Examining the role of individual movement in promoting coexistence in a spatially explicit prisoner's dilemma.

The emergence of cooperation is a major conundrum of evolutionary biology. To unravel this evolutionary riddle, several models have been developed within the theoretical framework of spatial game theory, focussing on the interactions between two general classes of player, "cooperators" and "defectors". Generally, explicit movement in the spatial domain is not considered in these models, with strategies moving via imitation or through colonisation of neighbouring sites. We present here a spatially explicit stochastic individual-based model in which pure cooperators and defectors undergo random motion via diffusion and also chemotaxis guided by the gradient of a semiochemical. Individual movement rules are derived from an underlying system of reaction-diffusion-taxis partial differential equations which describes the dynamics of the local number of individuals and the concentration of the semiochemical. Local interactions are governed by the payoff matrix of the classical prisoner's dilemma, and accumulated payoffs are translated into offspring. We investigate the cases of both synchronous and non-synchronous generations. Focussing on an ecological scenario where defectors are parasitic on cooperators, we find that random motion and semiochemical sensing bring about self-generated patterns in which resident cooperators and parasitic defectors can coexist in proportions that fluctuate about non-zero values. Remarkably, coexistence emerges as a genuine consequence of the natural tendency of cooperators to aggregate into clusters, without the need for them to find physical shelter or outrun the parasitic defectors. This provides further evidence that spatial clustering enhances the benefits of mutual cooperation and plays a crucial role in preserving cooperative behaviours.

Modelling contact spread of infection in host-parasitoid systems: vertical transmission of pathogens can cause chaos.

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we develop a mathematical model of contact spread infection to investigate the effect of introducing a parasitoid-vectored infection into a one-host-two-parasitoid competition model. We use a system of ordinary differential equations to investigate the separate influences of horizontal and vertical pathogen transmission on a model system appropriate for a variety of competitive situations. Computational simulations and steady-state analysis show that the transient and long-term dynamics exhibited under contact spread infection are highly complex. Horizontal pathogen transmission has a stabilising effect on the system whilst vertical transmission can destabilise it to the point of chaotic fluctuations in population levels. This has implications when considering the introduction of host pathogens for the control of insect vectored diseases such as bovine tuberculosis or yellow fever.

Disease induced dynamics in host-parasitoid systems: chaos and coexistence.

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we present a mathematical model of interactions between a host, two parasitoids and a pathogen which shows that the presence of an infection can preserve and promote diversity in such multi-species systems. Initially, we use a system of ordinary differential equations to investigate interactions between two species of parasitoids, a host and a host infection. We show that the presence of all four species is necessary for the system as a whole to persist, and that in particular, the presence of the pathogen is necessary for the coexistence of the two parasitoid species. The inclusion of infection induces a wide range of dynamics, including chaos, and these dynamics are robust for a wide range of parameter values. We then extend the model to include spatial effects by introducing random motility (diffusion) of all three species and examine the subsequent spatio-temporal dynamics, including travelling waves and other more complicated heterogeneous behaviour. The computational simulation results of the model suggest that infection in the hosts can blunt the effects of competition between parasitoids, allowing the weaker competitor to survive. Regardless of the nature of the stability of the coexistent steady state of the system, there is an initial period of transient dynamics, the length of which can be extended by an appropriate choice of initial conditions. The existence of these transient dynamics suggests that systems subject to regular restoration to a starting state, such as agro-ecosystems, may be kept in a continual state of dynamic transience, and this has implications for the use of natural enemies to control insect pests, the preservation of biodiversity in farmland habitats and the more general dynamics of disease processes.

Wolbachia infection suppresses both host defence and parasitoid counter-defence.

Endosymbiotic bacteria in the genus Wolbachia have been linked to several types of reproductive parasitism, which enhance their own transmission, while their direct effects on the host vary from beneficial to neutral or detrimental. Here, we report negative effects of infection on immunity-related traits of Drosophila simulans and the parasitoid wasp Leptopilina heterotoma. Infected D. simulans showed a reduced ability to encapsulate parasitoid eggs, compared to a tetracycline-treated, bacterium-free line. Challenging the two lines with a fungal pathogen, Beauveria bassiana, on the other hand, revealed no differences in survival. Moreover, elimination of Wolbachia was beneficial for the parasitoid wasp, as eggs laid by uninfected females suffered significantly lower encapsulation rates. We discuss possible origins of these fitness costs and their implications for infection dynamics and the interactions between host species.

