Testing metapopulation dynamics using genetic, demographic and ecological data

The metapopulation concept is a cornerstone in the recent history of ecology and evolution. However, determining whether a natural system fits a metapopulation model is a complex issue. Extinction-colonization dynamics are indeed often difficult to quantify because species detectability is not always 100%, resulting in an imperfect record of extinctions. Here, we explore whether combining population genetics with demographic and ecological surveys can yield more realistic estimates of metapopulation dynamics. We apply this approach to the freshwater snail Drepanotrema depressissimum in a fragmented landscape of tropical ponds. In addition to studying correlations between genetic diversity and demographical or ecological characteristics, we undertake, for the first time, a detailed search for genetic signatures of extinction-recolonization events using temporal changes in allele frequencies within sites. Surprisingly, genetic data indicate that extinction is much rarer than suggested by demographic surveys. Consequently, this system is better described as a set of populations with different sizes and immigration rates than as a true metapopulation. We identify several cases of apparent extinction owing to nondetection of low-density populations, and of aestivating individuals in desiccated ponds. More generally, we observed a frequent mismatch between genetic and demographical/ecological information at small spatial and temporal scales. We discuss the causes of these discrepancies and show how these two types of data provide complementary information on population dynamics and history, especially when temporal genetic samples are available.     

Fixation probabilities depend on life history: fecundity, generation time and survival in a burst-death model

The burst-death model has been developed to describe the life history of organisms with variable generation times and a burst of a fixed number of offspring. The model also includes an optional constant clearance rate, such as washout from a chemostat, and the possibility of sustained periods of population growth followed by severe bottlenecks, as in serial passaging. In this model, a beneficial mutation can either increase the burst rate or the burst size, or reduce the clearance rate, thus increasing survival. In this article we examine the effects of these three possible mechanisms on both the Malthusian fitness and the fixation probability of the lineage. We find that equivalent relative increases in the burst rate or burst size confer equivalent increases in the Malthusian fitness of a lineage, whereas increasing survival typically has a more moderate effect on Malthusian fitness. In contrast, for beneficial mutations that confer the same increase in fitness, mutations that increase survival are the most likely to fix, followed by mutations that increase the burst rate. Mutations that increase the burst size are the least likely to fix. These results imply that mutant lineages with the highest Malthusian fitness are not, in many cases, the most likely to escape extinction.     

The probability of evolutionary rescue: towards a quantitative comparison between theory and evolution experiments

Evolutionary rescue occurs when a population genetically adapts to a new stressful environment that would otherwise cause its extinction. Forecasting the probability of persistence under stress, including emergence of drug resistance as a special case of interest, requires experimentally validated quantitative predictions. Here, we propose general analytical predictions, based on diffusion approximations, for the probability of evolutionary rescue. We assume a narrow genetic basis for adaptation to stress, as is often the case for drug resistance. First, we extend the rescue model of Orr & Unckless (Am. Nat. 2008 172, 160–169) to a broader demographic and genetic context, allowing the model to apply to empirical systems with variation among mutation effects on demography, overlapping generations and bottlenecks, all common features of microbial populations. Second, we confront our predictions of rescue probability with two datasets from experiments with Saccharomyces cerevisiae (yeast) and Pseudomonas fluorescens (bacterium). The tests show the qualitative agreement between the model and observed patterns, and illustrate how biologically relevant quantities, such as the per capita rate of rescue, can be estimated from fits of empirical data. Finally, we use the results of the model to suggest further, more quantitative, tests of evolutionary rescue theory.     

