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

Stage duration distributions and intraspecific competition: a review of continuous stage-structured models

Stage structured models, by grouping individuals with similar demographic characteristics together, have proven useful in describing population dynamics. This manuscript starts from reviewing two widely used modeling frameworks that are in the form of integral equations and age-structured partial differential equations. Both modeling frameworks can be reduced to the same differential equation structures with/without time delays by applying Dirac and gamma distributions for the stage durations. Each framework has its advantages and inherent limitations. The net reproduction number and initial growth rate can be easily defined from the integral equation. However, it becomes challenging to integrate the density-dependent regulations on the stage distribution and survival probabilities in an integral equation, which may be suitably incorporated into partial differential equations. Further recent modeling studies, in particular those by Stephen A. Gourley and collaborators, are reviewed under the conditions of the stage duration distribution and survival probability being regulated by population density.

A method for detecting positive growth autocorrelation without marking individuals

In most ecological studies, within-group variation is a nuisance that obscures patterns of interest and reduces statistical power. However, patterns of within-group variability often contain information about ecological processes. In particular, such patterns can be used to detect positive growth autocorrelation (consistent variation in growth rates among individuals in a cohort across time), even in samples of unmarked individuals. Previous methods for detecting autocorrelated growth required data from marked individuals. We propose a method that requires only estimates of within-cohort variance through time, using maximum likelihood methods to obtain point estimates and confidence intervals of the correlation parameter. We test our method on simulated data sets and determine the loss in statistical power due to the inability to identify individuals. We show how to accommodate nonlinear growth trajectories and test the effects of size-dependent mortality on our method's accuracy. The method can detect significant growth autocorrelation at moderate levels of autocorrelation with moderate-sized cohorts (for example, statistical power of 80% to detect growth autocorrelation ρ² = 0.5 in a cohort of 100 individuals measured on 16 occasions). We present a case study of growth in the red-eyed tree frog. Better quantification of the processes driving size variation will help ecologists improve predictions of population dynamics. This work will help researchers to detect growth autocorrelation in cases where marking is logistically infeasible or causes unacceptable decreases in the fitness of marked individuals.

Developmental variability and stability in continuous-time host-parasitoid models

Insect host-parasitoid systems are often modeled using delay-differential equations, with a fixed development time for the juvenile host and parasitoid stages. We explore here the effects of distributed development on the stability of these systems, for a random parasitism model incorporating an invulnerable host stage, and a negative binomial model that displays generation cycles. A shifted gamma distribution was used to model the distribution of development time for both host and parasitoid stages, using the range of parameter values suggested by a literature survey. For the random parasitism model, the addition of biologically plausible levels of developmental variability could potentially double the area of stable parameter space beyond that generated by the invulnerable host stage. Only variability in host development time was stabilizing in this model. For the negative binomial model, development variability reduced the likelihood of generation cycles, and variability in host and parasitoid was equally stabilizing. One source of stability in these models may be aggregation of risk, because hosts with varying development times have different vulnerabilities. High levels of variability in development time occur in many insects and so could be a common source of stability in host-parasitoid systems.

Stochastic development in biologically structured population models

Variation in organismal development is ubiquitous in nature but omitted from most age- and stage-structured population models. I give a general approach for formulating and analyzing its role in density-independent population models using the framework of integral projection models. The approach allows flexible assumptions, including correlated development times among multiple life stages. I give a new Monte Carlo numerical integration approach to calculate long-term growth rate, its sensitivities, stable age-stage distributions and reproductive value. This method requires only simulations of individual life schedules, rather than iteration of full population dynamics, and has practical and theoretical appeal because it ties easily implemented simulations to numerical solution of demographic equations. I show that stochastic development is demographically important using two examples. For a desert cactus, many stochastic development models, with independent or correlated stage durations, can generate the same stable stage distribution (SSD) as the real data, but stable age-within-stage distributions and sensitivities of growth rate to demographic rates differ greatly among stochastic development scenarios. For Mediterranean fruit flies, empirical variation in maturation time has a large impact on population growth. The systematic model formulation and analysis approach given here should make consideration of variable development models widely accessible and readily extendible.

Superparasitism Evolution: Adaptation or Manipulation?

Superparasitism refers to the oviposition behavior of parasitoid females who lay their eggs in an already parasitized host. This often yields intense competition among larvae that are sharing the same host. Why would a female oviposit in such hostile habitat instead of looking for a better quality, unparasitized host? Here we present a continuous-time model of host-parasitoid interaction and discuss alternative scenarios. This model is first used to analyze the evolution of the superparasitism behavior of a solitary proovigenic parasitoid under both time and egg limitation. Then, following the recent discovery by Varaldi et al., we allow the parasitoid to be infected by a virus that alters the superparasitism behavior of its host to enhance its own horizontal transmission. The analysis of the coevolution of this manipulative behavior with the oviposition behavior of uninfected females clarifies and quantifies the conflict that emerges between the parasitoid and its virus. The model also yields new testable predictions. For example, we expect that uninfected parasitoids should superparasite less after coevolving with the manipulative virus. More generally, this model provides a theoretical framework for analyzing the evolution of the manipulation of parasitoid life-history traits by microparasites.

Appropriate models for the management of infectious diseases

BACKGROUND

Mathematical models have become invaluable management tools for epidemiologists, both shedding light on the mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we explain how substantial biases are introduced by two important, yet largely ignored, assumptions at the core of the vast majority of such models.

METHODS AND FINDINGS

First, we use analytical methods to show that (i) ignoring the latent period or (ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period) always results in underestimating the basic reproductive ratio of an infection from outbreak data. We then proceed to illustrate these points by fitting epidemic models to data from an influenza outbreak. Finally, we document how such unrealistic a priori assumptions concerning model structure give rise to systematically overoptimistic predictions on the outcome of potential management options.

CONCLUSION

This work aims to highlight that, when developing models for public health use, we need to pay careful attention to the intrinsic assumptions embedded within classical frameworks.