Modeling species dispersal with occupancy urn models

Models for species dispersal make various simplifications to facilitate analysis, such as ignoring spatial correlations or assuming equal probability of colonization among all sites within a dispersal neighborhood. Here we introduce a variation of the basic contact process (BCP) which allows us to separate the number of offspring produced from the neighborhood size, which are confounded in the original BCP. We then use classical results arising from probability models involving placing balls in urns to study our modified BCP, obtaining bounds for the critical value of the survival probability needed for the population to persist. We also use the probability urn calculations with a local-dispersal mean-field approximation to estimate equilibrium population density. These methods are able to include features such as unequal dispersal probabilities to different sites in the neighborhood, e.g., as would arise when dispersers have a fixed rate of mortality per distance traveled from the parent site. We also show how urn models allow one to generalize these results to two species competing for space.     

Within-species variation and measurement error in phylogenetic comparative methods

Most phylogenetically based statistical methods for the analysis of quantitative or continuously varying phenotypic traits assume that variation within species is absent or at least negligible, which is unrealistic for many traits. Within-species variation has several components. Differences among populations of the same species may represent either phylogenetic divergence or direct effects of environmental factors that differ among populations (phenotypic plasticity). Within-population variation also contributes to within-species variation and includes sampling variation, instrument-related error, low repeatability caused by fluctuations in behavioral or physiological state, variation related to age, sex, season, or time of day, and individual variation within such categories. Here we develop techniques for analyzing phylogenetically correlated data to include within-species variation, or "measurement error" as it is often termed in the statistical literature. We derive methods for (i) univariate analyses, including measurement of "phylogenetic signal," (ii) correlation and principal components analysis for multiple traits, (iii) multiple regression, and (iv) inference of "functional relations," such as reduced major axis (RMA) regression. The methods are capable of incorporating measurement error that differs for each data point (mean value for a species or population), but they can be modified for special cases in which less is known about measurement error (e.g., when one is willing to assume something about the ratio of measurement error in two traits). We show that failure to incorporate measurement error can lead to both biased and imprecise (unduly uncertain) parameter estimates. Even previous methods that are thought to account for measurement error, such as conventional RMA regression, can be improved by explicitly incorporating measurement error and phylogenetic correlation. We illustrate these methods with examples and simulations and provide Matlab programs.     

The effects of local spatial structure on epidemiological invasions.

Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade and persist in the short-term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlations between individuals, we are able to understand the role of spatial heterogeneity in invasion dynamics without the need for large-scale computer simulations. Here, a natural methodology is developed for modelling the behaviour of individuals in a fixed network. This formulation is applied to the spread of a disease through a structured network to determine invasion thresholds and some statistical properties of a single epidemic.     

Population Dynamics of the Endangered, Long-Lived Perennial Species, Ligularia sibirica

Ligularia sibirica is a relict wetland perennial plant species of the Czech and Slovak Republic. Explaining variation in population growth rate and identifying the causes of that variation is important for effective protection of such an endangered species. Matrix models based on four years of data of 11 populations were used to identify the pattern of variation in the demographic vital rates of this species, and to examine the causes of the variation such as population size and habitat type. Further, the matrix model was used to determine the population growth rate, longevity and risk of extinction of each population and to identify the specific vital rates that most affect population growth rate. The results showed that population growth rates were significantly different between years and populations. Temporal variation was mostly due to variable survival of adult individuals, while spatial variation was mainly driven by fertility of one small currently expanding population. Further, most studied populations of L. sibirica are performing well and only those growing in nitrogen-rich habitats have a high extinction risk. The results also indicate that all populations have low adult mortality, long-lived individuals (61.3?years on average) and some populations also show features of remnant populations (i.e., the persistence of populations in severe conditions in spite of no reproduction). Our results imply that detailed demographic data are needed to understand the long-term prospects of these populations. These data may serve as an early warning system for this species long before an obvious decline occurs in the populations.     

The relationships between habitat suitability,population size and body condition in a pond-breeding amphibian

The ecological niche of a species determines whether a species can persist and reproduce in a patch or not. The niche of a species is often described using habitat suitability models and indices. Accordingly, one may expect tight links between demography, phenotypes of individuals, population size, and habitat suitability. However, such links are not always found. Here, we study the relationship between a habitat suitability index that is commonly used for conservation assessments and metrics describing the performance at the level of populations and individuals. Using data from a metapopulation of a pond-breeding amphibian, the Great Crested Newt (Triturus cristatus), we show that habitat suitability predicts population size but not body condition. Ponds with higher suitability had a higher population size of newts, whereas population size correlated negatively with body condition of individuals. Our results are in line with previous studies showing no straightforward relationship between habitat suitability and body condition (a measure of individual performance) and the performance of populations. We suggest that a population size-dependent reduction of body condition may be a regulatory mechanism in newt populations.     

