Effects of sample size,number of markers,and allelic richness on the detection of spatial genetic pattern

The influence of study design on the ability to detect the effects of landscape pattern on gene flow is one of the most pressing methodological gaps in landscape genetic research. To investigate the effect of study design on landscape genetics inference, we used a spatially‐explicit, individual‐based program to simulate gene flow in a spatially continuous population inhabiting a landscape with gradual spatial changes in resistance to movement. We simulated a wide range of combinations of number of loci, number of alleles per locus and number of individuals sampled from the population. We assessed how these three aspects of study design influenced the statistical power to successfully identify the generating process among competing hypotheses of isolation‐by‐distance, isolation‐by‐barrier, and isolation‐by‐landscape resistance using a causal modelling approach with partial Mantel tests. We modelled the statistical power to identify the generating process as a response surface for equilibrium and non‐equilibrium conditions after introduction of isolation‐by‐landscape resistance. All three variables (loci, alleles and sampled individuals) affect the power of causal modelling, but to different degrees. Stronger partial Mantel r correlations between landscape distances and genetic distances were found when more loci were used and when loci were more variable, which makes comparisons of effect size between studies difficult. Number of individuals did not affect the accuracy through mean equilibrium partial Mantel r, but larger samples decreased the uncertainty (increasing the precision) of equilibrium partial Mantel r estimates. We conclude that amplifying more (and more variable) loci is likely to increase the power of landscape genetic inferences more than increasing number of individuals.     

Satellite Telemetry in Avian Research and Management: Sample Size Considerations

Abstract: Satellite tracking is currently used to make inferences to avian populations. Cost of transmitters and logistical challenges of working with some species can limit sample size and strength of inferences. Therefore, careful study design including consideration of sample size is important. We used simulations to examine how sample size, population size, and population variance affected probability of making reliable inferences from a sample and the precision of estimates of population parameters. For populations of >100 individuals, a sample >20 birds was needed to make reliable inferences about questions with simple outcomes (i.e., 2 possible outcomes). Sample size demands increased rapidly for more complex problems. For example, in a problem with 3 outcomes, a sample of >75 individuals will be needed for proper inference to the population. Combining data from satellite telemetry studies with data from surveys or other types of sampling may improve inference strength.     

Genetics of recent habitat contraction and reduction in population size: does isolation by distance matter?

Fragmentation and loss of natural habitats are recognized as major threats to contemporary flora and fauna. Detecting past or current reductions in population size is therefore a major aim in conservation genetics. Statistical methods developed to this purpose have tended to ignore the effects of spatial population structure. However in many species, individual dispersal is restricted in space and fine-scale spatial structure such as isolation by distance (IBD) is commonly observed in continuous populations. Using a simulation-based approach, we investigated how comparative and single-point methods, traditionally used in a Wright-Fisher (WF) population context for detecting population size reduction, behave for IBD populations. We found that a complex 'quartet' of factors was acting that includes restricted dispersal, population size (i.e. habitat size), demographic history, and sampling scale. After habitat reduction, IBD populations were characterized by a stronger inertia in the loss of genetic diversity than WF populations. This inertia increases with the strength of IBD, and decreases when the sampling scale increases. Depending on the method used to detect a population size reduction, a local sampling can be more informative than a sample scaled to habitat size or vice versa. However, IBD structure led in numerous cases to incorrect inferences on population demographic history. The reanalysis of a real microsatellite data set of skink populations from fragmented and intact rainforest habitats confirmed most of our simulation results.     

