Multilocus estimation of genetic structure within populations

Spatial structure of genetic variation within populations is well measured by statistics based on the distribution of pairs of individual genotypes, and various such statistics have been widely used in experimental studies. However, the problem of uncharacterized correlations among statistics for different alleles has limited the applications of multiallelic, multilocus summary measures, since these had unknown sampling distributions. Usually multiple alleles and/or multiple loci are required in order to precisely measure spatial structures, and to provide precise indirect estimates of the amount of dispersal in samples of reasonable size. This article examines the correlations among pair-wise statistics, including Moran I-statistics and various measures of conditional kinship, for different alleles of a locus. First the correlations are mathematically derived for random spatial distributions, which allow averages over alleles and loci to be used as more powerful yet exact test statistics for the null hypothesis. Then extensive computer simulations are conducted to examine the correlations among values for different alleles under isolation by distance processes. For loci with more than three alleles, the results show that the correlations are remarkably and perhaps surprisingly small, establishing the principle that then alleles behave as nearly independent realizations of space-time stochastic processes. The results also show that the correlations are largely robust with respect to the degree of spatial structure, and they can be used in a straightforward manner to form confidence intervals for averages. The results allow a precise connection between observations in experimental studies and levels of dispersal in theoretical models.     

Effect of sampling strategy on estimation of fine-scale spatial genetic structure in Androsace tapete (Primulaceae), an alpine plant endemic to Qinghai-Tibetan Plateau

The fine-scale spatial genetic structure (SGS) of alpine plants is receiving increasing attention, from which seed and pollen dispersal can be inferred. However, estimation of SGS may depend strongly on the sampling strategy,including the sample size and spatial sampling scheme. Here, we examined the effects of sample size and three spatial schemes, simple-random, line-transect, and random-cluster sampling, on the estimation of SGS in Androsace tapete, an alpine cushion plant endemic to Qinghai-Tibetan Plateau. Using both real data and simulated data of dominant molecular markers, we show that: (i) SGS is highly sensitive to sample strategy especially when the sample size is small (e.g., below 100); (ii) the commonly used SGS parameter (the intercept of the autocorrelogram) is more susceptible to sample error than a newly developed Sp statistic; and (iii) the random-cluster scheme is susceptible to obvious bias in parameter estimation even when the sample size is relatively large (e.g., above 200). Overall,the line-transect scheme is recommendable, in that it performs slightly better than the simple-random scheme in parameter estimation and is more efficient to encompass broad spatial scales. The consistency between simulated data and real data implies that these findings might hold true in other alpine plants and more species should be examined in future work.     

Sampling strategy for wild soybean (Glycine soja) populations based on their genetic diversity and fine-scale spatial genetic structure

A total of 892 individuals sampled from a wild soybean population in a natural reserve near the Yellow River estuary located in Kenli of Shandong Province (China) were investigated.Seventeen SSR (simple sequence repeat) primer pairs from cultivated soybeans were used to estimate the genetic diversity of the population and its variation pattern versus changes of the sample size (sub-samples),in addition to investigating the fine-scale spatial genetic structure within the population.The results showed relatively high genetic diversity of the population with the mean value of allele number (A) being 2.88,expected heterozygosity (He) 0.431,Shannon diversity index (/) 0.699,and percentage of polymorphic loci (P) 100%.Sub-samples of different sizes (ten groups) were randomly drawn from the population and their genetic diversity was calculated by computer simulation.The regression model of the four diversity indexes with the change of sample sizes was computed.As a result,27-52 individuals can reach 95% of total genetic variability of the population.Spatial autocorrelation analysis revealed that the genetic patch size of this wild soybean population is about 18 m.The study provided a scientific basis for the sampling strategy of wild soybean populations.     