Increased Extinction Potential of Insular Fish Populations with Reduced Life History Variation and Low Genetic Diversity

Theoretical work has shown that reduced phenotypic heterogeneity leads to population instability and can increase extinction potential, yet few examples exist of natural populations that illustrate how varying levels expressed diversity may influence population persistence, particularly during periods of stochastic environmental fluctuation. In this study, we assess levels of expressed variation and genetic diversity among demographically independent populations of tidewater goby (Eucyclogobius newberryi), show that reductions in both factors typically coincide, and describe how low levels of diversity contribute to the extinction risk of these isolated populations. We illustrate that, for this annual species, continuous reproduction is a safeguard against reproductive failure by any one population segment, as natural, stochastically driven salinity increases frequently result in high mortality among juvenile individuals. Several study populations deviated from the natural pattern of year-round reproduction typical for the species, rendering those with severely truncated reproductive periods vulnerable to extinction in the event of environmental fluctuation. In contrast, demographically diverse populations are more likely to persist through such periods through the continuous presence of adults with broader physiological tolerance to abrupt salinity changes. Notably, we found a significant correlation between genetic diversity and demographic variation in the study populations, which could be the result of population stressors that restrict both of these diversity measures simultaneously, or suggestive of a causative relationship between these population characteristics. These findings demonstrate the importance of biocomplexity at the population level, and assert that the maintenance of diversity contributes to population resilience and conservation of this endangered species.     

Density-structured models for plant population dynamics

Density-structured models are structured population models in which the state variable is the proportion of populations or sites in a small number of discrete density states. Although such models have rarely been used, they have the advantage that they are straightforward to parameterize, make few assumptions about population dynamics, and permit rapid data collection using coarse density assessment. In this article, we highlight their use in relating population dynamics to environmental variation and their robustness to measurement error. We show that density-structured models are able to accurately represent population dynamics under a wide range of conditions. We look at the effects of including a persistent seedbank and describe numerical approximations for the mean and variance of population size. For simulated data, we determine the extent to which the underlying continuous process may be inferred from density-structured data. Finally, we discuss issues of parameter estimation and applications for which these types of models may be useful.     

The effect of intraspecific sample size on type I and type II error rates in comparative studies

Comparative studies have increased greatly in number in recent years due to advances in statistical and phylogenetic methodologies. For these studies, a trade-off often exists between the number of species that can be included in any given study and the number of individuals examined per species. Here, we describe a simple simulation study examining the effect of intraspecific sample size on statistical error in comparative studies. We find that ignoring measurement error has no effect on type I error of nonphylogenetic analyses, but can lead to increased type I error under some circumstances when using independent contrasts. We suggest using ANOVA to evaluate the relative amounts of within- and between-species variation when considering a phylogenetic comparative study. If within-species variance is particularly large and intraspecific sample sizes small, then either larger sample sizes or comparative methods that account for measurement error are necessary.     

An agent-based modelling approach to estimate error in gyrodactylid population growth

Comparative studies of gyrodactylid monogeneans on different host species or strains rely upon the observation of growth on individual fish maintained within a common environment, summarised using maximum likelihood statistical approaches. Here we describe an agent-based model of gyrodactylid population growth, which we use to evaluate errors due to stochastic reproductive variation in such experimental studies. Parameters for the model use available fecundity and mortality data derived from previously published life tables of Gyrodactylus salaris, and use a new data set of fecundity and mortality statistics for this species on the Neva stock of Atlantic salmon, Salmo salar. Mortality data were analysed using a mark-recapture analysis software package, allowing maximum-likelihood estimation of daily survivorship and mortality. We consistently found that a constant age-specific mortality schedule was most appropriate for G. salaris in experimental datasets, with a daily survivorship of 0.84 at 13°C. This, however, gave unrealistically low population growth rates when used as parameters in the model, and a schedule of constantly increasing mortality was chosen as the best compromise for the model. The model also predicted a realistic age structure for the simulated populations, with 0.32 of the population not yet having given birth for the first time (pre-first birth). The model demonstrated that the population growth rate can be a useful parameter for comparing gyrodactylid populations when these are larger than 20-30 individuals, but that stochastic error rendered the parameter unusable in smaller populations. It also showed that the declining parasite population growth rate typically observed during the course of G. salaris infections cannot be explained through stochastic error and must therefore have a biological basis. Finally, the study showed that most gyrodactylid-host studies of this type are too small to detect subtle differences in local adaptation of gyrodactylid monogeneans between fish stocks.     

