Roger G. Bowers

Life-history trade-offs and the evolution of pathogen resistance: competition between host strains

The dynamics of a ‘resistant’ and a ‘susceptible’ strain of a self-regulated host species, in the presence of a directly transmitted pathogen, is investigated. The two strains trade off differences in pathogen transmissibility (as an aspect of pathogen resistance) against differences in birth rate and/or resistance to crowding. Depending on parameter values, either strain may be eliminated, or the two may coexist (along with the pathogen). Coexistence (polymorphism), unsurprisingly, requires an appropriate balance between the different advantages possessed by the two strains. The probability of coexistence through such a balance, however, varies nonlinearly with the degree of difference between the strains: coexistence is least likely between two very similar strains. Resistance is most likely to evolve in hosts with the characteristics of many insect pests. Moreover, with highly pathogenic pathogens, a ‘susceptible’ strain may exclude a ‘resistant’ strain because its higher growth rate is more effective against the pathogen than reduced transmissibility. ‘Resistance’ can reside in parameters other than those directly associated with the pathogen. Although no cycles arise and no chaotic behaviour is found, an oscillatory approach to equilibrium is commonly observed, signalling the possibility of observable oscillations in strain frequency in the (more variable) real world.

The evolution of resistance through costly acquired immunity.

We examine the evolutionary dynamics of resistance to parasites through acquired immunity. Resistance can be achieved through the innate mechanisms of avoidance of infection and reduced pathogenicity once infected, through recovery from infection and through remaining immune to infection: acquired immunity. We assume that each of these mechanisms is costly to the host and find that the evolutionary dynamics of innate immunity in hosts that also have acquired immunity are quantitatively the same as in hosts that possess only innate immunity. However, compared with resistance through avoidance or recovery, there is less likely to be polymorphism in the length of acquired immunity within populations. Long–lived organisms that can recover at intermediate rates faced with fast–transmitting pathogens that cause intermediate pathogenicity (mortality of infected individuals) are most likely to evolve long–lived acquired immunity. Our work emphasizes that because whether or not acquired immunity is beneficial depends on the characteristics of the disease, organisms may be selected to only develop acquired immunity to some of the diseases that they encounter.

Persistence and transmission of tick-borne viruses: Ixodes ricinus and louping-ill virus in red grouse populations

The population dynamics of tick-borne disease agents and in particular the mechanisms which influence their persistence are examined with reference to the flavivirus that causes louping-ill in red grouse and sheep. Pockets of infection cause heavy mortality and the infection probably persists as a consequence of immigration of susceptible hosts. Seroprevalence is positively associated with temporal variations in vectors per host, although variation between areas is associated with the abundance of mountain hares. The presence of alternative tick hosts, particularly large mammals, provides additional hosts for increasing tick abundance. Grouse alone can not support the vectors and the pathogen but both can persist when a non-viraemic mammalian host supports the tick population and a sufficiently high number of nymphs bite grouse. These alternative hosts may also amplify virus through non-viraemic transmission by the process of co-feeding, although the relative significance of this has yet to be determined. Another possible route of infection is through the ingestion of vectors when feeding or preening. Trans-ovarial transmission is a potentially important mechanism for virus persistence but has not been recorded with louping-ill and Ixodes ricinus. The influence of non-viraemic hosts, both in the multiplication of vectors and the amplification of virus through non-viraemic transmission are considered significant for virus persistence.

Epidemiological consequences of an incursion of highly pathogenic H5N1 avian influenza into the British poultry flock

Highly pathogenic avian influenza and in particular the H5N1 strain has resulted in the culling of millions of birds and continues to pose a threat to poultry industries worldwide. The recent outbreak of H5N1 in the UK highlights the need for detailed assessment of the consequences of an incursion and of the efficacy of control strategies. Here, we present results from a model of H5N1 propagation within the British poultry industry. We find that although the majority of randomly seeded incursions do not spread beyond the initial infected premises, there is significant potential for widespread infection. The efficacy of the European Union strategy for disease control is evaluated and our simulations emphasize the pivotal role of duck farms in spreading H5N1.

Renormalisation group calculations on a mixed-spin system in two dimensions

The real space renormalisation group of Niemeijer and van Leeuwen (1974) is applied to a mixed-spin Ising model on a simple quadratic lattice. The motivation is the investigation of critical phenomena in Ising models with less than the usual translational symmetry. The models in question are relevant to the study of ferrimagnetism. Two calculations, characterised by different block constructions, are performed and compared. Exponent values are found to be in good agreement with those suggested by the universality hypothesis. The utility of the renormalisation group for dealing with ferrimagnetism is demonstrated, but the high degree of labour involved in such an exercise is indicated.