The influence of landscape configuration and environment on population genetic structure in a sedentary passerine: insights from loci located in different genomic regions

The study of the factors structuring genetic variation can help to infer the neutral and adaptive processes shaping the demographic and evolutionary trajectories of natural populations. Here, we analyse the role of isolation by distance (IBD), isolation by resistance (IBR, defined by landscape composition) and isolation by environment (IBE, estimated as habitat and elevation dissimilarity) in structuring genetic variation in 25 blue tit (Cyanistes caeruleus) populations. We typed 1385 individuals at 26 microsatellite loci classified into two groups by considering whether they are located into genomic regions that are actively (TL; 12 loci) or not (NTL; 14 loci) transcribed to RNA. Population genetic differentiation was mostly detected using the panel of NTL. Landscape genetic analyses showed a pattern of IBD for all loci and the panel of NTL, but genetic differentiation estimated at TL was only explained by IBR models considering high resistance for natural vegetation and low resistance for agricultural lands. Finally, the absence for IBE suggests a lack of divergent selection pressures associated with differences in habitat and elevation. Overall, our study shows that markers located in different genomic regions can yield contrasting inferences on landscape‐level patterns of realized gene flow in natural populations.     

Landscape genetic inferences vary with sampling scenario for a pond‐breeding amphibian

A critical decision in landscape genetic studies is whether to use individuals or populations as the sampling unit. This decision affects the time and cost of sampling and may affect ecological inference. We analyzed 334 Columbia spotted frogs at 8 microsatellite loci across 40 sites in northern Idaho to determine how inferences from landscape genetic analyses would vary with sampling design. At all sites, we compared a proportion available sampling scheme (PASS), in which all samples were used, to resampled datasets of 2–11 individuals. Additionally, we compared a population sampling scheme (PSS) to an individual sampling scheme (ISS) at 18 sites with sufficient sample size. We applied an information theoretic approach with both restricted maximum likelihood and maximum likelihood estimation to evaluate competing landscape resistance hypotheses. We found that PSS supported low‐density forest when restricted maximum likelihood was used, but a combination model of most variables when maximum likelihood was used. We also saw variations when AIC was used compared to BIC. ISS supported this model as well as additional models when testing hypotheses of land cover types that create the greatest resistance to gene flow for Columbia spotted frogs. Increased sampling density and study extent, seen by comparing PSS to PASS, showed a change in model support. As number of individuals increased, model support converged at 7–9 individuals for ISS to PSS. ISS may be useful to increase study extent and sampling density, but may lack power to provide strong support for the correct model with microsatellite datasets. Our results highlight the importance of additional research on sampling design effects on landscape genetics inference.     

The computer program structure for assigning individuals to populations: easy to use but easier to misuse

The computer program Structure implements a Bayesian method, based on a population genetics model, to assign individuals to their source populations using genetic marker data. It is widely applied in the fields of ecology, evolutionary biology, human genetics and conservation biology for detecting hidden genetic structures, inferring the most likely number of populations (K), assigning individuals to source populations and estimating admixture and migration rates. Recently, several simulation studies repeatedly concluded that the program yields erroneous inferences when samples from different populations are highly unbalanced in size. Analysing both simulated and empirical data sets, this study confirms that Structure indeed yields poor individual assignments to source populations and gives frequently incorrect estimates of K when sampling is unbalanced. However, this poor performance is mainly caused by the adoption of the default ancestry prior, which assumes all source populations contribute equally to the pooled sample of individuals. When the alternative ancestry prior, which allows for unequal representations of the source populations by the sample, is adopted, accurate individual assignments could be obtained even if sampling is highly unbalanced. The alternative prior also improves the inference of K by two estimators, albeit the improvement is not as much as that in individual assignments to populations. For the difficult case of many populations and unbalanced sampling, a rarely used parameter combination of the alternative ancestry prior, an initial ALPHA value much smaller than the default and the uncorrelated allele frequency model is required for Structure to yield accurate inferences. I conclude that Structure is easy to use but is easier to misuse because of its complicated genetic model and many parameter (prior) options which may not be obvious to choose, and suggest using multiple plausible models (parameters) and K estimators in conducting comparative and exploratory Structure analysis.     

