Estimating relative fitness in asexually reproducing plant pathogen populations

Summary A mathematical model is presented and analysed to find the conditions under which changes in gene frequencies can be used in asexually reproducing populations for estimating fitness of single genes, for example, for estimating the fitnesses of unnecessary virulence genes relative to their corresponding avirulence genes. It is concluded that the underlying distribution of relative fitness of clones (genotypes) has to be unimodal and that many populations consisting of a mixture of distinguishable clones then provide the best experimental data for estimating relative fitness of single genes. An improved statistical test procedure, i.e. generalized logistic regression, is suggested for analysing changes in gene frequencies in population experiments with a mixture of distinguishable clones. A population study of Erysiphe graminis f.sp. hordei (Klug-Andersen 1980) provides data to illustrate the procedure in the case where the population consists of a large number of genotypes. A bimodal distribution of genotypes possessing the virulence gene is indicated here.     

Phylogeography and historical demography of the orchid bee <Emphasis Type="Italic">Euglossa iopoecila</Emphasis>: signs of vicariant events associated to Quaternary climatic changes

The aim of this study was to investigate whether Pleistocene climatic instability influenced the phylogeographic structure and historical demography of an endemic Atlantic Forest (AF) orchid bee, Euglossa iopoecila Dressler, which shows two main patterns of integument colors over of its geographical distribution. We based our analysis on the concatenated sequence of four mtDNA segments belonging to genes 16S (357 bp), Cytb (651 bp) and COI (1206 bp), totaling 2234 bp. Samples of E. iopoecila populations were collected in 14 AF remnants along its geographic distribution. Median-Joining haplotype networks, SAMOVA and BAPS results indicated three lineages (southern, central and northern clusters) for E. iopoecila, with two important phylogeographic ruptures. We found higher genetic diversity among samples collected in the central region of the AF, which coincides with predicted areas of climatic stability, according to recent AF stability–extinction model. The demographic analysis suggests that only the southern cluster had undergone recent population expansion, which probably started after the last glacial maximum (LGM). Our data suggest that the differentiation observed in the three mitochondrial lineages of E. iopoecila is the result of past disconnections and multiple extinction/recolonization events involving climate fluctuations. In terms of conservation, we would emphasize the importance of considering: (1) the region of the central clade as the location of the highest genetic diversity of mtDNA of E. iopoecila populations; (2) the philopatric behavior of females that tends to restrict mtDNA gene flow in particular, with direct implications for the conservation of the total genetic diversity in euglossine populations.     

How Levins’ dynamics emerges from a Ricker metapopulation model

Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively to explore the extinction dynamics of metapopulations, but they ignore the important role of local population dynamics. In this paper, we consider a stochastic metapopulation model where local populations follow a stochastic, density-dependent dynamics (the Ricker model), and use this framework to investigate the behaviour of the metapopulation on the brink of extinction. We determine under which circumstances the metapopulation follows a time evolution consistent with Levins’ dynamics. We derive analytical expressions for the colonisation and extinction rates (c and e) in Levins-type models in terms of reproduction, survival and dispersal parameters of the local populations, providing an avenue to parameterising Levins-like models from the type of information on local demography that is available for a number of species. To facilitate applying our results, we provide a numerical algorithm for computing c and e.     

The Effect of an Upper Limit to Population Size on Persistence Time

For a population with density-independent vital rates in a randomly varying environment, previous authors have calculated the probability that population size will first drop to some specified (arbitrary) low level at a given time (the first passage time distribution (FPTD), which may be interpreted as a distribution of extinction times). In this paper, we study the FPTD For a stochastic model of density-independent population growth which includes a hard upper limit to population size. We discuss the conditions under which this distribution may be approximated by the FPTD of a Wiener process with a reflecting boundary condition, for which an exact calculation is presented in an appendix. We compare the FPTD of the new model with its counterpart in the model without an upper limit. The most important effects of introducing the upper limit are: (a) ultimate extinction becomes certain; (b) if the long run growth rate in the absence of the upper boundary was small but positive, extinction within ecologically significant times is likely; (c) for larger values of the long run growth rate, persistence over ecologically significant times is almost certain. We discuss the implications of result (b) for conservation. Result (c) establishes that "density-vague" regulation can produce persistent, but bounded, populations.     