Sampling strategy for wild soybean ( Glycine soja ) populations based on their genetic diversity and fine-scale spatial genetic structure

A total of 892 individuals sampled from a wild soybean population in a natural reserve near the Yellow River estuary located in Kenli of Shandong Province (China) were investigated. Seventeen SSR (simple sequence repeat) primer pairs from cultivated soybeans were used to estimate the genetic diversity of the population and its variation pattern versus changes of the sample size (sub-samples), in addition to investigating the fine-scale spatial genetic structure within the population. The results showed relatively high genetic diversity of the population with the mean value of allele number (A) being 2.88, expected heterozygosity (He) 0.431, Shannon diversity index (I) 0.699, and percentage of polymorphic loci (P) 100%. Sub-samples of different sizes (ten groups) were randomly drawn from the population and their genetic diversity was calculated by computer simulation. The regression model of the four diversity indexes with the change of sample sizes was computed. As a result, 27–52 individuals can reach 95% of total genetic variability of the population. Spatial autocorrelation analysis revealed that the genetic patch size of this wild soybean population is about 18 m. The study provided a scientific basis for the sampling strategy of wild soybean populations. __________ Translated from Journal of Fudan University (Natural Science), 2006, 45(3): 322–327 [译自: 复旦学报 (自然科学版)]     

Demographic spatial genetic structure of the Neotropical tree, Jacaranda copaia

We used genotypes from six microsatellite loci and demographic data from a large mapped forest plot to study changes in spatial genetic structure across demographic stages, from seed rain to seedlings, juveniles, and adult diameter classes in the Neotropical tree, Jacaranda copaia. In pairwise comparisons of genetic differentiation among demographic classes, only seedlings were significantly differentiated from the other diameter classes; F(ST) values ranged from 0.006 to 0.009. Furthermore, only seedlings showed homozygote excess suggesting biparental inbreeding in the large diameter reproductive adults. We found very low levels of relatedness in the first distance class of trees, 1-26 cm diameter (F(ij) = 0.011). However, there was a 5- to 10-fold rise in relatedness in the smallest distance class, from the smallest to the largest tree diameter classes (F(ij) = 0.110 for individuals > 56 cm diameter). A variety of non-mutually exclusive mechanisms have been invoked perviously to explain such a pattern, including natural selection, history, or nonequilibrium population dynamics. The long-term demographic data available for this species allow us to evaluate these mechanisms. Jacaranda is a fast-growing, light-demanding species with low recruitment rates and high mortality rates in the smaller diameter classes. It successfully regenerates only in large light gaps, which occur infrequently and stochastically in space and time. These factors contribute to the nonequilibrium population dynamics and observed low genetic structure in the small size classes. We conclude that the pattern of spatial genetic transitions in Jacaranda is consistent with overlapping related generations and strong but infrequent periods of high recruitment, followed by long periods of population decline.     

Optimal death strategy of animal populations

Using Pontryagin's maximum principle, the optimal death strategy that maximizes the total reproduction of a population, which has the density dependent growth rate and the weight dependent reproduction, is investigated. As the result, it is shown that the optimal survival curve has a critical age, before which the mortality takes the highest admissible value and after which the lowest. In a population with this optimal death strategy, the change of resource level affects the length of the stage of high mortality. The switching age is explicitly calculated in a special case with a simple growth rate function and a simple weight dependence of reproduction. The average value of mortality or growth coefficient through the prereproductive stages are calculated and compared with the Le Cren's data, where trout was reared in varying resource levels.     

Regional and local spatial genetic structure of Siberian primrose populations in Northern Europe

We have investigated the local and regional scale genetic structure of Siberian primrose (Primula nutans) populations in Northern Europe. The genetic diversity and structure of fifteen populations sampled from the Bothnian Bay in Finland, the Barents Sea in Norway and the White Sea in Russia were assessed using eleven microsatellite markers. We investigated the distribution of genetic variation within and between populations, and studied the local genetic structure using spatial autocorrelation analysis. We found very low genetic and allelic diversity in the Bothnian Bay and Barents Sea populations, and only slightly higher in the White Sea population. The level of genetic differentiation between the regions was very high, whereas differentiation between the populations within the regions was moderate. We found no spatial structuring of populations in any region suggesting efficient dispersal on a local scale. Clonal reproduction seemed to have no effect on genetic structure.     

