J.V. Greenman

The role of shared parasites in the exclusion of wildlife hosts: Heterakis gallinarum in the ring‐necked pheasant and the grey partridge

1. A two-host shared-macroparasite model was parameterized from the results of infection and transmission experiments, to investigate whether apparent competition between the ring-necked pheasant (Phasianus colchicus) and the grey partridge (Perdix perdix), mediated via the shared nematode Heterakis gallinarum, could theoretically cause partridge exclusion. 2. Both the model created and the experiments conducted show that the bulk of H. gallinarum infection to partridges, when they occur in the same locations as pheasants, will be from the pheasants and not from the partridges themselves. This is due to R0 for the parasite being 1·23 when infecting pheasants, but only 0·0057 when infecting partridges. Thus, when the pheasant is present in the model the partridge population is impacted by the shared parasite but, when the pheasant is absent, the parasite is lost from the system. 3. Based on best available parameter estimates, the observed impact of H. gallinarum on the grey partridge may be sufficient to cause exclusion when the pheasant is present in the model. This supports the hypothesis that the UK grey partridge decline observed over the past 50 years may be partly due to apparent competition with pheasants. 4. Habitat separation between the two host species, where it decreases the rate of H. gallinarum transmission from the pheasant to the partridge, may allow them to co-exist in the field in the presence of the parasite. We predict, however, that grey partridge exclusion would still occur if separation was less than 43%.

The amplification of environmental noise in population models: causes and consequences.

Environmental variability is a ubiquitous feature of every organism’s habitat. However, the interaction between density dependence and those density‐independent factors that are manifested as environmental noise is poorly understood. We are interested in the conditions under which noise interacts with the density dependence to cause amplification of that noise when filtered by the system. For a broad family of structured population models, we show that amplification occurs near the threshold from stable to unstable dynamics by deriving an analytic formula for the amplification under weak noise. We confirm that the effect of noise is to sustain oscillations that would otherwise decay, and we show that it is the amplitude and not the phase that is affected. This is a feature noted in several recent studies. We study this phenomenon in detail for the Turchin and LPA models of population dynamics. We find that the degree of amplification is sensitive to both the noise input and life‐history stage through which it acts, that the results hold for surprisingly high levels of noise, and that stochastic chaos (as measured by local Lyapunov exponents) is a concomitant feature of amplification. Further, it is shown that the temporal autocorrelation, or “color,” of the noise has a major impact on the system response. We discuss the conditions under which color increases population variance and hence the risk of extinction, and we show that periodicity is sharpened when the color of the noise and dynamics coincide. Otherwise, there is interference, which shows how difficult it is in practice to separate the effects of nonlinearity and noise in short time series. The sensitivity of the population dynamics to noise when close to a bifurcation has wide‐ranging consequences for the evolution and ecology of population dynamics.

Differential impact of a shared nematode parasite on two gamebird hosts: implications for apparent competition

If the deleterious effects of non-specific parasites are greater on vulnerable host species than on reservoir host species then exclusion of the vulnerable host through apparent competition is more likely. Evidence suggests that such a mechanism occurs in interactions between the ring-necked pheasant (Phasianus colchicus), the grey partridge (Perdix perdix), and their shared caecal nematode Heterakis gallinarum. Modelling of the system predicts that the reduced parasite impact on the pheasant compared to the partridge results in the force of infection transmitted from pheasants to partridges being sufficient to cause partridge exclusion. Since the parasite impacts are currently estimated from correlational work, controlled infections were conducted to experimentally compare the impact of H. gallinarum on the two hosts and verify cause and effect. While challenged partridges showed reduced mass gain, decreased food consumption, and impaired caecal activity, in comparison to controls, the only detectable effect of parasite challenge on the pheasant was impaired caecal activity. The impact of H. gallinarum on challenged partridges conforms with previous correlational data, supporting the prediction that parasite-mediated apparent competition with the ring-necked pheasant may result in grey partridge exclusion. However, the observed decrease in the caecal activity of challenged pheasants could imply that H. gallinarum may also have an impact on the fecundity and survival of pheasants in the wild, particularly if food is limiting. If this is the case, the associated decrease in the force of infection to which the partridge is exposed may be sufficient to change the model prediction from partridge exclusion to pheasant and partridge coexistence.

