HOST-PARASITOID SYSTEMS IN PATCHY ENVIRONMENTS: A PHENOMENOLOGICAL MODEL

SUMMARY (1) A host-parasitoid model is presented which is intermediate in complexity between the Nicholson-Bailey model (in which the parasitoids search independently randomly in a homogenous environment) and complicated models for incorporating environmental patchiness (in which the overall distribution of parasitoid attacks is derived from detailed assumptions about their searching behaviour and about the spatial distribution of the hosts). The model assumes the overall distribution of parasitoid attacks per host to be of negative binomal form. There are consequently three biological parameters: two are the usual parasitoid 'area of discovery', a, and the host 'rate of increase', F; the third is the negative binomial clumping parameter, k. Such intermediate-level models have proved useful in sorting out ideas in the related disciplines of epidemiology and parasitology. (2) Empirical and theoretical arguments for using the negative binomial to give a phenomenological description of the essential consequences of spatial patchiness in models are surveyed. (3) A biological interpretation of the parameter k in host parasitoid models is offered. If the parasitoids be distributed among patches according to some arbitrary distribution which has a coefficient of variation CVp, and if the parasitoid attack distribution within a patch be Poisson, then the ensuing compound distribution can be approximated by a negative binomial which will have the same variance as the exact distribution provided k is identified as k = (I I/CVp)2. (4) Expressions are obtained for the equilibrium values of host and parasitoid popula- tions. These equilibria are stable if, and only if, k < 1; that is, provided there is sufficient clumping. (5) The dynamical effects of parasitoid aggregation in some respects mimic those introduced by mutual interference among parasitoids; the appropriate coefficient of 'psuedo-interference' is calculated.

[1]  C. S. Holling,et al.  A COMPETITION SUBMODEL FOR PARASITES AND PREDATORS , 1969, The Canadian Entomologist.

[2]  A. R. Sen,et al.  On the Line Transect Sampling Method , 1974 .

[3]  A Hastings,et al.  Spatial heterogeneity and the stability of predator-prey systems. , 1977, Theoretical population biology.

[4]  M. Solomon.  The Natural Control of Animal Populations , 1949 .

[5]  C. D. Kemp,et al.  Random Counts in Models and Structures. , 1971 .

[6]  R. May.  Dynamical aspects of host-parasite associations: Crofton's model revisited , 1977, Parasitology.

[7]  R. May,et al.  Aggregation of Predators and Insect Parasites and its Effect on Stability , 1974 .

[8]  T. R. E. Southwood,et al.  Ecological Methods with particular reference to the study of insect populations , 1967, Pedobiologia.

[9]  A. Nicholson,et al.  The Balance of Animal Populations.—Part I. , 1935 .

[10]  R. May,et al.  Regulation and Stability of Host-Parasite Population Interactions: I. Regulatory Processes , 1978 .

[11]  B P Zeigler,et al.  Persistence and patchiness of predator-prey systems induced by discrete event population exchange mechanisms. , 1977, Journal of theoretical biology.

[12]  R. May,et al.  STABILITY IN INSECT HOST-PARASITE MODELS , 1973 .

[13]  S. Jørgensen.  Models in Ecology , 1975 .

[14]  C. S. Holling.  The components of prédation as revealed by a study of small-mammal prédation of the European pine sawfly. , 1959 .

[15]  J. Lawton,et al.  Characteristics of successful natural enemies in models of biological control of insect pests , 1978, Nature.

[16]  D. Rosen,et al.  The area of discovery and searching strategy of a primary parasite and two hyperparasites , 1976 .

[17]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  John H. Lawton,et al.  On the Inadequacy of Simple Models of Mutual Interference for Parasitism and Predation , 1977 .

[19]  C. Krebs.  Ecology: The Experimental Analysis of Distribution and Abundance , 1973 .

[20]  L. Luckinbill,et al.  Coexistence in Laboratory Populations of Paramecium Aurelia and Its Predator Didinium Nasutum , 1973 .

[21]  W. Murdoch,et al.  Predation and Population Stability , 1975 .

[22]  R. Hilborn,et al.  The effect of spatial heterogeneity on the persistence of predator-prey interactions. , 1975, Theoretical population biology.

[23]  H. Crofton,et al.  A model of host–parasite relationships , 1971, Parasitology.

[24]  R. May,et al.  Consequences of helminth aggregation for the dynamics of schistosomiasis. , 1978, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[25]  Paul E. Smith.  Ecological Methods with Particular Reference to the Study of Insect Populations , 1979 .

[26]  W. Gurney,et al.  Predator-prey fluctuations in patchy environments , 1978 .

[27]  E. C. Pielou,et al.  An introduction to mathematical ecology , 1970 .

[28]  M. Hassell,et al.  New Inductive Population Model for Insect Parasites and its Bearing on Biological Control , 1969, Nature.

[29]  C. Huffaker.  Experimental studies on predation : dispersion factors and predator-prey oscillations , 1958 .

[30]  Roy M. Anderson,et al.  REGULATION AND STABILITY OF HOST-PARASITE POPULATION INTERACTIONS , 1978 .

[31]  J. F. Benson.  Intraspecific competition in the population dynamics of Bracon hebetor Say (Hymenoptera: Braconidae) , 1973 .

[32]  F. J. Anscombe,et al.  Sampling theory of the negative binomial and logarithmic series distributions. , 1950, Biometrika.

[33]  D. Rogers.  A MODEL FOR AVOIDANCE OF SUPERPARASITISM BY SOLITARY INSECT PARASITOIDS , 1975 .