Colonization dynamics of a clonal pioneer plant on a glacier foreland inferred from spatially explicit and size-structured matrix models

The regional distribution of a plant species is a result of the dynamics of extinctions and colonizations in suitable habitats, especially in strongly fragmented landscapes. Here, we studied the role of spatial dynamics of the long-lived, clonal pioneer plant Geum reptans occurring on glacier forelands in the European Alps. We used demographic data from several years and sites in the Swiss Alps in combination with dispersal data to parametrize a matrix model for G. reptans to simulate extinctions, colonizations and spatial spread of established populations on glacial forelands. We used different scenarios with varying germination rates, wind and animal dispersal capabilities, and modes of spatial spread (seed-only vs clonal spread), resulting in population growth rates (λ) ranging from 1.04 to 1.20. Our results suggest that due to the low germination rate (~1%) and the very limited wind dispersal distances (99.8% of seeds are dispersed < 5 m), G. reptans has a low probability of establishing new populations and a very low spatial spread by seed dispersal alone. In contrast to the low rate of establishment, the persistence of established populations is high and even populations of only a few individuals have an extinction probability of less than 25% within 100 years. This high persistency is partly due to clonal reproduction via aboveground stolons. Clonal reproduction increases the population size and contributes considerably to the spatial spread of established populations. Our simulation results together with the known pattern of molecular diversity of G. reptans indicate that the occurrence of populations of this species in the Alps is unlikely to be a result of recent colonizations by long-distance dispersal, but rather a result of post-glacial colonizations by large migrating populations that were fragmented when glaciers retreated. Additionally, our simulations suggest that the currently observed high rates of glacial retreat might be too fast for pioneer plants, such as G. reptans, to keep up with the retreating ice and therefore might threaten existing populations.     

Robust Identification of Local Adaptation from Allele Frequencies

Comparing allele frequencies among populations that differ in environment has long been a tool for detecting loci involved in local adaptation. However, such analyses are complicated by an imperfect knowledge of population allele frequencies and neutral correlations of allele frequencies among populations due to shared population history and gene flow. Here we develop a set of methods to robustly test for unusual allele frequency patterns and correlations between environmental variables and allele frequencies while accounting for these complications based on a Bayesian model previously implemented in the software Bayenv. Using this model, we calculate a set of “standardized allele frequencies” that allows investigators to apply tests of their choice to multiple populations while accounting for sampling and covariance due to population history. We illustrate this first by showing that these standardized frequencies can be used to detect nonparametric correlations with environmental variables; these correlations are also less prone to spurious results due to outlier populations. We then demonstrate how these standardized allele frequencies can be used to construct a test to detect SNPs that deviate strongly from neutral population structure. This test is conceptually related to F_ST and is shown to be more powerful, as we account for population history. We also extend the model to next-generation sequencing of population pools—a cost-efficient way to estimate population allele frequencies, but one that introduces an additional level of sampling noise. The utility of these methods is demonstrated in simulations and by reanalyzing human SNP data from the Human Genome Diversity Panel populations and pooled next-generation sequencing data from Atlantic herring. An implementation of our method is available from http://gcbias.org.     

Outbreeding depression in the common frog, <Emphasis Type="Italic">Rana temporaria</Emphasis>

Theory suggests that parental relatedness is a continuous variable with a fitness optimum that we heretoforth will refer to as optimal outbreeding. In the present paper, we test this proposition from a conservation (translocation) perspective. Amphibians are facing a global decline and many amphibian populations are today small and threatened by extinction. Because genetic differentiation is often high between amphibian populations, they could be particularly sensitive to outbreeding depression, e.g. due to breakdown of locally adapted gene complexes. We tested if outbreeding would reduce fitness in common frogs, Rana temporaria, crossed from a large and an isolated, small population, separated by 130km, using artificial fertilization. For females from the large population, tadpoles were significantly smaller and more malformed in crosses with males from the small population, than with males from the large population. For the small population, however, no significant paternal genetic effects could be found. The difference in response to outbreeding between populations was accompanied with significant differences in the importance of maternal effects. We conclude that care should be taken when translocating frogs between distantly related populations to avoid outbreeding depression.     

Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions

Population structure affects the relative influence of selection and drift on the change in allele frequencies. Several models have been proposed recently, using diffusion approximations to calculate fixation probabilities, fixation times, and equilibrium properties of subdivided populations. We propose here a simple method to construct diffusion approximations in structured populations; it relies on general expressions for the expectation and variance in allele frequency change over one generation, in terms of partial derivatives of a "fitness function" and probabilities of genetic identity evaluated in a neutral model. In the limit of a very large number of demes, these probabilities can be expressed as functions of average allele frequencies in the metapopulation, provided that coalescence occurs on two different timescales, which is the case in the island model. We then use the method to derive expressions for the probability of fixation of new mutations, as a function of their dominance coefficient, the rate of partial selfing, and the rate of deme extinction. We obtain more precise approximations than those derived by recent work, in particular (but not only) when deme sizes are small. Comparisons with simulations show that the method gives good results as long as migration is stronger than selection.     

Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion

In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t+ either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.This work was partially supported by the Centre National de la Recherche Scientifique through ATP 95939900     

Egg clumping,host plant selection and population regulation in Cactoblastis cactorum (Lepidoptera)

Summary Since the successful control of prickly pear cactus by Cactoblastis cactorum in Australia, populations of plants and moths have persisted at low densities in open woodland sites. A contagious egg distribution causes overcrowding of larvae on some plants but insures low levels or no attack of other plants. This prevents extinction of plants and insects. Cactoblastis moths choose plants with characteristics which may increase the success of their larvae. Field observations and cage experiments indicate that large, green cactuses near previously attacked cactuses receive more eggs. Plants which are actively photosynthesizing are also more attractive as oviposition sites. These oviposition preferences contribute to the observed contagious egg distribution.While open woodland Opuntia and Cactoblastis populations fluctuate around an equilibrium, pasture populations may better be described by the hide and seek model, with the woodland populations serving as refuges. Average plant quality and variation in quality are suggested as important components in the dynamics of this system.This paper is dedicated to the memory of our friend Mike Sabath.     

Designing gene drives to limit spillover to non-target populations

The prospect of utilizing CRISPR-based gene-drive technology for controlling populations has generated much excitement. However, the potential for spillovers of gene-drive alleles from the target population to non-target populations has raised concerns. Here, using mathematical models, we investigate the possibility of limiting spillovers to non-target populations by designing differential-targeting gene drives, in which the expected equilibrium gene-drive allele frequencies are high in the target population but low in the non-target population. We find that achieving differential targeting is possible with certain configurations of gene-drive parameters, but, in most cases, only under relatively low migration rates between populations. Under high migration, differential targeting is possible only in a narrow region of the parameter space. Because fixation of the gene drive in the non-target population could severely disrupt ecosystems, we outline possible ways to avoid this outcome. We apply our model to two potential applications of gene drives—field trials for malaria-vector gene drives and control of invasive species on islands. We discuss theoretical predictions of key requirements for differential targeting and their practical implications.     

Evaluating the local habitat history deepens the understanding of the extinction debt for endangered plant species in semi-natural grasslands

Habitat losses occur non-randomly within human-modified landscapes, resulting in high spatial heterogeneity of local habitat histories. Although local habitat history can modulate the existence of extinction debt (i.e., the number of populations predicted to become extinct) in a landscape, its role in detecting extinction debt has not been examined explicitly. We aimed to compare the detectability of extinction debt among populations of an endangered semi-natural grassland species, Echinops setifer (Compositae), in the grassland landscape of Mt. Aso, Japan. We classified populations into three groups that differed in local habitat history: stable (habitat loss ≤30% since the 1930s), moderately decreased (30% < loss ≤ 90%), and severely decreased (loss >90%). We then evaluated whether the effects of habitat areas during the 1930s and 2000s varied among groups to explain population size by GLMMs and estimated coefficient of explanatory variable by Bayesian MCMC methods. Within the groups, stable group showed significant positive relationships with both past and current habitat areas. The moderately decreased group only showed significant positive relationships with past habitat areas, indicating the existence of extinction debt in these populations. The severely decreased group only showed significant positive relationships with current habitat areas, indicating that they may have already paid their extinction debt because the rate of grassland loss exceeded the extinction threshold. Even within the same landscape, extinction debt varied in response to local habitat history. In spatially heterogeneous landscapes, evaluation of effects of local habitat history can elucidate the habitat-based extinction risks for plant populations.     

