations over 30 generations with simulated attack by E. canadensis at 3 indices of synchrony. Original host population 0.5, parasite female population 0.005 per square meter • 114 — xvii -ACKNOWLEDGMENTS I wish to acknowledge the stimulation and direction afforded by Dr. K. Graham and other members of the faculty of the Department of Zoology, while I was a graduate student i n that department. Dr. Graham has also provided advice and encouragement from the i n i t i a l outline of the problem through the prolonged period when the research was carried out, to the f i n a l c riticism of the manuscript. Most of the experimental work reported i n this thesis was carried out i n the Forest Research Laboratory, Sault Ste. Marie, Ont. and I am grateful to Mr. W. A. Reeks, officer-in-charge u n t i l 1965 and to Dr. G. W. Green, present officer-in-charge, for advice and encouragement i n conducting the research. Dr. P. J. Pointing and Dr. C. S. Holling, both former members of the staff of this laboratory, are sincerely thanked for their continued suggestions and criticisms of the experiments and analyses. Drs. Green, Holling and Pointing also reviewed the manuscript. Mr. D. C. Anderson prepared the photographs. - 1 -1. INTRODUCTION In recent years the study of insect population fluctuations has attracted the attention of increasing numbers of ecologists. The work of Morris (1963a) and his co-workers has amply illust r a t e d the complexity inherent i n such studies. Holling (1963, 1964) suggested that to obtain a greater understanding of these extremely complex relationships, effort should be concentrated on the processes that influence the fluctuations. He had previously developed (Holling 1959b) a simple mathematical model that described and p a r t i a l l y explained the i n i t i a l phases of parasite attack, which together with a model developed by Watt (1959) are the only effective mathematical treatments of the subject to date. The relative merits of the two models and the approaches they represent have already been discussed by Holling (1959b) and Morris (1963b). One of the aims of the current study i s to continue the assessment of these two models. In the models of Holling (1959b) and Watt (1959) and i n the previous studies of the numerical relations between hosts and parasites that they dealt with (Burnett 1951, 1954, 1956, 1958a, 1958b; DeBach and Smith 1941, 1947J UUyett 1949a, 1949b) i t was assumed that a l l hosts xrere equally available to a l l parasites. However, to mimic natural situations more closely, models must include the possibility that differential responses by host and parasite to various components of the environment may result i n less than perfect "overlap" between the parasite female and the attacked host stage. Thalenhorst (1950) refers to this aspect of the attack process as "coincidence" and correctly distinguishes between i t s spatial and temporal aspects, the l a t t e r generally designated as "synchrony." Thalenhorstfs study deals almost - 2 -exclusively with the def ini t ion and description of the various aspects of coincidence, however, and offers l i t t l e for the solution of the present problem. Doutt (1959) states " i t seems obvious that to achieve a host-parasite relationship the two species must f i r s t be seasonally, geographically, and ecologically coincident. But even when these requirements are met, the parasitic relationship may s t i l l not be established i f there are physical , psychological, physiological , or nutr i t ional b a r r i e r s , " indicating the several levels on which coincidence operates. At the f i r s t l e v e l , polyphagy among parasites, or their presence or absence i n the geographical range of a host are relevant. Franz (196U) points out that lack of spatial coincidence on a large scale can explain the outbreaks of harmful insects when introduced to a new environment and that b io logica l control i n these instances i s i n part an attempt to re-establish coincidence. The present study i s not concerned with this aspect of the problem, but with the second, more detailed level-where differences i n behaviour and development of parasite aid host affect coincidence. The physiological and nutr i t ional consequences of temporal coincidence or lack of i t are the subject of the majority of the meager l i s t of publications on coincidence. Buck and Keister (1956) suggest that the dipterous parasite Phorocera sp. " i s aroused from i t s diapause by the diapause-breaking hormone of the host (the saturniidNAgapema galbina (Clemens)) the two l i f e cycles being thereby synchronized." Klomp (1958) points out that the development of the tachinid Carcelia obesa Zett . i s activated by a stage i n the metamorphosis of the host, Bupalus piniarius L . Schoonhoven (1962), working with Eucarcelia  r u t i l l a V i l l . , another tachinid parasite of B. p iniar ius , believes that the parasite i s activated by a hormone associated with the adult development of the host. Similar relationships exist between hymenopterous parasites and their hosts (Klomp 1958; Lees 1955J Schoonhoven 1962). The importance of these mechanisms i n setting the stage for synchronization cannot be doubted. How-ever the physical factors affecting development may s t i l l reduce or eliminate the period during which adult female parasites and the attacked host stage are actually i n contact, even though the synchronizing mechanism has ensured that the appropriate stages occur i n the same season. Lack of spatial as dis t inct from temporal coincidence i s a function of the behavioural relations of host and parasite and of the physical l imitations of the parasites. For example, three species of Megarhyssa are l imited i n their host selection by differences i n ovipositor length (Heatwole and Davis 1965). The i n a b i l i t y of Ooencyrtus kuwanai (How.) to attack eggs i n the center of egg masses of Lymantria dispar (L), because of the length of i t s ovipositor, l imi ts i t s effectiveness (Franz 1964). The behavioural aspects of the study of spatial coincidence have been demonstrated by Burnett (19U8), who found that the temperature reactions of Encarsia formosa Gahan d i f f e r from those of i t s host Trialeurodes vaporariorum Westw. These differences could determine the proportion of the host population available for attack. The f i r s t aim of the present study i s to demonstrate, by investigations of Neodiprion ser t i fer (Geoff.) and several of i t s parasites, that external environmental factors and behavioural differences can result i n lack of temporal and spatial coincidence. The second aim is to develop a descriptively accurate 1 mathematical model using data based on intensive laboratory experiments with one of the parasites* The th i rd and f i n a l aim i s to use the model to simulate a variety of host-parasite interactions i n order to explore the consequences of - u -changing host and p a r a s i t e d e n s i t y , the e f f e c t of d i f f e r i n g degrees of temporal and s p a t i a l c o i n c i d e n c e , and the s i g n i f i c a n c e of these e f f e c t s on N . s e r t i f e r . Although the three p a r a s i t e species s t u d i e d were o r i g i n a l l y s e l e c t e d because they were common p a r a s i t e s of N. s e r t i f e r , they a l s o have other v i r t u e s . They represent a c r o s s - s e c t i o n o f the p a r a s i t e s of t h i s e x o t i c d e f o l i a t o r . The f i r s t s p e c i e s , Exenterus canadensis Prov., i s a n a t i v e ichneumonid t h a t has been a s s o c i a t e d w i t h N. s e r t i f e r throughout most of the l a t t e r 1 s h i s t o r y i n Canada and i s one of the few species a t t a c k i n g before the host spins i t s cocoon ( G r i f f i t h s 1959j Lyons 1963). The second species s t u d i e d i s a European ichneumonid, Pleolophus basizonus (Grav.), a m u l t i v o l t i n e cocoon p a r a s i t e t h a t was in t r o d u c e d i n t o Ontario from 1938 to 19U6 and has r e c e n t l y become a s i g n i f i c a n t m o r t a l i t y f a c t o r of cocoonsd l a r v a e of N. s e r t i f e r i n southwestern Ontario ( G r i f f i t h s 1961). I t was u t i l i z e d i n the i n t e n s i v e l a b o r a t o r y s t u d i e s which formed the b a s i s of the mathematical model, because of the ease w i t h which i t can be handled i n the l a b o r a t o r y . The t h i r d s p e c i e s , V i l l a sinuosa (Wd.) ( D i p t e r a : Bombyliidae), a u n i v o l t i n e cocoon p a r a s i t e , was for m e r l y abundant i n cocoon c o l l e c t i o n s ( G r i f f i t h s 1959) but l a t e l y has been obtained r a r e l y , making the c o l l e c t i o n of i n f o r m a t i o n on i t d i f f i c u l t . The d e c l i n e i n numbers i s s u f f i c i e n t i n i t s e l f t o arouse i n t e r e s t , and i t a l s o o f f e r s an i d e a l o pportunity to t e s t the p r e d i c t i v e value of the model using a minimum of i n f o r m a t i o n . 2. BIOLOGY OF NEODIPRION SERTIFER N . s e r t i f e r i s a P a l a e a r c t i c species that was f i r s t recorded i n North America i n 1925 (Hamilton 19U3) and i n Canada i n 1939 (Raizenne 1957). I t s present Canadian d i s t r i b u t i o n i s roughly t h a t p a r t of southern Ontario which - 5 -l i e s w e s t a n d s o u t h o f L a k e S i m c o e , w h e r e i t s p r i n c i p a l h o s t s , S c o t s p i n e P i n u s s y l v e s t r i s L . , r e d p i n e P . r e s i n o s a A i t . a n d j a c k p i n e P . b a n k s i a n a L a m b . , a r e g e n e r a l l y f o u n d i n p l a n t a t i o n s o f t r e e s l e s s t h a n 20 f e e t i n h e i g h t . I t h a s a l s o b e e n r e c o r d e d f r o m J a p a n e s e r e d p i n e , P . d e n s i f l o r a S . a n d Z . , a n d mugho p i n e , P . mugo T u r r a . ( S c h a f f n e r 1939). N . s e r t i f e r i s u n i v o l t i n e . I n s o u t h e r n O n t a r i o h a t c h i n g c o m m e n c e s i n t h e f i r s t h a l f o f May a n d c o n t i n u e s f o r one t o t w o w e e k s . The f e e d i n g l a r v a e a r e g r e g a r i o u s i n a l l s t a g e s a n d e a t o n l y t h e o l d f o l i a g e . F e e d i n g c o n t i n u e s u n t i l t h e l a t t e r h a l f o f J u n e , when t h e f u l l y - d e v e l o p e d l a r v a e d r o p t o t h e g r o u n d a n d s p i n c o c o o n s i n t h e l i t t e r . A d u l t s e m e r g e a n d o v i p o s i t f r o m e a r l y S e p t e m b e r t o l a t e a u t u m n . The e g g s a r e l a i d i n s l i t s c u t i n t h e e d g e s o f t h e c u r r e n t y e a r ' s n e e d l e s , e a c h n e e d l e r e c e i v i n g a r o w o f f r o m t w o t o e i g h t more o r l e s s u n i f o r m l y s p a c e d e g g s . The e g g a n d e a r l y l a r v a l s t a g e s o f N . s e r t i f e r a r e v i r t u a l l y f r e e o f p a r a s i t e a t t a c k . P a r a s i t e s a t t a c k f u l l y - d e v e l o p e d f e e d i n g l a r v a e ( t h e f o u r t h i n s t a r i n m a l e s a n d f i f t h i n s t a r i n f e m a l e s ) , a n d a l s o " p r e s p i n n i n g l a r v a e " w h i c h a r e t h e m o t i l e e a r l y p o r t i o n o f t h e p r e p u p a l s t a g e , e a s i l y s e p a r a t e d f r o m f e e d i n g l a r v a e b y d i f f e r e n c e s i n c o l o r a t i o n ( G r i f f i t h s 1959). M o u l t i n g t o t h e p r e s p i n n i n g l a r v a h a s b e e n o b s e r v e d i n t h e f i e l d t h r o u g h o u t t h e d a y . A p p r o x i m a t e l y o n e - t h i r d o f t h e m a t u r e l a r v a e d r o p t o t h e g r o u n d b e f o r e m o u l t i n g , b u t t h e m a j o r i t y g o t h r o u g h t h e f i n a l l a r v a l e c d y s i s o n t h e t r e e s w i t h i n , o r a t a s h o r t d i s t a n c e f r o m , t h e f e e d i n g c l u s t e r ( G r i f f i t h s 1959). H o w e v e r , o n l y a s m a l l p r o p o r t i o n o f t h e s e , u p t o t h r e e p e r c e n t a t C h a t s w o r t h , O n t a r i o ( L y o n s 1963) s p i n c o c o o n s i n t h e t r e e s . M o s t d r o p t o t h e g r o u n d w i t h i n 20 m i n u t e s t o 21; h o u r s a f t e r t h e l a s t l a r v a l - 6 -ecdysis, "before spinning cocoons. In ray insectary rearings the average time from the f i n a l l a r v a l moult to the completion of cocoon spinning was U8 hours i n both sexes. Lyons (l°63) however, reports that most larvae spin cocoons within 2k hours of the f i n a l l a r v a l moult. Clearly, individuals do not normally spend more than one or two days i n this "stage" and variable proportions of i t are spent on the tree and on the ground. W. ser t i fer populations pass through the prespiraiing "stage" i n two to three weeks ( F i g . 1). At the beginning of this period the population i s largely male, and at the end i t i s largely female. Most N. s e r t i f e r cocoons are spun at the sharp interface between the lowest l i t t e r stratum and the mineral s o i l . In open areas, where grass and other plants predominate, 90 per cent of the cocoons were found i n this posi t ion, seven per cent were found above i n the sparse l i t t e r , and three per cent were below i n the mineral layer . Within plantations, where needles cover the ground, 75 per cent of the cocoons were found at the l i t ter -mineral s o i l interface, 21 per cent i n the needle l i t t e r and four per cent i n the mineral s o i l (Griff i ths 1955). Cocoons are concentrated beneath the crowns of both open-grown trees and those i n plantations, the density of cocoons varying inversely with the distance from the trunk. Cocoons are only rarely found as far as 16 feet from the trunks of open-grown trees. Lyons (1963) has also noted the aggregated dis t r ibut ion of cocoons and states that i t generally conforms to the negative binomial model. The sex ra t io of N. ser t i fer during the cocoon stage varies from 67 to 76 - 7 -100. A-Bothwell (2 trees) • M * Males OMIMO Females 2 a: < i 11 frKif* i ''ffrin j • • i . i i • • • i • . . • i i i i • i 10 20 30 10 J U N E J U L Y O 200 Z Z a. <S) U J on Q -c a z 100 I i i • I Grand Bend (4 trees) • • • m * Males om'iiiio Females ""••0 ? 30 10 J U N E J U L Y F i g . 1 . N. s e r t i f e r prespinning l a r v a l population, as indicated by co l l e c -tions of larvae from trays under trees at two plots i n south-western Ontario, 1 9 5 3 ; Bothwell, d a i l y data; Grand Bend, two-day averages. - 8 -per cent females at Chatsworth, Ontario (Lyons 1963), where polyhedral virus disease (Bird 1953) does not occur. However, when this disease i s present i n the population, the proportion of females can be considerably reduced (Griff i ths 1959). 3. DEMONSTRATION OF COINCIDENCE IN NEODIPRION SERTIFER PARASITES 3.1 Methods The results reported i n this section have been obtained from several areas i n southern Ontario and over a considerable span of time. From 1952 to 1956 work was carried out near Strathroy, Mt. Brydges, Grand Bend and' Bothwell. In 1957 e f for t was concentrated at Elmira, and at Rosevi l le . In 1958, the f i e l d laboratory was moved to Chatsworth, although the work at Roseville was continued for two years. Chatsworth has remained the main site of f i e l d studies for the past seven years. A l l laboratory studies were carried out i n the Forest Research Laboratory, Sault Ste. Marie, Ontario. Much of the material presented i n this section was obtained by direct observation i n the f i e l d , or from routine collections and rearings of hosts over a number of years. Some information was obtained experimentally, how-ever, and the techniques used i n these w i l l be outlined below, their order being coincident with the appearance of the results from them. The seasonal course of P. basizonus parasitism was studied by exposing N. ser t i fer cocoons to attack i n the f i e l d i n two successive years. A number of wooden trays, each containing 50 cocoons i n I960 and 15 i n 1961, were set out i n the l i t t e r i n a red pine plantation, half i n shaded and half i n exposed s i t e s . In I960 eight trays were used, i n 1961, 20. Tha cocoons were protected from small mammal predators by coarse-mesh wire screening - 9 -placed on top and bottom of the trays. Trays were set out in mid-June and remained undisturbed until the end of October, but the cocoons in them were replaced weekly. Cocoons removed from trays were checked daily for parasite emergence both throughout the summer and also after three months in cold storage. The presence or absence of f i r s t instars of V. sinuosa in the soil was determined by the use of Tullgren funnels. A wire mesh tray was set inside the upper conical portion of a nine-inch metal funnel to hold the sample, and a collection bottle was placed beneath the funnel's lower end to collect the specimens. Above each of the ten funnels used, a 25-watt electric light bulb was suspended as a heat-light source. A sample consisted of a nine-inch diameter circle of l i t t e r and approximately one-half inch of the underlying mineral s o i l . A metal pie plate of nine inches diameter served both as a guide for cutting a sample from the ground and as a container for transporting i t . The sample was placed on the wire mesh in the funnel, the li t t e r upper-most. Animals within the sample, moving away from the heat-light source, dropped into the collecting bottle. The accumulation of material in each bottle was examined under a microscope daily and after seven days the N. sertifer cocoons in the sample were removed and the sample discarded. 3.2 Results 3.2.1 Exenterus canadensis Prov. 3.2.1.1 Biology. E. canadensis adults were present in the field,from May 29 until July 4 in 1959 and from May 29 until July 23 in I960. Adults were observed about infested trees from approximately 0800 hours until 1830 hours daily, at ambient air temperatures between 10°C and 26°C. - 10 -The mean longevity of 10 male adults i n rearing cages was 6.6 ± 1.0"** days. The l i f e span of 10 female adults that were permitted to oviposit averaged ?.£ ± 1.0 days, significantly longer than the average of 5*3 ± 0.7 days for 10 females that were denied the opportunity to oviposit (t = 3»5>lj p <.01). Mated E. canadensis females produce offspring of both sexes, v i r g i n females are arrhenotokous. The normal sex ratio i s apparently very close to £0 per cent females. In only one of the eight areas tested was there a preponderance of one sex, i n this case males (Table I ) . Both mated and un-mated females began to oviposit as soon as they were presanted with hosts. In cages, the average number of eggs l a i d per female per day w a 3 6.U ± 0.6, based on 32 field-collected females. E. canadensis oviposited significantly more frequently on prespinning larvae than on mature feeding stage larvae. This was true, whether larvae were offered singly, i n groups of one type, or i n pairs or groups containing both types together. Similar results were obtained from f i e l d collections of larvae (Table I I ) . Females oviposited more quickly on prespinning larvae than they did on mature feeding stages, although they required approximately the same time to reject larvae of both types (Table I I I ) . Prop (19$9) maintains that any difference i n attack on N. sertifer larvae by two European species of Exenterus i s caused by differences i n activity of the larvae. He l i s t s the various alarm reactions exhibited by these larvae, and points out that the presence of Exenterus i n a feeding colony of M. Standard error - 11 -TABLE I Summary of sex ratios of adult Exenterus canadensis i n various areas and years Area Year Number of Individuals Sex Ratio Females Males Females Males Mt. Brydges 1952 33 27 0.550 o.45o 1953 21 23 0.477 0.523 Strathroy 1952 21 16 0.568 0.432 1953 17 17 0.500 o.5oo Both-well 1952 27 33 o.45o o.55o Grand Bend 1953 10 ho 0.200 0.800* Bayfield 1955 19 29 0.396 0.604 Roseville 1957 31 20 0.608 0.392 Total 178 206 0.464 0.536 Significantly different from one-to-one ratio, probability less than .001. - 12 -TABLE I I Summary of experiments to show the concentration of ovipositions by Exenterus canadensis on prespinning larvae Type of Experiment Number of Para-sites Prespinning Larvae Mature Feeding Stage Larvae 2 Chi Tested ' Ac-cepted Re-jected Ac-cepted Re-jected Groups of hosts of one type only 21 135 222 17 200 62.34*** Groups of hosts of both types together 21 45 26 7 77 49.83*** Pairs of hosts 7 21 86 3 84 10.14*** Single hosts 12 59 175 13 105 9.72**" Field collected larvae - 1962 8 10 10 48 5.62* 1963 - 1 i . 