Fine-scale spatial genetic structure within continuous and fragmented populations of Trillium camschatcense

Spatial genetic structure (SGS) within populations was analyzed for the ling-lived understory perennial herb Trillium camschatcense using allozyme loci. We used Sp statistics to compare SGS between 2 life-history stages, juveniles (J) and reproductives (R), as well as between 2 populations, continuous and fragmented, with different habitat conditions. In the continuous population, significant SGS was detected in both stages but the extent was greatly reduced with the progress of the stage (J, Sp = 0.0475; R, Sp = 0.0053). We inferred that limited seed dispersal and subsequent random loss of individuals from the family patches are responsible for the J and R stage structures, respectively. The fragmented population differed in the patterns of SGS; significant structure was detected in the R stage, but not in the J stage (J, Sp = 0.0021; R, Sp = 0.0165) despite significant positive inbreeding coefficients (J, F(IS) = 0.251). The observed differences in the J-stage structures between populations may be explained by habitat fragmentation effects because reduced recruitment in the fragmented population prevents the development of maternal sibling cohort. Such comparative analysis between populations and life-history stages can be useful to understand the different underlying causes of SGS.     

The spatial structure of populations

1. Studies of the spatio-temporal dynamics and structure of populations have identified many categories of population type. However, recognized categories intergrade, making it difficult to assign empirical population systems to single categories.
2. We suggest that most population categories can be arranged along two axes that combine per capita birth (B), death (D), emigration (E) and immigration (I) rates. The 'Compensation Axis' describes the source-sink component of population structure, with source populations exporting individuals (B > D, E > I) and sinks and pseudosinks consuming individuals (B < D, E < I). The 'Mobility Axis' describes the involvement of a local population in regional (I + E) rather than local (B + D) processes, running from separate populations, through metapopulations, to patchy populations.
3. Each sample area within a spatially structured population system can potentially be assigned to a position along each of these axes, with individual sample areas weighted by local population size. The positions of these sample areas and their relative weightings allow the relative importance of different types of process to be judged. A worked exampled is provided, using the butterfly Hesperia comma . This approach shifts the emphasis from pattern (categories that real population systems do not fit) onto process.
4. In many systems, continuous variation in habitat quality and demographic parameters make clear distinctions between 'habitat' and 'non-habitat' difficult to sustain. In such cases, we advocate the use of a spatial grid system, with effects of patch size and isolation combined into a single, weighted distance function (neighbourhood).
5. The relative importance of different processes depends on the spatial scale at which the system is observed. This again emphasizes the value of a process-based approach.     

Contrasting spatial genetic structure in Annona crassiflora populations from fragmented and pristine savannas

In continuous populations, fine-scale genetic structure tends to be stronger in species with restricted pollen and seed dispersal. However, habitat fragmentation and disturbances can affect genetic diversity and spatial genetic structure due to disruption in ecological processes, such as plant reproduction and seed dispersal. In this study, we compared the genetic diversity and fine-scale spatial genetic structure (SGS) in two populations of Annona crassiflora (Annonaceae) in a pristine savanna Reserve (ESECAE) and in a fragmented disturbed savanna area (PABE), both in Cerrado biome in Central Brazil. The analyses were based on the polymorphism at 10 microsatellite loci. Our working hypothesis was that SGS is stronger and genetic diversity is lower in population at fragmented area (PABE) than at pristine area (ESECAE). Both populations presented high levels of polymorphism and genetic diversity and showed no sign of bottleneck for both Wilcoxon sign-rank test for heterozygosity excess (p > 0.05) and coalescent analyses (growth parameter g not different from zero), but population at fragmented area showed higher fixation index and stronger SGS. Besides, populations are significantly differentiated (F _ST = 0.239, R _ST = 0.483, p < 0.001 for both). Coalescent analyses showed high historical effective population sizes for both populations, high gene flow between ESECAE and PABE and recent time to most recent common ancestor (~37 k year BP). Our results suggest that despite the high genetic diversity, fragmentation and disturbance may have been affecting populations of this species increasing mating between closely related individuals leading to high fixation index and strong SGS.     

High genetic diversity and contrasting fine-scale spatial genetic structure in four seasonally dry tropical forest tree species

In this study we compared population structure, genetic diversity and fine-scale spatial genetic structure (SGS) in four Bignoniaceae tree species, Handroanthus chrysotrichus, H. impetiginosus, Tabebuia roseoalba and H. serratifolius in a remnant of seasonally dry tropical forest in Central-West Brazil, based on polymorphisms at six microsatellite loci. All species, except T. roseoalba, presented the inverted ‘J’ population structure indicating recruitment of juveniles. Juveniles presented a clumped distribution suggesting limitation in dispersal or patchy distribution of suitable microhabitat for recruitment. All species showed high levels of polymorphism and genetic diversity but without a clear pattern of distribution among life stages. The SGS was significant for all species, except T. roseoalba, but the pattern and strength of the spatial genetic structure differed among species. Handroanthus serratifolius had stronger SGS with significant kinship until 77 m. For H. impetiginosus and H. chrysotrichus, kinship was significant just until 23 and 6 m, respectively. Despite the high genetic diversity, all species showed low number of adults and high fixation indices suggesting that habitat fragmentation and disturbance have been affecting these populations in Central-West Brazil.     

