Effect of balancing selection on spatial genetic structure within populations: theoretical investigations on the self-incompatibility locus and empirical studies in Arabidopsis halleri

The effect of selection on patterns of genetic structure within and between populations may be studied by contrasting observed patterns at the genes targeted by selection with those of unlinked neutral marker loci. Local directional selection on target genes will produce stronger population genetic structure than at neutral loci, whereas the reverse is expected for balancing selection. However, theoretical predictions on the intensity of this signal under precise models of balancing selection are still lacking. Using negative frequency-dependent selection acting on self-incompatibility systems in plants as a model of balancing selection, we investigated the effect of such selection on patterns of spatial genetic structure within a continuous population. Using numerical simulations, we tested the effect of the type of self-incompatibility system, the number of alleles at the self-incompatibility locus and the dominance interactions among them, the extent of gene dispersal, and the immigration rate on spatial genetic structure at the selected locus and at unlinked neutral loci. We confirm that frequency-dependent selection is expected to reduce the extent of spatial genetic structure as compared to neutral loci, particularly in situations with low number of alleles at the self-incompatibility locus, high frequency of codominant interactions among alleles, restricted gene dispersal and restricted immigration from outside populations. Hence the signature of selection on spatial genetic structure is expected to vary across species and populations, and we show that empirical data from the literature as well as data reported here on three natural populations of the herb Arabidopsis halleri confirm these theoretical results.     

Synchrony, scale and temporal dynamics of rock partridge (Alectoris graeca saxatilis) populations in the Dolomites

1. Harvesting records of rock partridge ( Alectoris graeca saxatilis ) were examined first to identify the presence of cycles in a species with a southern European distribution and then to examine synchrony between populations at a range of scales.
2. Hunting records from 1965 to 1994 were obtained from 210 hunting areas and analysed at three spatial scales: subpopulation, population and metapopulation. Rock partridge exhibited cyclic fluctuations in about 40% of the time series with a period of 4–7 years. The results did not change with spatial scale. The density-dependent structure of the populations showed that most populations exhibited damped oscillations.
3. The proportion of populations that were in synchrony increased with scale from the population to metapopulation level. There was no decline in synchrony with distance but a large variation between populations irrespective of distance.
4. The populations clustered into dry and wet habitats, with those in the dry habitat being more cyclic. We suggest the lack of spatial synchrony with distance but greater synchrony within habitats may reflect the influence of stochastic events operating on populations with different density dependence structures.     

A theoretical study of population dynamics in the sheep tick

An analytical model describing incidence of mating in Ixodes ricinus (L.) is constructed and incorporated in a simple population model which predicts proportional growth rates of Ixodes populations as a function of host and parasite densities. The sensitivity of the population model to changes in parameter values is examined, and it is shown that there exists an optimum host population size for each of the Ixodes population sizes chosen. The significance of the results is discussed with respect to the spatial distribution of sheep tick populations.     

Effect of parental care and aggregation on population dynamics

Behavioral changes of animal species can influence the consequence of population dynamics. One of the most remarkable behaviors of animal species is the aggregation by which species can reduce predation risk as a consequence of dilution or the other effects by forming a group. Empirical studies have demonstrated that an incompatibility exists in aggregation since resource competition might become severe at the cost of reducing predation pressure from predatory species. Parental care by supplying the food consumed by adults to their juveniles would reduce the mortality of juvenile due to starvation, but it would reduce the reproduction rate at the same time. In this paper, we study a class of stage-structured resource-consumer models to investigate the effect of behavioral changes on population dynamics. It is shown that under the presence of trade-off in parental care, moderate degrees of parental care will be favored as maximizing the equilibrium density of consumers. For consumer species having a long maturation period, consumer species might get benefit from dilution effects as a result of aggregation despite the elevated resource competition. Aggregation gives rise to two different outcomes in consumer extinction. Resource exhaustion as a consequence of over-exploitation can induce extinction of consumers due to Allee effects if aggregation strongly mediates juvenile survival.     

Impact of simian immunodeficiency virus infection on chimpanzee population dynamics

