Mechanisms underlying host persistence following amphibian disease emergence determine appropriate management strategies

Emerging infectious diseases have caused many species declines, changes in communities and even extinctions. There are also many species that persist following devastating declines due to disease. The broad mechanisms that enable host persistence following declines include evolution of resistance or tolerance, changes in immunity and behaviour, compensatory recruitment, pathogen attenuation, environmental refugia, density‐dependent transmission and changes in community composition. Here we examine the case of chytridiomycosis, the most important wildlife disease of the past century. We review the full breadth of mechanisms allowing host persistence, and synthesise research on host, pathogen, environmental and community factors driving persistence following chytridiomycosis‐related declines and overview the current evidence and the information required to support each mechanism. We found that for most species the mechanisms facilitating persistence have not been identified. We illustrate how the mechanisms that drive long‐term host population dynamics determine the most effective conservation management strategies. Therefore, understanding mechanisms of host persistence is important because many species continue to be threatened by disease, some of which will require intervention. The conceptual framework we describe is broadly applicable to other novel disease systems.     

Modelling Foot-and-Mouth Disease Virus Dynamics in Oral Epithelium to Help Identify the Determinants of Lysis

Foot-and-mouth disease virus (FMDV) causes an economically important disease of cloven-hoofed livestock; of interest here is the difference in lytic behaviour that is observed in bovine epithelium. On the skin around the feet and tongue, the virus rapidly replicates, killing cells, and resulting in growing lesions, before eventually being cleared by the immune response. In contrast, there is usually minimal lysis in the soft palate, but virus may persist in tissue long after the animal has recovered from the disease. Persistence of virus has important implications for disease control, while identifying the determinant of lysis in epithelium is potentially important for the development of prophylactics. To help identify which of the differences between oral and pharyngeal epithelium are responsible for such dramatically divergent FMDV dynamics, a simple model has been developed, in which virus concentration is made explicit to allow the lytic behaviour of cells to be fully considered. Results suggest that localised structuring of what are fundamentally similar cells can induce a bifurcation in the behaviour of the system, explicitly whether infection can be sustained or results in mutual extinction, although parameter estimates indicate that more complex factors may be involved in maintaining viral persistence, or that there are as yet unquantified differences between the intrinsic properties of cells in these regions.     

New statistical tools for analyzing the structure of animal groups

The statistical characterization of the spatial structure of large animal groups has been very limited so far, mainly due to a lack of empirical data, especially in three dimensions (3D). Here we focus on the case of large flocks of starlings (Sturnus vulgaris) in the field. We reconstruct the 3D positions of individual birds within flocks of up to few thousands of elements. In this respect our data constitute a unique set. We perform a statistical analysis of flocks' structure by using two quantities that are new to the field of collective animal behaviour, namely the conditional density and the pair correlation function. These tools were originally developed in the context of condensed matter theory. We explain what is the meaning of these two quantities, how to measure them in a reliable way, and why they are useful in assessing the density fluctuations and the statistical correlations across the group. We show that the border-to-centre density gradient displayed by starling flocks gives rise to an anomalous behaviour of the conditional density. We also find that the pair correlation function has a structure incompatible with a crystalline arrangement of birds. In fact, our results suggest that flocks are somewhat intermediate between the liquid and the gas phase of physical systems.     

The effect of seasonal host birth rates on population dynamics: the importance of resonance

Many of the simple mathematical models currently in use often fail to capture important biological factors. Here we extend current models of insect-pathogen interactions to include seasonality in the birth rate. In particular, we consider the SIR model with self-regulation when applied to specific cases--rabbit haemorrhagic disease and fox rabies. In this paper, we briefly summarize the results of the model with a constant time-independent birth rate, a, which we then replace with the time dependent birth rate a(t), to investigate how this effects the dynamics of the host population. We can split parameter space into an area in which the model without seasonality has no oscillations, in which case a simple averaging rule predicts the behaviour. Alternatively, in the area where oscillations to the equilibrium do occur in the non-seasonal model, disease persistence is more complicated and we get more complex dynamical behaviour in this case. We apply resonance techniques to discover the structure of the subharmonic modes of the SIR model with self-regulation. We then look at whether many biological systems are likely to display these "resonant" dynamics and find that we would expect them to be widespread.     

