Adaptive host preference and the dynamics of host-parasitoid interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) "ideal free" parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) "evolving" parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

Differential cannibalism and population dynamics in a host-parasitoid system

The effects of host cannibalism on a host-parasitoid system were explored through experiment and modelling. In individual encounters between parasitized and unparasitized Plodia interpunctella larvae, parasitized larvae were more likely to be cannibalized. Inclusion of this differential cannibalism into a simple Lotka-Volterra-type model of host-parasitoid population dynamics generates alternative stable states-including stable coexistence and extinction of the parasitoid — which depend on starting conditions. Possible mechanisms for differential cannibalism, and its implications for studies of host-parasitoid populations and biological control programmes are discussed.     

A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

Dynamical consequences of harvest in discrete age-structured population models

The role of harvest in discrete age-structured one-population models has been explored. Considering a few age classes only, together with the overcompensatory Ricker recruitment function, we show that harvest acts as a weak destabilizing effect in case of small values of the year-to-year survival probability P and as a strong stabilizing effect whenever the survival probability approaches unity. In the latter case, assuming n=2 age classes, we find that harvest may transfer a population from the chaotic regime to a state where the equilibrium point (x₁*, x₂*) becomes stable. However, as the number of age classes increases (which acts as a stabilizing effect in non-exploited models), we find that harvest acts more and more destabilizing, in fact, when the number of age classes has been increased to n=10, our finding is that in case of large values of the survival probabilities, harvest may transfer a population from a state where the equilibrium is stable to the chaotic regime, thus exactly the opposite of what was found in case of n=2. On the other hand, if we replace the Ricker relation with the generalized Beverton and Holt recruitment function with abruptness parameter larger than 2, several of the conclusions derived above are changed. For example, when n is large and the survival probabilities exceed a certain threshold, the equilibrium will always be stable.Revised version: 18 September 2003     

Dynamical and statistical models of vertebrate population dynamics

Population dynamics methodology now powerfully combines discrete time models (with constant parameters, density dependence, random environment, and/or demographic stochasticity) and capture-recapture models for estimating demographic parameters. Vertebrate population dynamics has strongly benefited from this progress: survival estimates have been revised upwards, trade-offs between life history traits have been demonstrated, analyses of population viability and management are more and more realistic. Promising developments concern random effects, multistate and integrated models. Some biological questions (density dependence, links between individual and population levels, and diversification of life histories) can now be efficiently attacked.     

Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log–linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state–space model on log‐scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non‐autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state–space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.     

Infection dynamics of different Wolbachia-types within one host population

Wolbachia are widespread intracellular symbionts of arthropods which are known to cause several reproductive manipulations in their hosts, the commonest of which being cytoplasmic incompatibility (CI), male killing (MK), and the induction of parthenogenesis (PI). Strains of endosymbionts inducing one of these effects can be referred to as 'Wolbachia-types'. Here, we try to ascertain whether two of these Wolbachia-types can stably coexist within one population. We investigate this question by means of two discrete-time mathematical models which describe the dynamics of an infection of a host population with either CI- and MK- or CI- and PI-Wolbachia. We derive analytical solutions for two special cases of each model showing that stable coexistence of the respective Wolbachia-types is not possible if no doubly infected individuals occur within the population and that stable coexistence is possible when doubly infected hosts do exist and transmission of the endosymbionts is perfect. Moreover, we show that a population infected with either CI- or MK-Wolbachia at equilibrium can resist invasion of the respective other Wolbachia-type as a single infection. In contrast, a population infected with CI-Wolbachia can be invaded by PI-Wolbachia as a single infection with the CI-Wolbachia going extinct. Computer simulations confirmed these findings for the general models. We discuss our results with respect to the prevalence of the Wolbachia-types considered here and the emergence of PI- from CI-Wolbachia.     

