Partner intrinsic characteristics influence foraging trip duration, but not coordination of care in wandering albatrosses Diomedea exulans

Long-lived monogamous species gain long-term fitness benefits by equalizing effort during biparental care. For example, many seabird species coordinate care by matching foraging trip durations within pairs. Age affects coordination in some seabird species; however, the impact of other intrinsic traits, including personality, on potential intraspecific variation in coordination strength is less well understood. The impacts of pair members' intrinsic traits on trip duration and coordination strength were investigated using data from saltwater immersion loggers deployed on 71 pairs of wandering albatrosses Diomedea exulans. These were modeled against pair members' age, boldness, and their partner's previous trip duration. At the population level, the birds exhibited some coordination of parental care that was of equal strength during incubation and chick-brooding. However, there was low variation in coordination between pairs and coordination strength was unaffected by the birds' boldness or age in either breeding stage. Surprisingly, during incubation, foraging trip duration was mainly driven by partner traits, as birds which were paired to older and bolder partners took shorter trips. During chick-brooding, shorter foraging trips were associated with greater boldness in focal birds and their partners, but age had no effect. These results suggest that an individual's assessment of their partner's capacity or willingness to provide care may be a major driver of trip duration, thereby highlighting the importance of accounting for pair behavior when studying parental care strategies.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial' and ‘non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

Coevolution of group-living and aposematism in caterpillars: warning colouration may facilitate the evolution from group-living to solitary habits

BACKGROUND

Animals use diverse antipredator mechanisms, including visual signalling of aversive chemical defence (aposematism). However, the initial evolution of aposematism poses the problem that the first aposematic individuals are conspicuous to predators who have not learned the significance of the warning colouration. In one scenario, aposematism evolves in group-living species and originally persisted due to kin selection or positive frequency-dependent selection in groups. Alternatively, group-living might evolve after aposematism because grouping can amplify the warning signal. However, our current understanding of the evolutionary dynamics of these traits is limited, leaving the relative merit of these scenarios unresolved.

RESULTS

We used a phylogenetic comparative approach to estimate phenotypic evolutionary models to enable inferences regarding ancestral states and trait dynamics of grouping and aposematic colouration in a classic model system (caterpillars). We find strong support for aposematism at the root of the clade, and some (but weaker) support for ancestral solitary habits. Transition rates between aposematism and crypsis are generally higher than those between group-living and solitary-living, suggesting that colouration is more evolutionarily labile than aggregation. We also find that the transition from group-living to solitary-living states can only happen in aposematic lineage, suggesting that aposematism facilitates the evolution of solitary caterpillars, perhaps due to the additional protection offered when the benefits of grouping are lost. We also find that the high frequency of solitary, cryptic caterpillars is because this state is particularly stable, in that the transition rates moving towards this state are substantially higher than those moving away from it, favouring its accumulation in the clade over evolutionary time.

CONCLUSIONS

Our results provide new insights into the coevolution of colour and aggregation in caterpillars. We find support for an aposematic caterpillar at the root of this major clade, and for the signal augmentation hypothesis as an explanation of the evolution of aposematic, group-living caterpillars. We find that colouration is more labile than aggregation behaviour, but that the combination of solitary and cryptic habits is particularly stable. Finally, our results reveal that the transitions from group-living to solitary-living could be facilitated by aposematism, providing a new link between these well-studied traits.

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Dispersal polymorphism and mutation play significant roles during biological invasions, potentially leading to evolution and complex behaviour such as accelerating or decelerating invasion fronts. However, life-history theory predicts that reproductive fitness-another key determinant of invasion dynamics-may be lower for more dispersive strains. Here, we use a mathematical model to show that unexpected invasion dynamics emerge from the combination of heritable dispersal polymorphism, dispersal-fitness trade-offs, and mutation between strains. We show that the invasion dynamics are determined by the trade-off relationship between dispersal and population growth rates of the constituent strains. We find that invasion dynamics can be 'anomalous' (i.e. faster than any of the strains in isolation), but that the ultimate invasion speed is determined by the traits of, at most, two strains. The model is simple but generic, so we expect the predictions to apply to a wide range of ecological, evolutionary, or epidemiological invasions.