A host-host-pathogen model with free-living infective stages, applicable to microbial pest control

A model has been investigated of the dynamics of the interaction between two hosts which are both attacked by a common pathogen, where the pathogen has free-living infective stages the population size of which must itself be modelled explicitly, and where the host species do not interact with one another except through their shared pathogen. If either host interacted with the pathogen alone, three broad classes of dynamics would be possible: host regulation, pathogen persistence and pathogen extinction. Here, all possible types of combinations of hosts are examined: regulation-regulation (both hosts would be regulated if they interacted with the pathogen alone), regulation-persistence, regulation-extinction, persistence-persistence persistence-extinction and extinction-extinction. A wide range of dynamics is generated, including a number of patterns quite unlike those found in the one-host pathogen case (e.g. persistence in one host, elimination of the other host) and behaviour contingent on initial densities in the system. For clarity and pertinence, attention is focused on the case where one host is a pest, the pathogen is a potential microbial control agent, and the other host is a non-target species which it is undesirable to harm. The model suggests, broadly, that non-targets are unlikely to be seriously threatened in such cases, and also that non-targets, far from undermining pest control, are quite likely to contribute to its efficacy.

Host-Pathogen Systems in a Spatially Patchy Environment

A discrete model for a host–pathogen system is developed and is used to represent the dynamics in each patch within a landscape of n x n patches. These patches are linked by between-generation dispersal to neighbouring patches. Important results (compared to similar ‘coupled map lattice’ studies) include an increase in the likelihood of metapopulation extinction if the natural loss of pathogen particles is low, and the observation of a radial wave pattern (not previously reported) where the wavefront propagates uniformly from a central focus. This result has additional significance in that it permits the system to exhibit ‘intermittency’ between two quasi-stable spatial patterns: spirals and radial waves. With intermittent behaviour, the dynamics may look consistent when viewed at one time scale, but over a longer time scale they can alter dramatically and repeatedly between the two patterns. There is also evidence of clear links between spatial structure and temporal metapopulation behaviour in both the intermittent and ‘pure’ regions, verified by results from an algorithmic complexity measure and a spectral analysis of the temporal dynamics.

A network model of E. coli O157 transmission within a typical UK dairy herd: the effect of heterogeneity and clustering on the prevalence of infection.

Cattle are considered to be the main reservoir for Vero cytotoxin-producing Escherichia coli (VTEC) O157, a cause of food-poisoning (and even death) in humans. Here, the transmission of E. coli O157 within a typical UK dairy herd is modelled using a semi-stochastic network model. The model incorporates demographic as well as infection processes. Indirect transmission is modelled homogeneously, while direct transmission is modelled via a dynamic contact network. The aim was to investigate the effects of heterogeneity and clustering on the prevalence of infection within the herd and discover whether, particularly in terms of choosing an intervention strategy, it is necessary to include heterogeneity in direct contacts when modelling this sort of system. Results show that heterogeneity in direct contacts can make it more difficult for the pathogen to persist, particularly when the average number of contacts (per animal) in each group is small. They also show that the relationship between clustering and prevalence is not simple. For example, increasing the average number of contacts can increase clustering and prevalence. However, when the average number of contacts in each group is sufficiently high, higher clustering leads to lower prevalence. It would seem that clustering can aid the flow of infection under certain circumstances, but hinder it under others (probably by preventing wider dissemination). Further results show that indirect transmission (as it is modelled here) effectively removes the effect of heterogeneity in direct contacts. In terms of investigating proposed interventions, the results suggest that a network model would only be required if there was evidence to suggest that direct transmission was the major source of infection.

Host-Pathogen Cycles in Self-Regulated Forest Insect Systems: Resolving Conflicting Predictions

Anderson and May (1981) show that substituting realistic parameter values into a host-pathogen model with free-living infective stages (their model G) suggests that cyclic fluctuations observed in empirical studies of insect host-pathogen systems (Baltensweiler 1964; Varley et al. 1973) may be generated by the hostpathogen interactions alone. Recently, two studies have adapted model G to include the additional biological realism of host self-regulation (Bowers et al. 1993; Dwyer 1994). The results of these two studies are in conflict. Bowers et al. suggest hat self-regulation reduces the likelihood of cycles, whereas Dwyer suggests that the likelihood is greatly increased. Here we resolve the confusion caused by the conflicting predictions. First, we recall model G of Anderson and May (1981):

Explaining the Colour of Power Spectra in Chaotic Ecological Models

Power spectrum analysis is often used to determine whether population time series are dominated by particular frequencies. Results for chaotic time series are often reported in terms of the colour of the spectra whereby red spectra indicate a dominance of low frequency (long-term) fluctuations, white spectra indicate that all frequencies are equally dominant and blue spectra indicate a dominance of high frequency (short-term) fluctuations. Several studies have employed such analysis and much discussion has been provoked by an apparent conflict between the fact that the time series of natural populations produce reddened power spectra whereas chaotic, single species ecological models can produce blue, white or red spectra. Here, we resolve the question of which parameter values give rise to particular colour spectra by analysing simple models in terms of ‘universal’ parameters allowing direct comparisons between models to be drawn. This suggests that some models are not capable of producing reddened spectra, which would question their usefulness in describing ecological systems. The population behaviour associated with each colour spectrum is described and compared with models that incorporate simple modifications to represent delayed density dependence, spatial structure and environmental effects.