Adaptive feeding across environmental gradients and its effect on population dynamics

This paper analyzes a consumer's adaptive feeding response to environmental gradients. We consider a consumer-resource system where resources are distributed among many discrete resource patches. Each consumer exhibits a feeding morphology allowing it to remove resources from a patch down to some threshold density (or level) before having to seek resources elsewhere. Assuming consumers trade off resource extraction with patch access and predation, we show that for a given environment there often exists a single evolutionarily stable feeding threshold and it is an evolutionary attractor. We then investigate how the population dynamics of the resource and the consumer change as the environment changes. Two cases are considered: (i) all consumers exhibit a fixed feeding threshold that is adaptive for an intermediate environment; and (ii) the consumer population adapts and adopts the evolutionarily stable feeding threshold associated with the current environment. In less harsh environments (i.e., environments where consumers experience a lower risk of predation, or environments where resource patches are more abundant) the adaptive consumer population is predicted to evolve so that resources within a patch are depleted to lower densities. We show that the change in consumer density due to environmental change can be rather different depending on whether or not the population can adapt. In some situations we observe that when the consumer's environment becomes harsher, the consumer population may increase in density before a rapid crash to extinction. This result has implications for monitoring and managing a population.     

Multiple host use by a sap-sucking membracid: population consequences of nymphal development on primary and secondary host plant species

Aconophora compressa is a gregarious, sap-sucking insect that uses multiple host plant species. Nymphal host plant species (and variety) significantly affected nymphal survival, nymphal development rate and the subsequent size and fecundity of adults, with fiddlewood (Citharexylum spinosum) being significantly best in all respects. Nymphs that developed on a relatively poor host (Duranta erecta var “geisha girl”) and which were moved to fiddlewood as adults laid significantly fewer eggs (mean ± SE = 836 ± 130) than those that developed solely on fiddlewood (1,329 ± 105). Adults on geisha girl, regardless of having been reared as nymphs on fiddlewood or geisha girl, laid significantly fewer eggs (342 ± 83 and 317 ± 74, respectively) than adults on fiddlewood. A simple model that incorporates host plant related survival, development rate and fecundity suggests that the population dynamics of A. compressa are governed mainly by fiddlewood, the primary host. The results have general implications for understanding the population dynamics of herbivores that use multiple host plant species, and also for the way in which weed biological control host testing methods should be conducted. Handling Editor: Robert Glinwood     

Snowshoe hare optimal foraging and its implications for population dynamics

The results of an optimal foraging model using linear programming with constraints for feeding time, digestive capacity, sodium requirements, and energy requirements indicate that snowshoe hare (Lepus americanus) may forage as energy maximizers. The solution provides the quantities of major food classes (leaves, herbs, fungus, twigs) included in the diet. The species composition of each diet class also is determined using a simultaneous search model based upon the probability of encounter, the probability of sufficient item size, and the probability of sufficient quality. The results also indicate that hare life history parameters (weaning size, size at first reproduction, average adult size) and potential demographic changes in hare populations may be controlled by foraging considerations.     

Influence of parasitized adult reproduction on host-parasitoid dynamics: an age-structured model

In this work, we develop an age-structured model (based on delay-differential equations) to investigate the dynamics of host-parasitoid systems in which adults are the target of parasitism. The rare previous work dealing with such interactions assumes that hosts are functionally dead as soon as they are attacked. We relax this assumption and show that low reproduction rates of parasitized hosts can promote stability at the expense of cyclic behavior (either long term or generation cycles). Higher reproduction rates make the regulation of the host population by parasitoids impossible. As it is the case in models in which adults are subjected to attacks but do not reproduce, our model generates generation cycles for a larger set of parameter values than in models in which juveniles are attacked.     

The dynamical consequences of developmental variability and demographic stochasticity for host-parasitoid interactions

Few age-structured models of species dynamics incorporate variability and uncertainty in population processes. Motivated by laboratory data for an insect and its parasitoid, we investigate whether such assumptions are appropriate when considering the population dynamics of a single species and its interaction with a natural enemy. Specifically, we examine the effects of developmental variability and demographic stochasticity on different types of cyclic dynamics predicted by traditional models. We show that predictions based on the deterministic fixed-development approach are differentially sensitive to variability and noise in key life stages. In particular, we find that the demonstration of half-generation cycles in the single-species model and the multigeneration cycles in the host-parasitoid model are sensitive to the introduction of developmental variability and noise, whereas generation cycles are robust to the intrinsic variability and uncertainty that may be found in nature.     

