M. P. Hassell

The dynamics of arthropod predator-prey systems.

In this study of arthropod predador-prey systems Michael Hassell shows how many of the components of predation may be simply modeled in order to reveal their effects on the overall dynamics of the interacting populations. Arthropods, particularly insects, make ideal subjects for such a study because their generation times are characteristically short and many have relatively discrete generations, inviting the use of difference equation models to describe population changes. Using analytical models framed in difference equations, Dr. Hassell is able to show how the detailed biological processes of insect predator-prey (including host-parasitoid) interactions may be understood. Emphasizing the development and subsequent stability analysis of general models, the author considers in detail several crucial components of predator-prey models: the preys rate of increase as a function of density, non-random search, mutual interference, and the predators rate of increase as a function of predator survival and fecundity. Drawing on the correspondence between the models and field and laboratory data, Dr. Hassell then discusses the practical implications for biological pest control and suggests how such models may help to formulate a theoretical basis for biological control practices.

STABILITY IN INSECT HOST-PARASITE MODELS

where NS represents the survivors after Pt parasites have searched for Nt hosts resulting in P+ 1 parasite progenyt. All assumptions about parasite searching behaviour are here contained in the functionf[Pt,Nt]. If we consider the simplest case where the parasite population is specific and synchronized temporally with its host population, we can write the following generalized model for a host-parasite interaction:

Aggregation of Predators and Insect Parasites and its Effect on Stability

Searching animals, such as predators and insect parasites,t usually spend more time where their requisites are more plentiful, a behaviour that has an obvious selective advantage. Despite this, it is only from relatively recent work that aggregative responses to uneven prey distributions have been adequately quantified in terms of predator numbers, or the time spent by a predator, per unit areas of different prey density. This in turn is reflected in the relatively few predator-prey models that have allowed for such aggregative behaviour (Royama 1971; Hassell & Rogers 1972; Hassell & May 1973; Murdoch & Oaten 1974). These are in contrast to the many models (e.g. Lotka 1925; Volterra 1928; Thompson 1924; Nicholson & Bailey 1935; Watt 1959; Hassell & Varley 1969) where search is random, which effectively implies an even distribution of predators throughout the whole prey area and makes the particular types of prey distribution irrelevant to the model outcome. In an attempt to show how predator aggregation could affect stability, Hassell & May (1973) considered a simple modification of the Nicholson-Bailey model in which the prey survival was given by

The spatial dynamics of host-parasitoid systems

We consider models for host-parasitoid interactions in spatially patchy environments, where in each generation specified fractions of the host and parasitoid subpopulations in each patch move to adjacent patches. In most previous work of this general kind, the movement is not localized in this way, but involves «global» mixing of the populations prior to dispersal. A remarkable range of dynamical behaviour is exhibited by a mathematically explicit model with constant host reproductive rate, deterministically unstable local dynamics and dispersing hosts and parasitoids that only move to nearest-neighbour patches in a density-independent way

Discrete time models for two-species competition.

Abstract A discrete (difference) single age-class model for two-species competition is presented and its stability properties discussed. It resembles the Lotka-Volterra model in having linear zero growth isoclines, and thus, also in its general requirements for the coexistence of competing species. It differs in allowing the populations to show damped oscillations, stable cycles or even apparent “chaos” if competition is sufficiently severe. A similar two age-class model is discussed where there is both intra- and interspecific competition in one of the developmental stages, but only intraspecific competition in the other. Even this slight increase in complexity leads to markedly different properties. The zero growth curves become nonlinear and up to three equilibria between two competing species are possible.

Apparent competition structures ecological assemblages

Competition is a major force in structuring ecological communities. It acts directly or indirectly, in which case it may be mediated by shared natural enemies and is known as ‘apparent competition’. The effects of apparent competition on species coexistence are well known theoretically but have not previously been demonstrated empirically in controlled multigenerational experiments. Here we report on the population dynamic consequences of apparent competition in a laboratory insect system with two host species and a common parasitoid attacking them. We find that whereas the two separate, single host–single parasitoid interactions are persistent, the three-species system with the parasitoid attacking both hosts species (which are not allowed to compete directly) is unstable, and that one of the host species is eliminated from the interaction owing to the effects of apparent competition.