Microgeographic variation in Caiman latirostris

In theory, geographic scale is related to genetic variation at the population level, whereas microgeographic scale may reveal intra-population structure such as social groups and families. In the present work, both levels of genetic variation in the broad-snouted caiman (Caiman latirostris) were evaluated in small wetlands associated with the Piracicaba River and some of its tributaries in the state of S?o Paulo, Brazil. Genetic variation was determined using microsatellite DNA markers originally developed for the American alligator (Alligator mississipiensis) and previously tested in pedigreed captive broad-snouted caimans. Using these markers, we were able to detect variability among individuals from different sites, even those within a small geographic distance. Genetic results suggest that the groups sampled at each site are composed predominantly of related individuals. A possible combination of high mortality and low natality rates results in a low number of successfully dispersed individuals per generation. Future studies using a recently constructed Caiman latirostris microsatellite library (Zucoloto et al., 2002) might help us to understand metapopulation processes that may be occurring within this species.     

State-space models of individual animal movement

Detailed observation of the movement of individual animals offers the potential to understand spatial population processes as the ultimate consequence of individual behaviour, physiological constraints and fine-scale environmental influences. However, movement data from individuals are intrinsically stochastic and often subject to severe observation error. Linking such complex data to dynamical models of movement is a major challenge for animal ecology. Here, we review a statistical approach, state-space modelling, which involves changing how we analyse movement data and draw inferences about the behaviours that shape it. The statistical robustness and predictive ability of state-space models make them the most promising avenue towards a new type of movement ecology that fuses insights from the study of animal behaviour, biogeography and spatial population dynamics.     

Analysis of population genetic structure and variability using RAPD markers in the endemic and endangered Limonium dufourii (Plumbaginaceae)

Limonium dufourii (Plumbaginaceae) is a triploid species, with apomictic reproduction, endemic to the east mediterranean coast of Spain, where it is present in only six populations with a few individuals in most of them. L. dufourii is included in the Red List of Endangered Species by the IUCN. Genetic variation and population structure in this species has been studied using RAPDs. Twelve different primers provided 124 reliable bands of which 33 were polymorphic among the 165 individuals analysed. Those polymorphic bands were able to define 44 different patterns, of which all but six were present in only one population. Several methods for statistical evaluation have been used for intra- and interpopulation analysis of genetic variability. Relationships among patterns have led to the identification of four main clusters. Two of them show a perfect correspondence to the population of origin of those individuals that present them (Cullera and Torreblanca), and the other two (Groups A and B) include patterns found in individuals coexisting in the same populations (Marjal del Moro populations) and in El Saler. Most of the variation found in this species is due to differences among populations as shown by the analysis of molecular variance. This agrees with the expectation for an apomictic species such as L. dufourii . The analysis of homogeneity of variance shows that substantial differences in the amount of genetic variability present in the six populations exist. These results have been used to understand the evolutionary and demographic history of L. dufourii , which is a requisite in order to establish efficient conservation measures for this species.     

Relative contributions of fixed and dynamic heterogeneity to variation in lifetime reproductive success in kestrels (Falco tinnunculus)

Many species show large variation in lifetime reproductive success (LRS), with a few individuals producing the majority of offspring. This variation can be explained by factors related to individuals (fixed heterogeneity) and stochastic differences in survival and reproduction (dynamic heterogeneity). In this study, we study the relative effects of these processes on the LRS of a Dutch Kestrel population, using three different methods. First, we extended neutral simulations by simulating LRS distributions of populations consisting of groups with increasingly different population parameters. Decomposition of total LRS variance into contributions from fixed and dynamic heterogeneity revealed that the proportion of fixed heterogeneity is probably lower than 10% of the total variance. Secondly, we used sensitivities of the mean and variance in LRS to each parameter to analytically show that it is impossible to get equal contributions of fixed and dynamic heterogeneity when only one parameter differs between groups. Finally, we computed the LRS probability distribution to show that even when all individuals have identical survival and reproduction rates, the variance in LRS is large (females: 27.52, males: 12.99). Although each method has its limitations, they all lead to the conclusion that the majority of the variation in kestrel LRS is caused by dynamic heterogeneity. This large effect of dynamic heterogeneity on LRS is similar to results for other species and contributes to the evidence that in most species the majority of individual variation in LRS is due to dynamic heterogeneity.     

Are geometric morphometric analyses replicable? Evaluating landmark measurement error and its impact on extant and fossil Microtus classification

Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis‐based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining >30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis‐specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations.     