A unified framework for analysis of individual-based models in ecology and beyond

Individual-based models, ‘IBMs’, describe naturally the dynamics of interacting organisms or social or financial agents. They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. Here, we resolve this problem with a general mathematical framework for IBMs containing interactions of an unlimited level of complexity, and derive equations that reliably approximate the effects of space and stochasticity. We provide software, specified in an accessible and intuitive graphical way, so any researcher can obtain analytical and simulation results for any particular IBM without algebraic manipulation. We illustrate the framework with examples from movement ecology, conservation biology, and evolutionary ecology. This framework will provide unprecedented insights into a hitherto intractable panoply of complex models across many scientific fields.

Individual-based models are widely used to simulate complex systems of interacting agents. Here the authors provide a mathematical framework that automates the analysis of any model in a wide class, facilitating a deeper understanding of the scientific questions these models are used to address.

Controlling invasive rodents via synthetic gene drive and the role of polyandry

House mice are a major ecosystem pest, particularly threatening island ecosystems as a non-native invasive species. Rapid advances in synthetic biology offer new avenues to control pest species for biodiversity conservation. Recently, a synthetic sperm-killing gene drive construct called t-Sry has been proposed as a means to eradicate target mouse populations owing to a lack of females. A factor that has received little attention in the discussion surrounding such drive applications is polyandry. Previous research has demonstrated that sperm-killing drivers are extremely damaging to a male's sperm competitive ability. Here, we examine the importance of this effect on the t-Sry system using a theoretical model. We find that polyandry substantially hampers the spread of t-Sry such that release efforts have to be increased three- to sixfold for successful eradication. We discuss the implications of our finding for potential pest control programmes, the risk of drive spread beyond the target population, and the emergence of drive resistance. Our work highlights that a solid understanding of the forces that determine drive dynamics in a natural setting is key for successful drive application, and that exploring the natural diversity of gene drives may inform effective gene drive design.

The evolution of variance in sequential defences

The defences used by organisms against predators display a great degree of variability. Defence phenotypes can differ substantially among individuals of the same species, and a single individual can itself deploy a variety of defences. Here, we use a mathematical model that includes mutation and selection to understand the evolutionary origin of this variability in a population of a species that deploys defences sequentially ("first" and "second" defences). Typically, the first defence evolves to have lower variance, i.e. appears more closely accumulated around the ideal phenotype, than the second defence (even when the breaching the first defence incurs more fitness loss than breaching the second defence with the other parameters the same for both defences). However, if the first defence is much less effective in repelling predators, or is much less tolerant of deviation from the ideal phenotype, then the first defence can evolve to have higher variance than the second. Other factors like mutation strength and the losses in the fitness when each defence fails also influence the defence variance. Larger mutation rate incurs larger equilibrium variances, and when the comparative importance in fitness of one defence increases, then the ratio between the variances of this defence and the other defence decreases. Sequentially acting defences are found in many organisms, so we encourage empirical research to test our theoretical predictions.

Sexual cannibalism and population viability

Some behaviours that typically increase fitness at the individual level may reduce population persistence, particularly in the face of environmental changes. Sexual cannibalism is an extreme mating behaviour which typically involves a male being devoured by the female immediately before, during or after copulation, and is widespread amongst predatory invertebrates. Although the individual-level effects of sexual cannibalism are reasonably well understood, very little is known about the population-level effects. We constructed both a mathematical model and an individual-based model to predict how sexual cannibalism might affect population growth rate and extinction risk. We found that in the absence of any cannibalism-derived fecundity benefit, sexual cannibalism is always detrimental to population growth rate and leads to a higher population extinction risk. Increasing the fecundity benefits of sexual cannibalism leads to a consistently higher population growth rate and likely a lower extinction risk. However, even if cannibalism-derived fecundity benefits are large, very high rates of sexual cannibalism (>70%) can still drive the population to negative growth and potential extinction. Pre-copulatory cannibalism was particularly damaging for population growth rates and was the main predictor of growth declining below the replacement rate. Surprisingly, post-copulatory cannibalism had a largely positive effect on population growth rate when fecundity benefits were present. This study is the first to formally estimate the population-level effects of sexual cannibalism. We highlight the detrimental effect sexual cannibalism may have on population viability if (1) cannibalism rates become high, and/or (2) cannibalism-derived fecundity benefits become low. Decreased food availability could plausibly both increase the frequency of cannibalism, and reduce the fecundity benefit of cannibalism, suggesting that sexual cannibalism may increase the risk of population collapse in the face of environmental change.