NONSTATIONARY PATTERNS OF ISOLATION‐BY‐DISTANCE: INFERRING MEASURES OF LOCAL GENETIC DIFFERENTIATION WITH BAYESIAN KRIGING

Patterns of isolation‐by‐distance (IBD) arise when population differentiation increases with increasing geographic distances. Patterns of IBD are usually caused by local spatial dispersal, which explains why differences of allele frequencies between populations accumulate with distance. However, spatial variations of demographic parameters such as migration rate or population density can generate nonstationary patterns of IBD where the rate at which genetic differentiation accumulates varies across space. To characterize nonstationary patterns of IBD, we infer local genetic differentiation based on Bayesian kriging. Local genetic differentiation for a sampled population is defined as the average genetic differentiation between the sampled population and fictive neighboring populations. To avoid defining populations in advance, the method can also be applied at the scale of individuals making it relevant for landscape genetics. Inference of local genetic differentiation relies on a matrix of pairwise similarity or dissimilarity between populations or individuals such as matrices of between pairs of populations. Simulation studies show that maps of local genetic differentiation can reveal barriers to gene flow but also other patterns such as continuous variations of gene flow across habitat. The potential of the method is illustrated with two datasets: single nucleotide polymorphisms from human Swedish populations and dominant markers for alpine plant species.     

Hierarchical genetic structure of native masu salmon populations in Hokkaido,Japan

Identification of the spatial extent of genetic structuring that may be influenced by evolutionary, ecological and historical factors is critical for effective conservation or management strategies. Masu salmon Oncorhynchus masou is commonly distributed in Far East, however, many local populations have been under threats of decline due to habitat destruction, overexploitation, and genetic introgression. To reveal the spatial genetic structure of native masu salmon populations in Hokkaido, masu salmon samples were collected from 16 rivers in which there was no official record of artificial releases of any masu salmon stock and were analyzed using 15 microsatellite loci. A Bayesian assignment test revealed that masu salmon populations were divided into two genetically distinct groups: the northeastern and southwestern groups. For within-group genetic structure, all populations, except for geographically proximate populations, were significantly different from each other. AMOVA revealed that genetic variation at among-group level based on groups identified assignment test was greater than that of groups based on geographic locations. There was no significant IBD for the 16 populations. However, the Mantel test revealed significant IBD for the northeastern group, but did not for the southwestern group. This study suggested that native masu salmon populations in Hokkaido exhibit a hierarchical genetic structure that is largely a result of their precise homing behavior. The results of this study also highlight the importance of defining populations by using genetic data rather than by using predefined populations based on geographic locations for the correct determination of genetic structure.     

spagedi: a versatile computer program to analyse spatial genetic structure at the individual or population levels

spag e d i version 1.0 is a software primarily designed to characterize the spatial genetic structure of mapped individuals or populations using genotype data of codominant markers. It computes various statistics describing genetic relatedness or differentiation between individuals or populations by pairwise comparisons and tests their significance by appropriate numerical resampling. spag e d i is useful for: (i) detecting isolation by distance within or among populations and estimating gene dispersal parameters; (ii) assessing genetic relatedness between individuals and its actual variance, a parameter of interest for marker based inferences of quantitative inheritance; (iii) assessing genetic differentiation among populations, including the case of haploids or autopolyploids.     

Variance of Neutral Genetic Variances within and between Populations for a Quantitative Character

The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.     

Inference of hazel grouse population structure using multilocus data: a landscape genetic approach