38 108 51 664 46.70*** * Significant at the .02 level . ' Significant at the .01 level . Significant at the .001 level. - 13 ~ TABLE I I I Time spent by Exenterus canadensis adults i n contact with two types of potential hosts Host Parasite Number of Mean Time Stage Reaction Cases i n Contact Prespinning larvae Oviposit 95 2.8 mins. Feeding stage larvae Oviposit 15 6.1 mins. Prespinning larvae Reject 191 0.8 mins. Feeding stage larvae Reject 174 0.6 mins. - 14 -s e r t i f e r can e l i c i t them. E. canadensis also e l i c i t s alarm reactions i n N. s e r t i f e r feeding colonies, although i t s movements are so stealthy i t does so infrequently. In the laboratory, N. s e r t i f e r larvae exhibited alarm reactions i n only 61 of 3f>9 confrontations witft £. canadensis. There was no s i g n i f i c a n t difference i n the number of alarm reactions between feeding stage and pre-spinning larvae, nor did the absence of host alarm reactions influence oviposition (Table IV). Superparasitism by E. canadensis i s common i n both the laboratory and the f i e l d . However, the d i s t r i b u t i o n of eggs on f i e l d - c o l l e c t e d hosts i s not random, but i s described by the negative binomial equation (Table V ) . In the laboratory, the egg d i s t r i b u t i o n i s adequately described by the Poisson, (Table V) and although there are too few data to t e s t the f i t of the negative binomial, no overdispersion i s indicated by the c r i t e r i o n developed by Blackman (1942). The eggs of E. canadensis are l a i d externally and embedded i n the host's integument, a type of attachment that has been noted also i n E. abruptorius Thurib., E. adspersus Htg., E. d i p r i o n i s Eoh. and E. amictorius (Panz.) by Barclay (1938). The preferred oviposition s i t e on the host i s the dorsal or laterodorsal portion of the second and t h i r d thoracic and f i r s t f i v e abdominal segments. Ninety-three per cent of 132 eggs recorded were found i n t h i s area. The incubation period of E. canadensis eggs varies from eight to f i f t e e n days, with an average of 9.8 ± 0.8 days. The f i r s t - i n s t a r l a r v a emerges from the egg through a s l i t which extends along the whole exposed length of the egg. The egg remains gradually turn brown and are conspicuous on the host - 1 5 -TABLE IV Comparison of effect of host alarm reactions on oviposition and rejection by Exenterus canadensis Type of Larvae No Alarm Reaction Alarm Reaction Chi 2 Oviposit Reject Oviposit Reject Prespinning larvae 65 118 13 30 0.412 Feeding stage larvae 12 103 4 1.945 Type of Reaction No Alarm Reaction Alarm Reaction Pre-spinning Larvae Feeding Stage Larvae Pre-spinning Larvae Feeding Stage Larvae Chi 2 Oviposition 65 12 13 4 0.614 Rejection 118 103 30 14 3.223 Total 183 115 43 18 1.790 Chi for significance at the .05 level * 3.841, TABLE V Distribution of Exenterus canadensis eggs on Neodiprion sertifer prespinning larvae Number Field Data1 0 Laboratory datac of Eggs per Host Observed Poisson Negative Binomial Observed Poisson Calculated Chi Z Calculated Chi 2 Calculated 0 1943 1907.100 0.676 1942.500 0.0001 625 627.26 0.008 1 l 5 l 215.310 19.208 i55 .ao 0.114 117 112.09 0.215 2 34 12.154 39.268 28.88 0.908 7 10.02 N 3 4 6 1 0.457^ 0.013J 90.730 6.40 \ 1.53 / 0.109 1 0 0.60 > 0.03 J 0.659 5 0 0 6 0 2135 2135.034 149.882* 2134.52 1.131 750 75o.oo 0.882 A Pooled data for 1957, 1958, 1961, 1962, 1963-2 Pooled data for 1957, 1958. Significant beyond the .001 level. - 17 -integument for some weeks. Typically eggs do not hatch u n t i l after the host has spun i t s cocoon; however, they w i l l do so i n a saturated atmosphere, where N. sertifer prespinning larvae w i l l not construct a cocoon. Larvae feed externally throughout their entire development. When more than one egg has been l a i d on one host, the supernumerary larvae invariably die i n the f i r s t or second instar without overt signs of damage. The v a r i a b i l i t y i n larval development under constant temperatures of 1$°C and 20°G was so great that no difference between the average times was detectable and the data were grouped. The approximate duration, i n days, of the various instars are as follows: f i r s t , 22; second, 6; third, 31; fourth, 13>J and f i f t h , 9, exclusive of the time required to spin a cocoon. Hosts are apparently l i t t l e affected by the feeding of the f i r s t three instars of E. canadensis. There is no noticeable change i n the appearance of the host during this period, and they can usually withstand feeding by a single parasite for almost six weeks, and the attacks of several individuals for at least one week, without losing the a b i l i t y to pupate and form an adult. In the f i e l d , f i r s t instars of E. canadensis were present from mid-June to mid-July, second and third instars up to the la t t e r part of August, and fourth and f i f t h instars from then u n t i l the end of September. When feeding i s finished, the fully-developed E. canadensis larva spins a thin whitish cocoon within the host cocoon. The majority of parasite cocoons were spun while larvae were s t i l l at rearing temperatures. The remainder did so while being held at 5«5>°C, preparatory for storage at 0°C. - 18 -A l l specimens overwintered as eonymphs. Spring development was slower at 11? °C than at 20 °C i n a l l spring developmental stages, but i t was most marked i n the pupal stage, the average duration of which was doubled at the lower temperature (Table ¥1). Very rarely both laboratory-reared specimens and those obtained i n the f i e l d completed development to the adult without overwintering or remained within the host cocoon an extra 12 months, and emerged after having spent a second winter i n the host cocoon. 3*2.1.2. Temporal coincidence. E. canadensis overwinters as an eonymph and, therefore, a l l individuals must commence spring development at the same stage. Because small changes i n temperature greatly influence spring development times (Table VI), i t seems reasonable to assume that emergence of this species could occur over a prolonged period i n the f i e l d , depending upon the temperatures reached at the s i t e . In a test of development under natural conditions i n 1959, the f i r s t adult emerged 10 days earlier i n an exposed site as compared with a shaded s i t e . Temperatures beneath the l i t t e r i n the exposed site averaged approximately 3°C higher i n May and h°C higher i n June than i n the shaded s i t e . In two more extreme sites, differences of nearly 6°C were consistently recorded i n I960 (Table VII). Wallace and Sullivan (1963) recorded 6°C differences between l i t t e r temperatures i n exposed and shaded sites throughout the whole early summer i n the Chatsworth area. The marked response of E. canadensis to the temperature at the host cocoon-spinning site can apparently result i n a prolonged period when the adult parasite population i s present i n the f i e l d . Fig. 2 indeed shows that E. canadensis adults were present from the time the host was i n the second and - 19 -TABLE VI Spring development of Exenterus canadensis at l5°C and 20 °C Stage 15 °c 20 °C Average Range Average Range Eonymph 10 days 4-21 days 6 days 6-13 days Pronymph 8 days days 7 days 3-10 days Pupa 26 days 21-28 days 13 days 10-17 days Total kZ days 32-53 days 26 days 23-30 days - 20 -TABLE VII Average temperatures at five possible cocoon-spinning sites °C Period S i t e 1 1 2 3 4 5 May 1 - 31, 1 9 5 9 13 . 4 10.1 June 1 - 2 9 , 1 9 5 9 19.2 i 5 . i May 7 -31, I960 1 6 . 4 1 5.1 10 .6 June 1 -30, I960 20.8 17 .8 1 4.0 June 1 -19, I960 2 4 . 1 i 19.6 15.2 Site 1 - beneath open-grown tree, sunlight for part of each day • Site 2 - beneath tree i n plantation, no sunlight. Site 3 - i n open, no shade from trees. Site 4 - beneath open-grown tree, sunlight for part of each day. Site 5 - beneath tree i n plantation, no sunlight. - 21 -third instar until after the last host had dropped from the trees. In the following year at the same plantation, adults were present from the time the host was in the third and fourth instar until over three weeks after they had dropped from the trees. Fig. 2 also shows that some individual parasites must have died before the preferred host stage became available for attack, since the average l i f e span of ovipositing females is only 9.5 days. Other adults spent a part of their l i f e before or after prespinning larvae were present. Those that emerge too early to attack prespinning larvae do have the opportunity to attack feeding stages, although they do not attack this stage as readily as the preferred host stage (Table II). Moreover, approx-imately half of the eggs deposited on feeding stages arc sloughed off with the final larval ecdysis. Attack on feeding stages in the absence of pre-spinning larvae may have one advantage, however, since the l i f e of the parasite may be prolonged until the preferred stage becomes available. A schematic illustration of the effects of asynchrony on this species is given in Fig. 3A. 3.2.1.3 Spatial coincidence. The majority of N. sertifer larvae moult to prespinning larvae on the trees, and spend a short time there before dropping to the ground. The remaining larvae do not undergo their final larval moult until they have dropped to the ground. E. canadensis attacked the host on the ground both in exposed sites and in the shade. In addition, E. canadensis attacked host larvae which were s t i l l on the trees, although i t concentrated its attack on hosts in the lower portions. Significantly higher parasitism occurred i n the lower half of ten foot trees than in the upper half (chi 2 = 5«05j p = approx. .02), and there was no attack on prespinning - 22 -i F i g . 2'. The presence of N. ser t i fer larvae and of E . canadensis adults i n the f i e l d , Chatsworth, Ontario, 1959-- 23 -DISTANCE FROM TRUNK (FEET) c DISTANCE FROM TRUNK (FEET) F i g . 3. Schematic presentation oi' coincidence between N. sertifer and E. canadensis. A. Temporal coincidence, solid line indicates host density, broken line parasite adult density. B and C. Spatial coincidence, distribution of prespinning larvae beneath and beyond the crown projection of an open grown tree (B) and those of two adjacent trees in a plantation (C). Cross-hatched areas indicate where attack by E. canadensis can occur. - 21;-larvae confined on trays i n the crowns of trees at a height of ten feet. Thalenhorst (1950) made similar observations on Exenterus spp. attacking Diprion pini L. This cannot be considered a lack of spatial coincidence, however, since a l l larvae must pass through the lower part of the tree as they drop from branch to branch to the ground, i n passing from the three-dimensional la r v a l environment to the essentially two-dimensional cocoon environment. Pig. 3B and C il l u s t r a t e the effects of spatial coincidence schematic-a l l y . 3.2.2 Pleolophus basizonus (Gray.) 3.2.2.1. Biology. The mean l i f e span of P. basizonus adults was 18.0 ± 0.8 days for both sexes, based on 92 specimens maintained at 20°C and 70% R.H. P. basizonus i s multi-voltine and i n the f i e l d i t s attacks on N. sertifer cocoons set out i n the l i t t e r continued from mid-June u n t i l the end of September. Mated females of this species produce offspring of both sexes, vi r g i n females produce only males. The sex ratio of emergents from f i e l d attacked cocoons remained at approximately 55 per cent females through two successive f i e l d seasons. The oviposition rate of P. basizonus was investigated by offering newly-emerged parasites a surplus of host cocoons. Daily oviposition reaches a maximum of 3»68 ± 0.15 eggs after approximately four days and this maximum i s maintained u n t i l the female i s 9 to 10 days old. Thereafter, egg production declines rapidly (Fig. k ) * Ovipositing females contain increasing - 25 -numbers of "mature" eggs as their age increases, up to a maximum at age k days, "mature" eggs being defined as those approximately the same size as oviposited eggs. It i s assumed that since such eggs are s t i l l i n the ovarioles they are not actually ready for oviposi t ion. Twenty-six ovipositing females, age k to 8 days, had an average of 4.30 + 0.32 "mature" eggs i n their ovaries. When females are deprived of hosts, eggs accumulate i n the ovarioles. There i s no storage i n the oviducts, and, because "mature" eggs are large relat ive to the size of the ovarioles, the maximum storage capacity of the female i s roughly one egg i n each of the 8 ovarioles . Twenty-five females that had reached their maximum oviposition rate before being deprived of hosts for four days contained an average of 8.Ok ± 0 .51 mature eggs on dissect ion. Forty females treated s imi lar ly and then offered an excess of cocoons l a i d an average of 7 .25 ± 0.26 eggs on the f i r s t and.2.09 ± 0.14 on the second day after deprivation. Most of the stored eggs i n these i n d i -viduals must therefore have become t ruly mature, and ready for oviposit ion. Females that have been deprived of hosts from emergence also accumulate mature eggs i n the ovarioles, but the rate of accumulation i s slower during the f i r s t few days of their l i f e since egg production i s lower during that period. When offered cocoons these females also show a marked increase i n ovipositions on the f i r s t day followed by a decrease on the second day. P . basizonus attacks N. 3ertifer after the la t ter has spun i t s cocoon. The several phases of development passed i n the cocoon were offered i n pairs to females to determine whether preferences exist for any of them. There i s an indication of selection of female eonymphs over pronymphs, but since this was not apparent when male eonymphs and pronymphs were tested this may have - 26 -Fig. 4 . Daily er;g production of P. basizonus vhen offered a surplus of host cocoons. After day l^, when the number of feraa.les dropped below 1 0 , a 2-day average was used. V e r t i c a l l i n e s through each point represent ± 2 S . E . - 27 -been a chance difference. A limited number of tests indicated no selection between pupae and prepupae. Parasites avoided dead prepupae, and strongly selected female prepupae over male prepupae (Table VIII). Preliminary studies on the methods by which this selection i s made indicate that the parasite responds to the size of the host cocoon rather than to i t s contents, and that of the two primary dimensions of the cocoon, length and diameter, the latter may prove to be the determining factor i n selection. The oviposition process i n P. basizonus i s rather prolonged, requiring an average of 21.3 ± 1.16 minutes i n 100 ovipositions observed i n the laboratory. Only one egg was l a i d at each of these ovipositions. Therefore, the presence of more than one egg i n a host, observed i n both f i e l d col-lections and i n laboratory studies, indicates that superparasitism occurs. I t was not possible to obtain enough data from f i e l d collections to assess the nature of the distribution of eggs i n hosts, because of low densities i n the study areas. However a large body of data on egg distribution was obtained i n the laboratory studies. A series of experiments was made i n which each of five densities of parasites were offered each of six densities of female host cocoons. The distribution of eggs per cocoon was determined at each of the host and parasite densities and the observed distribution compared with those of the Poisson and negative binomial • In only 3 of the 30 cases were the observed data accurately described by the Poisson dis-tribution, whereas they were described by the negative binomial distribution i n 21 of the 30 cases (Table IX). P. basizonus i s an ectoparasite and the egg i s generally found loose i n the host cocoon. Morris et a l (1937) observed oviposition on one host and -28 -TABLE VIII Tests to determine the reaction of Pieolophus basizonus to the various developmental phases, found i n the host cocoon Host Phase Number Offered Number Attacked C h T Female pronymph Female eonymph M a l e pronymph Male eonymph Female pupa Female prepupa Female prepupa FemaHe dead Male eonymph Female eonymph Male pronymph Female pronymph 75 121 4o 43 22 30 305 116 188 320 84 89 4.95 0.91 0.71 134.73* 131.39 41.42' Significant beyond the .001 l e v e l . - 29 -TABLE IX Chi 2 values obtained when observed distributions of Pleolophus basizonus eggs per cocoon are compared to Poisson and negative binominal distributions Host Density-Parasite Density Number of Cocoons Poisson Negative Binomial 9 2 18 2 32 2 48 2 72 2 126 2 9 4 18 4 32 4 1*8 4 72 4 126 4 9 7 18 7 32 7 48 7 72 7 126 7 9 10 18 10 32 10 48 10 72 10 126 10 9 15 18 15 32 15 48 15 72 15 126 15 45o 900 1600 2400 1800 2520 270 540 960 1440 1440 1890 180 360 64o 960 1440 2520 135 270 480 720 1080 1890 135 270 480 720 1080 1890 8.59** 28.98*** 47.58*** 14.56*** 4.11 0.00 18.82 88.92' 155.34*** 6.26* 79 J T 5.59 .•3HH4-6.13 4o.58f** 167.13 528.47*** 43.38*** 40.50 58.38' 296.38*** 136.01" 49-20" 43.47*** 102 .61*** 1155.93 4676.61*** 15573.35* 0.97 0.45 0.11 0.01 1.18 0.01 1.74 1.61 7.19 0.69 0.07 0.23 3.95. 6.64* 0.75 7.06 0.22 2.84 4.83 6.98' 3.63 5.46 14.86' 7.73 7.56 39.18 56.88 Significant beyond the .05 level. Significant beyond the .01 level. Significant beyond the .001 level. - 30 -noted that the egg was " l i g h t l y attached" to the thoracic pleural region. This may be the normal procedure, the egg being dislodged when the host i s removed from the cocoon. At a constant temperature of 20°C, the average incubation period of P. basizonus eggs is 2,2 ± 0.05 days and the larvae require an average of 8.9 ± 0.15 days to complete development. The larvae then spin rather flimsy white cocoons within ths host cocoons and pass through the eonymphal phase of the prepupa i n 3*9 ± 0.19 days* The pronyirphal phase, i t s beginning indicated by the f i r s t appearance of the imaginal eye, and subsequently characterized by the constriction of the thorax from the abdomen, averases 1.7 ±- 0.07 days, and the pupal period 8.0 ± 0.09 days. The whole develop-mental period from oviposition to adult emergence requires 24.5 ± 0.25 deys at 20°C, and ranges from 76.8 ± 1=64 days at 10°C to 20.4 ± 0.40 days at 25°C, the lower and upper l imits of continuous development. In a l l attacks that occurred i n ths f i e l d up to mid-August, parasites developed without interruption, when reared under natural conditions. From that date on, however, approximately half overwintered as eonymphs and did not resume development u n t i l after they were removed from cold storage i n the spring. At 18°C, prepupae of this stock commenced the pronymphal phase 7.8 ± 0.77 days after removal from 0°C cold storage, spent 2.0 +. 0.15 days i n that phase and 10.5 ± 0.25 days as pupae. Total spring development required 20.5 ± 1«06 days. The times needed to complete development at other temperatures are shown i n Table X. There was no s t a t i s t i c a l difference i n the mortality of parasites reared on the two host sexes, nor was there any difference i n mortality - 31 -TABLE X Post-larval development of Pleolophus basizonus after three months at 0°C Rearing Total Temperature Development Time 5 . 5°c 9 9 . 1 ± 6 . 8 8 days 1 0 . 0 6 1 . 6 ± 5 . 9 9 " 1 5 . 0 28.2 ± 1 . 5 8 » 1 8 . 0 2 0 . 5 ± 1 . 0 6 » 2 5 . 0 1 2.6 * 0.1*1. " - 32 -between parasites reared on eonymphs and pronymphs or on prepupae and pupae. Hosts attacked by this parasite cannot complete development even i f the parasite f a i l s to develop, because the adult parasite paralyzes the host before ovipositing on i t . When superparasitism occurs, the supernumerary eggs or f i r s t instars are destroyed by the f i r s t emerging larva. The placing of 1, 2, 3, U, $> 6 and 9 eggs i n cocoons with paralyzed hosts had no effect on the size of the resultant adults or on their sex ratio, nor was there a significant decrease i n number of progeny produced at any of the levels of super-parasitism, compared to that with no superparasitism. There was however, a s t a t i s t i c a l l y significant increase i n development time of 1 1/2 days i n those cases where there were S> or more eggs per host compared to those with one egg per host. 3.2.2.2 Temporal coincidence. P. basizonus adults are present i n the f i e l d from mid-June to the end of September, as shown by their attack on N. sertifer cocoons exposed i n wooden trays for one-week intervals during that period. The f i r s t N, sertifer prespinning larvae generally appear i n early June (Pigs. 1, 2), hence cocoons of the current generation are present and subject to attack by mid-June. Since trays were not placed i n the f i e l d before mid-June, however, there i s no concrete evidence to indicate that there i s perfect synchrony between the adults emerging from the overwintering generation of P. basizonus and their hosts. Considering the spring develop-ment times (Table X) and l i t t e r temperatures observed i n May and June (Table VII) i t i s l i k e l y that some adults do emerge too early to attack the current generation. If overwintering cocoons of the previous generation are present - 33 -( G r i f f i t h s 19$9), they may be u t i l i z e d by e a r l y emerging p a r a s i t e s . Over-wintering has never been recorded at Chatsworth, however, and there asynchrony between f i r s t generation P. basizonus adults and i t s host seems l i k e l y . There i s no problem of asynchrony between the second 'generation adults of t h i s species and i t s host, since host cocoons are present i n the ground from mid-June u n t i l September. Sawfly adult emergence gradually depletes the host population f o r a t h i r d generation of p a r a s i t e s . The probable appearance of temporal r e l a t i o n s between P. basizonus and N. s e r t i f e r i s i l l u s t r a t e d i n F i g . 