Hair snaring and molecular genetic identification for reconstructing the spatial structure of Eurasian lynx populations

Non-invasive genetic sampling (NGS) is being increasingly applied in wildlife monitoring and population genetic research. This study was designed to evaluate the use of NGS for reconstructing the spatial structure of populations of large felids. We developed a procedure for reliably genotyping individuals of Eurasian lynx (Lynx lynx) from samples obtained through a hair-trapping scheme based on a network of lynx scent-marking sites. The spatial locations of the identified genotypes were matched with the home ranges distribution of radio-tracked individuals, thus cross-checking the accuracy of the two methods. We analyzed DNA extracted from 170 hair samples and 11 blood samples from live-trapped lynx collected in 2004–2009 in the Bia?owie?a Primeval Forest, Poland. We obtained PCR products in 96 (67%) hair samples; 82 (85%) of them were reliably genotyped at 12 autosomal microsatellite loci following a multiple-tubes protocol and stringent quality-controls of the data set. The sample included 29 distinct genotypes; 18 were found only in hair samples, five were determined only in live-trapped animals, and six in both hair and blood samples. Based on linkage disequilibrium we estimated an effective population size N_e = 20.3 (90% CI = 15–28). The total population size estimated with Capwire was N_c = 32 (95% CI = 25–37) in close agreement with the observed number of genotypes. The genotypes obtained from hair samples were re-sampled on average 3.9 times and 50% of them were recorded for more than one year. The spatial distribution of six hair-genotypes was consistent with their home ranges obtained by radio-tracking in the same period. The distribution ranges of hair-trapped genotypes overlapped on average in 86.4% (mode 100%) with home ranges of the corresponding individuals. Hair-trapping and molecular identification is a reliable method for reconstructing the spatial organization of lynx population. It is likely to be also efficiently used in other rare and endangered species of felids in combination with data from other monitoring techniques, such as radio- and snow-tracking and photo-trapping.     

Optimal sampling time selection for parameter estimation in dynamic pathway modeling

Systems Biology is an emerging research area, which considers mathematical representations of inter- and intra-cellular dynamics. Among the many research problems that have been addressed, dynamic modeling of signal transduction pathways has received increasing attention. The usual approach to represent intra-cellular dynamics are nonlinear, usually ordinary, differential equations. The purpose of the models is to test and generate hypothesis of specific pathways and it is therefore required to estimate model parameters from experimental data. The experiments to generate data are complex and expensive, as a consequence of which the time series available are usually rather short, with few if any replicates. Almost certainly, not all variables one would like to include in a model can be measured. Parameter estimation is therefore an important research problem in Systems Biology and the focus of this paper. In particular, we are interested in optimizing the sampling time selection in order to minimize the variance of the parameter estimation error. With few sampling time points feasible, their selection is of practical importance in experimental design. Finally, the theoretical results are supported with an application.     

Nuclear and chloroplast genetic structure indicate fine-scale spatial dynamics in a neotropical tree population

Dicorynia guianensis is a canopy tree, endemic to the tropical rain forest of French Guiana. We compared generational and spatial genetic structure for maternally and biparentally inherited markers in two cohorts (adult and seedling) in order to infer processes shaping the distribution of genetic diversity. The study was conducted on a 40 ha study plot located at Paracou near Kourou, where 172 adults trees and 375 saplings were sampled. Aggregation of trees was therefore suggested at different distances, ranging from 100 to 400 m. There was a strong link between demographic and genetic spatial structures at small distances (less than 100 m) that is likely to be the consequence of restricted seed dispersal. Genetic differentiation was more pronounced between spatial aggregates than between cohorts. Despite the spatial differentiation, the species was able to maintain high levels of diversity for maternal genomes, suggesting rapid turnover of aggregates. Spatial autocorrelation was larger for chloroplast than nuclear markers indicating a strong asymmetry between pollen and seed flow. Fixation indices indicated a lower heterozygote deficiency for the adults, maybe because of gradual elimination of selfed trees. Genetic relatedness at lower distances was higher in adult trees than in saplings, as a result of generation overlapping in the adult cohort. Overall, our results confirm earlier biological knowledge about the dispersion mechanisms of the species, and lead to an enhanced role of spatial processes in the dynamics of genetic diversity of D. guianensis.     