Biased movement at a boundary and conditional occupancy times for diffusion processes

Motivated by edge behaviour reported for biological organisms, we show that random walks with a bias at a boundary lead to a discontinuous probability density across the boundary. We continue by studying more general diffusion processes with such a discontinuity across an interior boundary. We show how hitting probabilities, occupancy times and conditional occupancy times may be solved from problems that are adjoint to the original diffusion problem. We highlight our results with a biologically motivated example, where we analyze the movement behaviour of an individual in a network of habitat patches surrounded by dispersal habitat.

Estimates of coextinction risk: how anuran parasites respond to the extinction of their hosts

Amphibians are known as the most threatened vertebrate group. One of the outcomes of a species' extinction is the coextinction of its dependents. Here, we estimate the extinction risk of helminth parasites of South America anurans. Parasite coextinction probabilities were modeled, assuming parasite specificity and host vulnerability to extinction as determinants. Parasite species associated with few hosts were the most prone to extinction, and extinction risk varied amongst helminth species of different taxonomic groups and life cycle complexity. Considering host vulnerability in the model decreased the extinction probability of most parasites species. However, parasite specificity and host vulnerability combined to increase the extinction probabilities of 44% of the helminth species reported in a single anuran species.

When can species abundance data reveal non-neutrality?

Species abundance distributions (SAD) are probably ecology's most well-known empirical pattern, and over the last decades many models have been proposed to explain their shape. There is no consensus over which model is correct, because the degree to which different processes can be discerned from SAD patterns has not yet been rigorously quantified. We present a power calculation to quantify our ability to detect deviations from neutrality using species abundance data. We study non-neutral stochastic community models, and show that the presence of non-neutral processes is detectable if sample size is large enough and/or the amplitude of the effect is strong enough. Our framework can be used for any candidate community model that can be simulated on a computer, and determines both the sampling effort required to distinguish between alternative processes, and a range for the strength of non-neutral processes in communities whose patterns are statistically consistent with neutral theory. We find that even data sets of the scale of the 50 Ha forest plot on Barro Colorado Island, Panama, are unlikely to be large enough to detect deviations from neutrality caused by competitive interactions alone, though the presence of multiple non-neutral processes with contrasting effects on abundance distributions may be detectable.

Predictive systems ecology

Human societies, and their well-being, depend to a significant extent on the state of the ecosystems that surround them. These ecosystems are changing rapidly usually in response to anthropogenic changes in the environment. To determine the likely impact of environmental change on ecosystems and the best ways to manage them, it would be desirable to be able to predict their future states. We present a proposal to develop the paradigm of predictive systems ecology, explicitly to understand and predict the properties and behaviour of ecological systems. We discuss the necessary and desirable features of predictive systems ecology models. There are places where predictive systems ecology is already being practised and we summarize a range of terrestrial and marine examples. Significant challenges remain but we suggest that ecology would benefit both as a scientific discipline and increase its impact in society if it were to embrace the need to become more predictive.