Ion permeation and selectivity of OmpF porin: a theoretical study based on molecular dynamics,Brownian dynamics,and continuum electrodiffusion theory

Three different theoretical approaches are used and compared to refine our understanding of ion permeation through the channel formed by OmpF porin from Escherichia coli. Those approaches are all-atom molecular dynamics (MD) in which ions, solvent, and lipids are represented explicitly, Brownian dynamics (BD) in which ions are represented explicitly, while solvent and lipids are represented as featureless dielectrics, and Poisson-Nernst-Planck (PNP) electrodiffusion theory in which both solvent and local ion concentrations are represented as a continuum. First, the ability of the different theoretical approaches in reproducing the equilibrium average ion density distribution in OmpF porin bathed by a 1M KCl symmetric salt solution is examined. Under those conditions the PNP theory is equivalent to the non-linear Poisson-Boltzmann (PB) theory. Analysis shows that all the three approaches are able to capture the important electrostatic interactions between ions and the charge distribution of the channel that govern ion permeation and selectivity in OmpF. The K(+) and Cl(-) density distributions obtained from the three approaches are very consistent with one another, which suggests that a treatment on the basis of a rigid protein and continuum dielectric solvent is valid in the case of OmpF. Interestingly, both BD and continuum electrostatics reproduce the distinct left-handed twisted ion pathways for K(+) and Cl(-) extending over the length of the pore which were observed previously in MD. Equilibrium BD simulations in the grand canonical ensemble indicate that the channel is very attractive for cations, particularly at low salt concentration. On an average there is 1.55 K(+) inside the pore in 10mM KCl. Remarkably, there is still 0.17 K(+) on average inside the pore even at a concentration as low as 1microM KCl. Secondly, non-equilibrium ion flow through OmpF is calculated using BD and PNP and compared with experimental data. The channel conductance in 0.2M and 1M KCl calculated using BD is in excellent accord with the experimental data. The calculations reproduce the experimentally well-known conductance-concentration relation and also reveal an asymmetry in the channel conductance (a larger conductance is observed under a positive transmembrane potential). Calculations of the channel conductance for three mutants (R168A, R132A, and K16A) in 1M KCl suggest that the asymmetry in the channel conductance arises mostly from the permanent charge distribution of the channel rather than the shape of the pore itself. Lastly, the calculated reversal potential in a tenfold salt gradient (0.1:1M KCl) is 27.4(+/-1.3)mV (BD) and 22.1(+/-0.6)mV (PNP), in excellent accord with the experimental value of 24.3mV. Although most of the results from PNP are qualitatively reasonable, the calculated channel conductance is about 50% higher than that calculated from BD probably because of a lack of some dynamical ion-ion correlations.     

Coupled molecular dynamics and continuum electrostatic method to compute the ionization pKa’s of proteins as a function of pH. Test on a large set of proteins

A computational method, to predict the pKa values of the ionizable residues Asp, Glu, His, Tyr, and Lys of proteins, is presented here. Calculation of the electrostatic free-energy of the proteins is based on an efficient version of a continuum dielectric electrostatic model. The conformational flexibility of the protein is taken into account by carrying out molecular dynamics simulations of 10 ns in implicit water. The accuracy of the proposed method of calculation of pKa values is estimated from a test set of experimental pKa data for 297 ionizable residues from 34 proteins. The pKa-prediction test shows that, on average, 57, 86, and 95% of all predictions have an error lower than 0.5, 1.0, and 1.5 pKa units, respectively. This work contributes to our general understanding of the importance of protein flexibility for an accurate computation of pKa, providing critical insight about the significance of the multiple neutral states of acid and histidine residues for pKa-prediction, and may spur significant progress in our effort to develop a fast and accurate electrostatic-based method for pKa-predictions of proteins as a function of pH.     