Microsatellite analysis of demographic genetic structure in fragmented populations of the tropical tree Symphonia globulifera

We developed genetic markers for three microsatellite loci in the tropical tree Symphonia globulifera and used them to examine the demographic genetic consequences of forest fragmentation. High levels of genetic variation were revealed in samples of adults, saplings, and seedlings. The more-variable loci exhibited less stability in allelic composition across sites and stages. The number of alleles per hectare (ha) of forest was similar when continuous forest plots were compared to plots from fragmented forest for all three stages. This pattern also held for the number of unique multilocus adult and sapling genotypes, but the number of unique seedling genotypes per ha of fragmented forest greatly exceeded expectations based on continuous forest data, probably due to the concentration of seeds into remnant forest patches by foraging bats. Significant inbreeding and genetic differentiation were most often associated with the fragmented forest and the seedlings. Finally, principal component analysis reaffirmed that a bottleneck, acting in concert with pre-existing genetic structure in the adults, had led to enhanced and rapid divergence in the seedlings following deforestation, a result that is of central interest for landscape management.     

Effects of multiple founder populations on spatial genetic structure of reintroduced American martens

Reintroductions and translocations are increasingly used to repatriate or increase probabilities of persistence for animal and plant species. Genetic and demographic characteristics of founding individuals and suitability of habitat at release sites are commonly believed to affect the success of these conservation programs. Genetic divergence among multiple source populations of American martens (Martes americana) and well documented introduction histories permitted analyses of post‐introduction dispersion from release sites and development of genetic clusters in the Upper Peninsula (UP) of Michigan <50 years following release. Location and size of spatial genetic clusters and measures of individual‐based autocorrelation were inferred using 11 microsatellite loci. We identified three genetic clusters in geographic proximity to original release locations. Estimated distances of effective gene flow based on spatial autocorrelation varied greatly among genetic clusters (30–90 km). Spatial contiguity of genetic clusters has been largely maintained with evidence for admixture primarily in localized regions, suggesting recent contact or locally retarded rates of gene flow. Data provide guidance for future studies of the effects of permeabilities of different land‐cover and land‐use features to dispersal and of other biotic and environmental factors that may contribute to the colonization process and development of spatial genetic associations.     

Noninvasive genetic sampling allows estimation of capercaillie numbers and population structure in the Bohemian Forest

Wildlife conservation and management of endangered species requires reliable information on the size and structure of populations. One of the flagship species in European wildlife conservation is the forest-dwelling capercaillie (Tetrao urogallus), where several populations are endangered. In the Bohemian Forest, e.g., the population severely declined 30 years ago with only 100 birds remaining in 1985. Subsequently, breeding and release programs were conducted to supplement the local population. The current distribution and population size, however, remained unknown. With recent habitat changes and increasing recreational activities, a reliable population estimate to inform conservation plans was needed. A team of scientists and volunteers collected fresh capercaillie droppings covering an area of about 120,000 ha. We genotyped ten microsatellite loci to estimate the current population size and to determine the population’s spatial and genetic structure. Population size and density estimators revealed a population size of approximately 500 individuals, which is thus one of the two largest relict populations in the low mountain ranges of temperate Europe. The population clustering revealed gene flow across the entire study area. Several genotypes were documented with multiple recaptures at spatial distances between 10 and 30 km additionally corroborating gene flow across the entire landscape of the study area. Males were more closely related than females on small spatial scales up to 3 km, indicating lower dispersal rates in males. We conclude that the population currently appears to have a viable size and shows unrestricted gene flow across state borders and management units of the entire Bohemian Forest. However, long-term viability of this population requires a transboundary strategy to sustainably protect and monitor this isolated capercaillie population in Central Europe.