The speed of range shifts in fragmented landscapes

Species may be driven extinct by climate change, unless their populations are able to shift fast enough to track regions of suitable climate. Shifting will be faster as the proportion of suitable habitat in the landscape increases. However, it is not known how the spatial arrangement of habitat will affect the speed of range advance, especially when habitat is scarce, as is the case for many specialist species. We develop methods for calculating the speed of advance that are appropriate for highly fragmented, stochastic systems. We reveal that spatial aggregation of habitat tends to reduce the speed of advance throughout a wide range of species parameters: different dispersal distances and dispersal kernel shapes, and high and low extinction probabilities. In contrast, aggregation increases the steady-state proportion of habitat that is occupied (without climate change). Nonetheless, we find that it is possible to achieve both rapid advance and relatively high patch occupancy when the habitat has a "channeled" pattern, resembling corridors or chains of stepping stones. We adapt techniques from electrical circuit theory to predict the rate of advance efficiently for complex, realistic landscape patterns, whereas the rate cannot be predicted by any simple statistic of aggregation or fragmentation. Conservationists are already advocating corridors and stepping stones as important conservation tools under climate change, but they are vaguely defined and have so far lacked a convincing basis in fundamental population biology. Our work shows how to discriminate properties of a landscape's spatial pattern that affect the speed of colonization (including, but not limited to, patterns like corridors and chains of stepping stones), and properties that affect a species' probability of persistence once established. We can therefore point the way to better land use planning approaches, which will provide functional habitat linkages and also maintain local population viability.

Dispersal polymorphism and the speed of biological invasions

The speed at which biological range expansions occur has important consequences for the conservation management of species experiencing climate change and for invasion by exotic organisms. Rates of dispersal and population growth are known to affect the speed of invasion, but little is known about the effect of having a community of dispersal phenotypes on the rate of range expansion. We use reaction-diffusion equations to model the invasion of a species with two dispersal phenotypes into a previously unoccupied landscape. These phenotypes differ in both their dispersal rate and population growth rate. We find that the presence of both phenotypes can result in faster range expansions than if only a single phenotype were present in the landscape. For biologically realistic parameters, the invasion can occur up to twice as fast as a result of this polymorphism. This has implications for predicting the speed of biological invasions, suggesting that speeds cannot just be predicted from looking at a single phenotype and that the full community of phenotypes needs to be taken into consideration.

Downscaling species occupancy from coarse spatial scales

The measurement and prediction of species' populations at different spatial scales is crucial to spatial ecology as well as conservation biology. An efficient yet challenging goal to achieve such population estimates consists of recording empirical species' presence and absence at a specific regional scale and then trying to predict occupancies at finer scales. So far the majority of the methods have been based on particular species' distributional features deemed to be crucial for downscaling occupancy. However, only a minority of them have dealt explicitly with specific spatial features. Here we employ a wide class of spatial point processes, the shot noise Cox processes (SNCP), to model species occupancies at different spatial scales and show that species' spatial aggregation is crucial for predicting population estimates at fine scales starting from coarser ones. These models are formulated in continuous space and locate points regardless of the arbitrary resolution that one employs to study the spatial pattern. We compare the performances of nine models, calibrated at regional scales and demonstrate that a very simple class of SNCP, the Thomas process, is able to outperform other published models in predicting occupancies down to areas four orders of magnitude smaller than the ones employed for the parameterization. We conclude by explaining the ability of the approach to infer spatially explicit information from spatially implicit measures, the potential of the framework to combine niche and spatial models, and the possibility of reversing the method to allow upscaling.

Seasonality, cohort-dependence and the development of immunity in a natural host-nematode system

Acquired immunity is known to be a key modulator of the dynamics of many helminth parasites in domestic and human host populations, but its relative importance in natural populations is more controversial. A detailed long-term dataset on the gastrointestinal nematode Trichostrongylus retortaeformis in a wild population of European rabbits (Oryctolagus cuniculus) shows clear evidence of seasonal acquired immunity in the age-structured infection profiles. By fitting a hierarchy of demographic infection-immunity models to the observed age-structured infection patterns, we are able to quantify the importance of different components (seasonality, immunity and host age structure) of the parasite dynamics. We find strong evidence that the hosts' immunocompetence waxes and wanes with the seasons, but also contains a lifelong cohort factor, possibly acting through a maternal effect dependent on the host's month of birth. These observations have important and broad implications for the ecology of parasite infection in seasonal natural herbivore systems.