5A. 3.2.2.3 S p a t i a l coincidence. The s i t e s through which P. basisonus adulta search f o r host cocoons were determined by p l a c i n g wooden trays containing cocoons i n micro-environments ranging from the deep shade encountered under closely-grown Scots pine 10 to 15 f e e t high, to the exposed areas between small trees and i n c l e a r i n g s . Attack occurred throughout the season over the whole range of micro-environments t e s t e d . Attack also occurred i n cocoons that had been spun i n trees and i n those fastened there with thread f o r weekly periods throughout the season. The attacks i n trees occurred from one to s i x f e e t above ground, the highest l e v e l t e s t e d . Good s p a t i a l coincidence between P. basizonus and N. s e r t i f e r cocoons e x i s t s on the h o r i z o n t a l plane, and i n that p o r t i o n of the v e r t i c a l plane that i s above the ground. However, since most N. s e r t i f e r cocoons are spun beneath the needle l i t t e r on the ground, i t was necessary to t e s t the a b i l i t y of P. basizonus adults to penetrate needle l i t t e r . This was done by burying N. s e r t i f e r cocoons under various depths of whole and crushed needles i n two-foot square cages, and recording the number of eggs l a i d by s i x parasites - 3k ->• i— CO z L U Q DEPTH OF COCOONS BELOW SURFACE (MM) Fig. 5. Schematic presentation of coincidence between N. sertifer and P. basizonus. A. Temporal coincidence, solid line indicates host density, broken line parasite adult density. B apd C Spatial coincidence. The frequency distributions indicate the distribu-tion of host cocoons beneath the surface, the cross-hatched area the number of host cocoons available for attack in B, an area of shallow lit t e r , and C, an area of deep l i t t e r . - 35 -during a five-day period. Whole, uncompacted red and jack pine needles apparently did not seriously impede adults since attack on cocoons buried beneath layers of needles 2$ and $0 mm. thick did not di f f e r significantly (Fig. 6 A ) . When layers of crushed needles, which approximate l i g h t l y compacted natural l i t t e r , were used, attack was v i r t u a l l y confined to cocoons less than 13 mm. from the surface (Fig. 6B). No attack occurred on cocoons protected by 2$ mm. of crushed l i t t e r , when there were no cocoons above them (Fig. 6C). A schematic i l l u s t r a t i o n of the effect of cocoon depth on attack by P. basizonus i s given i n Fi g . 5B and C. 3.2.3 V i l l a sinuosa (Wd.) 3.2.3.1 Biology. Adults were observed in the f i e l d from June 12 to July 30, 1959, and from June 27 to August 12, 1?60. Both sexes were present through-out these periods. Two attempts to determine the adult l i f e span of this species have apparently underestimated i t . Nine field-captured adults kept individually i n 12 x 12 x 14 inch wire-screen cages with a supply of crushed raisins and honey lived an average of only 2.2 days (range one to six days). The mean period between marking and f i n a l recapture of 16 adults i n a mark-and-re-capture experiment was only 3.8 days (range two to six days). Yet ten adult females up to two days old had no large "mature" eggs i n the ovaries, while 31 field-collected females of unknown age had from 2 to 325 "mature" eggs. It seems l i k e l y , therefore, that the confinement or handling of adults shortened their l i f e span. - 36 -2 5 -X »-Q . LU O oi 50 A 20 B 2 2 c o o WHOLfc NEEDLES CRUSHED NEEDLES F i g . 6. A b i l i t y of P. basizonus adults to attack N. s e r t i f e r cocoons buried i n various depths of whole and crushed needles. The figures'at the bottom of each column are the d a i l y number of eggs l a i d per female. The figures within the ovals i n the columns are the per cent of the t o t a l attack that occurred at that l e v e l . 100 cocoons ana si x iemales were used i n each experiment. - 37 -The sex ra t io of V . sinuosa adults was determined by examining 200 pinned, specimens from 12 cocoon collections made i n southwestern Ontario over a period of six years. In no case did the sex ra t io from any one area and year d i f f e r s t a t i s t i c a l l y from the average for a l l areas and years, which was 52.0 per cent females. V . sinuosa parasitizes cocooned larvae of N. s e r t i f e r . F i r s t - i n s t a r parasite larvae have been recovered from cocoons but the egg stage ha3 never been found. These facts , plus the evidence from the l i terature that many bombyliids deposit their eggs i n the ground and not i n contact with the host (Shelford 1913; Richter and Fluke 1935,* Linsley and MacSwain 1957; Sweetman 1958), led to the use of Tullgren funnels to determine the oviposition habits of V . sinuosa. In 1959, s o i l samples were taken from areas with bare s o i l on the surface, with s o i l covered by a l i t t e r of dead vegetation only, and with s o i l covered with a layer of l i v i n g grass. Although these s o i l samples were taken when f i r s t - i n s t a r larvae of V. sinuosa were present i n the f i e l d only two of the 3 2 samples taken i n areas with grass cover contained f i r s t - i n s t a r larvae, while 11 of the 2 8 samples i n the other two categories contained l i v i n g f i r s t - i n s t a r larvae. This difference is significant ( c h i 2 = 7.76; p <(.0l), and i n addition to indicating that eggs are deposited i n the s o i l , also shows a preference by adults for oviposition on bare ground or ground covered only with dead vegetation, compared to grass-covered ground. F i r s t - i n s t a r larvae were very much overdispersed i n the samples by the c r i t e r i o n established by Blackman (19U2), indicating a tendency i n the adults to confine their oviposition to certain l imited areas. In spite of the tendency for adults to concentrate their ovipositions i n restr ic ted areas, - 38 -superparasitism was rare. Only two cocoons containing more than one V. sinuosa larvae were found i n approximately 130 parasitized hosts collected i n 1957• In both there was a dead f i r s t - i n s t a r and a living second-instar which developed normally. As stated earlier, deposited eggs of this species have never been observed. The earliest stage found, f i r s t instar, was extracted from s o i l samples from mid-July to the end of August. None were found i n the weekly samples from mid-May to mid-July or from late August to mid-September. Seven f i r s t - i n s t a r larvae kept on moist sand lived an average of 10.6 days (range 2 to 21) after extraction from the s o i l . Their method of penetration into the host cocoon i s unknown, and those obtained within host cocoons are indistinguishable from those obtained from the s o i l . Larvae found i n cocoons spent an average ?.l i 1.2 days i n the f i r s t instar at 20°G and LU.8 ± l.k days at 1$%. A l l l a rval stages feed externally. The f i r s t instar apparently produces a paralyzing agent that renders the host immobile and prevents i t s further development even i f parasite feeding ceases. First-instar larvae were found i n weekly collections of host cocoons throughout August and September, and made up the majority of V. sinuosa larvae obtained u n t i l mid-August. Second-instar larvae began appearing as early as f i r s t - i n s t a r larvae, but only became numerous by mid-August. After the end of August their numbers declined. Third-instar larvae were obtained i n increasing numbers from mid-August u n t i l the end of the season. Mature larvae, i.e., those third instars that had completely consumed the host, were found i n collections as early as mid-August. They made up the majority of the popula-tion by mid-September, and overwintered i n that stage, although approximately - 39 -10 per cent did not develop beyond the second ins tar . Larvae placed, i n 0°C cold storage for three months as second instars resumed and completed develop-ment after being restored to rearing temperatures indicating that these individuals could survive under natural conditions. Mature larvae pupated 10 days after removal from cold storage to 20°C rearings. Larvae that had overwintered as second instars reached the pupal stage 19 days after removal from cold storage to 20°C. Both then required 30 days to complete development. "When reared at 15°C after cold storage, an average of 37 days elapsed before pupation and only 20 per cent had reached the adult stage after two months at that temperature. 3.2.3.2- Temporal coincidence. N. ser t i fer i s i n the cocoon from mid-June to late September. In both 1959 and I960, the f i r s t V . sinuosa adults were observed i n the f i e l d less than one week after cocoon spinning had started. In 1959 they were present u n t i l July 30, i n I960 u n t i l August 12. Asynchrony, therefore i s unlikely i n this species (Fig . 7A). 3.2.3.3 Spatial coincidence. The spatial l imitations of V . sinuosa o v i -posit ion si te preferences are sharply defined, as indicated by s o i l samples and cocoon col lec t ions . Fourteen f i r s t - i n s t a r larvae were obtained from 25 s o i l samples collected i n open exposed sites i n 1957, whereas only one was obtained from the same number of samples collected i n deep shade. Of nearly 600 cocoons obtained i n collections from open areas i n 1957, 12.5 per cent contained V . sinuosa larvae, while only O.k per cent of a similar number of cocoons collected from shaded areas contained V . sinuosa larvae . I t was pointed out i n an ear l ier section that N. ser t i fer cocoons are more - ko -co Z LU o ' J U N E J U L Y A U G U S T S E P T E M B E R to Z C r o w n P r o j e c t i o n • i i i ! B D I S T A N C E F R O M T R U N K (FEET) co Z LU Q C r o w n P r o j e c t i o n 1 1 1 1 1 wmi i i i i i D I S T A N C E F R O M T R U N K (FEET ) F i g . 7» Schematic presentation oi' coincidence between N. s e r t i f e r and V. sinuosa• A. Temporal coincidence, s o l i d l i n e indicates host density, broken l i n e parasite adult density. B and C. Spati a l coincidence, d i s t r i b u t i o n of host cocoons beneath and beyond the crown projection of an open grown tree(B) and those of two adjacent trees i n plantation (C). Cross-hatched areas indicate where attack by V. sinuosa adults can occur. - i n -frequently spun i n the shade of trees. A further i l l u s t r a t i o n of this was given when the cocoon density i n 1 0 of the 9 inch diameter circular s o i l samples made i n open sites for f i r s t - i n s t a r larvae assessment were compared with a similar number of identical samples made i n deep shade on the same day. The former contained an average of 0 . 3 sound N. sertifer cocoons per sample, the latter 5 « 2 . Although V. sinuosa adults do not deposit their eggs i n those positions where N. sertifer cocoons are most concentrated, i t i s s t i l l possible that they exercise some selection for hosts within the limited area of their a c t i v i t i e s . This can be determined by comparing the density of host cocoons i n s o i l samples that contained V. sinuosa f i r s t instars with those that did not. The mean number of host cocoons i n samples that produced f i r s t instars did not differ from that found i n a l l open area samples ("t" = . 5 2 ; p * . 6 0 ) . The d i f f i c u l t i e s encountered by V. sinuosa with spatial coincidence are schematically shown i n Fig. 7B and C. I i . SIMULATION OF COINCIDENCE U«l Introduction In the previous section i t has been demonstrated that lack of coincidence i s possible between N. sertifer and the three parasites studied. In one species, E. canadensis, spatial coincidence i s nearly perfect, while lack of temporal coincidence may play an important role; i n another species, 7. sinuosa, temporal coincidence i s perfect, and lack of spatial coincidence lim i t s attack; i n the third species, P. basizonus, both temporal and spatial coincidence may be less than perfect. The effects xhich such lack of coinci-dence can have on both parasite and host must now be determined. I t would be a Herculean task to do so while working i n the f i e l d . Therefore, efforts were transferred to the laboratory, where the essential variables could be manipula-ted at w i l l , and the confusing array of factors that characterize conditions i n the f i e l d could be eliminated. In order to be reasonably r e a l i s t i c , however, i t was necessary to explore the interactions between degrees of coincidence on.the one hand and the effects of host and parasite density on the other. This was dona by choosing one of the species of parasites, (P. basizonus.) as an analogue of a l l parasite species, and by showing experimentally how various combinations of host and parasite density affected attack. With this information i t was then possible to introduce degree of coincidence into the system, and to study i t s effects. h*2 Methods The hosts used i n the laboratory experiments were cocoons of N. s e r t i f e r . They were chosen not only because they are the actual host stage of two of the parasites studied, but also because they require l i t t l e handling. Large numbers of cocoons can be obtained simply by mass rearing late feeding-stage larvae i n the f i e l d and shipping the newly spun cocoons to the laboratory, where they can be stored u n t i l needed. They may be kept up to one year at 0°C with no development and very l i t t l e mortality. The parasite used was P . basizonus, again not only because i t was one of the species studied, but also because i t i s an ideal experimental animal i n many respects. I t mates and oviposits readily under laboratory conditions. Its l i f e span i s quite short and uninterrupted by diapause requirements at room temperature. Its immature stages require no attention. In addition, a great deal was already known about i t s behaviour, the appearance of immature - U3 -stages, i t s host preferences and handling techniques. The cage used for the experimental universe was k by 8 feet with walls of 1 x li inch lumber, and a removable top consisting of a wooden frame and fine-mesh nylon screen (Fig. 8, 9). The size selected was the maximum practicable one, after several smaller cages had been eliminated because they were not large enough to obtain a changing response by the parasites to host density. Even i n the large cage a functional response to host density was obtained only after the introduction of barriers to make i t more d i f f i c u l t for parasites to locate hosts. These consisted of 2£3 glass v i a l s , i n 2 3 rows with 11 vials per row, giving a spacing of 3 1/2 inches between vials and a border of 1 3 A inches between the cage side and the nearest v i a l s to i t . The v i a l s , which were 13 mm. i n diameter and 2 0 mm. high, were kept upright and their position i n the cage determined by placing them i n holes 13 mm. i n diameter and approximately 3 mm. deep. Preliminary tests showed that the parasites were able to walk into and out of these v i a l s and to oviposit successfully on cocoons within them. The cage was lighted by two UO-watt fluorescent tubes i n a reflector suspended approximately 18 inches above the floor of the cage. A sheet of white paper supported on a wooden frame between the light source and the cage served to diffuse the l i g h t (Fig. 8). The resulting light gradient i n the cage had no significant effect on the distribution of attack i n five preliminary experiments, each involving two females and lasting two days. Four identical cages were used, supported one above the other by a 2 x h inch frame, (Fig. 8) i n a rearing room where a temperature of 20°C, relative humidity of 6$% and a daily photoperiod of 16 hours was maintained. A number of preliminary tests were made to establish the range of host densities over - uu -F i g . 8. Experimental cages i n place on the rack. A. Diffusion screen between l i g h t source and cage. - US -F i g . 10. The mechanical arm used to capture parasite females when cocoons were about to be changed. It has been put i n the ca^e through a capture port. - k6 -which changes i n amount of attack occurred, that i s , to establish the gross outline of the functional response curve to host density. This was necessary since the most important point to be considered i n selecting host densities to be used i n the f i n a l experiments was that they should be wall-distributed along the rising phase of the functional response curve. Ihfe second consider-ation was that the densities should be within the range of natural cocoon populations. The third and least important consideration was the necessity of keeping host cocoons equidistant from each other i n the cage. The six densities chosen are l i s t e d i n Table XI. In order to reduce the observed v a r i a b i l i t y i n oviposition rates among individuals, the lowest parasite density used was two females per cage. A high density was needed to show interference between females i f this occurred. Considering the practical limitations of the parasite rearing program, the largest number of females that could be regularly expected was l£. Three densities between these extremes were selected giving a t o t a l of five parasite densities, as l i s t e d i n Table XI. The number of replicates at each host and parasite density was largely determined by the desire to have approximately the same number of parasite days of information from each host-parasite combination (Table XII). Practical considerations of supplies of hosts and parasites and of time available are responsible for the failure to make the numbers of parasite days completely uniform. The reduction i n number of replicates at high host and low parasite densities (Table XII) was necessitated by a shortage of hosts. I t was f e l t that the results obtained at these host and parasite levels were reliable enough to permit this reduction. - 4 7 -TABLE XI Conversion of parasite and host densities to numbers per square meter Parasite Density Host Density Number Number Number Number per Cage per Sq. M. per Cage per Sq. M. 2 0.71 9 3.17 4 i . i a 18 6.35 7 2.47 32 11.29 10 3.53 48 16.93 15 5.29 72 2$.40 126 44.44 - 48 -TABLE XII Number of replicates at each host and parasite density Eost Parasite Density Density 2 4 1 10 15 9 10 6 4 3 3 18 10 6 4 3 3 32 10 6 4 3 3 48 10 6 4 3 3 72 5 4 4 3 3 126 4 3 4 3 3 - 49 -The particular host and parasite density i n any one experiment was determined randomly within the limits of two restrictions. F i r s t , an equal ncmber of replicates of each host and parasite density was assigned to each of the four cages i n order to eliminate the possibility of small undetected differences between cages affecting the results. Second, i t was occasionally necessary to delay an experiment at the higher parasite densities because of a temporary shortage of females. Parasites were obtained for the experiments i n the following manner. Each day a number of pairs of newly-emerged adults were set up i n 4 x 4 x 4 inch-wooden cages with crushed raisins and two or three female sawfly cocoons. Three days later, the cocoons were removed from the cages and opened to determine i f eggs had been l a i d i n them. Females that had oviposited were then considered "standardized" and ready for use: they were at least three days old, had had an opportunity to mate and had oviposited. The small number of females that had not oviposited were destroyed. Occasionally, when not enough three-day-old standardized females were available, these were kept with cocoons another 24 hours and then used with additional three-day-old standardized females i n an experiment. Also, a number of standardized females were kept as "stand-ins" for each experiment to replace females that had escaped or died during experiments. The "stand-ins" were offered new cocoons daily. Only 38 females died and h$ females escaped i n the 4200 parasite-days of the experiments. Each experiment ran for five days . On the f i r s t morning of an experiment, clean vials were placed i n the cage, four raisins were distributed randomly i n the cage, the predetermined number of female cocoons were placed i n shell vials - 5 0 -i n the standard pattern for that host density, the cage was closed and placed on the rack. Then the standardized females, which had been transferred from stock rearing cages to screw top vials with screen ends, were introduced into the cage through the "introduction ports," circular holes i n the side of