In conservation and management of species it is important to make inferences about gene flow, dispersal and population structure. In this study, we used 613 georeferenced tissue samples from hazel grouse (Bonasa bonasia) where each individual was genotyped at 12 microsatellite loci to make inference on population genetic structure, gene flow and dispersal in northern Sweden. Observed levels of genetic diversity suggest that Swedish hazel grouse do not suffer loss of genetic diversity compared with other grouse species. We found significant F(IS) (deviation from Hardy-Weinberg expectations) over the entire sample using jack-knifed estimators over loci, which is most likely explained by a Wahlund effect. With the use of spatial autocorrelation methods, we detected significant isolation by distance among individuals. Neighbourhood size was estimated in the order of 62-158 individuals corresponding to a dispersal distance of 950-1500 m. Using a spatial statistical model for landscape genetics to infer the number of populations and the spatial location of genetic discontinuities between these populations we found indications that Swedish hazel grouse are divided into a northern and a southern population. We could not find a sharp border between these two populations and none of the observed borders appeared to coincide with any potential geographical barriers.These results imply that gene flow appears somewhat unrestricted in the boreal taiga forests of northern Sweden and that the two populations of hazel grouse in Sweden may be explained by the post-glacial reinvasion history of the Scandinavian Peninsula.     

Extending phylogeography to account for lineage fusion

Secondary contact between long isolated populations has several possible outcomes. These include the strengthening of preexisting reproductive isolating mechanisms via reinforcement, the emergence of a hybrid lineage that is distinct from its extant parental lineages and which occupies a spatially restricted zone between them, or complete merging of two populations such that parental lineages are no longer extant (“lineage fusion” herein). The latter scenario has rarely been explicitly considered in single‐species and comparative phylogeographic studies, yet it has the potential to impact inferences about population history and levels of congruence. In this paper, we explore the idea that insights into past lineage fusion may now be possible, owing to the advent of next‐generation sequencing. Using simulated DNA sequence haplotype datasets (i.e., loci with alleles comprised of a set of linked nucleotide polymorphisms), we examined basic requirements (number of loci and individuals sampled) for identifying cases when a present‐day panmictic population is the product of lineage fusion, using an exemplar statistical framework—approximate Bayesian computation. We found that with approximately 100 phased haplotype loci (each 400 bp long) and modest sample sizes of individuals (10 per population), lineage fusion can be detected under rather challenging scenarios. This included some scenarios where reticulation was fully contained within a Last Glacial Maximum timeframe, provided that mixing was symmetrical, ancestral gene pools were moderately to deeply diverged, and the lag time between the fusion event and gene pool sampling was relatively short. However, the more realistic case of asymmetrical mixing is not prohibitive if additional genetic data (e.g., 400 loci) are available. Notwithstanding some simplifying assumptions of our simulations and the knowledge gaps that remain about the circumstances under which lineage fusion is potentially detectable, we suggest that the recent release from data limitation allows phylogeographers to expand the scope of inferences about long‐term population history.     

Pedigree reconstruction in wild cichlid fish populations

It is common practice to use microsatellites to detect parents and their offspring in wild and captive populations, in order to reconstruct a pedigree. However, correct inference is often constrained by a number of factors, including the absence of demographic data and ignorance regarding the completeness of parental sampling. Here we present a new Bayesian estimator that simultaneously estimates the pedigree and the size of the unsampled population. The method is robust to genotyping error, and can estimate pedigrees in the absence of demographic data. Using a large-scale microsatellite assay in four wild cichlid fish populations of Lake Tanganyika (1000 individuals in total), we assess the performance of the Bayesian estimator against the most popular assignment program, Cervus. We found small but significant pedigrees in each of the tested populations using the Bayesian procedure, but Cervus had very high type I error rates when the size of the unsampled population was assumed to be lower than what it was. The need of pedigree relationships to infer adaptive processes in natural populations places strong constraints on sampling design and identification of multigenerational pedigrees in natural populations.     

Estimation of population parameters and recombination rates from single nucleotide polymorphisms

Some general likelihood and Bayesian methods for analyzing single nucleotide polymorphisms (SNPs) are presented. First, an efficient method for estimating demographic parameters from SNPs in linkage equilibrium is derived. The method is applied in the estimation of growth rates of a human population based on 37 SNP loci. It is demonstrated how ascertainment biases, due to biased sampling of loci, can be avoided, at least in some cases, by appropriate conditioning when calculating the likelihood function. Second, a Markov chain Monte Carlo (MCMC) method for analyzing linked SNPs is developed. This method can be used for Bayesian and likelihood inference on linked SNPs. The utility of the method is illustrated by estimating recombination rates in a human data set containing 17 SNPs and 60 individuals. Both methods are based on assumptions of low mutation rates.     

