Andrew Hoyle

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.

The evolution of costly acquired immune memory

A key feature of the vertebrate adaptive immune system is acquired immune memory, whereby hosts launch a faster and heightened response when challenged by previously encountered pathogens, preventing full infection. Here, we use a mathematical model to explore the role of ecological and epidemiological processes in shaping selection for costly acquired immune memory. Applying the framework of adaptive dynamics to the classic SIR (Susceptible-Infected-Recovered) epidemiological model, we focus on the conditions that may lead hosts to evolve high levels of immunity. Linking our work to previous theory, we show how investment in immune memory may be greatest at long or intermediate host lifespans depending on whether immunity is long lasting. High initial costs to gain immunity are also found to be essential for a highly effective immune memory. We also find that high disease infectivity and sterility, but intermediate virulence and immune period, increase selection for immunity. Diversity in host populations through evolutionary branching is found to be possible but only for a limited range of parameter space. Our model suggests that specific ecological and epidemiological conditions have to be met for acquired immune memory to evolve.

Evolutionary Behaviour, Trade-Offs and Cyclic and Chaotic Population Dynamics

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.

Optimising Antibiotic Usage to Treat Bacterial Infections

The increase in antibiotic resistant bacteria poses a threat to the continued use of antibiotics to treat bacterial infections. The overuse and misuse of antibiotics has been identified as a significant driver in the emergence of resistance. Finding optimal treatment regimens is therefore critical in ensuring the prolonged effectiveness of these antibiotics. This study uses mathematical modelling to analyse the effect traditional treatment regimens have on the dynamics of a bacterial infection. Using a novel approach, a genetic algorithm, the study then identifies improved treatment regimens. Using a single antibiotic the genetic algorithm identifies regimens which minimise the amount of antibiotic used while maximising bacterial eradication. Although exact treatments are highly dependent on parameter values and initial bacterial load, a significant common trend is identified throughout the results. A treatment regimen consisting of a high initial dose followed by an extended tapering of doses is found to optimise the use of antibiotics. This consistently improves the success of eradicating infections, uses less antibiotic than traditional regimens and reduces the time to eradication. The use of genetic algorithms to optimise treatment regimens enables an extensive search of possible regimens, with previous regimens directing the search into regions of better performance.

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.

Sexually antagonistic co-evolution: a model and an empirical test

Models reveal that sexually antagonistic co‐evolution exaggerates female resistance and male persistence traits. Here we adapt an established model by including directional sexual selection acting against persistence. We find similar equilibria to previous models showing that sexually antagonistic co‐evolution can be limited by counteracting sexual, as well as, natural selection. We tested the model using empirical data for the seaweed fly, Coelopa ursina, in which body size acts as a persistence and a resistance trait. Our model can generate continuous co‐evolutionary cycles and stable equilibria, however, all simulations using empirically derived parameter estimates reach stable equilibria. Thus, stable equilibria might be more common in nature than continuous co‐evolutionary cycles, suggesting that sexual conflict is unlikely to promote speciation. The model predicts male biased sexual size dimorphism for C. ursina, comparable with empirically observed values. Male persistence is shown to be more sensitive than female resistance to changes in model parameters.

A limited host immune range facilitates the creation and maintenance of diversity in parasite virulence.

A vast theoretical literature has explored the evolutionary dynamics of parasite virulence. The classic result from this modelling work is that, assuming a saturating transmission–virulence trade-off, there is a single evolutionary optimum where the parasite optimizes the epidemiological R0. However, there are an increasing number of models that have shown how ecological and epidemiological feedbacks to evolution can instead result in the creation and maintenance of multiple parasite strains. Here, we fully explore one such example, where recovered hosts have a limited ‘immune range’ resulting in partial cross-immunity to parasite strains that they have not previously encountered. Taking an adaptive dynamics approach, we show that, provided this immune range is not too wide, high levels of diversity can evolve and be maintained through multiple branching events. We argue that our model provides a more realistic picture of disease dynamics in vertebrate host populations and may be a key explanatory factor in the high levels of parasite diversity seen in natural systems.

Can possible evolutionary outcomes be determined directly from the population dynamics

Traditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria - one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply.

Reproductive trade-offs may moderate the impact of Gyrodactylus salaris in warmer climates.

Gyrodactylus salaris is a notifiable freshwater ectoparasite of salmonids. Its primary host is Atlantic salmon (Salmo salar), upon which infections can cause death, and have led to massive declines in salmon numbers in Norway, where the parasite is widespread. Different strains of S. salar vary in their susceptibility, with Atlantic strains (such as those found in Norway) exhibiting no resistance to the parasite, and Baltic strains demonstrating an innate resistance sufficient to regulate parasite numbers on the host causing it to either die out or persist at a low level. In this study, Leslie matrix and compartmental models were used to generate data that demonstrated the population growth of G. salaris on an individual host is dependent on the total number of offspring per parasite, its longevity and the timing of its births. The data demonstrated that the key factor determining the rate of G. salaris population growth is the time at which the parasite first gives birth, with rapid birth rate giving rise to large population size. Furthermore, it was shown that though the parasite can give birth up to four times, only two births are required for the population to persist as long as the first birth occurs before a parasite is three days old. As temperature is known to influence the timing of the parasites first birth, greater impact may be predicted if introduced to countries with warmer climates than Norway, such as the UK and Ireland which are currently recognised to be free of G. salaris. However, the outputs from the models developed in this study suggest that temperature induced trade-offs between the total number of offspring the parasite gives birth to and the first birth timing may prevent increased population growth rates over those observed in Norway.

PEPA'd Oysters: Converting Dynamic Energy Budget Models to Bio-PEPA, Illustrated by a Pacific Oyster Case Study

We present a Bio-PEPA (Biochemical-Performance Evaluation Process Algebra) computational model for the Pacific oyster, derived from a DEB (Dynamic Energy Budget) mathematical model. Experience with this specific model allows us to propose a generic scheme for translation between the widely-used DEB theory and Bio-PEPA. The benefits of translation are that a range of novel analysis tools become available, therefore improving the potential to understand complex biological phenomena at a systems level. This work also provides a link between biology, mathematics and computer science: such interlinking of disciplines is the core of the systems approach to biology.