Like human immunodeficiency virus type 1 (HIV-1), simian immunodeficiency virus of chimpanzees (SIVcpz) can cause CD4+ T cell loss and premature death. Here, we used molecular surveillance tools and mathematical modeling to estimate the impact of SIVcpz infection on chimpanzee population dynamics. Habituated (Mitumba and Kasekela) and non-habituated (Kalande) chimpanzees were studied in Gombe National Park, Tanzania. Ape population sizes were determined from demographic records (Mitumba and Kasekela) or individual sightings and genotyping (Kalande), while SIVcpz prevalence rates were monitored using non-invasive methods. Between 2002-2009, the Mitumba and Kasekela communities experienced mean annual growth rates of 1.9% and 2.4%, respectively, while Kalande chimpanzees suffered a significant decline, with a mean growth rate of -6.5% to -7.4%, depending on population estimates. A rapid decline in Kalande was first noted in the 1990s and originally attributed to poaching and reduced food sources. However, between 2002-2009, we found a mean SIVcpz prevalence in Kalande of 46.1%, which was almost four times higher than the prevalence in Mitumba (12.7%) and Kasekela (12.1%). To explore whether SIVcpz contributed to the Kalande decline, we used empirically determined SIVcpz transmission probabilities as well as chimpanzee mortality, mating and migration data to model the effect of viral pathogenicity on chimpanzee population growth. Deterministic calculations indicated that a prevalence of greater than 3.4% would result in negative growth and eventual population extinction, even using conservative mortality estimates. However, stochastic models revealed that in representative populations, SIVcpz, and not its host species, frequently went extinct. High SIVcpz transmission probability and excess mortality reduced population persistence, while intercommunity migration often rescued infected communities, even when immigrating females had a chance of being SIVcpz infected. Together, these results suggest that the decline of the Kalande community was caused, at least in part, by high levels of SIVcpz infection. However, population extinction is not an inevitable consequence of SIVcpz infection, but depends on additional variables, such as migration, that promote survival. These findings are consistent with the uneven distribution of SIVcpz throughout central Africa and explain how chimpanzees in Gombe and elsewhere can be at equipoise with this pathogen.     

Effect of mixed infection on TB dynamics

Poor living conditions,overcrowding and strain diversity are some of the factors that influence mixed infection in Tuberculosis (TB) at the population level.We formulate a mathematical model for mixed infection in TB using nonlinear ordinary differential equa-tions where such factors were represented as probabilities of acquiring mixed infection.A qualitative analysis of the model shows that it exhibits multiple endemic equilibria and backward bifurcation for certain parameter values.The reactivation rate and trans-mission rate of individuals with mixed infection were of importance as well as the prob-abilities for latent individuals to acquire mixed infection.We calculate the prevalence of mixed infection from the model and the effect of mixed infection on TB incidence,TB prevalence and Mycobacterium tuberculosis (MTB) infection rate.Numerical simu-lations show that mixed infection may explain high TB incidences in areas which have a high strain diversity,poor living conditions and are overcrowded even without HIV.     

Physical control of plankton population abundance and dynamics in intertidal rock pools

Little is known about the population structure and dynamics of plankton of intertidal rock pools. A numerical model was developed for rock pool plankton with growth limited by both tidal washout and the stress associated with adverse conditions in high-shore pools. This model predicts that a stress tolerant species will tend to have maximum population densities in high-shore pools and that populations will fluctuate in opposite phase to the spring-neap tidal cycle. Conversely, where a species is susceptible to stress in high-shore pools, the maximum population density is likely to occur lower on the shore, and numbers in upper shore pools will cycle in phase with the spring-neap cycle. These two alternative predictions were sufficient to classify the dynamics of the most abundant species in time series taken from rock pools in the Isle of Man. The dinoflagellate Oxyrrhis marina followed the predictions of the stress tolerant model. In comparison, the spatiotemporal patterns of other taxa, including a ciliate, a dinoflagellate and cryptophytes, suggested stress-susceptible life histories.     

Trophic interaction modifications: an empirical and theoretical framework

Consumer–resource interactions are often influenced by other species in the community. At present these ‘trophic interaction modifications’ are rarely included in ecological models despite demonstrations that they can drive system dynamics. Here, we advocate and extend an approach that has the potential to unite and represent this key group of non‐trophic interactions by emphasising the change to trophic interactions induced by modifying species. We highlight the opportunities this approach brings in comparison to frameworks that coerce trophic interaction modifications into pairwise relationships. To establish common frames of reference and explore the value of the approach, we set out a range of metrics for the ‘strength’ of an interaction modification which incorporate increasing levels of contextual information about the system. Through demonstrations in three‐species model systems, we establish that these metrics capture complimentary aspects of interaction modifications. We show how the approach can be used in a range of empirical contexts; we identify as specific gaps in current understanding experiments with multiple levels of modifier species and the distributions of modifications in networks. The trophic interaction modification approach we propose can motivate and unite empirical and theoretical studies of system dynamics, providing a route to confront ecological complexity.     

Effect of selenium and Ascaridia galli infection on antioxidant biomarkers in broiler chickens: a mathematical model for parasite reduction and host growth

The activity of selenium-dependent glutathione peroxidase (GPX), liver concentration of vitamin E, and plasma and liver selenium levels were used for estimation of the antioxidant status of broiler chickens infected with Ascaridia galli. These biomarkers were recorded in an experiment covering 70 days p.i. At the same time the establishment rate of A. galli in chicken intestines, gain in the host body weight and chicken survival were studied. Broiler chickens (Cobb hybrids) were infected with 1450 embryonated A. galli eggs and treated with Sel-plex. A mathematical model was applied to determine the rate of nematode reduction and the relative rate of gain of host body weight, which are essential kinetic parameters of parasite-host interaction. The activity of GPX increased with both elevated selenium and reduced infection levels. The concentrations of selenium and vitamin E, and the GPX activity in the infected chickens demonstrated a similar pattern of change with time after day 30 p.i. The supplementation of the broilers with dietary selenium in the form of Sel-plex improved their antioxidant status. Increases by 29% in vitamin E concentration, 15% in GPX activity, and 22% in liver selenium concentration, respectively, were recorded in the infected and treated, compared to infected and untreated broilers.     