TESTING INFERENCES ABOUT MICRO-EVOLUTIONARY PROCESSES BY MEANS OF SPATIAL AUTOCORRELATION ANALYSIS

We generated numerous simulated gene-frequency surfaces subjected to 200 generations of isolation by distance with, in some cases, added migration or selection. From these surfaces we assembled six data sets comprising from 12 to 15 independent allele-frequency surfaces, to simulate biologically plausible population samples. The purpose of the study was to investigate whether spatial autocorrelation analysis will correctly infer the microevolutionary processes involved in each data set. The correspondence between the simulated processes and the inferences made concerning them is close for five of the six data sets. Errors in inference occurred when the effect of migration was weak, due to low gene frequency differential or low migration strength; when selection was weak and against a background with a complex pattern; and when a random process—isolation by distance—was the only one acting. Spatial correlograms proved more sensitive to detecting trends than inspection of gene-frequency surfaces by the human eye. Joint interpretation of the correlograms and their clusters proved most reliable in leading to the correct inference. The inspection and clustering of surfaces were useful for determining directional components. Because this method relies on common patterns across loci, as many gene frequencies as feasible should be used. We recommend spatial autocorrelation analysis for the detection of microevolutionary processes in natural populations.     

How do SNP ascertainment schemes and population demographics affect inferences about population history?

Background

The selection of variable sites for inclusion in genomic analyses can influence results, especially when exemplar populations are used to determine polymorphic sites. We tested the impact of ascertainment bias on the inference of population genetic parameters using empirical and simulated data representing the three major continental groups of cattle: European, African, and Indian. We simulated data under three demographic models. Each simulated data set was subjected to three ascertainment schemes: (I) random selection; (II) geographically biased selection; and (III) selection biased toward loci polymorphic in multiple groups. Empirical data comprised samples of 25 individuals representing each continental group. These cattle were genotyped for 47,506 loci from the bovine 50 K SNP panel. We compared the inference of population histories for the empirical and simulated data sets across different ascertainment conditions using F_ST and principal components analysis (PCA).

Results

Bias toward shared polymorphism across continental groups is apparent in the empirical SNP data. Bias toward uneven levels of within-group polymorphism decreases estimates of F_ST between groups. Subpopulation-biased selection of SNPs changes the weighting of principal component axes and can affect inferences about proportions of admixture and population histories using PCA. PCA-based inferences of population relationships are largely congruent across types of ascertainment bias, even when ascertainment bias is strong.

Conclusions

Analyses of ascertainment bias in genomic data have largely been conducted on human data. As genomic analyses are being applied to non-model organisms, and across taxa with deeper divergences, care must be taken to consider the potential for bias in ascertainment of variation to affect inferences. Estimates of F_ST, time of separation, and population divergence as estimated by principal components analysis can be misleading if this bias is not taken into account.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1469-5) contains supplementary material, which is available to authorized users.     