A new theory for the evolution of polyandry as a means of inbreeding avoidance

We propose a novel theory for the evolution of polyandry driven by genetic benefits to females whose offspring interbreed. In species with an ecology characterized by frequent colonization of new habitat patches, consanguineous matings may be common during the early stages of colonization, but genetic diversity may grow as new colonizers arrive. We show that with levels of inbreeding depression similar to those found in predominantly inbreeding populations, a polyandrous female can benefit her descendants since matings among her brood are mainly between half siblings rather than full siblings. We examine the invasion by a polyandrous phenotype using explicit genetic models in which costs of inbreeding are themselves subject to selection. In common with other models of inbreeding, we find that underlying high levels of inbreeding tend to purge deleterious recessive alleles, and hence these are unlikely to maintain sufficient inbreeding depression to favour polyandry. However, if costs of inbreeding are due to overdominance, biologically realistic levels of inbreeding depression result in genetic benefits large enough to favour polyandry provided it is not too costly. The potential significance of polyandry as a mechanism to reduce inbreeding in grandchildren will depend upon the genetic basis of inbreeding depression in natural, inbreeding populations.

Species–area relationships from a spatially explicit neutral model in an infinite landscape

We use recently developed technical methods to study species-area relationships from a spatially explicit extension of Hubbell's neutral model on an infinite landscape. Our model includes variable dispersal distances and exhibits qualitatively different behaviour from the cases of nearest-neighbour dispersal and finite periodic landscapes that have previously been studied. We show that different dispersal distances and even different dispersal kernels produce identical species-area curves up to rescaling of the two axes. This scaling property provides a straightforward method for fitting the model to empirical data. The species-area curves display all three phases observed empirically and enable the exponent describing the power law relationship for species-area curves to be identified as the gradient at the central phase. This exponent can take all values between 0 and 1 and is given by a simple function of the speciation rate, independent of all other model variables.

Intracellular demography and the dynamics of Salmonella enterica infections

An understanding of within-host dynamics of pathogen interactions with eukaryotic cells can shape the development of effective preventive measures and drug regimes. Such investigations have been hampered by the difficulty of identifying and observing directly, within live tissues, the multiple key variables that underlay infection processes. Fluorescence microscopy data on intracellular distributions of Salmonella enterica serovar Typhimurium (S. Typhimurium) show that, while the number of infected cells increases with time, the distribution of bacteria between cells is stationary (though highly skewed). Here, we report a simple model framework for the intensity of intracellular infection that links the quasi-stationary distribution of bacteria to bacterial and cellular demography. This enables us to reject the hypothesis that the skewed distribution is generated by intrinsic cellular heterogeneities, and to derive specific predictions on the within-cell dynamics of Salmonella division and host-cell lysis. For within-cell pathogens in general, we show that within-cell dynamics have implications across pathogen dynamics, evolution, and control, and we develop novel generic guidelines for the design of antibacterial combination therapies and the management of antibiotic resistance.

Modeling of infection shows that heterogeneities in bacterial burden per host cell need not be explained by differences in host cell permissiveness; this has important implications for understanding the ecology of infection.

Space and stochasticity in population dynamics

Organisms interact with each other mostly over local scales, so the local density experienced by an individual is of greater importance than the mean density in a population. This simple observation poses a tremendous challenge to theoretical ecology, and because nonlinear stochastic and spatial models cannot be solved exactly, much effort has been spent in seeking effective approximations. Several authors have observed that spatial population systems behave like deterministic nonspatial systems if dispersal averages the dynamics over a sufficiently large scale. We exploit this fact to develop an exact series expansion, which allows one to derive approximations of stochastic individual-based models without resorting to heuristic assumptions. Our approach makes it possible to calculate the corrections to mean-field models in the limit where the interaction range is large, and it provides insight into the performance of moment closure methods. With this approach, we demonstrate how the buildup of spatiotemporal correlations slows down the spread of an invasion, prolongs time lags associated with extinction debt, and leads to locally oscillating but globally stable coexistence of a host and a parasite.