Understanding extinction debts: spatio–temporal scales,mechanisms and a roadmap for future research

Extinction debt refers to delayed species extinctions expected as a consequence of ecosystem perturbation. Quantifying such extinctions and investigating long‐term consequences of perturbations has proven challenging, because perturbations are not isolated and occur across various spatial and temporal scales, from local habitat losses to global warming. Additionally, the relative importance of eco‐evolutionary processes varies across scales, because levels of ecological organization, i.e. individuals, (meta)populations and (meta)communities, respond hierarchically to perturbations. To summarize our current knowledge of the scales and mechanisms influencing extinction debts, we reviewed recent empirical, theoretical and methodological studies addressing either the spatio–temporal scales of extinction debts or the eco‐evolutionary mechanisms delaying extinctions. Extinction debts were detected across a range of ecosystems and taxonomic groups, with estimates ranging from 9 to 90% of current species richness. The duration over which debts have been sustained varies from 5 to 570 yr, and projections of the total period required to settle a debt can extend to 1000 yr. Reported causes of delayed extinctions are 1) life‐history traits that prolong individual survival, and 2) population and metapopulation dynamics that maintain populations under deteriorated conditions. Other potential factors that may extend survival time such as microevolutionary dynamics, or delayed extinctions of interaction partners, have rarely been analyzed. Therefore, we propose a roadmap for future research with three key avenues: 1) the microevolutionary dynamics of extinction processes, 2) the disjunctive loss of interacting species and 3) the impact of multiple regimes of perturbation on the payment of debts. For their ability to integrate processes occurring at different levels of ecological organization, we highlight mechanistic simulation models as tools to address these knowledge gaps and to deepen our understanding of extinction dynamics.     

Past and potential future population dynamics of three grouse species using ecological and whole genome coalescent modeling

Studying demographic history of species provides insight into how the past has shaped the current levels of overall biodiversity and genetic composition of species, but also how these species may react to future perturbations. Here we investigated the demographic history of the willow grouse (Lagopus lagopus), rock ptarmigan (Lagopus muta), and black grouse (Tetrao tetrix) through the Late Pleistocene using two complementary methods and whole genome data. Species distribution modeling (SDM) allowed us to estimate the total range size during the Last Interglacial (LIG) and Last Glacial Maximum (LGM) as well as to indicate potential population subdivisions. Pairwise Sequentially Markovian Coalescent (PSMC) allowed us to assess fluctuations in effective population size across the same period. Additionally, we used SDM to forecast the effect of future climate change on the three species over the next 50 years. We found that SDM predicts the largest range size for the cold‐adapted willow grouse and rock ptarmigan during the LGM. PSMC captured intraspecific population dynamics within the last glacial period, such that the willow grouse and rock ptarmigan showed multiple bottlenecks signifying recolonization events following the termination of the LGM. We also see signals of population subdivision during the last glacial period in the black grouse, but more data are needed to strengthen this hypothesis. All three species are likely to experience range contractions under future warming, with the strongest effect on willow grouse and rock ptarmigan due to their limited potential for northward expansion. Overall, by combining these two modeling approaches, we have provided a multifaceted examination of the biogeography of these species and how they have responded to climate change in the past. These results help us understand how cold‐adapted species may respond to future climate changes.     

Modelling population dynamics in a unicellular social organism community using a minimal model and evolutionary game theory

Most unicellular organisms live in communities and express different phenotypes. Many efforts have been made to study the population dynamics of such complex communities of cells, coexisting as well-coordinated units. Minimal models based on ordinary differential equations are powerful tools that can help us understand complex phenomena. They represent an appropriate compromise between complexity and tractability; they allow a profound and comprehensive analysis, which is still easy to understand. Evolutionary game theory is another powerful tool that can help us understand the costs and benefits of the decision a particular cell of a unicellular social organism takes when faced with the challenges of the biotic and abiotic environment. This work is a binocular view at the population dynamics of such a community through the objectives of minimal modelling and evolutionary game theory. We test the behaviour of the community of a unicellular social organism at three levels of antibiotic stress. Even in the absence of the antibiotic, spikes in the fraction of resistant cells can be observed indicating the importance of bet hedging. At moderate level of antibiotic stress, we witness cyclic dynamics reminiscent of the renowned rock–paper–scissors game. At a very high level, the resistant type of strategy is the most favourable.     