The evolution of oscillatory behavior in age-structured species

A major challenge in ecology is to explain why so many species show oscillatory population dynamics and why the oscillations commonly occur with particular periods. The background environment, through noise or seasonality, is one possible driver of these oscillations, as are the components of the trophic web with which the species interacts. However, the oscillation may also be intrinsic, generated by density‐dependent effects on the life history. Models of structured single‐species systems indicate that a much broader range of oscillatory behavior than that seen in nature is theoretically possible. We test the hypothesis that it is selection that acts to constrain the range of periods. We analyze a nonlinear single‐species matrix model with density dependence affecting reproduction and with trade‐offs between reproduction and survival. We show that the evolutionarily stable state is oscillatory and has a period roughly twice the time to maturation, in line with observed patterns of periodicity. The robustness of this result to variations in trade‐off function and density dependence is tested.

Pathogen exclusion from eco-epidemiological systems.

Increasing concerns about the changing environment and the emergence of pathogens that cross species boundaries have added to the urgency of understanding the dynamics of complex ecological systems infected by pathogens. Of particular interest is the often counterintuitive way in which infection and predation interact and the consequent difficulties in designing control strategies to manage the system. To understand the mechanisms involved, we focus on the pathogen exclusion problem, using control maps (on which the network of exclusion thresholds are plotted) in order to readily identify which exclusion strategies will work and why others will not. We apply this approach to the analysis of parasite exclusion in two game bird ecologies. For higher dimensions, we propose a computational scheme that will generate the optimal exclusion strategy, taking into account all operational constraints on the pathogen invasion matrix, populations, and controls. The situation is further complicated when external forcing distorts pathogen thresholds. This distortion is highly sensitive to the lags between forcing components, a sensitivity that can be exploited by management using correctly lagged cyclically varying controls to reduce the effort involved in pathogen exclusion.

Phase control of resonant systems: Interference, chaos and high periodicity

Much progress has been made in understanding the effect of periodic forcing on epidemiological and ecological systems when that forcing acts on just one part of the system. Much less is known about situations in which several parts of the system are affected. In this case the interaction between the impacts of the different forcing components can lead to reinforcement of system responses or to their interference. This interference phenomenon is significant if some forcing components are anthropogenic for then management might be able to exercise sufficient control to bring about suppression of undesirable aspects of the forcing, for example resonant amplification and the problems this can cause. We set out the algebraic theory when forcing is weak and illustrate by example what can happen when forcing is strong enough to create subharmonics and chaotic states. Phase is the key control variable that can bring about interference, advantageously shift nonlinear response curves and create periodic states out of chaos. The phenomenon in which high period fluctuations appear to be generated by low period forcing is examined and different mechanisms compared in a two-strain epidemiological model. The effect of noise as a source of high period fluctuations is also considered.

Exclusion of Generalist Pathogens in Multihost Communities

Knowing how to control a pathogen that infects more than one host species is of increasing importance because the incidence of such infections grows with continuing environmental change. Of concern are infections transmitted from wildlife to humans or livestock. To determine which options are available to control a pathogen in these circumstances, we analyze the pathogen invasion matrix for the multihost susceptible‐infected‐susceptible model. We highlight the importance of both community structure and the column sum or row sum index, an indicator of both force of infection and community stability. We derive a set of guidelines for constructing culling strategies and suggest a hybrid strategy that has the advantages of both the bottom‐up and the top‐down approaches, which we study in some detail. The analysis holds for an arbitrary number of host species, enabling the analysis of large‐scale ecological systems and systems with spatial dimensions. We test the robustness of our methods by making two changes in the structure of the underlying dynamic model, adding direct competition and introducing frequency‐dependent infection transmission. In particular, we show that the introduction of an additional host can eliminate the pathogen rather than eliminate the resident host. The discussion is illustrated with a reference to bovine tuberculosis.

Threshold dynamics for periodically forced ecological systems: The control of population invasion and exclusion

Ecosystems are under increasing threat as a result of anthropogenic activity, through pollution, unregulated harvesting, habitat destruction and the inadvertent spread of pathogens and vertebrate and non-vertebrate species through global transportation links. Many of the necessary interventions to restore or restructure natural ecosystems require the exclusion of a population from the ecosystem or the inclusion of a population if robust biodiversity is the objective. The problem of how best to bring this about is not easy to solve in highly nonlinear systems, especially if the system is exposed to significant time varying external forces. We wish here to build on the understanding gained from previous work by developing an algebraic methodology that yields explicit formulae to analyse the effect of moderate multi-component forcing on the invasion/exclusion process. This can be of assistance to management in designing suitable intervention strategies if one or more of the forcing components is under management control. We apply this methodology to look at three important issues, involving the relationships between resonance and control, between vaccination policy and the stage structure of a disease and between apparent competition and coexistence.