the cage, normally closed with a rubber stopper (Fig. 9). The cage was l i g h t l y sprayed with water at that time and again at 1700 nr., otherwise i t remained undisturbed u n t i l the second morning. On the second morning the females i n the experimental cages were confined under small petri plates, an operation carried out using a simple'-mechanical arm device through one of the three "capture ports," small openings approx-imately 3 x h inches i n the side of each cage, and normally closed by a sliding plexiglass door (Fig. 9, 10). When a l l females had been captured, the cage was lowered to the floor, the top removed and the cocoons replaced with new ones. The cage was then replaced on the rack and the females released. A new experiment was started every morning for four consecutive mornings. On the f i f t h day no experiment was started because there were only four cages and each experiment ran for five days. Cocoons were changed every day. Clean vi a l s were used only at the beginning of each experiment, when the cage was also thoroughly cleaned out. The cocoons from each experiment were opened and examined immediately. The attacked hosts were replaced i n their cocoons with one parasite egg, and placed i n shell v i a l s to provide part of the supply of parasites for future experi-ments. Attacked hosts from the standardization tests and from the "stand-ins" were also treated i n this way. If too few attacked hosts were obtained from these sources on any one day, the surplus eggs that were almost invariably - 5 1 -obtained were placed i n cocoons that contained coddled hosts. Mortality i n rearings on coddled hosts was only s l i g h t l y greater than that from hosts paralyzed by parasites. In this manner, approximately 60 attacked hosts were set up every day, allowed to develop at 20°C for 16 days, and then examined d a i l y for emergents to use for standardization tes ts . This system was quite e f f i c i e n t , requiring a minimum of effort and also u t i l i z i n g as few host cocoons as possible . In order to generalize the results obtained i n these experiments, a l l measurements of host and parasite density were converted to the number per square meter before analysis of the results was started. The resultant densities are given i n Table X I . k>3 Results The analysis of the results of the experiments involved the handling of f ive basic sets of data-host density, parasite density, time, the number of eggs l a i d and the number of hosts attacked. The two ways i n which attack was measured are indicative of the two kinds of responses involved. One of these was measured as the number of eggs l a i d per parasite and one as the number of hosts attacked per parasite . The former i s a measure of the number of attacks completed per parasite irrespective of whether a particular host receives one or more attacks, i . e . , irrespective of superparasitism. The lat ter i s a measure of the number of hosts that have been attacked at least once, and i s intimately bound up xdth superparasitism. Since a host i s k i l l e d by one attack as effect ively as by many, this measure i s d i r e c t l y related to host mortality, a lso . The number of attacks ( i . e . , number of eggs la id) per para-site i s the more basic of these two kinds of functional responses. The f i r s t - 5 2 -step i n the analysis, therefore, was to determine how the number of attacks i s affected by the two key variables - parasite density and host density. When the nature of the relation between number of attacks and density was revealed i t led logically to a demonstration of how this response was affected by the length of time parasite and host are together, i.e., by the degree of syn-chrony. Attention was then directed to a consideration of how attacks are distributed among hosts, so that number of hosts attacked can be expressed as a function of parasite and host density. Since data were obtained at six host densities and five parasite densities during a five day period, there i s a total of 1 5 0 blocks of data, each replicated three to 1 0 times. Each step i n the analysis requires the arrange-ment of these data into various sub-sets. To explore the effects of parasite density on number of attacks, for example, the data were divided into 30 sub-sets each of which contained data from one of the six host densities on one of the five days. Within each sub-set, therefore, everything was constant except parasite density, and the exact role of parasite density could be demonstrated. Similarly, the other steps i n the analysis required arrangement of data i n different sub-sets to isolate the influence of the specific variable concerned. In this step-like fashion, the intricate action and interaction of the various responses and variables were revealed. In the f i r s t step, the effect of parasite density on the number of attacks or eggs l a i d per parasite was demonstrated using the 30 sub-sets of data described above. This produced a family of 30 curves i n which number of attacks was plotted against parasite density. A sample of four such curves i s shown i n Fig. 11. The slope of the line of best f i t differed significantly - 5 3 -from zero i n only four of these curves, and i n each case the difference was positive. It i s interesting too, that 19 of the remaining slopes are positive (Table XIII). This i s significantly more than would be expected on the assump-tion of equal distribution of positive and negative slopes, and suggests some "f a c i l i t a t i o n " between parasites. To investigate this possibility and the counteracting influences of interference further, parasite density should have been increased. However, since rearing f a c i l i t i e s were hard-pressed to supply the highest parasite density then i n use, an attempt was made to assess attack at higher parasite densities by using smaller, one-foot square cages. Two parasite densities were tested, one female per cage and 10 females per cage. The former i s arithmetically comparable to approximately 32 females i n the large cage or 10.76 females per Bquare meter, the latter to 320 females i n the large cage or 107*58 per square meter, both very much higher than the highest densities actually used i n large cages. At both parasite densities, one cocoon was provided per cage. When the parasite density was one female per cage, there were 3«05 ± .26 eggs l a i d per female per day (99 female days). At a parasite density of 10, there was an average of 2.88 eggs per female per day (ikh female days). It i s impossible to calculate a standard error for the lat t e r mean, since the contribution of individual females to each day's ovi-position cannot be determined. It i s obvious that the two means are not significantly different, however, since the latter l i e s within the range of two standard errors of the former. Thus, the assumption of f a c i l i t a t i o n at high parasite densities i s not substantiated. The above calculations and experiments shoV that parasite density has l i t t l e effect on attack, and that i f f a c i l i t a t i o n and interference are signif-icant components of the response, they mask each other's action. Since the 11. Relation between number oi' attacks per female and density of female P. basizonus; experimental data and l i n e of best f i t calculated by the method of least squares• TABLE XIII Relation between number of attacks per parasite and parasite density i n Pleolophus basizonus slopes of l ines of best f i t and "t" values obtained when slope compared to zero slope Host Density Day 1 Day 2 Day 3 Day 4 Day 5 SLopo " t » Slope »t M Slope » t " Slope "t" Slope "t" 3.17 +0.026 0.388 +0.109 3 -313* +0.143 2.129 +0.122 2 .709 +0.082 2.118 6.35 +0.039 1.323 +0.117 2.433 +0.048 1.492 +0.047 1.096 +o.o55 i . o 4 i LI.29 +0.004 0.122 -0 e034 1.397 +o .004 0.102 -0.026 0.334 -o .o4o 0.520 16.93 +0.134 0.598 +0.033 1.127 +o .049 1.184 +0.078 2.166 +o .075 1.558 2$.hO +0.044 0.952 -0.042 0.788 -0.090 1.216 -0.043 1.123 -0.083 1.586 44.44 +0.098 2.478 +o .155 4.688** +0.144 3-543* +0.123 1.974 +0.144 3-699* Significant at . 05 l e v e l . * * Significant at .02 l e v e l . - $6" attack per parasite i s a constant at a l l parasite densities, the t o t a l attack may, therefore, be expressed as a linear function of the number of parasites present. Because changing parasite density did not affect the number of attacks per parasite, the 150 blocks of data can be now pooled into only five sub-sets, each representing one of the five experiment days, to explore the effects of host density on attack. The relation between parasite attack and host density for a l l five sub-sets i s shown i n Figs. 12, 13, and lU. A l l these functional response curves show the gradually decreasing rate of increase i n attack characteristic of the Type 2 response curves described by Holling (1959a). Two models exist which have been shown to describe adequately this kind of response, one developed by Watt (1959) and one by Holling (1959b). The form of the Watt (1959) model which i s most applicable here i s the one l n which both the number of hosts offered and the number of parasites present are known. This i s or, transposing - 57 -HOSTS PER SQUARE METER F i g . 12. The re ia t i on between number of attacks per parasite and host density in P. basizonus on the1 i i r s t and second days of ex-periments . The solid line i : i that predicted by the equation oi* Holling (1959b), the broken line that predicted by the equation of Watt (1959). - 58 -H O S T S P E R S Q U A R E M E T E R F i g . 13. The r e l a t i o n between number o i attacks per parasite and host density i n P. basizonus on the' t h i r d and fourth days of experi-ments . The s o l i d l i n e i s that predicted by the equation of Holling (1959b), the broken l i n e that predicted by the equation of Watt (1959) • - 5 9 -DAY 5 10 2 0 3 0 4 0 5 0 HOSTS PER SQUARE METER F i g . H i . The r e l a t i o n between number of att a c k s per p a r a s i t e and host density i n P. basizonus on the f i f t h day of experiments . The s o l i d l i n e i s that p r e d i c t e d by the equation of R o l l i n g ( 1 9 5 9 b ) , the broken l i n e t h a t p r e d i c t e d by the equation of Watt ( 1 9 5 9 ) . - 60 -where - the total number of eggs l a i d per square meter Np - the number of parasites per square meter - the i n i t i a l number of hosts available per square meter K - the maximum number of eggs that can be l a i d per parasite during the period the N q are available. and a and b are positive constants, designated by Watt (l?6l) as measures of searching efficiency and depression of searching efficiency from intra-specific competition, respectively. If the number of attacks per parasite i n the experimental cage i s design-ated as A, the number of parasites i n the experimental cage as P and the area of the cage i n square meters as C, then N » A.P A ~c~ and «= A T p which can be substituted i n equation ( l ) . Equation (l) must now be transformed into a linear form so that i t s usefulness i n describing the data may be determined by the least squares method. It becomes l n aJLjNp 1 - b (2) - 61 -Since there i s no interference between parasites, the term 1 - b, which i s a measure of interference i s 0 and equation (2) becomes l n / K \ - a N Q (3) The b e s t v a l u e o f K c a n now b e d e t e r m i n e d b y a n i t e r a t i v e t e c h n i q u e , t h e b e s t v a l u e b e i n g t h a t w h i c h m a x i m i z e s t h e c o r r e l a t i o n c o e f f i c i e n t f o r t h e r e g r e s s i o n i n (3)» The H o l l i n g (1959b) " d i s c " e q u a t i o n , o r b a s i c f u n c t i o n a l r e s p o n s e e q u a t i o n i s - - .. M Np = 1""+ ab N"Q w h e r e TQ - t h e n u m b e r o f d a y s h o s t a n d p a r a s i t e a r e i n contact a - t h e r a t e o f s u c c e s s f u l d i s c o v e r y p e r u n i t o f s e a r c h i n g t i m e , o r , s i n c e a l l s p a t i a l c o m p o n e n t s o f (k) a r e i n S q u a r e m e t e r s , t h e a r e a i n s q u a r e m e t e r s s u c c e s s f u l l y s w e p t o u t i n a u n i t o f s e a r c h i n g t i m e b - t h e t i m e i n d a y s s p e n t i n " h a n d l i n g " p e r e g g l a i d . T h e l e f t h a n d s i d e o f t h e e q u a t i o n N A / N p , c a n a g a i n be r e p l a c e d b y A . The s t r a i g h t - l i n e f o r m o f t h i s e q u a t i o n t h e n i s A - - abA + T p a (5") *0 ° w i t h w h i c h t h e d e s c r i p t i v e p o w e r o f t h e e q u a t i o n f o r t h e d a t a c a n b e d e t e r m i n e d , a n d c o m p a r e d w i t h t h e W a t t e q u a t i o n b y t h e l e a s t s q u a r e s m e t h o d . - 62 -Holling (1959b) has pointed out that i t i s possible to obtain a value of K from the basic functional response equation by use of the re la t ion bK - T c from which K - T c (6) b~ There are several comparisons that can be made between equations (3) and (5). F i r s t , from equation (3) the value of the y-lntercept should be zero. In calculations using the P. basizonus data, the y-intercept was not zero, a suggestion that the descriptive power of the model i n this instance i s not good. Further, i t was impossible to calculate a "best" K using the technique suggested by Watt (1959) i n one of the f i v e subsets of data, again suggesting the inadequacy of the equation. The sums of squares of deviations of the observed data from the calculated data are greater with the Watt model than with the Holl ing model (Table XIV). This i s i l l u s t r a t e d i n F i g s . 12, 13, and lh i n which the curves predicted by the two equations are compared with the data. The superior descriptive power of the Holling model, especially on days 2, 3 and U, i s c lear . It i s not possible to determine the v a r i a b i l i t y of these data, since the individual contribution of parasite females i n the experiments i s unknown. However, each point i s based on attack by from 123 to 1U7 females. One other comparison between these two models i s possible. Values of K, the maximum number of eggs that can be l a i d per parasite per day, can be - 63 -TABLE XIV Comparison of equations developed by Holling (1959b) and Watt (1959) i n describing the functional response of Pleolophus basizonus to host density Exp't. Boiling Equation Watt Equation A • K(l • 1 A • abN0 Day $um of Squares a b K • Sum»of Squares K 1 0.1655 0.1291 0.2959 3.3795 0.1900 2.080 2 0.3175 0.3324 0.3023 3.3080 1.6993 4.400 3 0.2305 0.5119 0.2762 3.6206 2.3960 4.000 4 0.2181 0.5487 0.3018 3.3135 2.9762 3.600 5 0.2368 0.5009 0.2737 3*6536 0.77091 3.2001 It was impossible to obtain a value of K by the iterative technique. K used i s the lowest one possible. - 64-obtained from both of them. An independent measure of this parameter i s also available from earlier experiments i n which females were offered a surplus of cocoons throughout their lives (Fig. 4). This value of K, using only data for those days when attack was maximal, i s 3«68 ± .15, based on 105 females. The predicted K values from the Holling model show less variation and are consist-ently closer to the true value than are those from the Watt model (Table XIV). On the basis of this evidence we must assume that the parasites under study here are behaving i n a fundamentally different way from that predicted by the Watt model, and that the Holling model describes the experimental data adequately. The value of the parameter a, the instantaneous rate of discovery, i n -creases with time (Table XIV). Preliminary work indicated that an explanation of this observed increase i n a probably l i e s i n changes i n the size of the odour f i e l d given off by the host, one of the subcomponents of this component l i s t e d by Holling (1961). Any attempt to carry this study of a to the point where an explanatory submodel could be developed would take us too far from our main objective, hoxraver, and i t must await a more propitious time. In the testing of the model that follows, the calculated values of a appearing i n Table XIV have been used. The value of the parameter b, handling time, remained relatively constant over the five days of experiments (Table XIV), indicating that the "standardization" technique was adequate. The values for b given i n Table XIV are fractions of one day and they are more easily understood when they are converted to hours. They then range from 6.57 to 7*26 hours. Ae the actual oviposition process requires an average of only 21.3 minutes or 0.36 hours, - 6 5 -i t is obvious that handling time must involve something more than oviposition. It must also involve a "refractory period" during which the female is unable to oviposit, probably because there are no eggs ready for oviposition. The use of a constant value for b with standardized females is justified* However, i t has already been demonstrated that females do not reach their maximum oviposition rate and thus a constant value of b until they are several days old (Fig. 4). To deal xd.th host-parasite systems where synchrony is not perfect, therefore, we must have a submodel to describe the temporal changes in oviposition rate. The data upon which this submodel can be based are given in Fig. i i . It was noted earlier that the number of "mature" eggs in ovipositing females increased with age up to a maximum at four days, suggesting that the reason for the increase in oviposition is an increase in rate of egg production with time. The b submodel can thus be made explanatory as well as descriptive i f i t can be expressed in terms of the rate of egg production. The logical mathematical form of this submodel, which must be able to express temporal changes in rate of production leading to an asymptotic level, is the logistic equation. It has the form 1+e where y - the rate of egg production per day per female K - maximum daily egg production per female T - the age of the parasite female in days and d and f are constants defining the slope and position of the curve. We may readily obtain numerical values for d and f, the only unknown values in equation (7) by transforming i t to a linear form - 66 -( 8 ) and solving for d and f, giving 7 = 3 - 6 8 0 1 . 