A New Metric of Inclusive Fitness Predicts the Human Mortality Profile

Biological species have evolved characteristic patterns of age-specific mortality across their life spans. If these mortality profiles are shaped by natural selection they should reflect underlying variation in the fitness effect of mortality with age. Direct fitness models, however, do not accurately predict the mortality profiles of many species. For several species, including humans, mortality rates vary considerably before and after reproductive ages, during life-stages when no variation in direct fitness is possible. Variation in mortality rates at these ages may reflect indirect effects of natural selection acting through kin. To test this possibility we developed a new two-variable measure of inclusive fitness, which we term the extended genomic output or EGO. Using EGO, we estimate the inclusive fitness effect of mortality at different ages in a small hunter-gatherer population with a typical human mortality profile. EGO in this population predicts 90% of the variation in age-specific mortality. This result represents the first empirical measurement of inclusive fitness of a trait in any species. It shows that the pattern of human survival can largely be explained by variation in the inclusive fitness cost of mortality at different ages. More generally, our approach can be used to estimate the inclusive fitness of any trait or genotype from population data on birth dates and relatedness.     

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature. Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.     

Adaption,neutrality and life-course diversity

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non-genetic and also non-environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non-genetic, non-environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life-course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non-genetic non-environmental variation.     

Dispersal and individual quality in a long lived species

The idea of differences in individual quality has been put forward in numerous long-term studies in long-lived species to explain differences in lifetime production among individuals. Despite the important role of individual heterogeneity in vital rates in demography, population dynamics and life history theory, the idea of "individual quality" is elusive. It is sometimes assumed to be a static or dynamic individual characteristic. When considered as a dynamic trait, it is sometimes assumed to vary deterministically or stochastically, or to be confounded with the characteristics of the habitat. We addressed heterogeneity in reproductive performance among individuals established in higher-quality habitat in a long-lived seabird species. We used approaches to statistical inference based on individual random effects permitting quantification of heterogeneity in populations and assessment of individual variation from the population mean. We found evidence of heterogeneity in breeding probability, not success probability. We assessed the influence of dispersal on individual reproductive potential. Dispersal is likely to be destabilizing in species with high site and mate fidelity. We detected heterogeneity after dispersal, not before. Individuals may perform well regardless of quality before destabilization, including those that recruited in higher-quality habitat by chance, but only higher-quality individuals may be able to overcome the consequences of dispersal. Importantly, results differed when accounting for individual heterogeneity (an increase in mean breeding probability when individuals dispersed), or not (a decrease in mean breeding probability). In the latter case, the decrease in mean breeding probability may result from a substantial decrease in breeding probability in a few individuals and a slight increase in others. In other words, the pattern observed at the population mean level may not reflect what happens in the majority of individuals.     

A computational approach to studying ageing at the individual level

The ageing process is actively regulated throughout an organism''s life, but studying the rate of ageing in individuals is difficult with conventional methods. Consequently, ageing studies typically make biological inference based on population mortality rates, which often do not accurately reflect the probabilities of death at the individual level. To study the relationship between individual and population mortality rates, we integrated in vivo switch experiments with in silico stochastic simulations to elucidate how carefully designed experiments allow key aspects of individual ageing to be deduced from group mortality measurements. As our case study, we used the recent report demonstrating that pheromones of the opposite sex decrease lifespan in Drosophila melanogaster by reversibly increasing population mortality rates. We showed that the population mortality reversal following pheromone removal was almost surely occurring in individuals, albeit more slowly than suggested by population measures. Furthermore, heterogeneity among individuals due to the inherent stochasticity of behavioural interactions skewed population mortality rates in middle-age away from the individual-level trajectories of which they are comprised. This article exemplifies how computational models function as important predictive tools for designing wet-laboratory experiments to use population mortality rates to understand how genetic and environmental manipulations affect ageing in the individual.     

Learned social preference in zebrafish

How social aggregations arise and persist is central to our understanding of evolution, behavior, and psychology. When social groups arise within a species, evolutionary divergence and speciation can result. To understand this diversifying role of social behavior, we must examine the internal and external influences that lead to nonrandom assortment of phenotypes. Many fishes form aggregations called shoals that reduce predation risk while enhancing foraging and reproductive success. Thus, shoaling is adaptive, and signals that maintain shoals are likely to evolve under selection. Given the diversity of pigment patterns among Danio fishes, visual signals might be especially important in mediating social behaviors in this group. Our understanding of pigment pattern development in the zebrafish D. rerio allows integrative analyses of how molecular variation leads to morphological variation among individuals and how morphological variation influences social interactions. Here, we use the zebrafish pigment mutant nacre/mitfa to test roles for genetic and environmental determinants in the development of shoaling preference. We demonstrate that individuals discriminate between shoals having different pigment pattern phenotypes and that early experience determines shoaling preference. These results suggest a role for social learning in pigment pattern diversification in danios.