Metapopulation models for extinction threshold in spatially correlated landscapes

Simple analytical models assuming homogeneous space have been used to examine the effects of habitat loss and fragmentation on metapopulation size. The models predict an extinction threshold, a critical amount of suitable habitat below which the metapopulation goes deterministically extinct. The consequences of non-random loss of habitat for species with localized dispersal have been studied mainly numerically. In this paper, we present two analytical approaches to the study of habitat loss and its metapopulation dynamic consequences incorporating spatial correlation in both metapopulation dynamics as well as in the pattern of habitat destruction. One approach is based on a measure called metapopulation capacity, given by the dominant eigenvalue of a "landscape" matrix, which encapsulates the effects of landscape structure on population extinctions and colonizations. The other approach is based on pair approximation. These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence. In contrast to the pair approximation based approaches, the metapopulation capacity based approach allows us to consider species with long as well as short dispersal range and landscapes with spatial correlation at different scales. The two methods make dissimilar assumptions, but the broad conclusions concerning the consequences of spatial correlation in the landscape structure are the same. Our results show that increasing correlation in the spatial arrangement of the remaining habitat increases patch occupancy, that this increase is more evident for species with short-range than long-range dispersal, and that to be most beneficial for metapopulation size, the range of spatial correlation in landscape structure should be at least a few times greater than the dispersal range of the species.     

Evolutionary constraints on structural similarity in orthologs and paralogs

Although a quantitative relationship between sequence similarity and structural similarity has long been established, little is known about the impact of orthology on the relationship between protein sequence and structure. Among homologs, orthologs (derived by speciation) more frequently have similar functions than paralogs (derived by duplication). Here, we hypothesize that an orthologous pair will tend to exhibit greater structural similarity than a paralogous pair at the same level of sequence similarity. To test this hypothesis, we used 284,459 pairwise structure‐based alignments of 12,634 unique domains from SCOP as well as orthology and paralogy assignments from OrthoMCL DB. We divided the comparisons by sequence identity and determined whether the sequence‐structure relationship differed between the orthologs and paralogs. We found that at levels of sequence identity between 30 and 70%, orthologous domain pairs indeed tend to be significantly more structurally similar than paralogous pairs at the same level of sequence identity. An even larger difference is found when comparing ligand binding residues instead of whole domains. These differences between orthologs and paralogs are expected to be useful for selecting template structures in comparative modeling and target proteins in structural genomics.     

Pair-edge approximation for heterogeneous lattice population models

To increase the analytical tractability of lattice stochastic spatial population models, several approximations have been developed. The pair-edge approximation is a moment-closure method that is effective in predicting persistence criteria and invasion speeds on a homogeneous lattice. Here we evaluate the effectiveness of the pair-edge approximation on a spatially heterogeneous lattice in which some sites are unoccupiable, or "dead". This model has several possible interpretations, including a spatial SIS epidemic model, in which some sites are occupied by immobile host-species individuals while others are empty. We find that, as in the homogeneous model, the pair-edge approximation is significantly more accurate than the ordinary pair approximation in determining conditions for persistence. However, habitat heterogeneity decreases invasion speed more than is predicted by the pair-edge approximation, and the discrepancy increases with greater clustering of "dead" sites. The accuracy of the approximation validates the underlying heuristic picture of population spread and therefore provides qualitative insight into the dynamics of lattice models. Conversely, the situations where the approximation is less accurate reveals limitations of pair approximation in the presence of spatial heterogeneity.     

Multiplicative moments and measures of persistence in ecology

Ecologists and epidemiologists have begun focusing on demographic stochasticity and spatial heterogeneity as important biological factors. With high-powered computers simulation of such systems is a common modelling technique; however we lack a detailed understanding of the processes involved. Moment closure approximations provide a simple method which can be used to capture the main features of a wide variety of stochastic models and to gain a more intuitive understanding. In this paper we give an alternative variation based on multiplicative moments which is equivalent to taking a novel third-order cumulant approximation. The differential equations for these multiplicative moments are far more robust than their additive counterparts. We use this technique to consider the behaviour and persistence of finite metapopulations for two common ecological systems.     

Correlations between habitat use and body shape in a phrynosomatid lizard (Urosaurus ornatus): a population-level analysis

Recent ecomorphological studies have shown that the predicted correlations between morphology and ecology on broad taxonomic levels are often obscured when comparing more closely related groups. Among species, comparisons of lizards often indicate very little support for adaptive radiations into novel habitats. As few population level studies have been performed, we compared body, head and limb shape between four populations of Urosaurus ornatus living in structurally distinct habitats (cliffs, rocks, trees and boulders). Surprisingly, clear correlations between habitat use and body shape among populations were found, most of which were in good accordance with a priori biomechanical predictions (e.g. flat body and head for extreme climbers; long distal hindlimb segments for jumpers and runners; narrow body and long tail for tree dwelling lizards). This indicates that populations of Urosaurus ornatus are seemingly 'adapted' to the habitat they live in. However, quantification of performance and behaviour are needed to determine the adaptive nature of these observations.     