Spatial structure and dynamics of breeding bird populations at a distribution margin,southern California

Aim Local‐scale processes at species distribution margins can affect larger‐scale distribution dynamics, but are rarely studied. The objective of this research was to elucidate the nature of distribution limits by studying the comparative structure, dynamics and environmental associations of breeding bird populations at their distribution margin. We hypothesized that climate is principally responsible for setting distribution limits, whereas biotic habitat features are more strongly associated with distribution patterns within the range. Location Southern California, USA. Methods During 2005–2007 we studied the distribution patterns of breeding birds in three study areas, each spanning a low‐elevation (200–1800 m) desert scrub‐to‐chaparral gradient. We used logistic regression with hierarchical partitioning to assess the independent effects of environmental variables (e.g. climate versus habitat) on distributions. We tested for shifts in the relative importance of these environmental variables in determining distribution limits versus within‐range patterns, and we also compared higher‐ and lower‐elevation groups of species. Results Distribution patterns were highly variable among species, but were remarkably static over the three study areas and 3‐year study period. Across species, habitat floristic variables performed relatively well at explaining distribution patterns. For higher‐elevation species (chaparral birds), climate was relatively important in setting their lower distribution limits, and there was a shift to a greater importance of biotic habitat (mainly habitat structural variables) for determining within‐range patterns. Relationships were more mixed for lower‐elevation species (desert scrub birds), but with respect to distribution limits, biotic habitat variables tended to be more important relative to climate than we observed for chaparral birds. Main conclusions Along this warm, arid elevational gradient, higher‐elevation chaparral birds are more limited by climate at their lower margin than are lower‐elevation desert birds at their upper margin, suggesting that climate plays a strong role (relative to other values) in excluding non‐desert birds from desert. However, given the strong differences among species, predictive distribution models will need to be individually tailored, and for most species biotic habitat variables were of greater importance than climate in determining limits. This research highlights the usefulness of studying environmental relationships at distribution margins and the importance of considering biotic relationships in forecasting distribution shifts under changing climates.     

Dynamic sampling bias and overdispersion induced by skewed offspring distributions

Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population expansions. The resulting allele-frequency fluctuations are large and, therefore, challenge standard models of population genetics, which assume sufficiently narrow offspring distributions. While the neutral dynamics backward in time can be readily analyzed using coalescent approaches, we still know little about the effect of broad offspring distributions on the forward-in-time dynamics, especially with selection. Here, we employ an asymptotic analysis combined with a scaling hypothesis to demonstrate that over-dispersed frequency trajectories emerge from the competition of conventional forces, such as selection or mutations, with an emerging time-dependent sampling bias against the minor allele. The sampling bias arises from the characteristic time-dependence of the largest sampled family size within each allelic type. Using this insight, we establish simple scaling relations for allele-frequency fluctuations, fixation probabilities, extinction times, and the site frequency spectra that arise when offspring numbers are distributed according to a power law.     

Smooth ROC curves and surfaces for markers subject to a limit of detection using monotone natural cubic splines

The use of ROC curves in evaluating a continuous or ordinal biomarker for the discrimination of two populations is commonplace. However, in many settings, marker measurements above or below a certain value cannot be obtained. In this paper, we study the construction of a smooth ROC curve (or surface in the case of three populations) when there is a lower or upper limit of detection. We propose the use of spline models that incorporate monotonicity constraints for the cumulative hazard function of the marker distribution. The proposed technique is computationally stable and simulation results showed a satisfactory performance. Other observed covariates can be also accommodated by this spline‐based approach.     