Asymptotically exact analysis of stochastic metapopulation dynamics with explicit spatial structure

We describe a mathematically exact method for the analysis of spatially structured Markov processes. The method is based on a systematic perturbation expansion around the deterministic, non-spatial mean-field theory, using the theory of distributions to account for space and the underlying stochastic differential equations to account for stochasticity. As an example, we consider a spatial version of the Levins metapopulation model, in which the habitat patches are distributed in the d-dimensional landscape Rd in a random (but possibly correlated) manner. Assuming that the dispersal kernel is characterized by a length scale L, we examine how the behavior of the metapopulation deviates from the mean-field model for a finite but large L. For example, we show that the equilibrium fraction of occupied patches is given by p(0)+c/L(d)+O(L(-3d/2)), where p(0) is the equilibrium state of the Levins model and the constant c depends on p(0), the dispersal kernel, and the structure of the landscape. We show that patch occupancy can be increased or decreased by spatial structure, but is always decreased by stochasticity. Comparison with simulations show that the analytical results are not only asymptotically exact (as L-->infinity), but a good approximation also when L is relatively small.

Investigations of cattle herd breakdowns with bovine tuberculosis in four counties of England and Wales using VETNET data

Cattle herd breakdown (HBR) with bovine tuberculosis (BTB) was investigated for farms in four counties of England and Wales outside southwest England from 1986 to early 2000. Data from the national database of TB testing history (VETNET) were used. Factors that influenced HBR included calendar time, herd size, number of cattle tested, the test type, the inter-test interval and spatial grouping of farms. Herd tests other than routine herd tests had an increased risk of HBR in all four counties. In all counties, the risk of HBR increased with calendar time and in Shropshire a test interval of 3 years was associated with an increased risk of HBR compared with a 1-year test interval. In Staffordshire and Sussex, a 4-year test interval was associated with a lower risk of HBR compared with a 1-year test interval. There was no evidence of spatial clustering of HBR in West Glamorgan (equal spatial risk in a 15-30 km radius) and weak evidence of spatial clustering in Shropshire (7-15 km) and Sussex (5-10 km). In Staffordshire, there was evidence of spatial (2-4 km) and time (3-4 years) clustering of HBR. The locally increased rate of testing following a confirmed HBR increased the detection of infected herds but did not prevent local spread in two of the four counties (Shropshire and Staffordshire) since the rate of HBR increased linearly from 1988 to 2000. The main conclusion is that there were both local and distant components of spread.

Peak shift and epidemiology in a seasonal host-nematode system

Insight into the dynamics of parasite-host relationships of higher vertebrates requires an understanding of two important features: the nature of transmission and the development of acquired immunity in the host. A dominant hypothesis proposes that acquired immunity develops with the cumulative exposure to infection, and consequently predicts a negative relationship between peak intensity of infection and host age at this peak. Although previous studies have found evidence to support this hypothesis through between-population comparisons, these results are confounded by spatial effects. In this study, we examined the dynamics of infection of the nematode Trichostrongylus retortaeformis within a natural population of rabbits sampled monthly for 26 years. The rabbit age structure was reconstructed using body mass as a proxy for age, and the host age-parasite intensity relationship was examined for each rabbit cohort born from February to August. The age-intensity curves exhibited a typical concave shape, and a significant negative relationship was found between peak intensity of infection and host age at this peak. Adult females showed a distinct periparturient rise in T. retortaeformis infection, with higher intensities in breeding adult females than adult males and non-breeding females. These findings are consistent with the hypothesis of an acquired immune response of the host to a parasite infection, supporting the principle that acquired immunity can be modelled using the cumulative exposure to infection. These findings also show that seasonality can be an important driver of host-parasite interactions.

Farming and the fate of wild nature

World food demand is expected to more than double by 2050. Decisions about how to meet this challenge will have profound effects on wild species and habitats. We show that farming is already the greatest extinction threat to birds (the best known taxon), and its adverse impacts look set to increase, especially in developing countries. Two competing solutions have been proposed: wildlife-friendly farming (which boosts densities of wild populations on farmland but may decrease agricultural yields) and land sparing (which minimizes demand for farmland by increasing yield). We present a model that identifies how to resolve the trade-off between these approaches. This shows that the best type of farming for species persistence depends on the demand for agricultural products and on how the population densities of different species on farmland change with agricultural yield. Empirical data on such density-yield functions are sparse, but evidence from a range of taxa in developing countries suggests that high-yield farming may allow more species to persist.