0 5 9 -( 9 ) l+e The relation between the observed and calculated daily egg production i s given i n Table XV. In order to use the submodel with the functional response submodel (equation h) to predict the number of attacks at different degrees of asyn-chrony, i t i s necessary to convert the rate of egg production into i t s reciprocal, the time to produce and oviposit one egg, which i s b, handling time. The b submodel thus i s The predictive value of the functional response and handling time sub-models was assessed with two s t a t i s t i c a l tests. F i r s t the calculated values were compared to the observed values using linear regression. Second, the slope of this straight line was compared to a slope of one, the slope to be expected i f the predictive value of the straight line was perfect. The results of these two tests indicate that the descriptive powers of the two submodels are quite adequate (Table XVI). The handling time submodel, i n conjunction with the basic functional response submodel, enables us to deal with asynchrony resulting from parasites starting attack some time after hosts become available, i.e., late emerging 1.059 - 1.223T b = 1 + e (10) - 67 -T A B U : xv Comparisons of observed daily ovipositions of Pleolophus basizonus and that predicted by the b submodel Day Observed Predicted 0.5 1.U+1 l.kk 1 1.12 1.99 2 2.82 2.9k 3 3.12 3.43 h 3.63 3.60 5 3.62 3.66 6 3.70 3.67 7 3.71 3.68 8 3.70 3.68 Based on dissections of newly emerged females 0 - 1 days old. - 68 -TABLE XVI Test of Holling (1959b) model, using b submodel and a from data Exp*t. Day r «ttt 1 0.9603 0.2185 2 0.9480 0.0348 3 0.9616 0.4493 4 0.9533 0.4071 5 0.9586 0.2448 r for significance at .01 level « 0.874. " t " for significance at .05 level « 2.776. - 6 9 -parasites. However, females deprived of hosts, i.e., early emerging parasites, apparently behave differently since they accumulate eggs i n their ovarioles and deposit them i n a "burst" of ovilpasition when hosts are present. We cannot assume that the handling time submodel gives an adequate description and explanation of the oviposition behaviour of P. basizonus u n t i l we have determined whether i t can deal with early emergents. Deprived females accumulate a maximum of eight eggs i n three days. This i s known from dissections and i s also predicted by equation (9), the sum of the f i r s t three days' egg production equalling 8.26 eggs (Table XV). Beyond age three days, the number of stored eggs remains constant at eight. When hosts are provided* stored eggs are nearly a l l oviposited the f i r s t day. The value of b, handling time, for the f i r s t day's attack by early emerging females, can thus be determined either as the reciprocal of the accumulated values of daily egg production from equation (9) up to age three days, or as the reciprocal of the maximum egg storage capacity, beyond that age. The f i n a l step i n dealing with attack by early emerging parasites i s to determine whether a relation exists between the b submodel and attack after the f i r s t day's i n i t i a l increase. I t was found that no significant s t a t i s t i c a l difference existed between attack by normal females on their f i r s t day and that by deprived females on their f i r s t day after the i n i t i a l "burst" of activity. This relation held up to normal age of 13 days with only two exceptions (Table XVII). I t i s thus possible to use the b submodel to deter-mine the value of b to be used for deprived females simply hy substituting attack day n + 1 i n deprived females for attack day n i n normal females. The functional response to parasite and host density and the interaction - 70 - . TABI8 XVII Relation betxreen daily oviposition rates of normal and deprived females of Pleolophus basizonus Day 1 Normal Females Deprived Females " t " Mean No. eggs l a i d N Mean No. eggs l a i d N 1 1.12 50 1.07 15 0.166 2 2.82 45 2.40 15 0.970 3 3.12 43 2.87 15 0.667 4 3.63 41 3.27 15 0.882 5 3.62 34 4.67 15 2 .226* 6 3-70 27 4.67 15 1.974 7 3-71 24 4.27 15 1.059 8 3.70 20 4.4o 15 1.352 9 3.35 4o 3.40 15 0.094 10 3.43 35 3.36 14 0.115 11 3.18 33 2.79 14 0.596 12 1.95 19 3.43 14 2.463** 13 1.87 15 2.43 14 0.881 For normal females equals age, for deprived females equals days after i n i t i a l "burst" of oviposition following deprival. Significant at .04 l e v e l . Significant at .02 l e v e l . - 71 -between these and time have new been explored, and i t only remains to discover the r e l a t i o n between the number of eggs l a i d , the number of hosts attacked and mortality. In short, superparasitism must be accounted f o r . The r e l a t i o n between superparasitism and host and parasite mortality has already been shown to be quite simple. The number of supernumerary eggs, up to 8 per host, can-not increase host mortality over that ensuing when only one parasite egg i s present, and i t has been demonstrated that i t does not decrease the probabi-l i t y of one of the parasites reaching maturity. To predict the number of hosts and parasites present i n generation n + l , therefore, i t i s merely necessary to know the number of hosts attacked at l e a s t once i n generation n. This involves the study of the d i s t r i b u t i o n of eggs among hosts, f o r which the 1^0 blocks of data must again be rearranged into sub-sets, i n th i s case, one f o r each host and parasite density, a t o t a l of 30. The d i s t r i b u t i o n of eggs i n hosts i s adequately described by the negative binomial equation i n 21 of the 30 subsets of data, while only three of the 30 subsets are adequately described by the Poisson equation (Table IX). However, attention must now be concentrated, not on the actual numbers of eggs per host, but on the number of hosts that have one or more eggs. This i s most simply done by determining the number of hosts that have no eggs and subtract-ing t h i s figure from the t o t a l number of hosts offered f o r attack. When the zero categories of the two d i s t r i b u t i o n s are compared, none of the 30 observed zero categories d i f f e r s i g n i f i c a n t l y from that predicted by the negative binomial, while nearly one-third of the Poisson d i s t r i b u t i o n s had s i g n i f i c a n t c h i 2 i n the zero category alone. The deviation of calculated from observed zero categories i s f i v e per cent or less i n 28 of the 30 negative binomial calcu l a t i o n s , while i t i s f i v e per cent or less i n only 1E> of the Poisson calculations (Table XVIII). Further, when the 30 values of k, the index of - 72 -dispersion obtained i n negative binomial calculations, were plotted against the number of eggs l a i d per host offered, the slope of the straight line obtained did not differ from zero ("t" = .241$ p approximately . 8 0 ) , indicating that the value of k did not vary with attack. A more stringent comparison of these two distributions, and one that u t i l i z e s data more closely connected with the present needs, i.e., the 3 0 sub-sets of experimental data on number of eggs l a i d and number of hosts attacked at each host and parasite density, involves the equations by which the zero category of the two distributions are determined. If eggs were randomly distributed, the number of hosts containing no eggs would be given by -aN /N A 0 NQe and the number of hosts attacked, N H A, by -aNA/NQ \ (11) %A " %V~Q The linear transformation of equation ( l l ) i s N o .4343 log\ N - N 0 HA * a "1 ^0 (12) An equation may also be constructed comparable to (11) based on the negative binomial distribution, the zero category of which i s (Bliss 1953) - 73 -TABLE XVIII Comparison between observed zero categories and those calculated by the Poisson and negative binomial distributions Per cent Deviation from Observed Distr ibution Less than 0.1* 0.1 - 1.0* 1 - 5 * 5 - i o * More than 10* Negative Binomial 10 11 7 2 0 Poisson 1 3 11 5 10 - 74 -f - N 0 o T a. N where q = 1 + A ¥"k 0 From these can be determined the number of hosts attacked i f eggs were distributed contagiously NHA - W 0 " Ng , ( W ) A \ k and, transforming equation (13) to a linear form l o g T N 0 ] - k | log (NQk + NA) - log (N Qk)| (14) N 0 ~ NHA, Equation-(14) must be handled by an iterative technique, the correct value of k w i l l be that value that equals the slope. Its predictive ab i l i t y may be compared to that of equation (12) by regression analysis of the two straight l i n e s . Equation (12) gave a correlation coefficient of .821 + .060, equation (14) a correlation coefficient of .984 ± .006. The value of k was .7800. We now have a submodel that w i l l predict the number of eggs l a i d given only the number of hosts offered, equation ( 4 ) , and one that w i l l predict the number of hosts attacked given only the number of eggs l a i d and the number of hosts offered, equation ( 1 3 ) . Algebraically, i t would be straightforward to substitute equation (4) for N A i n equation (13). to obtain a single model, - 75 -but, prac t i ca l ly , i t i s better to leave them separate, especially i n those cases where the effects of the handling time submodel, equation (10), are incorporated. A f i n a l test of the three submodels was made using values of a from Table XIV, and 150 blocks of data, 30 on each of the f ive experiment days. The rela-t i o n between the observed number of hosts attacked and that predicted by the combined use of the three submodels are shown for each day separately i n F i g s . 15 to 19• The correlation coefficient i s extremely high i n every case,, and i n none of the cases did the l ine of best f i t d i f f e r s ignif icant ly from that for perfect predict ion. h*k Simulation of the effects of lack of coincidence In this section the model and the parameters obtained for P. basizonus w i l l be used f i r s t , to show the effect of lack of coincidence at a number of host and parasite densi t ies . Then the appropriate parameters for E . canadensis and V . sinuosa w i l l be estimated and u t i l i z e d i n a similar manner to compare the interspecif ic effects of coincidence. Only the effects of lack of coincidence i n a single generation w i l l be dealt with here, the long-term effects w i l l be l e f t u n t i l the following section. In these and a l l remaining simulations a l l parasites of one species are assumed to emerge on the same day and have the same l i f e span. Lack of temporal coincidence, or asynchrony, results when parasite females spend part of their l i f e span out of contact with the appropriate host stage, by emerging too early, or too l a t e . The index of synchrony, I , S i s that proportion of the female parasite's l i f e span that i s spent i n contact with the host. - 76 -F i g . 15. The relation between observed number of hosts attacked on f i r s t day of experiments and that predicted by the combined basic functional response, handling time and superparasitism submodels Line of best f i t calculated by least squares method, r = .930; "t" obtained when slope of line of best f i t compared to that for perfect prediction - .61b. - 77 -F i g . 16. The r e l a t i o n between observed number of hosts attacked on second day of experiments and that p r e d i c t e d by the combined b a s i c f u n c t i o n a l response, handling time and superparasitism submodels. Line of best f i t c a l c u l a t e d by l e a s t squares method, r = .967; " t " obtained when slope of l i n e of best f i t compared t o that f o r p e r f e c t p r e d i c t i o n .301. - 78 -F i g . 17. The relat ion between observed number of hosts attacked on third day of experiments and that predicted by the combined basic fun-ct ional response, handling time and superparasitism submodels. Line of best f i t calculated by least squares method, r = .961j "t" obtained when slope of line of best f i t compared to that for perfect prediction .778. - 79 -F i g . 18. The relation between observed number oi' hosts attacked on fourth day of experiments and that predicted by ithe.combined basic funct-ional response, handling tine and superparasitism submodels • Line of best f i t calculated by least -squares jinethod. r = . 9 7 1 ; " t " obtained when slope of line o i ' best-ifit cdmbarea! <-to that for perfect prediction . 7 9 2 . - 80 -DAY 5 < x Z u a UJ i i i i L 5 10 OBSERVED N H A jk i i i F i g . 1 9 . The r e l a t i o n between observed number of hosts attacked on f i f t h day of experiments and that predicted by the combined basic f u n c t i o n a l response, handling time and superparasitism submodels. Line of best f i t calculated by l e a s t squares method, r = . 9 6 7 ; " t " obtained when slope of l i n e of best f i t compared to that f o r perfect p r e d i c t i o n . 4 2 1 . -BI-OS) where T - the number of days the parasite i s i n contact with the host c Tp - parasite female adult l i f e span. The operation of equation ( l £ ) i s i l l u s t r a t e d graphically i n F i g . 20, which shows the effects of •various degrees of early and late emergence of parasite females with 15-day adult l i f e span (that assigned to P. basizonus i n this and following sections), on a host with a 15-day susceptible period. Although the length of the host susceptible period does not enter into the calculation of the index of synchrony, i t s effect i s obvious from F i g . 20 and equation (l5)• Parasites cannot enjoy perfect synchrony with hosts whose susceptible period i s shorter than the parasite adult l i f e span. Host suscept-i b l e periods longer than the parasite adult l i f e span increase the probability of perfect synchrony, but do not affect the index of synchrony when asyn-chrony occurs. Lack of spatial coincidence i s also indicated by an index, the index of coincidence, I^, which i s the proportion of the host population that i s susceptible to attack. With perfect coincidence the host population D equals N Q , the number of hosts offered, but, when a proportion P of the hosts are protected from attack then D - N + P 0 (16) N (17) and I - 82 -| — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — r — i — i — i — | — r I s = 0-6 I . . . . I . . . . 1 • • • L _ ! i I I I I I I I I 1 1 1 1—1 1 1 1 1 1 1—I TIME - DAYS 20. Schematic representation ol' synchrony between a host (cross-hatched block) that is vulnerable to attack i'or 15 days and a parasite (open blocks) whose female adults live 15 days. The changes in handling time based on the b submodel are shown within each parasite block. - 83 -kJiJL Pleolophus basizonus The interaction between synchronyj number of hosts attacked and host density at constant b and parasite density of one female per square meter, i s shown i n Fig. 21. The parameter values used are given i n Table XIX. (It w i l l be noted i n Table XIX that the value for a, the rate of successful discovery, . 5 5 0 0 , i s higher than any of the experimental values given i n Table XI?. It was pointed out i n an earlier section that observed changes i n a i n Table XIV were believed to be related to changes i n the odour f i e l d surrounding the host cocoon. I t has been assumed that this odour f i e l d reaches a maximum radius i n a relatively short time compared to the period cocoons are present, and that the best estimate of a based on these assumptions about i t s subcomponent, radius of odour f i e l d , would be a constant numerically close to the largest figure obtained experimentally). The direct relation between N„. and I at any constant i s obvious. The HA S 0 asymptotes of the curves w i l l occur at a lower and a lower as the index of synchrony decreases. The divergence of the curves i n F i g . 21 over their r i s i n g phases illus t r a t e s the greater effect of asynchrony at high host density than at low. This i s demonstrated even more dramatically i n Table XX, N * 1. P At the lowest host density (N - l ) , a 60 per cent reduction i n I causes only 0 o a decrease of approximately 16 per cent i n the number of hosts attacked, while at the highest host density (N Q - l\$0), the reduction of Ig and i 3 almost equal. At low host density superparasitism i s high, and reduction i n the number of eggs l a i d merely results i n a lessening of supernumerary eggs, with l i t t l e decrease i n the number of hosts destroyed. At high host density, how-ever, parasites are ovipositing at their maximum rate, and reduction i n time i n contact with the host i s c r i t i c a l , since superparasitism i s low and the - 8U -21. Simulations of number of hosts attacked at various host densities and with four i n d i c e s of synchrony, using P. basizonus parameters, b constant, parasite density 1 per square meter. - 85 -TABLE X S Parameter values used, i n simulation studies Parameter P. basizonus E. canadensis v. sinuosa N. ser t i fer a 0.5500 0.5UiO 0.1+000 -. b 0.27171 0.0521 0.0320 -k 0.7800 0.2732 0.1260 -Life Span 15 days 9 days 7 days 2 2-3 weeks 2 1/2-3 mos. 3 Sex Ratio 50* 9 50* S 50* ? 75* ? No. eggs per Female - - - 100 I n i t i a l Pop'n. 0.005 $/M2 o.oo5 ?/fa2 0.005 S/M2 0.5/M2 Other Mortality 75*1 75* 75* 97 -5*1 Genera-tions per Year i 1 l 1 1 In certain simulations these parameters were changed; the changes w i l l be noted where applied. Period prespinning larvae available for attack. Period cocoons available for attack. - 86 -TABIE XX Effect of varying degrees of asynchrony on attack by three species of parasites N o h P. basizonus E . canadensis V. sinuosa N p - 1 N p = 5 N p - 1 Np = 5 N p - 1 N p = 5 1 1.0 100 .o 1 100.0 100.0 100.0 100.0 i 100'.0 0.8 96.1+ 98.9 94.5 95.8 93-9 95.6 0.6 91.7 97.9 87.3 93.0 84.8 91.1 0.1+ 83-3 94.7 81.8 88.7 78.8 86.7 50 1.0 100.0 100.0 100.0 100.0 100.0 100.0 0.8 89.1 95-7 92 .2 95.9 92.9 95.7 0.6 75.5 89-4 81.6 90.2 83.4 89.8 0.1+ 57-8 79.3 74.5 86.1 75.0 84.4 45o 1.0 100.0 100.0 100.0 100.0 100.0 100.0 0.8 82.0 86.9 85.4 91.8 88.6 93-4 0.6 63.0 71.5 67.8 80.7 74.4 84.5 0.1+ 43.1 52.6 57.6 73-3 62.6 76.4 The number of hosts attacked i s expressed as a percentage of that occurring at perfect synchrony at each host and parasite density. - 87 -number of eggs laid and number of hosts attacked are nearly identical (Table XXI). A fivefold increase in parasite density produces a negligible increase in number of hosts attacked at low host density, and decreasing the synchrony again has l i t t l e effect on number of hosts attacked because of the "buffering" effect of superparasitism (Table XX). Under these circumstances, super-parasitism i s extremely high. Increasing the host density increases the host destruction, although even at the highest host density tested, a fivefold increase in parasite density causes only slightly over a threefold increase in number of hosts attacked. At these extreme host and parasite densities, large numbers of parasite eggs are lost through superparasitism, but the rate of decrease in number of hosts attacked with decreasing synchrony is slightly less than at low parasite density and high host density (Table XX, XXI). The simulation of P. basizonus-N. sertifer interactions can be made more realistic by the introduction of the handling time submodel. The values of b are plotted against parasite age in each of the rectangles representing para-sites in Fig. 20. From these i t can be seen that decreasing synchrony decreases the proportion of time late-emerging parasites spend ovipositing at their maximum rate. However, the only noteworthy difference between late-emerging parasites using constant b or the b submodel is a slight but consist-ent reduction in attack in the latter (Table XXI, XXII). The changes in b with age in early-emerging parasites are also shown in Fig. 20. The gradual decrease in the value of b with deprivation culminating in the high rate of oviposition on the f i r s t day of contact are shown, as is the return to conditions similar to that in late emerging parasites after this - 88 -TABLE XXI Number of eggs laid and number of hosts attacked by Pleolophus basizonus at three host densities, two parasite densities and four indices of synchrony, with handling time constant h N p = 1 Np = 5 0 NA NHA NA NHA 1 1.00 0.80 0.60 0.40 7*18 5.74 4.30 2.87 0.84 0.81 0.77 0.70 35.90 28.70 21.55 14.35 0.95 0.94 0.93 0.90 5o 1 .00 0.80 0.60 0.40. 48.70 38.96 29.22 19.48 23.43 20.87 17.68 13.55 243.50 194.80 146.10 97.40 39.33 37 .63 35.16 31.17 45o 1.00 0.80 0.60 0.40 54.41 43.53 32.65 21.76 47.82 39.23 30.15 20.61 272.05" 217.65 163.25 108.80 162 .39 141.12 116.05 85.45 - 89 -TABLE XXII Number of eggs l a i d and number of hosts attacked by Pleolophus basizonus at five host densities and two parasite densities by late and early emerging parasites, using handling time submodel h = 1 \ » 5 \ NHA \ % A 1 0.6L1 4-24 0.77 21.20 0.93 0.6E 4.27 0.77 21.37 0.93 10 0.6L 18.68 6.15 93.40 8.65 0.6E 19.73 6.26 98.66 8.70 50 0.6L 26.95 16.81 134.75 34.40 0.6E 29.90 17.92 149 -50 35.37 150 0.6L 29.11 23.86 145.55 70.15 0.6E 32.88 26.35 164.40 74.35 300 0.6L 29.71 26.70 148.55 9565 0.6E 33.74 29.92 167.70 103.56 45o 0.6L 29.91 27.82 149.56 108.85 0.6E 34.03 31.36 170.15 119.40 L indicates late-emerging parasites; E 11 early-emerging parasites. - 90 -i n i t i a l burst of attack. Only one index of synchrony was used to compare early and late emergents. The former showed small differences in number of eggs laid and no difference in number of hosts attacked at low host density, but in-creasingly greater differences as host density increased, the early-emerging parasites being able to take increasing advantage of the increased oviposition activity on the f i r s t day of contact as host density increased (Table XXII). The effect of lack of spatial coincidence in one generation is straight-forward, since i t results in a decrease in the number of hosts offered for attack, that i s , a movement to the left on the functional response curve (Pig. 21). Clearly, host density is important in determining the effect of lack of coincidence, protection of a small proportion of the hosts has a proportion-ately greater effect at low than at high densities. There i s also an obvious interrelation between temporal and spatial coincidence, the effect of the latter being less at low indices of synchrony than at high. 1+.1+.2 Exenterus canadensis The simulations that have been done on this species and on V. sinuosa are based on the assumption that the basic functional response equation developed by Holling (l9!?9b) to describe the relation between number of eggs laid and host density will apply. Holling (I9!>9b) showed that its descriptive power was adequate for several other species of parasites, and i t has been demon-strated to be so for P. basizonus in this study. The biological reality and universality of its parameters in attack have been pointed out by Holling (1961). An estimate of the maximum number of ovipositions per day in E. canadensis was made using the mean of the six most productive of the 6 U - 91 -female days of oviposition available, 1 ? . 2 eggs per day* The reciprocal of t h i s , . 0 5 2 1 , i s handling time b . A numerical value for the rate of discovery a can be obtained by substituting the number of egss l a i d at a known host density and the value of b i n equation (5), giving an estimate of a of . 5 U i i - 0 . It has already been noted that the supernumerary eggs i n superparasitism are distributed contagiously (Table V ) . The value of k i n the negative binomial equation from these data, . 2 7 3 2 , i s the one used i n the simulations. The l i f e span of adult parasites has been estimated at 9 days. The parameter values used are l i s t e d i n Table XLX. In this and the following section the indices of synchrony are s l i g h t l y different from those used for P. basizonus because the periods that parasites were i n contact with hosts were measured i n whole days. F i g . 