Effects of tick population dynamics and host densities on the persistence of tick-borne infections

The transmission and the persistence of tick-borne infections are strongly influenced by the densities and the structure of host populations. By extending previous models and analysis, in this paper we analyse how the persistence of ticks and pathogens, is affected by the dynamics of tick populations, and by their host densities. The effect of host densities on infection persistence is explored through the analysis and simulation of a series of models that include different assumptions on tick-host dynamics and consider different routes of infection transmission. Ticks are assumed to feed on two types of host species which vary in their reservoir competence. Too low densities of competent hosts (i.e., hosts where transmission can occur) do not sustain the infection cycle, while too high densities of incompetent hosts may dilute the competent hosts so much to make infection persistence impossible. A dilution effect may occur also for competent hosts as a consequence of reduced tick to host ratio; this is possible only if the regulation of tick populations is such that tick density does not increase linearly with host densities.     

Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution

The effect of dispersal on population size and stability is explored for a population that disperses passively between two discrete habitat patches. Two basic models are considered. In the first model, a single population experiences density-dependent growth in both patches. A graphical construction is presented which allows one to determine the spatial pattern of abundance at equilibrium for most reasonable growth models and rates of dispersal. It is shown under rather general conditions that this equilibrium is unique and globally stable. In the second model, the dispersing population is a food-limited predator that occurs in both a source habitat (which contains a prey population) and a sink habitat (which does not). Passive dispersal between source and sink habitats can stabilize an otherwise unstable predator-prey interaction. The conditions allowing this are explored in some detail. The theory of optimal habitat selection predicts the evolutionarily stable distribution of a population, given that individuals can freely move among habitats so as to maximize individual fitness. This theory is used to develop a heuristic argument for why passive dispersal should always be selectively disadvantageous (ignoring kin effects) in a spatially heterogeneous but temporally constant environment. For both the models considered here, passive dispersal may lead to a greater number of individuals in both habitats combined than if there were no dispersal. This implies that the evolution of an optimal habitat distribution may lead to a reduction in population size; in the case of the predator-prey model, it may have the additional effect of destabilizing the interaction. The paper concludes with a discussion of the disparate effects habitat selection might have on the geographical range occupied by a species.     

Temporal variation in feeding morphology and size-structured population dynamics in fishes

Considerable variation in morphology associated with resource use is a classic example of local adaptation to the environment. We demonstrate that a temporal change in feeding morphology might occur within a population. In a 5-year natural field experiment, we estimated gill raker morphology, resource density and population dynamics of the roach and its competitor, the perch. Despite a variation in density of zooplankton resources and perch across years, no change in roach density was observed. However, gill raker morphology in roach covaried with size structure of the zooplankton resource across years. A laboratory experiment confirmed that gill raker morphology has a great effect on roach foraging efficiency on zooplankton and that there is a functional trade-off with regard to zooplankton foraging. We suggest that the response in gill raker structure is an adaptation to deal with the rapid population dynamics of zooplankton, which are in turn mediated by changes in the size structure of the competing perch.     

Comparative dynamics of three models for host-parasitoid interactions in a patchy environment

Phenomenological models represent a simplified approach to the study of complex systems such as host-parasitoid interactions. In this paper we compare the dynamics of three phenomenological models for host-parasitoid interactions developed by May (1978), May and Hassell (1981) and May et al. (1981). The essence of the paper by May and Hassell (1981) was to define a minimum number of parameters that would describe the interactions, avoiding the technical difficulties encountered when using models that involve many parameters, yet yielding a system of equations that could capture the essence of real world interactions in patchy environments. Those studies dealt primarily with equilibrium and coexistence phenomena. Here we study the dynamics through bifurcation analysis and phase portraits in a much wider range of parameter values, carrying the models beyond equilibrium states. We show that the dynamics can be either stable or chaotic depending on the location of a damping term in the equations. In the case of the stable system, when host density dependence acts first, a stable point is reached, followed by a closed invariant curve in phase space that first increases then decreases, finally returning to an asymptotically stable point. Chaos is not seen. On the other hand, when parasitoid attack occurs before host density dependence, chaos is inevitably apparent. We show, as did May et al. (1981) and stated earlier byWang and Gutierrez (1980), that the sequence of events in host-parasitoid interactions is crucial in determining their stability. In a chaotic state the size of the host (e.g., insect pests) population becomes unpredictable, frequently becoming quite large, a biologically undesirable outcome. From a mathematical point of view the system is of interest because it reveals how a strategically placed damping term can dramatically alter the outcome. Our study, reaching beyond equilibrium states, suggests a strategy for biological control different from that of May et al. (1981).