Changing environmental spectra influence age-structured populations: increasing ENSO frequency could diminish variance and extinction risk in long-lived seabirds

As global climate changes, there is increasing need to understand how changes in the frequencies of environmental variability affect populations. Age-structured populations have recently been shown to filter specific frequencies of environmental variability, favoring generational frequencies, and very low frequencies, a phenomenon known as cohort resonance. However, there has been little exploration of how changes in the spectra of environmental signals will affect the stability and persistence of age-structured populations. To examine this issue, we analyzed a likely example to show how changes in the frequency of an influential climate phenomenon, the El Niño-Southern Oscillation (ENSO), could affect a marine bird population. We used a density-dependent, age-structured population model to calculate the transfer function (i.e., the frequency-dependent sensitivity) of Brandt’s cormorant (Phalacrocorax penicillatus), a representative marine bird species known to be influenced by ENSO. We then assessed how the population would be affected by ENSO forcing that was doubled and halved in frequency. The transfer function indicated this population is most sensitive to variance at low frequencies, but does not exhibit the sensitivity to generational frequencies (cohort resonance) observed in shorter-lived species. Doubling the frequency of ENSO unexpectedly resulted in higher mean adult population abundance, lower variance, and lower probability of extinction, compared to forcing with the historical or reduced ENSO frequency. Our results illustrate how long-lived species with environmentally driven variability in recruitment, including many species of marine birds and fish, may respond in counterintuitive ways to anticipated changes in environmental variability.     

Patterns of differentiation among wild rabbit populations Oryctolagus cuniculus L. in arid and semiarid ecosystems of north-eastern Australia

Feral rabbit populations in Australia have generally been managed using localized control procedures. While these procedures may result in local extinctions, persistence of populations will depend on the probability of recolonization. Genetic markers developed using temperature gradient gel electrophoresis (TGGE) combined with heteroduplex analysis (HA) of mitochondrial DNA (mtDNA) were used to characterize the degree of subdivision and extent of gene flow within and among rabbit populations distributed over large distances (up to 1000 km) in southern Queensland (QLD) and north-west New South Wales (NSW), Australia. TGGE analyses revealed significant heterogeneity in mtDNA control region haplotype frequencies. From heterogeneity χ² tests, it was evident that the differentiation observed was largely attributable to five sites which were located in the semiarid eastern region, whereas haplotype frequencies were homogeneous throughout the arid western region. These results suggest that there are independent population systems within the study area. The extent of gene flow among local populations within each system is related to the spatial configuration of acceptable habitat patches and the persistence of the populations is determined by the probability of recolonization following local extinction. These data suggest that to provide better overall control of rabbit populations, different management strategies may be necessary in arid and semiarid ecosystems. In arid south-west QLD and north-west NSW, where extensive gene flow occurs over large distances, rabbit populations should be managed at a regional level. In semiarid eastern QLD, where gene flow is restricted and populations are more isolated, localized control procedures may provide effective short-term relief. These results indicate that in nonequilibrium systems with patchy distribution of individuals, the interpretation of migration rate from estimates of gene flow obtained using existing genetic models must include an understanding of the spatial and temporal scales over which population processes operate.     

Spatial genetic structure and reproductive success in fragmented and continuous populations of<Emphasis Type="Italic">Primula vulgaris</Emphasis>

In Flanders (northern Belgium),Primula vulgaris, a self-incompatible long-lived perennial herb, is rare and consists of a network of fragmented populations in the intensively used agricultural landscape. We investigated genetic variation and structure using 27 allozyme loci in 41 populations, and reproductive success to assess the effect of fragmentation on gene flow and the influence of the nearest neighbouring (large and/or highly genetically diverse) population on within-population genetic variation and reproductive success. Isolation by distance was found among and within populations. Smaller and more isolated populations showed a slight loss of allelic variation, but maintained high levels of observed heterozygosity. They were not more differentiated from each other than large populations. No significant difference in the regression slopes of the spatial autocorrelation analysis was found between two continuous populations and two groups of fragmented populations with similar distance classes. Multiple regression showed that population allelic richness and reproductive success were higher when the nearest neighbouring population was genetically more diverse. These results suggest moderate current gene flow within and among populations rather than historical gene flow. We conclude that small and isolated populations ofP. vulgaris should be considered not only as remnants of previously larger populations, but also as potential stepping stones insuring gene flow processes. For conservation, all highly variable and flowering populations should be considered, irrespective of their size or their isolation from large and continuous populations.     