Evolutionary trade-offs at two time-scales: competition versus persistence

The evolution of many natural systems is complicated due to dynamics at a mixture of time-scales. This is especially true when there is a trade-off between large reproductive rates and long-term persistence; such behaviour is frequently observed in disease models. In this paper, a simple partial differential equation model is formulated which describes the evolutionary dynamics of two disease strains in a metapopulation: one strain is a better short-term competitor; the other has greater persistence. By considering the behaviour of means and higher-order moments, analytical expressions for the evolutionary behaviour are produced in the case when the two strains are phenotypically close.     

The coevolution of long‐term pair bonds and cooperation

The evolution of social traits may not only depend on but also change the social structure of the population. In particular, the evolution of pairwise cooperation, such as biparental care, depends on the pair‐matching distribution of the population, and the latter often emerges as a collective outcome of individual pair‐bonding traits, which are also under selection. Here, we develop an analytical model and individual‐based simulations to study the coevolution of long‐term pair bonds and cooperation in parental care, where partners play a Snowdrift game in each breeding season. We illustrate that long‐term pair bonds may coevolve with cooperation when bonding cost is below a threshold. As long‐term pair bonds lead to assortative interactions through pair‐matching dynamics, they may promote the prevalence of cooperation. In addition to the pay‐off matrix of a single game, the evolutionarily stable equilibrium also depends on bonding cost and accidental divorce rate, and it is determined by a form of balancing selection because the benefit from pair‐bond maintenance diminishes as the frequency of cooperators increases. Our findings highlight the importance of ecological factors affecting social bonding cost and stability in understanding the coevolution of social behaviour and social structures, which may lead to the diversity of biological social systems.     

Spatially structured superinfection and the evolution of disease virulence

When pathogen strains differing in virulence compete for hosts, spatial structuring of disease transmission can govern both evolved levels of virulence and patterns in strain coexistence. We develop a spatially detailed model of superinfection, a form of contest competition between pathogen strains; the probability of superinfection depends explicitly on the difference in levels of virulence. We apply methods of adaptive dynamics to address the interplay of spatial dynamics and evolution. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. Both pair approximation and simulation of the detailed model indicate that spatial structure constrains disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.     

A centuries-long epidemic of scrapie in British sheep?

The apparent persistence of scrapie in British sheep for more than 250 years is difficult to explain. Susceptibility to scrapie is associated with particular alleles at a single locus, the PrP gene. As the only known effect of these alleles is to confer susceptibility to a fatal disease, natural selection is expected to reduce their frequency, as has been observed in practice during scrapie outbreaks in single sheep flocks. Susceptibility alleles, and hence scrapie itself, are therefore expected to become rare, yet the disease remains widespread. We suggest that the paradox of scrapie's persistence can be explained by the exceptionally long time-scales inherent in the epidemiology of the disease. It is proposed that scrapie should be regarded as epidemic in British sheep but, unlike more familiar epidemics, which have time-scales of months or years, the scrapie epidemic has a time-scale of centuries. This interpretation implies that scrapie should eventually disappear from the sheep population.     

The coevolution of warning signals

It has long been recognized that defended prey tend to be conspicuous. Current theories suggest that the association ('aposematism') has arisen because predators more readily learn to avoid attacking defended phenotypes when they are conspicuous. In this paper, I consider why such psychology has evolved. In particular, I argue that aposematism may have evolved not because of an independent and pre-existing receiver bias, but because the conspicuousness of a prey item provides a reliable indicator of its likelihood of being defended. To develop my case I consider how warning signals might coevolve in a system containing a number of predators, whose foraging behaviour is also subject to selection. In these cases, models readily show that the greater the conspicuousness of a novel prey item, the more likely that it has been encountered by other predators and survived. As a consequence, naive predators should be less likely to attack highly conspicuous novel prey on encounter, or at least more inclined to attack them cautiously. This adaptive predator behaviour will greatly facilitate the spread of aposematic phenotypes from extreme rarity, which in turn will enhance selection for forms of predator behaviour under which aposematism will coevolve even more readily.     

Complex ecological models with simple dynamics: From individuals to populations

The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for food of different types. The degree of competition as well as the predation pressure are dependent upon these activities. Preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study the effect of a change in the average individual behaviour of the animals on interspecific relationships. Computer simulations of the whole sets of equations are compared to simulations of the reduced sets of equations.     