Seasonal population dynamics of ticks,and its influence on infection transmission: A semi-discrete approach

In this paper, a simple semi-discrete (ticks’ feeding is assumed to occur only during the summers of each year) model for tick population dynamics is presented. Conditions for existence, uniqueness, and stability of a positive equilibrium are found; the system is then studied numerically using parameter estimates calibrated for the tick Ixodes ricinus in Trentino, Italy, and the sensitivity to parameters is examined. Then, this model is extended to consider a tick-transmitted infection of one species of hosts, while other hosts are incompetent to the infection. Assuming, for simplicity, that the infection is not affecting the total number either of hosts or ticks, a threshold condition for infection persistence is obtained. The dependence of the equilibrium infection prevalence on parameters is studied numerically; in particular, we considered how infection prevalence depends on host densities. This analysis reveals that a ‘dilution effect’ occurs both for competent and for incompetent hosts; this means that, besides a lower threshold for host densities for infection to persist, there exists also an upper threshold: if host densities were higher than the upper threshold, the infection would go to extinction. Numerically, it is found that, for realistic parameter values, the upper threshold is not much higher than observed densities.     

Seasonal population dynamics of ticks, and their influence on infection transmission: a semi-discrete approach

A semi-discrete model for tick population dynamics is presented, whereby tick feeding is assumed to occur only during summers of each year. Conditions for existence, uniqueness, and stability of a positive equilibrium were found; the system was then studied numerically using parameter estimates calibrated for the tick Ixodes ricinus in Trentino, Italy, and the sensitivity to parameters was examined. This model was then extended to consider tick-transmitted infection of one species of hosts, while other hosts are incompetent to the infection. Assuming, for simplicity, that the infection is not affecting the total number of either hosts or ticks, a threshold condition for infection persistence was obtained. The dependence of the equilibrium infection prevalence on parameters was studied numerically; in particular, we considered how infection prevalence depends on host densities. This analysis reveals that a dilution effect occurs both for competent and for incompetent hosts. This means that, besides a lower threshold for host densities for infection to persists, there also exists an upper threshold: if host densities were higher than the upper threshold, the infection would go to extinction. Numerically, it was found that the upper threshold was not much higher than observed densities for realistic parameter values.     

Effect of resource subsidies on predator-prey population dynamics: a mathematical model

The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.     

Genetic load,inbreeding depression,and hybrid vigor covary with population size: An empirical evaluation of theoretical predictions

Reduced population size is thought to have strong consequences for evolutionary processes as it enhances the strength of genetic drift. In its interaction with selection, this is predicted to increase the genetic load, reduce inbreeding depression, and increase hybrid vigor, and in turn affect phenotypic evolution. Several of these predictions have been tested, but comprehensive studies controlling for confounding factors are scarce. Here, we show that populations of Daphnia magna, which vary strongly in genetic diversity, also differ in genetic load, inbreeding depression, and hybrid vigor in a way that strongly supports theoretical predictions. Inbreeding depression is positively correlated with genetic diversity (a proxy for N_e), and genetic load and hybrid vigor are negatively correlated with genetic diversity. These patterns remain significant after accounting for potential confounding factors and indicate that, in small populations, a large proportion of the segregation load is converted into fixed load. Overall, the results suggest that the nature of genetic variation for fitness‐related traits differs strongly between large and small populations. This has large consequences for evolutionary processes in natural populations, such as selection on dispersal, breeding systems, ageing, and local adaptation.     

Cheaters must prosper: reconciling theoretical and empirical perspectives on cheating in mutualism

Cheating is a focal concept in the study of mutualism, with the majority of researchers considering cheating to be both prevalent and highly damaging. However, current definitions of cheating do not reliably capture the evolutionary threat that has been a central motivation for the study of cheating. We describe the development of the cheating concept and distill a relative‐fitness‐based definition of cheating that encapsulates the evolutionary threat posed by cheating, i.e. that cheaters will spread and erode the benefits of mutualism. We then describe experiments required to conclude that cheating is occurring and to quantify fitness conflict more generally. Next, we discuss how our definition and methods can generate comparability and integration of theory and experiments, which are currently divided by their respective prioritisations of fitness consequences and traits. To evaluate the current empirical evidence for cheating, we review the literature on several of the best‐studied mutualisms. We find that although there are numerous observations of low‐quality partners, there is currently very little support from fitness data that any of these meet our criteria to be considered cheaters. Finally, we highlight future directions for research on conflict in mutualisms, including novel research avenues opened by a relative‐fitness‐based definition of cheating.