Stochastic and spatial dynamics of nematode parasites in farmed ruminants

Host-parasite systems provide powerful opportunities for the study of spatial and stochastic effects in ecology; this has been particularly so for directly transmitted microparasites. Here, we construct a fully stochastic model of the population dynamics of a macroparasite system: trichostrongylid gastrointestinal nematode parasites of farmed ruminants. The model subsumes two implicit spatial effects: the host population size (the spatial extent of the interaction between hosts) and spatial heterogeneity ('clumping') in the infection process. This enables us to investigate the roles of several different processes in generating aggregated parasite distributions. The necessity for female worms to find a mate in order to reproduce leads to an Allee effect, which interacts nonlinearly with the stochastic population dynamics and leads to the counter-intuitive result that, when rare, epidemics can be more likely and more severe in small host populations. Clumping in the infection process reduces the strength of this Allee effect, but can hamper the spread of an epidemic by making infection events too rare. Heterogeneity in the hosts' response to infection has to be included in the model to generate aggregation at the level observed empirically.

Spatial parasite transmission, drug resistance, and the spread of rare genes

The transmission of many parasitic worms involves aggregated movement between hosts of "packets" of infectious larvae. We use a generic metapopulation model to show that this aggregation naturally promotes the preferential spread of rare recessive genes, compared with the expectations of traditional nonspatial models. A more biologically realistic model also demonstrates that this effect could explain the rapid observed spread of recessive or weakly dominant drug-resistant genotypes in nematode parasites of sheep. This promotion of a recessive trait arises from a novel mechanism of inbreeding arising from the metapopulation dynamics of transmission.

Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape

Foot-and-mouth is one of the world's most economically important livestock diseases. We developed an individual farm-based stochastic model of the current UK epidemic. The fine grain of the epidemiological data reveals the infection dynamics at an unusually high spatiotemporal resolution. We show that the spatial distribution, size, and species composition of farms all influence the observed pattern and regional variability of outbreaks. The other key dynamical component is long-tailed stochastic dispersal of infection, combining frequent local movements with occasional long jumps. We assess the history and possible duration of the epidemic, the performance of control strategies, and general implications for disease dynamics in space and time.

Is it feasible to plan secondary care services for coronary heart disease rationally? A quantified modelling approach for a UK Health Authority

BACKGROUND

Coronary heart disease (CHD) is the major cause of mortality in the UK. This paper explores the difficulties facing health authorities in applying a rational and needs based approach to the planning of hospital based services and describes a simple model used to bring available information to bear on this problem.

METHOD

Published estimates of CHD incidence were identified and methodologies were critically appraised. Estimates were extrapolated to a district population. A three month cohort study of patients with suspected CHD was undertaken within a district general hospital and a model of these clinical pathways was used to examine the volumes of patients and services required to meet the estimated levels of need.

RESULTS

From published studies, estimates of CHD incidence ranged from 83 to 3600 per 100 000. From the cohort study, of patients referred with possible CHD 62% received a definitive diagnosis of CHD, 56% underwent an exercise ECG, 16% received an angiogram, 4% received a CABG and 2% a PTCA. Using these figures together with the cohort study, estimated activity ranges from 247 to 6475 surgical interventions per million population compared with the National Service Framework for Coronary Heart Disease recommendations of 1500 procedures per million.

CONCLUSIONS

Current research on CHD incidence gives a very wide variation in estimated need. This makes its value for service planning questionable and the model highlights a need for further high quality research. The model provides a link between epidemiological research and secondary care service planning and supports the implementation of recommendations within the National Service Framework for Coronary Heart Disease.

Drug-resistant parasites and aggregated infection--early-season dynamics

We investigate the effect of spatial aggregation in the infection dynamics of nematode parasites in ruminants. We show that a high degree of spatial aggregation is likely to lead to a dramatically enhanced rate of invasion by drug-resistant strains.

Public health and primary care collaboration--a case study

This paper describes the approach of one total purchasing project (TPP) to health needs assessment (HNA) and identifies issues that require consideration when undertaking HNA in primary care. It discusses the advantages of adopting a Health Authority (HA) HNA strategy and the development of a decision-making process for implementing this and other strategies to address possible areas of identified need. The prerequisites, advantages and potential difficulties of this approach are highlighted and related to the needs of primary care groups (PCGs) for addressing health needs and population health.