Insect endosymbionts: manipulators of insect herbivore trophic interactions?

Throughout their evolutionary history, insects have formed multiple relationships with bacteria. Although many of these bacteria are pathogenic, with deleterious effects on the fitness of infected insects, there are also numerous examples of symbiotic bacteria that are harmless or even beneficial to their insect host. Symbiotic bacteria that form obligate or facultative associations with insects and that are located intracellularly in the host insect are known as endosymbionts. Endosymbiosis can be a strong driving force for evolution when the acquisition and maintenance of a microorganism by the insect host results in the formation of novel structures or changes in physiology and metabolism. The complex evolutionary dynamics of vertically transmitted symbiotic bacteria have led to distinctive symbiont genome characteristics that have profound effects on the phenotype of the host insect. Symbiotic bacteria are key players in insect-plant interactions influencing many aspects of insect ecology and playing a key role in shaping the diversification of many insect groups. In this review, we discuss the role of endosymbionts in manipulating insect herbivore trophic interactions focussing on their impact on plant utilisation patterns and parasitoid biology.

Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems.

When searching for hosts, parasitoids are observed to aggregate in response to chemical signalling cues emitted by plants during host feeding. In this paper we model aggregative parasitoid behaviour in a multi-species host-parasitoid community using a system of reaction-diffusion-chemotaxis equations. The stability properties of the steady-states of the model system are studied using linear stability analysis which highlights the possibility of interesting dynamical behaviour when the chemotactic response is above a certain threshold. We observe quasi-chaotic dynamic heterogeneous spatio-temporal patterns, quasi-stationary heterogeneous patterns and a destabilisation of the steady-states of the system. The generation of heterogeneous spatio-temporal patterns and destabilisation of the steady state are due to parasitoid chemotactic response to hosts. The dynamical behaviour of our system has both mathematical and ecological implications and the concepts of chemotaxis-driven instability and coexistence and ecological change are discussed.

Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications.

A mathematical model of the spatio-temporal dynamics of a two host, two parasitoid system is presented. There is a coupling of the four species through parasitism of both hosts by one of the parasitoids. The model comprises a system of four reaction-diffusion equations. The underlying system of ordinary differential equations, modelling the host-parasitoid population dynamics, has a unique positive steady state and is shown to be capable of undergoing Hopf bifurcations, leading to limit cycle kinetics which give rise to oscillatory temporal dynamics. The stability of the positive steady state has a fundamental impact on the spatio-temporal dynamics: stable travelling waves of parasitoid invasion exhibit increasingly irregular periodic travelling wave behaviour when key parameter values are increased beyond their Hopf bifurcation point. These irregular periodic travelling waves give rise to heterogeneous spatio-temporal patterns of host and parasitoid abundance. The generation of heterogeneous patterns has ecological implications and the concepts of temporary host refuge and niche formation are considered.

Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations.

In this paper we develop a general mathematical model describing the spatio-temporal dynamics of host-parasitoid systems with forced generational synchronisation, for example seasonally induced diapause. The model itself may be described as an individual-based stochastic model with the individual movement rules derived from an underlying continuum PDE model. This approach permits direct comparison between the discrete model and the continuum model. The model includes both within-generation and between-generation mechanisms for population regulation and focuses on the interactions between immobile juvenile hosts, adult hosts and adult parasitoids in a two-dimensional domain. These interactions are mediated, as they are in many such host-parasitoid systems, by the presence of a volatile semio-chemical (kairomone) emitted by the hosts or the hosts' food plant. The model investigates the effects on population dynamics for different host versus parasitoid movement strategies as well as the transient dynamics leading to steady states. Despite some agreement between the individual and continuum models for certain motility parameter ranges, the model dynamics diverge when host and parasitoid motilities are unequal. The individual-based model maintains spatially heterogeneous oscillatory dynamics when the continuum model predicts a homogeneous steady state. We discuss the implications of these results for mechanistic models of phenotype evolution.