Inference of population structure under a Dirichlet process model

Inferring population structure from genetic data sampled from some number of individuals is a formidable statistical problem. One widely used approach considers the number of populations to be fixed and calculates the posterior probability of assigning individuals to each population. More recently, the assignment of individuals to populations and the number of populations have both been considered random variables that follow a Dirichlet process prior. We examined the statistical behavior of assignment of individuals to populations under a Dirichlet process prior. First, we examined a best-case scenario, in which all of the assumptions of the Dirichlet process prior were satisfied, by generating data under a Dirichlet process prior. Second, we examined the performance of the method when the genetic data were generated under a population genetics model with symmetric migration between populations. We examined the accuracy of population assignment using a distance on partitions. The method can be quite accurate with a moderate number of loci. As expected, inferences on the number of populations are more accurate when theta = 4N(e)u is large and when the migration rate (4N(e)m) is low. We also examined the sensitivity of inferences of population structure to choice of the parameter of the Dirichlet process model. Although inferences could be sensitive to the choice of the prior on the number of populations, this sensitivity occurred when the number of loci sampled was small; inferences are more robust to the prior on the number of populations when the number of sampled loci is large. Finally, we discuss several methods for summarizing the results of a Bayesian Markov chain Monte Carlo (MCMC) analysis of population structure. We develop the notion of the mean population partition, which is the partition of individuals to populations that minimizes the squared partition distance to the partitions sampled by the MCMC algorithm.     

The trouble with isolation by distance

The genetic population structure of many species is characterised by a pattern of isolation by distance (IBD): due to limited dispersal, individuals that are geographically close tend to be genetically more similar than individuals that are far apart. Despite the ubiquity of IBD in nature, many commonly used statistical tests are based on a null model that is completely non-spatial, the Island model. Here, I argue that patterns of spatial autocorrelation deriving from IBD present a problem for such tests as it can severely bias their outcome. I use simulated data to illustrate this problem for two widely used types of tests: tests of hierarchical population structure and the detection of loci under selection. My results show that for both types of tests the presence of IBD can indeed lead to a large number of false positives. I therefore argue that all analyses in a study should take the spatial dependence in the data into account, unless it can be shown that there is no spatial autocorrelation in the allele frequency distribution that is under investigation. Thus, it is urgent to develop additional statistical approaches that are based on a spatially explicit null model instead of the non-spatial Island model.     

Challenges and regulatory experiences with non‐inferiority trial design without placebo arm

For a non‐inferiority trial without a placebo arm, the direct comparison between the test treatment and the selected positive control is in principle the only basis for statistical inference. Therefore, evaluating the test treatment relative to the non‐existent placebo presents extreme challenges and requires some kind of bridging from the past to the present with no current placebo data. For such inference based partly on an indirect bridging manipulation, fixed margin method and synthesis method are the two widely discussed methods in the recent literature. There are major differences in statistical inference paradigm between the two methods. The fixed margin method employs the historical data that assess the performances of the active control versus a placebo to guide the selection of the non‐inferiority margin. Such guidance is not part of the ultimate statistical inference in the non‐inferiority trial. In contrast, the synthesis method connects the historical data to the non‐inferiority trial data for making broader inferences relating the test treatment to the non‐existent current placebo. On the other hand, the type I error rate associated with the direct comparison between the test treatment and the active control cannot shed any light on the appropriateness of the indirect inference for faring the test treatment against the non‐existent placebo. This work explores an approach for assessing the impact of potential bias due to violation of a key statistical assumption to guide determination of the non‐inferiority margin.     

Primates and Cameras

Field-based primate studies often make population inferences using count-based indices (e.g., individuals/plot) or distance sampling; the first does not account for the probability of detection and thus can be biased, while the second requires large sample sizes to obtain precise estimates, which is difficult for many primate studies. We discuss photographic sampling and occupancy modeling to correct for imperfect detection when estimating system states and dynamics at the landscape level, specifically in relation to primate ecology. We highlight the flexibility of the occupancy framework and its many applications to studying low-density primate populations or species that are difficult to detect. We discuss relevant sampling and estimation procedures with special attention to data collection via photographic sampling. To provide tangible meaning to terminology and clarify subtleties, we use illustrative examples. Photographic sampling can have many advantages over observer-based sampling, especially when studying rare or elusive species. Combining photographic sampling with an occupancy framework allows inference to larger scales than is common in primate studies, addresses uncertainty due to the observation process, and allows researchers to examine questions of how landscape-level anthropogenic changes affect primate distributions.