2 2 shows that when the number of hosts attacked i s plotted against the number of hosts offered at various indices of synchrony for this species, there i s again an obvious decrease i n N with I at constant N . The o v i -HA S "J posit ion rate of this species i s higher than that of P. basizonus, however, and consequently the functional response curve does not become asymptotic at the highest host density used i n the calculations. The number of hosts attacked by E_. canadensis i s only s l i g h t l y affected by decrease i n synchrony at low host density. At the highest host density calculated, the decrease i n hosts destroyed i s more nearly equal to decrease i n synchrony (Table XXIII), but since this host density i s s t i l l on the r i s i n g phase of the functional response curve (F ig . 2 2 ) far this species, and hosts are not so abundant as to reduce superparasitism to a negligible amount, the large reduction i n eggs l a i d with increasing asynchrony i s not so f a i t h f u l l y - 92 -22. Simulations of number of hosts attacked at various host densities and with k indices of synchrony using E. canadensis parameters. Parasite density 1 per square meter. - 93 -reproduced i n numbers of hosts attacked as i t was i n P. basizonus (Table XX). The larger number of eggs l a i d by P. basizonus at low host densities i s simply a reflection of that species' longer l i f e span (Table XXI, XXIII). I f I g = .60 for P. basizonus, a period i n contact of nine days i s compared with the same period i n contact for E. canadensis, Ig = 1.0, the true relation between them i s seen. As with P. basizonus a fivefold increase i n numbers of E. canadensis produced only a ininor increase i n number of hosts attacked at low host densi-tie s , the large increase i n number of eggs l a i d being lost i n superparasitism (Table XXIII). At high host density the fivefold increase i n parasites results i n an approximately twofold increase i n number of hosts attacked, but there was less decrease i n supernumerary eggs than there was i n P. basizonus with a similar increase in host density. This i s a reflection of the specific re-actions of these two species to "high" host density. The maximum density used i n these simulations, USO per square meter, or approximately 1,800,000 per acre, would be a truly high N. sertifer population under natural conditions«. If "high" density i n terms of parasite attack i s defined as one where the functional response curve i s asymptotic, then i t i s also high to P. basizonus, but i t i s not to E. canadensis. h*h»3 V i l l a sinuosa The biology of this species i s not well known and i t w i l l be necessary to make several assumptions to calculate the necessary parameter values. How-ever, i f the model w i l l provide reasonable predictions with assumed parameter values, i t s general usefulness should be evident. There i s very l i t t l e direct evidence of superparasitism i n this species, - 91 -TABLE X X I I I Number of eggs l a i d and number of hosts attacked by Exenterus canadensis at three host densities, two parasite densities and four indices of synchrony h NP = 1 N p - 5 WA NHA NA % 1 1.00 4.76 0.55 23.80 0.71 0.78 3-70 0.52 18.50 0.68 0.56 2.65 0.48 13.25 0:66 o.lu+ 2.12 0.45 10.60 0.63 50 1.00 101.37 22.06 506.85 31.51 0.78 78.84 20.35 394.20 30.23 0.56 56.31 18.00 281.55 28.41 0.44 45.05 16.43 225.25 27.12 450 1.00 160.41 91.78 802.05 190.72 0.78 124-76 78.38 623.80 175.11 0.56 89.12 62 -.27 445.60 153.85 0.44 71.29 52.86 356.hB 139.72 -95-F i r s t instar larvae are contagiously distributed i n s o i l samples obtained from exposed sites where host cocoons are scarce, and are absent from shaded sites where host cocoons are ooncentrated. Assuming that this contagion remains after the f i r s t instar larvae have entered the host, the value of k obtained from their distribution i n the s o i l , .1260, w i l l serve as an estimate of this parameter. Oviposition i s not synonymous with attack i n this species, and there must be considerable loss of eggs and f i r s t instars after oviposition and before the host cocoon i s penetrated. This loss has been assumed to amount to 75 per cent of the number of eggs oviposited. Using the average number of "mature" eggs i n the 10 per cent of field-collected females with the highest egg counts as a starting point, and assuming that this average represents two day's ovi-position, the value of b was estimated at .0320. The l i f e span of adults has been estimated at seven days. To estimate the rate of successful discovery a i t was necessary to rely entirely on comparison with the two better-known species already dealt with. Each subcomponent of a was examined i n each species and a relative value as-signed to i t . The sum of these estimates gave a relative value for a i n the three species. Since the actual value was known for P. basizonus and E. canadensis i t was then possible to calculate a value for V. sinuosa of .1*000. Although lack of temporal coincidence i n V. sinuosa appears to be un-l i k e l y , i t would be interesting to compare the effects of asynchrony i n this species with the two already studied, considering i t temporarily as a hypothetical species having a rate of successful discovery similar to the other two species, handling time indicative of an egg-laying rate approximately -96-eight times that of P. basizonus and twice that of E . canadensis, and a dispersion coefficient approximately one-sixth that of P. basizonus and one-half that of E. canadensis (Table XIX). Attack by V, sinuosa resembles that by E. canadensis more closely than pasizonus because the functional response curve f a i l s to l e v e l off at the highest host densities used ( F i g . 23). At low and intermediate host densities, V . sinuosa lays fewer eggs and attacks fewer hosts than the other two species, even when allowance i s made for i t s shorter assigned l i f e span. At the highest host density tested, the number of eggs l a i d i s greater, but the number of hosts attacked i s less than the other two species, indicating that i t s greater egg laying rate i s more than overcome by the wastage of eggs caused by their dis tr ibution (Table XXIV). A f i v e f o l d increase i n parasite density produces less increase i n V . sinuosa attack than i n P. basizonus and E . canadensis a l so . At low host density and both parasite densities tested, V . sinuosa attack i s reduced more with decreasing synchrony than i s that of the other two species. At the highest host density tested, however, V . sinuosa attack i s affected less by reduction i n synchrony (Table XX). The la t ter host density i s not "high" for V . sinuosa according to the def ini t ion already stated that relates high host density i n a given parasite species to the density where attack becomes asymptotic, and the "buffering" effect of superparasitism that i s evidently characteristic of the r is ing phase of the functional response equation i s s t i l l preventing the one-to-one relat ion between number of hosts attacked and asynchrony seen i n P. basizonus. The effects of lack of spatial coincidence are again best i l l u s t r a t e d by functional response curves ( F i g . 23) • A change i n the proportion of protected - 97 -F i g . 2 3 . Simulations of number of hosts attacked at various host densities and with h indices of synchrony, using V . sinuosa parameters. Parasite density 1 per square meter. - 98 -TABLE XXIV Number of eggs l a i d and number of hosts attacked by V i l l a sinuosa at three host densities, two parasite densities and four indices of synchrony N o N p = 1 N p - 5 NA *RL NA NHA 1 1.00 2 ".76 0.33 13.80 o.45 0.79 2 .17 0.31 10.85 0.43 0.57 1.58 0.28 7-90 0.41 0.1+3 1.18 0.26 5.90 0.39 50 1.00 85-37 14.32 426.85" 20.66 0.79 67.07 13.30 335*35 19.77 0.57 48.78 11.95 243.90 18.56 0.43 36.59 10.74 182 .95 17.43 45o 1.00 186.39 75.41 931.95 136.10 0.79 146.45 66.83 732 .25 127.05 0.57 106 61 56.13 532 65 114.95 0.43 79.88 47.17 399.40 103.95 - 99 -cocoons w i l l have a greater effect on the attack by V. sinuosa than P. basizonus (Pig. 2 1 ) . For instance, an index of coincidence of 0 . 6 6 at a host density of !i50 cocoons per square meter would reduce N Q to approximately 3 0 0 . With perfect synchrony, Nj^ for V. sinuosa would be reduced from approximately 7 6 to 5 8 , a 2k per cent reduction, whereas for P. basizonus the reduction would be from 1+8 to 1+5, or approximately 6 per cent. 1+.5 Simulation of host-parasite interactions The interrelations of coincidence, host density, parasite density and attack i n one generation have been considered and i t i s now necessary to introduce a historical element into the calculations to follow the effects of lack of coincidence through a succession of host and parasite generations. To do this the necessary parameters for a host population that w i l l grossly mimic —* s e r^l^ e r must be established. The interactions must also be kept as simple as possible, so that the effect of those characteristics under study are not masked by interference from unrelated elements. The host characteristics must permit populations to increase i n the absence of parasites or when parasites are scarce, and must also allow for the elimination of the host when attack i s high. Ideally the same host characteristics should be used i n every system generated so that the effects of coincidence can be compared without corrections for changes i n host parameters. A number of host characteristics must be included: (a) Sex rati o . Griffiths (1959) and Lyons ( 1 9 6 3 ) provide an adequate estimate of 7 5 per cent females. (b) Number of eggs l a i d per female. 100 was selected as a r e a l i s t i c approx-imation based on several published estimates. - 100 -(c) l\himber of generations per year. N. ser t i fer has one. (d) The period during which susceptible host stage i s available for attack. Prespinning larvae were assumed to be available f o r two to three weeks, cocoons two and one-half to three months. (e) I n i t i a l host density. Only those situations i n which the i n i t i a l popula-t ion was low were simulated. To keep the calculations simple i t was assumed that only one migration to a given area occurred. An i n i t i a l host density of 0.5 per square meter was used i n a l l simulations. (f) Mortality from other factors . This was assumed to be constant and there-fore density independent. After some preliminary calculations a value of °7«5> per cent was selected, which approximates estimates of mortality given by Lyons (1963). With th is mortality and the other relevant factors already selected and i n the absence of parasites, the host required 13 generations to exceed a density of 750 per square meter. This density, which i s approximately 3,000,000 per acre, was chosen as the upper density l i m i t . It i s extremely unlikely that densities would ever exceed this figure i n the late l a r v a l or cocoon stage under t y p i c a l f i e l d conditions. Certain constant parasite parameters i n addition to those already estimated were needed a lso . The sex ra t io of a l l three species was set at j>0 per cent females. In the E . canadensis and V . sinuosa calculations, there was only one parasite generation per year. I n i t i a l l y i t was assumed that P. basizonus also had only one generation per year, but i n the second set of calculations with this species i t was more r e a l i s t i c a l l y assumed to have two. The i n i t i a l parasite density was selected to simulate the introduction by chance or otherwise of 0.005 females per square meter or approximately 20 females per acre. - 101 -It i s also necessary to establish a figure for parasite mortality. A constant density independent mortality of 75 per cent was selected. This i s lower than that for the host since there i s mortality implicit i n the function-a l response to host density, and i n losses through superparasitism. A summary of host and parasite parameters i s given i n Table XLX. Lack of spatial or temporal coincidence, when introduced into the system, was assumed to operate unchanged from generation to generation. The number of parasite females available for attack i n the next generation (n + 1) was determined by multiplying the number of hosts attacked i n genera-tion n from equation (13) by the parasite sex ratio (.50) and parasite survival (.25). N_ n+l n n 1 + (.50) (.25) (18) using a value of N previously obtained from equation (It.). ^n The number of hosts available for attack i n the next generation was determined by multiplying the number of hosts not attacked by the host sex ratio (.75), fecundity (100), and the survival from other mortality factors, (.025). Jn+1 -N. n 1 + ^n * 7 (.75) (100) (.025) (1?) - 102 -The i n i t i a l host-parasite system simulated was made as simple as possible. P. basizonus parameters were used with constant handling time, and only one parasite generation per year. Only lack of spatial and temporal coincidence were var ied . In these and most other simulations, calculations were ..stopped after 2$ to 35 host generations for pract ical reasons, since the work was done on a desk calculator . When a host-parasite system i s calculated using the basic functional response equation (1+) only, P. basizonus parameters, and perfect synchrony (I « s1.0), the parasite eliminates the host, i . e . , reduces i t s number to zero, S i n the 10th generation. When Ig=0.8, the host i s eliminated i n the 11th generation. In this case, of course, we are assuming that the parasite does not superparasitize. I f the effect of superparasitism is now added to this system by the use of the superparasitism submodel (equation 13), the parasite no longer eliminates the host at perfect synchrony, but both go through a series of osci l la t ions with decreasing peaks of density, and both apparently eventually become stable (Table XXV). The changes i n host density with time are shown i n F i g . 2l+. Parasite density follows a similar pattern to host density except that i t s peaks occur 1 to 2 generations after that of the host. Similar results are obtained at indices of synchrony down to 0 .6 , increasing asyn-chrony resulting i n longer periods between peaks and higher host and parasite densities at the peaks (Table XXV). Presumably the end result , s t a b i l i t y , i s the same, although the f i n a l densities w i l l be higher. The maximum parasite densities i n the f i r s t osci l la t ions at less than perfect synchrony are very high . - 103 -NUMBER OF GENERATIONS F i g . 2 4 . Fluctuations of host populations over 35 generations with sim-ulated attack by P. basizonu1;, 1 generation per year, b constant, at 4 indices of synchrony. ""Original host population 0.5* parasite female population 0.005 per square meter. TABLE XXV Effect of changing synchrony and coincidence on times to reach peaks and their height with Pleolophus basizonus, b constant one generation per year h lc F i r s t Peak Second Peak Third Peak Host Para. Host Para. Host Para. Time Density Density Time Density Density Time Density Density 1 . 0 1 .0 9 kO .7 6.6 22 1 3 . 4 2 . 0 34 7.3 1 .0 0 . 8 1 .0 11 119.2 17 .8 25 2 3 . 5 3 . 5 0 . 6 1 . 0 12 194.2 28.2 28 33.9 4 . 9 0 . 5 1 .0 13 878.4 2 . 4 1 . 0 0 . 9 10 55.2 8 . 3 23 6.4 0 . 4 1 . 0 0.75 l l 9 8 . 0 13.1 30 1 .0 0 . 6 ik 223.4 26.5 30 1 .0 0 . 5 18 853.2 7 2 . 4 - 105 -Only when the index of synchrony drops to 0.5 does the basic pattern change (F ig . 21+). Now the parasite i s unable to control the host and the density of the host increases u n t i l i t passes the upper density l i m i t of 750 per square meter. Under these conditions, parasite densities always remain low, reaching only 2.1+ per square meter when the host had reached the upper l i m i t . Parasites had no effect on the host at this index of synchrony because the time required by the host to reach the upper density l imit i s the same as when no parasites are i n the system, i . e . 13 generations. When the spatial coincidence of host and parasite i s changed, so that a constant proportion of the host i s protected from attack i n each generation, the method of calculating the number of hosts available for attack must be altered from that shown i n equation (19). From equation (17) we can obtain the i n i t i a l number of hosts available for attack N, '01* N01 - W L (20) Where i s the i n i t i a l host population, i n the present calculations, 0.5 per square meter. The i n i t i a l protected host population i s , from equation (16) P l - D l - % L = D 1 ( l - IG) (21) The host density i n the second and subsequent generations i s obtained by the following calculat ion: N_ 0_ P l (1.875) (22) - 106 -and the number of hosts offered and protected i n the second and subsequent generations are obtained from equations (20) and (21). The results with less than perfect spatial coincidence are grossly similar to those obtained with asynchrony up u n t i l the f i r s t peak (Table XXV, F i g . 25). However, beyond this peak a marked change occurs. With imperfect spat ial co-incidence subsequent osci l lat ions are quickly damped, the host and parasite density becoming almost constant at a low l e v e l . As lack of coincidence i s increased, the decline i n density after the f i r s t peak becomes very slow and apparently would reach a steady density only after a large number of genera-t ions . When the index of coincidence has reached 0.5, the host exceeds the upper density l i m i t i n 18 generations, only f ive more than are required to do so i n the absence of parasites. A s tr iking difference between I g = 0.5 and 1^  « 0.5 i s that at the former the parasite density i s very low while at the lat ter i t i s very high when the upper density l i m i t i s reached (Table XXV). In the second set of host-parasite systems, i t was assumed that P. basizonus has two generations per year. To do this i t was necessary to divide both the host and parasite density-independent mortality factors into two parts. For the host, a smaller proportion (50 per cent) was assumed to occur between the f i r s t (summer) and second (overwintering) parasite generation, a larger proportion (95 per cent) after the second parasite generation, when the host was overwintering. The total effect of the two density-independent host mortalities was the same as when only one parasite generation was present. However, i t was not r e a l i s t i c to assume that the to ta l density-independent parasite mortality should be the same as previously. The overwintering genera-t ion of the parasite was assumed to have only a s l i g h t l y smaller loss than - 107 -25. Fluctuations of host populations over 35 generations with sim-ulated attack by P. basizonus, 1 generation per year, b_ constant, at 5 indices of coincidence. Original host population 0 . 5 , parasite female population 0.005 per square meter. - 108 -occurred with one generation (70 per cent) . The summer generation of para-s i tes , exposed to mortality factors for a very short period, but at a time when predators, e t c . , are active and abundant, was assumed to have a loss of 50 per cent. Equation (l8) was again used for calculation of the parasite female population for attack i n the next generation but the hosts attacked by the f i r s t or summer generation of parasites were multiplied by a survival factor of .50, while those attacked by the second or overwintering parasite genera-t ion were multiplied by a survival factor of .30. The hosts for attack by the f i r s t parasite generation were obtained as previously, with equation ( 1 9 ) , using the sex rat io and fecundity as before and survival of .05• The hosts available for attack by the second parasite generation were determined by multiplying the hosts not attacked by the f i r s t parasite generation only by a survival factor of .50. When spatial coincidence was imperfect, the number of protected hosts i n each generation was determined as previously (equation 21). Since they were protected from attack by both parasite generations they did not enter into the calculation of the hosts available for attack by the second parasite generation. The effect of two generations per year with perfect synchrony and co-incidence is s tr iking (Fig . 26). Oscil lat ions are more frequent, but the peaks are very much lower than when only one parasite generation exists (Fig . 