ECOLOGICAL STRATEGIES AND POPULATION PARAMETERS

Habitat is the template against which evolutionary pressures fashion the ecological strategy of a species; the instability-stability habitat spectrum gives rise to the r-K-selection continuum. Habitat stability for any animal is conveniently expressed by τ/H (τ = generation time and H = the length of time the habitat remains suitable for food harvesting). In animals whose habitats have a value of τ/H approaching unity, one generation will not affect the resources available to the next. The strategy for these habitats can allow overshooting of the equilibrium. In animals with permanent habitats (τ/H very small), overshooting, with the consequent overexploitation of resources, will be selected against. The logistic equation cannot represent a situation that involves overshooting. A more realistic approach arises from the consideration of the difference equation (2) which includes a time delay between density-dependence acting and the subsequent population change. Its three basic parameters are the equilibrium population (N*), the finite growth rate of the population (λ), and the density-dependent moderator (b), which is related to the return time (Tr = 1/b) near equilibrium. Characteristics of successful r- and K-strategists are investigated using the model and conclusions summarized above. While we accept that many vertebrates may have arisen as a result of K-selection (in comparatively stable geological periods), many groups within these taxa will have their population parameters modified toward those characteristics for the type of habitat they occupy (table 1). Really successful K-strategists become precisely adapted to a very permanent (in generation terms) habitat type, they become larger in size, and, because of their extreme K-type population parameters, they lose their plasticity for selection. When their habitats change owing to major environmental variations in geological time, these species become extinct. This, we suggest, is the ecological explanation of Copes rule.

THE PERSISTENCE OF HOST-PARASITOID ASSOCIATIONS IN PATCHY ENVIRONMENTS. I. A GENERAL CRITERION

In this article we show that, for host-parasitoid interactions in a heterogeneous environment and with discrete generations, the dynamic effects of any patterns of distribution of searching parasitoids can be assessed within a common, simple framework. The populations are regulated if the distribution of searching parasitoids is sufficiently heterogeneous. Specifically, the square of the coefficient of variation (CV2) of the searching parasitoids per host must exceed unity. This criterion is demonstrated to apply approximately, in general and also in several specific cases. We further show that CV2 may be partitioned into a density-dependent component caused by the response of parasitoids to host density per patch and a density-independent component. Population regulation is enhanced as much by density-independent as by density-dependent heterogeneity.

The Dynamics of Multiparasitoid-Host Interactions

In this paper, we have explored the dynamics of some simple multiparasitoid models, concentrating on the factors affecting coexistence and equilibrium levels. As a prelude, a one parasitoid-one host system is examined since this provides the basic submodel for parasitism that is used throughout. This is followed by a system with two parasitoid species attacking the same host species, a system with facultative hyperparasitoids, and finally one with hosts, parasitoids, and hyperparasitoids. In each case, the conditions permitting the three species to coexist are examined and, by introducing a host rate of increase that is density dependent, we also show the extent to which parasitism can depress the host equilibrium below its carrying capacity. The results are discussed within the context of biological control. We conclude that the practice of multiple parasitoid introductions, and the use of parasitoids with high searching efficiency and a marked ability to seek out patches of high host density, are sound strategies for maximizing the depression in the host equilibrium populations and for ensuring that they remain locally stable. While obligate hyperparasitoids will always lead to an increase in host equilibria, truly facultative hyperparasitoids can be classed with other primary parasitoids as candidates for use in multiple introduction programs.

FORAGING STRATEGIES, POPULATION MODELS AND BIOLOGICAL CONTROL: A CASE STUDY

SUMMARY (4) A population model based on that of May (1978), but with k from the negative binomial now a function of host density as observed for Cyzenis, is analysed and the stability properties displayed. (5) This general model for parasitism is included in a more detailed model for the winter moth and Cyzenis at Wytham Wood. It shows Cyzenis to play a minor part in the winter moth population dynamics, which is largely governed by the destabilizing effects of the key-factor and the stabilizing effects of the density dependent soil mortality. (6) A model for the winter moth and CyzeMis in Nova Scotia is developed. Cyzenis is assumed to search in the manner found for Wytham Wood, but the other components are derived from the studies of Embree (1965, 1966). The model predicts the successful biological control of the winter moth that has been observed in Nova Scotia following the introduction of Cyzenis. The reasons for the very different performances of Cyzenis at Wytham Wood and Nova Scotia are discussed.