On the distribution of allele frequencies in a diffusion model

An expression is derived and values tabulated for the expected allele frequencies and their variances, arranged in decreasing order in a population, from the finite and infinite alleles diffusion model in Watterson (1976). The neutral model and also a model with heterozygote selection are considered. Some observed ABO blood group allele frequencies are compared with the tabulated expected frequencies in the neutral three allele model. This extends the results of Watterson and Guess (1977) who tabulate the expected value of the most common allele. One test of neutrality previously advocated is to consider the distribution of F, the population homozygosity, conditional on G, the product of allele frequencies. However it is shown here that for a large number of alleles, F and G are asymptotically independent, the test would not be a good one in this case. A limit theorem is derived for the distribution of allele frequencies in the neutral model when the mutation rate is large. In this case F is shown to be asymptotically normal. An inequality is derived for the probability that the oldest allele in a population is amongst the r most frequent types. An inequality is also found for the probability that a sample will only contain representatives of the r most frequent allele types in the population.     

The polymorphism frequency spectrum of finitely many sites under selection

The distribution of genetic polymorphisms in a population contains information about evolutionary processes. The Poisson random field (PRF) model uses the polymorphism frequency spectrum to infer the mutation rate and the strength of directional selection. The PRF model relies on an infinite-sites approximation that is reasonable for most eukaryotic populations, but that becomes problematic when is large ( greater, similar 0.05). Here, we show that at large mutation rates characteristic of microbes and viruses the infinite-sites approximation of the PRF model induces systematic biases that lead it to underestimate negative selection pressures and mutation rates and erroneously infer positive selection. We introduce two new methods that extend our ability to infer selection pressures and mutation rates at large : a finite-site modification of the PRF model and a new technique based on diffusion theory. Our methods can be used to infer not only a "weighted average" of selection pressures acting on a gene sequence, but also the distribution of selection pressures across sites. We evaluate the accuracy of our methods, as well that of the original PRF approach, by comparison with Wright-Fisher simulations.     

The genetic structure of the European breeding populations of a declining farmland bird,the ortolan bunting (<Emphasis Type="Italic">Emberiza hortulana</Emphasis>), reveals conservation priorities

Anthropogenic activities, such as agricultural intensification, caused large declines in biodiversity, including farmland birds. In addition to demographic consequences, anthropogenic activities can result in loss of genetic diversity, reduction of gene flow and altered genetic structure. We investigated the distribution of the genetic variation of a declining farmland and long-distance migratory bird, the ortolan bunting Emberiza hortulana, across its European breeding range to assess the impact of human-driven population declines on genetic diversity and structure in order to advise conservation priorities. The large population declines observed have not resulted in dramatic loss of genetic diversity, which is moderate to high and constant across all sampled breeding sites. Extensive gene flow occurs across the breeding range, even across a migratory divide, which contributes little to genetic structuring. However, gene flow is asymmetric, with the large eastern populations acting as source populations for the smaller western ones. Furthermore, breeding populations that underwent the largest declines, in Fennoscandia and Baltic countries, appear to be recently isolated, with no gene exchange occurring with the eastern or the western populations. These are signs for concern as declines in the eastern populations could affect the strength of gene flow and in turn affect the western populations. The genetic, and demographic, isolation of the northern populations make them particularly sensitive to loss of genetic diversity and to extinction as no immigration is occurring to counter-act the drastic declines. In such a situation, conservation efforts are needed across the whole breeding range: in particular, protecting the eastern populations due to their key role in maintaining gene flow across the range, and focussing on the northern populations due to their recent isolation and endangered status.     

Calculating the time to extinction of a reactivating virus, in particular bovine herpes virus

The expected time to extinction of a herpes virus is calculated from a rather simple population-dynamical model that incorporates transmission, reactivation and fade-out of the infectious agent. We also derive the second and higher moments of the distribution of the time to extinction. These quantities help to assess the possibilities to eradicate a reactivating infection. The key assumption underlying our calculations is that epidemic outbreaks are fast relative to the time scale of demographic turnover. Four parameters influence the expected time to extinction: the reproduction ratio, the reactivation rate, the population size, and the demographic turn-over in the host population. We find that the expected time till extinction is very long when the reactivation rate is high (reactivation is expected more than once in a life time). Furthermore, the infectious agent will go extinct much more quickly in small populations. This method is applied to bovine herpes virus (BHV) in a cattle herd. The results indicate that without vaccination, BHV will persist in large herds. The use of a good vaccine can induce eradication of the infection from a herd within a few decades. Additional measures are needed to eradicate the virus from a whole region within a similar time-span.