2 ^ ) « Decreasing coincidence s l i g h t l y results i n a greater i n i t i a l peak density (Table XXVI), but, as with only one parasite generation per year, a damping of - 1 0 9 -the subsequent oscillations follows (Fig. 2 6 , Table X X V I ) . When a greater proportion of the host population i s protected from attack (IQ = O.JjO), a very pronounced damping occurs after the fir s t peak which would apparently result eventually in a stable population at a much higher density than with fewer protected hosts. With two parasite generations per year the host does not "escape" from the parasite's regulation until a higher proportion of the hosts are protected than with one parasite generation per year - IQ = 0.1+0 compared to IQ = 0.5>0. Also the "escape" is a slower process, the upper density limit was not reached until host generation 28 with two parasite generations and I C = 0.1+0 (Table X X V I ) . Early emergence of the fir s t generation parasites i.e., when the f i r s t six days are wasted, has a pronounced effect, peaks of host density being much higher. Also the damping effect noted with lack of spatial coincidence is not evident (Fig. 2 6 ) . When the handling time submodel is introduced into the simulations, only minor differences are evident up to the f i r s t peak of host density (Tables XXVI and X X V I I ) . Thereafter, however, the simulations incorporating the handling time submodel have consistently lower host densities than those using a constant b. This is true at perfect coincidence, at reduced spatial coinci-dence and also when the fi r s t generation of parasites emerge early. The calculations involving E. canadensis were simplified by assuming that a l l host individuals are sufficiently long-lived to be available to the parasites for the whole period the parasites are present. As host character-istics and parasite mortality are unchanged (Table X I X ) the effects on coincidence of changes in the model parameters only can now be determined. - 110 -. 2 6 . Fluctuations of overwintering host populations over 25 generations with simulated attack by P. basizonus, 2 generations per year, b constant, with h combinations of lack of temporal and spatial coincidence. Original host population 0 . 5 , parasite female population 0 . 0 0 5 per square meter. - I l l TABLE XXVI Effect of changing synchrony and coincidence on times to reach peaks and their height with Pleolophus basizonus, b constant two generations per year h F i r s t Peak Second Peak Third Peak Host Para. Density Host Para. Density Host Para. Density Time Density Time Density Time Density 1.0 1.0 6 6.2 4-4 0.3 20 3.4 0.2 1.0 0.9 6 7.9 0.5 13 3.0 0.2 21 2 .5 0.1 1.0 0 .5 9 33.3 1.3 1.0 0.4 28 780 70 0.6E1 1.0 7 12.6 1.0 15 7.8 0.6 22 5 . 5 0.4 Early emergents i n f i r s t generation, perfect synchrony i n second generation. - 112 -TABLE XXVII Effect of changing synchrony and coincidence on times to reach peaks and their height •with Pleolophus basizonus, b submodel two generations per year h I c F i r s t Peak Second Peak Third Peak Host Para. Density Host Para. Density Host Para. Density Time Density Time Density Time Density 1.0 1.0 6 6.7 0.5 13 2.6 0.1 20 2.3 0.1 1.0 0.9 6 7-3 0.5 12 2.6 0.1 17 2.3 0.1 0 . 6E 1 1.0 7 13.0 1.1 15 4.2 0.3 22 3.6 0.2 Early emergents i n f i r s t generation, perfect synchrony i n second generation. - 113 -As with P. basizomis, when there was no superparasitism ( i « e . , when only the basic functional response equation was used), the host was eliminated by the 10th generation. With superparasitism and perfect synchrony the host population increased to a peak at the 10th generation and then declined (Fig . 27)• E . canadensis required one more generation to reach the f i r s t peak than P. basizonus and both host and parasite density were s l i g h t l y higher at that point (Tables XXV, XXVIII). Comparisons of the effects of asynchrony are d i f f i c u l t because the indices of synchrony d i f f e r s l i g h t l y from one species to the other, but both host and parasite reach higher densities when attacked by E . canadensis than when attacked by P. basizonus. The host escaped regulation by both E . canadensis and P. basizonus at approximately the same degree of asynchrony. The str iking difference between these two species appears after the f i r s t peak. With indices of synchrony greater than O.kk at which the host population escapes the parasite 's regulation, E . canadensis - N. sert ifer populations become essentially stable after one peak (Fig . 27). When being attacked by P. basizonus, the host populations osci l late with decreasing amplitude over the period tested (Fig . 2k). The f i n a l set of simulations were those using the parameters obtained for V . sinuosa. In the absence of superparasitism the host was eliminated i n 12 generations, but with superparasitism the host density increased steadily u n t i l i t passed the upper density l i m i t i n the 2kth generation even under conditions of perfect coincidence. Decreasing coincidence produced a more rapid increase i n host density. Although parasite densities also became extremely high they did not change the direction of the host population trend. This species i s unable to regulate host numbers under the conditions of these simulations. - l l l i -300 -Z co O X 200 100 l s = 1 0 0 0 - - - - 0 Ig = 0-78 •••••••iitiima Ig — 0*56 10 20 N U M B E R O F G E N E R A T I O N S 27. Fluctuations of host populations over 3 0 generations with simulated attack by E . canadensis at 3 indices of synchrony. Original host population 0 . 5 , parasite i'emale population 0 . 0 0 5 per square meter--115" -TABLE XXVIII Effect of changing synchrony on time to reach peaks and their heights with Exenterus canadensis h F i r s t Peak Second Peak Host Para. Density Host Para. Density Time Density Time Density 1 . 0 0 1 . 0 1 0 59 .0 8 . 3 0 . 7 8 1 . 0 1 1 120.2 16.1+ 0 . 5 6 1 . 0 1 3 3 7 6 . 7 5 0 . 4 o.kk 1 . 0 1 3 7U5-5 8 . 8 - 1 1 6 -5 . DISCUSSION It was pointed out i n the introduction that one of the aims of this study was to present further evidence of the relative merits of the attack models developed by Holling ( 1 9 5 9 b ) and Watt ( 1 9 5 9 ) * The superior descriptive power of the Holling "disc equation" or basic functional response equation has been demonstrated, as has the u t i l i t y of the Holling equation as a basis for explanation of relations between host and parasite. This i s the great merit of the Holling approach, as pointed out by Morris ( 1 9 6 3 b ) . An attempt to explain the role of the basic functional response equation component "instantaneous rate of discovery" was not j u s t i f i e d since to do so would not have greatly forwarded the major interest, the study of coincidence. I t was necessary to treat "handling time" more thoroughly, however, since the observed relation between this component and parasite age could alter the effects of coincidence. The need for a submodel to describe temporal changes i n ovigenesis i s confined to those types of parasite that were described by Flanders ( 1 9 5 0 ) as synovigenic. In proovigenic species, where ovigenesis i s largely over before oviposition begins, the refractory subcomponent of hand-l i n g time would presumably be zero, and a submodel unnecessary. Complex submodels may be required i n some cases, as i n those instances when there i s a relation between host-feeding and egg production (Edwards 1 9 5 4 b ; Bartlett 1 9 6 4 ) . It was found that interference between P. basizonus females had no effect on attack, and calculations were based on this finding, not only for that species, but also for the other two. It i s possible that interference can occur when two females contact each other while searching, causing enough "disturbance" to push one or both into a refractory period or to lower their - 117 -rate of search. The probability of such interference would be a function of parasite density. It i s more l i k e l y , however, that interference results from encounters between parasite females while one of them i s ovipositing, when i t w i l l be a function of handling time and parasite density. When the parasite density i s constant, the shorter the interval between ovipoSitions and the longer the period spent ovipositing, the greater i s the l ikel ihood of inter -ference. At high parasite density, of course, this l ikel ihood i s increased. This re la t ion explains many of the examples of interference recorded i n the l i t e r a t u r e . Burnett (1953) shoxred a marked decrease i n attack per parasite with increasing parasite density i n 2l+-hour experiments i n which 2 to 6k Dahlbominus fuscipennis (Zett .) attacked 25 N. ser t i fer cocoons. Ullyett (1936) pointed out that D. fuscipennis requires more than 21+ hours to complete one oviposition, making interference almost inevitable at the higher parasite densities used by Burnett. A similar explanation w i l l serve for the inter -ference demonstrated i n the same two species under more natural conditions (Burnett 1956), and for the effect of attack by Nasonia (Mormoniella) vitripennis (Walker) on puparia of Muse a domestic a L . (DeBach and Smith 191+7). In the la t ter case three of the six parasite densities used exceeded host densities by 2 1/2, 5 and 7 1/2 times and the experiments lasted 2l+ hours. Edwards (1954a) pointed out that N. vitripennis requires from 1 1/2 to 6 1/2 hours to oviposit and that i t repeats the oviposition process several times on the same host, spending 20 to 30 minutes wandering about on the host between oviposit ions. Ullyet t (I9l+9b) found that increasing the density of Cryptus inornatus Pratt had no effect on the number of eggs l a i d per day per female on prepupae of Loxostege f r u s t a l i s Walk., even though he had actually observed contacts - 118 -between females during the attack process and found that i t interrupted o v i -p o s i t i o n a c t i v i t i e s . This ichneumonid has an oviposition rate of only two eggs per day. I t also exhibits some discrimination between attacked and un-attacked hosts, avoiding further oviposition on the former. Discrimination may be considered as a un i d i r e c t i o n a l temporal extension of interference, i n which the presence of one parasite influences behaviour of other parasites f o r a greater or lesser period after oviposition has been completed. Our interest has been confined to -those species that do not exhibit t h i s f a c u l t y , but read-i l y deposit eggs i n hosts that have already received eggs of the same species. The presence of more than one P. basizonus egg on a host did not decrease the p o s s i b i l i t y of one of them maturing. However, t h i s i s not so i n some parasite species. Pramanik and Choudhury (1963) found that increasing the number of Brae on greeni Ashmead from one to f i v e per host increased parasite l a r v a l mortality, decreased the development period, decreased adult s i z e , shortened adult l i f e span and lowered fecundity. Salt (1936) found that when more than one egg of Trichogramma evanescens Westw. was deposited per host there was increased mortality, although the size of the host influenced the outcome. For these parasites the number of eggs per host would have to be determined to treat the effects of superparasitism mathematically. However, i f i t can be shown that supernumerary eggs do not affect important parasite c h a r a c t e r i s t i c s , a very simple superparasitism submodel can be used i n which the number of hosts attacked i s the difference between the number offered and the number not attacked. Only an adequate mathematical description of the number of hosts not attacked i s required. I have already pointed out the form the submodel would take i f either the Poisson or the negative binomial equations adequately describe the zero category i n the observed egg - 119 -d i s t r i b u t i o n . To explain the observed dis tr ibution, however, i t s origin must be described. The eggs of P. basizonus were distributed contagiously at a l l parasite and host densities tested i n the laboratory when only large female cocoons were offered. This species selects larger cocoons over smaller ones and strongly avoids oviposition i n cocoons containing dead hosts, so that the presence of contagion i n egg distr ibution i n natural populations where a l l these types of host are present, would not be unexpected. However, to explain the observed contagion when only large female cocoons were offered w i l l require further categorization of female cocoons. Contagion i n egg distr ibution of E . canadensis has been demonstrated i n the f i e l d and i t s absence noted i n cages. These observations suggest that a difference i n a v a i l a b i l i t y of hosts may cause the overdispersion noted under natural conditions. A proportion of the prespinning larvae i n the f i e l d reach that stage while s t i l l within the protection of the l a r v a l cluster , while others moult at a distance from the cluster , on the tree or on the ground. The la t ter are more l i k e l y to be attacked than the former. The short duration of the individual prespinning stages may also be important i n determining egg d i s t r i -bution, since some short-term meteorological conditions may favour rapid migration to spinning sites and rapid spinning while others may favour attack and hence superparasitism. Because of inadequate knowledge of V . sinuosa we can only speculate about the egg or f i r s t instar distr ibution of this species. A large proportion of host cocoons collected contain no V. sinuosa f i r s t instars i f a l l possible cocoon spinning sites are sampled. Also, f i r s t instar larvae are contagiously - 120 -distributed i n those areas that do y i e l d them. With this l imited knowledge i t was assumed that they are overdispersed i n the host, even though there i s no direct evidence of egg distr ibution to support i t . Although these reasons can be advanced to j u s t i f y use of the negative binomial equation as a basis for our superparasitism submodel, i t i s possible that the Poisson distr ibution would provide a better description for other species. However, deviation from the Poisson might be common i n parasites that do exhibit superparasitism, since any factor that tends to make one host more attractive or more accessible than another w i l l lead toward contagion. Neither the Poisson nor the negative binomial dis tr ibution may describe the observed egg distr ibution i n some species. When the egg distr ibution of Encarsia formosa Qahan, a chalcid studied by Burnett (1958a) i s analyzed i t is found that they are randomly distributed at f ive of the 11 host and para-site densities , they are contagiously distributed at four densities and i n the remaining two are not described adequately by either equation. It i s note-worthy that i n the six cases where i t could be calculated, a negative binomial dis t r ibut ion described the zero category better than the Poisson. In Chelonus  texanus Cress. , a braconid attacking the eggs of Lepidoptera (Ullyett 19l+9a), the type of egg dis t r ibut ion among hosts dif fered with host and parasite density. At low host density, eggs were contagiously distributed, at s l i g h t l y higher host density both equations described the distributions adequately. At s t i l l higher host density, eggs were randomly distr ibuted. At the highest host density the Poisson no longer was an adequate description and the charac-t e r i s t i c dis t r ibution of a parasite that avoids superparasitism appears. When parasite density i s increased at a constant host density, overdispersion again - 121 -appears. The same characteristics are apparently common to the ichneumonid Cryptus inornatus Pratt (Dlly e t t 19U9b). The p o s s i b i l i t y of lack of coincidence i n the f i e l d has been demonstrated by studies of the parasites of N. s e r t i f e r , and laboratory experiments with P. basizonus have provided data for a mathematical treatment of attack, s p a t i a l and temporal coincidence. The effect of lack of s p a t i a l coincidence i n one generation i s a very straightforward one. To v i s u a l i z e i t s effects i t i s simply necessary to determine the number of unprotected hosts at a given host density and f i n d the effect on the number of hosts attacked d i r e c t l y from the functional response curves ( F i g . 21, 22 and 23). Temporal coincidence or asynchrony, however, has been shown to be a complex subject because of the i n t e r -actions of host and parasite density and superparasitism. The effects of host and parasite density may be separated from those of superparasitism by dealing separately with the basic functional response submodel and the superparasitism submodel. The basic functional response submodel (equation h ) may be written where T , as noted previously, i s the number of days the parasite i s i n contact with the host, and i s equal to (equation V?) T I P S Tplg can be substituted for T c i n the basic functional response equation to give - 122 -aN N "* •( ° F )Vs ( 2 3 ) 1 + abNQ With host and parasite density constant there i s a direct linear relation between number of eggs laid and index of synchrony. The slope of this line is a measure of the detrimental effect of asynchrony on number of eggs laid, and varies with the parasite parameters in equation (23) as well as with host and parasite density. The slopes of the lines obtained using the appropriate data in Tables XXI, XXILT, and XXIV* are summarized in Table XXIX. The direct linear relation between number of eggs laid and parasite density has already been demonstrated and its relation to synchrony is the same (Table XXIX). The effect of host density on the slope of this line and hence on the effect of asynchrony, i s direct but non-linear. Specific parasite characteristics will have more effect at low host density and the relative importance in their effect on asynchrony and attack wil l decrease as host density increases. At host densities above the asymptotic attack level on the functional response curve, the effect of host density on the slope of equation (23) is lessened. This is clear from the slopes shown in Table XXIX for P. basizonus. Increasing the host density from 1+50 to 900 per square meter only increases the slope of equation (23) for this species from 5U.1+ to 5U.8. The effect of superparasitism can be added by substituting equation (23) for in the superparasitism submodel (equation 13). The equation would be simpler to comprehend i f the single letter L were substituted for the bracketed portion of equation (23), giving - 123 -TABLE X X I X Slopes of lines obtained when number of eggs l a i d i s plotted against synchrony P. basizonus E. canadensis V. sinuosa 0 Np - 1 % - 5 N p - 1 N p = 5 N p - 1 N p =5 1 7.2 35.9 4.7 23.6 2.8 13.9 48.7 243-5 100.6 502.9 85.6 427.9 450 54.4 272.1 159.1 795-7 186.9 924-3 - 1 2 4 -N = N HA 0 LT I P S NJc ) k ( 2 4 ) 1 + It is now possible to see where asynchrony enters into the determination of the number of hosts attacked, and i t is clear that i t must operate through number of eggs laid. Changing synchrony and host density give the typical families of functional response curves illustrated in Figs. 2 1 , 2 2 and 2 3 . Since host den-sity and number of eggs laid are both determined before equation ( 2 4 ) i s used, this equation i s evidently a very specific one, the result produced depending entirely on the value of the parasite parameter k. Small values of k, indicat-ing high overdispersion, will result in lower numbers of hosts attacked at any given host density and number of eggs laid, than will large values of k, which are indicative of low overdispersion. Although i t is beyond the scope of this study to investigate the effect of individual parasite parameters on attack, i t is obvious that, by the use of equations ( 2 3 ) and ( 2 4 ) the value of a given species of parasite as a regula-tory agent at different host densities and over a range of asynchrony could be assessed, given only the adult l i f e span, rate of successful searching, hand-ling time, and, provided eggs are contagiously distributed, the value of the dispersion coefficient. One of the more obvious results of the generation of host-parasite systems undertaken in Section 4 . 