Variations in the diet of introduced Norway rats (Rattus norvegicus) inferred using stable isotope analysis

The presence of introduced Norway rats Rattus norvegicus has raised concerns for the fate of the large least auklet Aethia pusilla colony situated at Sirius Point, Kiska Island, Alaska. Previous studies have documented extreme interannual variation in least auklet reproductive success and potential drastic population declines, both of which have been attributed to the varying abundance of, and predation by, Norway rats. A diet study would resolve the uncertainty that remains about the role of rats in the auklet's reproductive failure and the colony's decline. Our main objectives here were to quantify the variation in diet of introduced Norway rats and assess predation on least auklets. Using stable isotope analysis we document wide variability in rat diet dependent on location and provide direct evidence that Norway rats are preferentially preying on least auklets at Sirius Point. In conclusion, we hypothesize that the observed wide variability in rat diet will contribute to the persistence of rats on Kiska long after auklets have been extirpated. The persistence of rats enabled by their foraging plasticity will increase their effects by creating ecological traps within which prospecting individuals will fall and be depredated. This has large conservation consequences as it suggests that when seabirds are extirpated recolonization by prospecting birds is virtually impossible and island ecosystems will continue to be negatively affected and altered as long as introduced predators, such as rats, remain within them.     

Interactions between Social Structure,Demography, and Transmission Determine Disease Persistence in Primates

Catastrophic declines in African great ape populations due to disease outbreaks have been reported in recent years, yet we rarely hear of similar disease impacts for the more solitary Asian great apes, or for smaller primates. We used an age-structured model of different primate social systems to illustrate that interactions between social structure and demography create ‘dynamic constraints’ on the pathogens that can establish and persist in primate host species with different social systems. We showed that this varies by disease transmission mode. Sexually transmitted infections (STIs) require high rates of transmissibility to persist within a primate population. In particular, for a unimale social system, STIs require extremely high rates of transmissibility for persistence, and remain at extremely low prevalence in small primates, but this is less constrained in longer-lived, larger-bodied primates. In contrast, aerosol transmitted infections (ATIs) spread and persist at high prevalence in medium and large primates with moderate transmissibility;, establishment and persistence in small-bodied primates require higher relative rates of transmissibility. Intragroup contact structure – the social network - creates different constraints for different transmission modes, and our model underscores the importance of intragroup contacts on infection prior to intergroup movement in a structured population. When alpha males dominate sexual encounters, the resulting disease transmission dynamics differ from when social interactions are dominated by mother-infant grooming events, for example. This has important repercussions for pathogen spread across populations. Our framework reveals essential social and demographic characteristics of primates that predispose them to different disease risks that will be important for disease management and conservation planning for protected primate populations.     

Metapopulation moments: coupling, stochasticity and persistence

1.  Spatial heterogeneity has long been viewed as a reliable means of increasing persistence. Here, an analytical model is developed to consider the variation and, hence, the persistence of stochastic metapopulations. This model relies on a novel moment closure technique, which is equivalent to assuming log-normal distributions for the population sizes.
2.  Single-species models show the greatest persistence when the mixing between subpopulations is large, so spatial heterogeneity is of no benefit. This result is confirmed by stochastic simulation of the full metapopulation.
3.  In contrast, natural-enemy models exhibit the greatest persistence for intermediate levels of coupling. When the coupling is too low, there are insufficient rescue effects between the subpopulations to sustain the dynamics, whereas when the coupling is too high all spatial heterogeneity is lost.
4.  The difference in behaviour between the one- and two-species models can be attributed to the oscillatory nature of the natural-enemy system.     

Spread rate for a nonlinear stochastic invasion

Despite the recognized importance of stochastic factors, models for ecological invasions are almost exclusively formulated using deterministic equations [29]. Stochastic factors relevant to invasions can be either extrinsic (quantities such as temperature or habitat quality which vary randomly in time and space and are external to the population itself) or intrinsic (arising from a finite population of individuals each reproducing, dying, and interacting with other individuals in a probabilistic manner). It has been long conjectured [27] that intrinsic stochastic factors associated with interacting individuals can slow the spread of a population or disease, even in a uniform environment. While this conjecture has been borne out by numerical simulations, we are not aware of a thorough analytical investigation. In this paper we analyze the effect of intrinsic stochastic factors when individuals interact locally over small neighborhoods. We formulate a set of equations describing the dynamics of spatial moments of the population. Although the full equations cannot be expressed in closed form, a mixture of a moment closure and comparison methods can be used to derive upper and lower bounds for the expected density of individuals. Analysis of the upper solution gives a bound on the rate of spread of the stochastic invasion process which lies strictly below the rate of spread for the deterministic model. The slow spread is most evident when invaders occur in widely spaced high density foci. In this case spatial correlations between individuals mean that density dependent effects are significant even when expected population densities are low. Finally, we propose a heuristic formula for estimating the true rate of spread for the full nonlinear stochastic process based on a scaling argument for moments. Received: 19 October 1998 / Revised version: 1 September 1999 / Published online: 4 October 2000