The longitudinal distribution and community dynamics of zooplankton in a regulated large river: a case study of the Nakdong River (Korea)

The longitudinal distribution and seasonal dynamics of zooplankton were examined along a 200-km section of the middle to lower Nakdong River, Korea. Zooplankton was sampled twice a month from January 1995 to December 1997 at five sites in the main river channel. There was considerable longitudinal variation in total zooplankton abundance (ANOVA, p < 0.001). All major zooplankton groups (rotifers, cladocerans, copepodids and nauplii) increased significantly with distance downstream along the river. There also were statistically significant seasonal differences in zooplankton abundance at the sampling sites (ANOVA, p < 0.01). Zooplankton abundance was high in spring and fall and low in summer and winter. The seasonal pattern of rotifers was similar to that of total zooplankton. This reflected the fact that rotifers (Brachionus calyciflorus, B. rubens, Keratella cochlearis and Polyarthra spp.) strongly dominated the zooplankton community at all locations. Among the macrozooplankton, small-bodied cladocerans (e.g. Bosmina spp.) dominated; the abundance of large-bodied cladocerans (e.g. Daphnia) was negligible (0–5 ind. l^–1). Among the environmental variables considered, partial residence time seemed to play the most important role in determining characteristics of the river zooplankton community.     

Generation time and the stability of sex-determining alleles in oyster populations as deduced using a gene-based population dynamics model

Crassostrea oysters are protandrous hermaphrodites. Sex is thought to be determined by a single gene with a dominant male allele M and a recessive protandrous allele F, such that FF animals are protandrous and MF animals are permanent males. We investigate the possibility that a reduction in generation time, brought about for example by disease, might jeopardize retention of the M allele. Simulations show that MF males have a significantly lessened lifetime fecundity when generation time declines. The allele frequency of the M allele declines and eventually the M allele is lost. The probability of loss is modulated by population abundance. As abundance increases, the probability of M allele loss declines. Simulations suggest that stabilization of the female-to-male ratio when generation time is long is the dominant function of the M allele. As generation time shortens, the raison d’être for the M allele also fades as mortality usurps the stabilizing role. Disease and exploitation have shortened oyster generation time: one consequence may be to jeopardize retention of the M allele. Two alternative genetic bases for protandry also provide stable sex ratios when generation time is long; an F-dominant protandric allele and protandry restricted to the MF heterozygote. In both cases, simulations show that FF individuals become rare in the population at high abundance and/or long generation time. Protandry restricted to the MF heterozygote maintains sex ratio stability over a wider range of generation times and abundances than the alternatives, suggesting that sex determination based on a male-dominant allele (MM/MF) may not be the optimal solution to the genetic basis for protandry in Crassostrea.     

The Quaternary evolutionary history,potential distribution dynamics,and conservation implications for a Qinghai–Tibet Plateau endemic herbaceous perennial,Anisodus tanguticus (Solanaceae)

Various hypotheses have been proposed about the Quaternary evolutionary history of plant species on the Qinghai–Tibet Plateau (QTP), yet only a handful of studies have considered both population genetics and ecological niche context. In this study, we proposed and compared climate refugia hypotheses based on the phylogeographic pattern of Anisodus tanguticus (three plastid DNA fragments and nuclear internal transcribed spacer regions from 32 populations) and present and past species distribution models (SDMs). We detected six plastid haplotypes in two well‐differentiated lineages. Although all haplotypes could be found in its western (sampling) area, only haplotypes from one lineage occurred in its eastern area. Meanwhile, most genetic variations existed between populations (F_ST = 0.822). The SDMs during the last glacial maximum and last interglacial periods showed range fragmentation in the western area and significant range contraction in the eastern area, respectively, in comparison with current potential distribution. This species may have undergone intraspecific divergence during the early Quaternary, which may have been caused by survival in different refugia during the earliest known glacial in the QTP, rather than geological isolation due to orogenesis events. Subsequently, climate oscillations during the Quaternary resulted in a dynamic distribution range for this species as well as the distribution pattern of its plastid haplotypes and nuclear genotypes. The interglacial periods may have had a greater effect on A. tanguticus than the glacial periods. Most importantly, neither genetic data nor SDM alone can fully reveal the climate refugia history of this species. We also discuss the conservation implications for this important Tibetan folk medicine plant in light of these findings and SDMs under future climate models. Together, our results underline the necessity to combine phylogeographic and SDM approaches in future investigations of the Quaternary evolutionary history of species in topographically complex areas, such as the QTP.