5 , was the apparent tendency of host and parasite den-sity to oscillate with decreasing amplitude, and to tend toward a steady state, although because of the practical difficulties of computation, few of the - 12$ -calculations were carried to that point . It i s possible to determine mathemat-i c a l l y whether a theoretical steady state can be reached. The method of determining the host density i n the next generation i s given i n equation (19). If the host sex ra t io , fecundity and survival from mortality factors other than the parasite under study are grouped under the term H , and U is sub-sti tuted for the denominator, equation (19) may be written N n N0 H (25) ° n + l - n "tj n From this equation i t i s obvious that the change i n host density from one generation to the next i s determined by the ra t io H /U. I f U ^ H , then N_ ) N ; i f u ) H , then N <(N J i f U = H , host density i n the two un+i u n °n+l N ° n succeeding generations w i l l be equal. Since the term H i s a constant i n the calculations, i t may be profitable to examine that part of equation (19) which we designated U. When there i s no change i n host density i n two succeeding generations H = U =( 1 + A j (26) and for a given value of k , the value of the ra t io N ^ /HQ during this period can be calculated readi ly . Let this value be E . and N A - E N Q (2?) - 126 -This temporary equilibrium i n host density w i l l be maintained only i f the value of N , the parasite density, does not disturb i t . Equation (l8), with P which the parasite density i n the next generation i s determined, can be altered as equation (19) was above, to where R i s a constant involving the parasite sex ratio and survival from mortality factors, and H i s as i n equation (26). The host density necessary for a permanent steady state can now be determined by substituting equations (27) and (28) i n the basic functional response equation (h) and solving for N • Doing so gives n+1 (28) This i s a simple quadratic equation of the form Ax + Bx + C => 0 that can be solved by use of the quadratic formula 2A and, since the C component of the quadratic formula i s zero this simplifies to HE (30) T_(aRH - aR) - HEab The necessary parasite density for a stable host-parasite relation i s obtained from (28) using N from (30) and U » H. The only necessary condition - 1 2 7 -for a theoretical stable host-parasite population i s that there be a real solution to equation ( 3 0 ) . It can be readily determined whether a steady density of host and para-site i s possible at any degree of asynchrony from equation ( 3 0 ) by substituting values of T c from equation (l£). P. basizonus and E. canadensis w i l l eventually reach an equilibrium with N. sertifer under the prescribed conditions at a l l indices of synchrony down to approximately 0 . 3 , but V. sinuosa w i l l not do so even at perfect synchrony (Table XXX), largely because of the high value of E or N ^ / NQ required. This ratio, which i s determined solely by the value of k, given a constant host factor H (equation 2 6 ) , i s a measure of the degree of superparasitism allowed i f s t a b i l i t y i s to be reached and maintained. By following a comparable set of arguments, i t i s also possible to deter-mine whether steady states can exist with less than perfect spatial coincidence. Equation ( 2 2 ) can be re-written as N ° n equation ( 2 0 ) and equation ( 2 1 ) can be substituted i n i t , and the necessary value of U for a stable population determined. It i s U = I C H ( 3 1 ) 1 + I Q H - H Here a much more complex relationship exists, the value of II required for a stable population being no longer constant, but varying with the index of coincidence. Also, since U was originally substituted f o r j l + % V N 0 K - 128 -TABLE XXX Effect of changing synchrony on steady host and parasite densities using constant host and parasite factors of 1.875 and 0.125 respectively Steady Steady Species V N o Host Female Density Parasite Density P. basizonus 1.0 0.966 2.868 0.167 0.8 4.015 0.234 0.6 6.690 0.390 0.4 20.062 1.170 0.3 30194 1761 0.2« E. canadensis 1.0 2.454 11.359 0.663 0.8 15.442 0.901 0.6 24.105 1.406 0.4 54.912 3.203 0.3 152.371 8.888 0.2' V. sinuosa 1.0' 18.368 _ Produces an inadmissible solution to equation (30). - 129 -to find the ratio N /N for stability the equation k 1 + - H 0 must be solved. Note that N„AL or E also varies with index of coincidence. A 0 However, i t is s t i l l possible to substitute in the basic functional response equation to get but a different value of U and E must be calculated for each index of coincidence. The calculated values for steady host and parasite densities with changing spatial' coincidence are given in Table BEXI. P. basizonus can attain a steady density with 1+0 per cent of the host population continually protected from attack, while E. canadensis (calculations for which were done only to allow comparison with P. basiz onus) cannot do so with more than 2$ per cent protected, V. sinuosa is incapable of doing so, as already noted in Table XXX. A l l the results presented in Table XXXI are well within the host density limits set by consideration of natural conditions. At least one of the host densities in Table XXX is beyond these limits. This brings up the difficulty inherent in such theoretical calculations. There is no indication from them of the time required to reach equilibrium, nor of the maxima and minima of the oscillations through which the population passed in reaching i t . To find these the tedious ; generation-by-generation calculations shown in an earlier section must be used. For example, with P. basizonus and E. canadensis at any index of synchrony below 0 . 6 , the fir s t maximum of host density wil l be beyond the maximum allow-able density (Fig. 2 4 and 27). Hence the equilibrium densities given in UEN 0 - 0 (32) - 130 -TABLE XXXX Effect of changing spatial coincidence on steady host and parasite densities using constant host and parasite factors of 1.875 and 0.125 respectively Species XC Host Density Protected Hosts Hosts Offered Female Parasite Density P. basizonus 1.0 2.868 0 2.868 0.167 0.9 3.803 0.380 3.423 0.222 0.75 7.332 1.833 5.499 0.428 0.6 65.235 26.094 39.141 3.805 0.5' E. canadensis 1.0 11.359 0 11.359 0.663 0.9 19.288 1.929 17.359 1.125 0.75 108.182 27.046 ,81.136 6.311 0.6' V. sinuosa 1.0' Produces an inadmissible solution to equation (30). - 131 -Table XXX for lower indices of synchrony produce maxima that would not be tolerated when generating host-parasite systems. There i s no disagreement between Table XXXI and F i g . 22, which shows the effect of lack of spatial coincidence on a P. basizonus system. Bailey, Nicholson and Williams (1962) have discussed the theoretical implications of a host-parasite system i n which a part of the host population i s inaccessible to the parasite. Their systems consist of a specif ic parasite attacking under constant environmental conditions, the interacting generations of host and parasite being perfectly synchronized, the host mortality constant. They assume that superparasitism does not occur. They also assume, as we have done, that the host dis tr ibution i s discontinuous, one part being accessible, the other inaccessible to a l l parasites. Under these conditions, they maintain that a steady state i s possible only i f the proportion of the hosts that are inaccessible i s less than the reciprocal of the power of increase of the host i n the absence of parasites. In our terminology, a steady state i s only possible i f (1 - 1^) ^ l / H . Nothing has been found i n this study to disprove this conclusion, since i r r a t i o n a l solutions to equation (32) were obtained when the protected population became less than l / H , or 0.533 of the total population (Table XXXI). But a steady state can be impossible when protected hosts form a considerably smaller proportion of the host population, and this i s a specific character of the parasite . The inclusion of inaccessible hosts i n the system tends to increase the degree of s t a b i l i t y i n some cases because osci l la t ions are damped but s t a b i l i t y exists i n two of the three species studies xtfithout protected hosts and i t w i l l not exist i n one species at a l l under the conditions postulated. Our general conclusion i s that i t takes considerable disruption of the system to prevent the eventual attainment of - 132 -s t a b i l i t y rather than that i t can be attained only under c e r t a i n conditions. Considerable d i s r u p t i o n of synchrony i s t o l e r a t e d , as an example, and eventual s t a b i l i t y s t i l l r e s u l t s (Table XXX). It i s d i f f i c u l t to generalize on the e f f e c t of asynchrony from the host-p a r a s i t e systems generated. S p e c i f i c d ifferences are marked. V. sinuosa was unable to l i m i t host numbers. The other two species did so. In these two species, the height of the f i r s t peak of host density increased with decreasing synchrony ( F i g . 2l+, 27), and both species eventually reached a stable host and parasite density (Table XXX). Beyond that there i s l i t t l e s i m i l a r i t y between them. With P. basizonus, the host density f l u c t u a t e d through a number of o s c i l -l a t i o n s , the distance from peak to peak, the height of peaks and presumably the time to s t a b i l i t y i n c r e a s i n g with decreasing synchrony. E. canadensis, how-ever, reached s t a b i l i t y i n approximately 18 generations at p e r f e c t synchrony as in d i c a t e d by both F i g . 27 and Table XXX, a f t e r only one peak. The time to s t a b i l i t y apparently increased as synchrony decreased, but the number of peaks remained constant at one. When lack of s p a t i a l coincidence i s increased with P. basizonus, a damping of the o s c i l l a t i o n s occurs ( F i g . 25), but steady d e n s i t i e s are s t i l l p o s s i b l e . At low coincidence, as at low synchrony, the parasite i s unable to contain the host, but i n the former case the parasite density i s high, i n the l a t t e r i t i s low, when the host passes the upper density l i m i t (Table XXV). Decreasing index of coincidence reduces the number of o s c i l l a t i o n s and t h e i r amplitude. Increasing the number of P. basizonus generations to two per year r e s u l t s i n a considerable decrease i n host d e n s i t i e s , although the frequency of fl u c t u a t i o n s i s increased ( F i g . 26). I t i s worth noting here, too, that under - 133 -these conditions lack of coincidence greater than l/H is tolerated. When the fi r s t of the two annual P. basizonus generations is asynchronous, higher peaks and longer intervals between peaks occur. Throughout this discussion a realistic maximum for the number of hosts present has been used, but this limitation has had l i t t l e effect on the results. It cannot be expected that the other limitations imposed on the systems will be as inconsequential. For instance, H the host factor, and R the parasite factor are important enough to justify a closer examination of their roles in the course of events. It should be pointed out in passing that the mortality components and perhaps also the other components of the host and parasite factors are, in reality, probably functions of host and parasite density. The places where these constants enter the present model are the places where, i n the future, models describing and explaining their actions will mesh with the present one. The relation between those two constants and host and parasite density can be determined from equation (27). If H is substituted for U in this equation to indicate that the population is stable, then _0 = H (33) N p RH - R The value of the right hand side of this equation, using the constants utilized in the simulations, is 17.III.. This is the ratio between steady host and para-site densities for both P. basizonus and E. canadensis in Table XXX, and also in Table XXXI, i f the basis i s host density rather than hosts offered. This suggests that, provided R is not species specific, the number of hosts required -13U -per parasite for equilibrium is independent of the parasite species involved, a rather startling conclusion. The specific differences noted previously are not invalidated however, since no allowance is made for differences in time spent in contact with the host. This must be adjusted to maintain a system with steady density. For instance, i f the steady host and parasite density for perfect synchrony with E. canadensis (Table XXIII), and the parameters for P. basizonus are used together, the next generation's host and parasite density will not be the same as the previous generation's unless the time in contact is set at 7«1S> days. Similar calculations using P. basiz onus host and parasite densities for perfect synchrony and E. canadensis parameters require a time in contact of 29 days - much longer than my estimate of E. canadensis adult longevity. The existence of steady states depend^on a real-is t i c host-»parasite contact period which is spe cies-specif i c . Nevertheless, equation (33) can be used to investigate the effect of host and parasite characteristics on steady density. Since H consists of the sex ratio, fecundity and survival from other factors for the host and R consists of the sex ratio and survival from other factors for the parasite, an increase in either may be brought about by a reduction in the mortality factors that are affecting i t or an increase in fecundity or the proportion of females in the population. Conditions favourable to the parasite, for instance, will bring about a reduction in the right hand side of equation (33) and hence reduce the number of both hosts and parasites necessary to reach equilibrium. Obviously, too, any change in either one of the host or parasite factors can upset an existing equilibrium and lead to greater or less destruction of the host in the following generation. Variability in these two factors from year to year such as occurs under natural conditions will preclude the possibility - 135 -of a steady state being reached or maintained. The d i f f i c u l t y of applying the theoretical findings of this study to natural situations i s clear when the variations i n other factors affecting both host and parasite are considered. Also the environment i n which both find themselves i s not a stable one, since the trees upon which the host feeds are increasing i n size. This affects not only the micro-environment of the immature stages on the trees, but also that of the cocoon by increasing shade, changing the ground cover and changing the depth and character of the l i t t e r . However, several facts do emerge. P. basizonus appears to be capable of regulating N. sertifer numbers even when handicapped by reduced temporal and spatial coincidence (Figs. 2U, 25, 26). It can maintain i t s e l f at low host and parasite densities, when a proportion of the hosts are inaccessible to i t , and does so with remarkably l i t t l e change i n numbers from generation to generation. This conclusion i s confirmed by the history of this species i n Canada. Approximately a decade elapsed between i t s release and i t s recovery some f i f t y miles from the nearest release point (Griffiths 1961). During that period, annual collections of N. ser t i f e r were made throughout the infested area of southwestern Ontario by the Forest Insect and Disease Survey. Lyons (1963) has also noted the recent occurrence of this species i n areas of low host density. Efficiency at low host density i s probably a function of long-evity and of the ab i l i t y of P. basizonus to store mature eggs when ovipositions are infrequent. This permits the female to take advantage of more of the en-counters with hosts than would be possible i f no storage occurred. The main advantage of storage of mature eggs during host absence appears to be as a - 136 -compensatory mechanism to overcome the difficulties of early emergence. As host densities increase, however, the low rate of egg production of this parasite becomes disadvantageous, resulting in a levelling-off of its functional response to host density at a low attack rate and a low host density. E. canadensis also i s capable of reducing N. sertifer numbers under the conditions set out in our simulations (Fig. 27). It differs from P. basizonus, however, in the speed with which fluctuations in host and parasite density are damped. This species s t i l l maintained itself from generation to generation when nearly half of its adult l i f e span each year was spent out of contact with the host. Calculations for this species have been simplified by assuming that individual prespinning larvae, which are the preferred host stage, are present for the whole period that the host population is present. Attempts to make allowance for the actual available period of individual hosts would have required much more complex computations, since the effects of superparasitism would have had to be assessed more frequently. Also, the number of individuals escaping attack would have been increased, since the probability of attack is a function of period of exposure. The introduction of short individual l i f e spans for the host would thus have produced results similar to that obtained with less than perfect coincidence. One major effect of lack of synchrony in E. canadensis could be on the sex ratio of the host in the next generation. Male hosts are available for attack earlier than female hosts (Fig. 1). Early emergence of a considerable propor-tion of the parasite population could result in more attack on male than female hosts. V. sinuosa is incapable of causing a decrease in host numbers even with - 137 -perfect coincidence. I t was noted, however, that parasite numbers continued to increase with host numbers, which may account for the observed abundance of V. sinuosa i n the earlier work on I . sertifer i n southwestern Ontario (Griffiths 1959)• Populations of the host had b u i l t up rapidly and were then very quickly reduced by the application of a virus disease (Bird 1953). The virus, which destroys developing larvae, caused a drastic reduction i n the subsequent cocoon population i n that generation. However, V. sinuosa density i n that generation was determined by the number of hosts present i n the previous generation* Hence, large numbers of V. sinuosa attacked reduced populations of N. sertifer and produced heavy parasitism. N. sertifer numbers continued to decrease rapidly because of virus infection and V. sinuosa continued to enjoy a numerical advantage for several generations. It i s only under conditions such as these that V. sinuosa i s obtained. At low host densities i t s inefficient method of distributing i t s offspring coupled with i t s avoidance of areas of concentration of hosts render i t relatively ineffective. - 138 -6 . REFERENCES Bailey, V . A . , A . J . Nicholson and E . J . Williams. 1962. Interaction between hosts and parasites when some host individuals are more d i f f i c u l t to f ind than others. J . Theoret. B i o l . 3:1-18. Barclay, J . M. 1938. The oviposition habits of some species of the genus Exenterus parasitic on sawfly larvae. 69th Annu. Rep. Ent . Soc. Ont. 29-31. Bart le t t , B. R. 1964. Patterns i n the host-feeding habit of adult parasitic Hymenoptera. Ann. ent. Soc. Amer. 57:344-350. B i r d , F . T . 1953. The use of a virus disease i n the biological control of" the European pine sawfly, Neodiprion ser t i fer (Ueoffr . ) . Canad. Ent . 85:437-446. Blackman, 0. E . 1942. S t a t i s t i c a l and ecological studies i n the distr ibution of species i n plant communities. 1. 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Amer. 4965-59• — « — . 1958a. Effect of host dis t r ibution on the reproduction of Encarsia formosa Gahan. (Hymenoptera: Chalcidoidae). Canad. Ent. 90:179-191. 1958b. Dispersal of an insect parasite over a small p l o t . Canad. Ent . 90:279-283. Debach, P . , and H. S. Smith. 194l. The effect of host density on the rate of reproduction of entomophagous parasites. J . Econ. Ent . 34:741-745. - 139 -Debach, P ., and H. S. Smith. 191+7 • Effects of parasite population density on rate of change of host and parasite populations. Ecology. 28:290-298, Doutt, R. L. 1959« The biology of parasitic Hymenoptera. Annu. Rev. Ent. 4:161-182. Edwards, R. L. 1954a. The host-finding and oviposition behaviour of Mormoniella vitripennis (Walker) (Hymenoptera: Pteromalidae), a parasite of muscoid f l i e s . Behaviour.: 7:88-111. — 1954b. The effect of diet on egg maturation and resorption i n Mormoniella vitripennis (Hymenoptera: Pteromalidae). Quart. J. micr. S c i . 95:459-468. Flanders, S. E. 1950. 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E . 1913. The l i f e history of a bee f l y (Spogostylum anale Say) parasite of the larva of a t iger beetle (Cicindela scutel lar is Say v a r . lecontei Hald.) (Bombyliidae). Ann. ent. Soc. Amer. 6:213-225. Sweetman, H . L . 1958. The principles of b io logica l control . Wm. C . Brown Co. Dubuque, Iowa, U . S . A . Thalenhorst, W. 1950. Die Koinzidenz als gradologisches problem. Eine synokologische studie. Z . angew. Ent . 32:1-48. U l l y e t t , G. C . 1936. The physical ecology of Microplectron fuscipennis Zet t . B u l l . ent. Res. 27:195-217. 1949a. Distribution of progeny by Chelonus texanus Cress. (Hymenoptera: Ichneumon!dae). Canad. Ent . 8l:25-44« 1949b. Distr ibution of progeny by Cryptus inornatus Pratt (Hymenoptera: Ichneumon!dae). Canad. Ent . 81:285-299• Wallace, D . R., and C . R. S u l l i v a n . 1963» Laboratory and f i e l d investigations of the effect of temperature on the development o f Neodiprion sert i fer (Geoff.) i n the cocoon. Canad. Ent . 95:105l-1066. Watt, K . E . F . 1959. A mathematical model for the effect of densities of attacked and attacking species on the number attacked. Canad. Ent . 91: 129-144• 1961. Mathematical models for use i n insect pest contro l . C^nad. E n t . Suppl. 19, 62 pp. 

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