The probability distribution under a population divergence model of the number of genetic founding lineages of a population or species

The composition of genetic variation in a population or species is shaped by the number of events that led to the founding of the group. We consider a neutral coalescent model of two populations, where a derived population is founded as an offshoot of an ancestral population. For a given locus, using both recursive and nonrecursive approaches, we compute the probability distribution of the number of genetic founding lineages that have given rise to the derived population. This number of genetic founding lineages is defined as the number of ancestral individuals that contributed at the locus to the present-day derived population, and is formulated in terms of interspecific coalescence events. The effects of sample size and divergence time on the probability distribution of the number of founding lineages are studied in detail. For 99.99% of the loci in the derived population to each have one founding lineage, the two populations must be separated for 9.9N generations. However, only approximately 0.87N generations must pass since divergence for 99.99% of the loci to have <6 founding lineages. Our results are useful as a prior expectation on the number of founding lineages in scenarios that involve the evolution of one population from the splitting of an ancestral group, such as in the colonization of islands, the formation of polyploid species, and the domestication of crops and livestock from wild ancestors.     

Comparing risk factors for population extinction

Extinction risk of natural populations of animals and plants is enhanced by many different processes, including habitat size reduction and toxic chemical exposure. We develop a method to evaluate different risk factors in terms of the decrease in the mean extinction time. We choose a population model with logistic growth, environmental and demographic stochasticities with three parameters (intrinsic growth rate r, carrying capacity K, and environmental noise sigma(2)(e)). The reduction in the habitat size decreases carrying capacity K only, whilst toxic chemical exposure decreases survivorship (or fertility) and in effect reduces both r and K. We derived a formula for the reduction in habitat size that decrease the mean extinction time by the same magnitude as a given level of toxic chemical exposure. In a large population (large K) or in a slowly growing population (small r), a small decrease in survivorship can cause the extinction risk increase corresponding to a significant reduction in the habitat size. This conclusion depends also on the nonlinearity of dose-effect relationship. To illustrate the method, we analyse a freshwater fish, Japanese crucian carp (Carassius auratus subsp.) in Lake Biwa.     

Genetic rescue and inbreeding depression in Mexican wolves

Although inbreeding can reduce individual fitness and contribute to population extinction, gene flow between inbred but unrelated populations may overcome these effects. Among extant Mexican wolves (Canis lupus baileyi), inbreeding had reduced genetic diversity and potentially lowered fitness, and as a result, three unrelated captive wolf lineages were merged beginning in 1995. We examined the effect of inbreeding and the merging of the founding lineages on three fitness traits in the captive population and on litter size in the reintroduced population. We found little evidence of inbreeding depression among captive wolves of the founding lineages, but large fitness increases, genetic rescue, for all traits examined among F1 offspring of the founding lineages. In addition, we observed strong inbreeding depression among wolves descended from F1 wolves. These results suggest a high load of deleterious alleles in the McBride lineage, the largest of the founding lineages. In the wild, reintroduced population, there were large fitness differences between McBride wolves and wolves with ancestry from two or more lineages, again indicating a genetic rescue. The low litter and pack sizes observed in the wild population are consistent with this genetic load, but it appears that there is still potential to establish vigorous wild populations.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS

Previous attempts to model the joint action of selection and mutation in finite populations have treated population size as being independent of the mutation load. However, the accumulation of deleterious mutations is expected to cause a gradual reduction in population size. Consequently, in small populations random genetic drift will progressively overpower selection making it easier to fix future mutations. This synergistic interaction, which we refer to as a mutational melt-down, ultimately leads to population extinction. For many conditions, the coefficient of variation of extinction time is less than 0.1, and for species that reproduce by binary fission, the expected extinction time is quite insensitive to population carrying capacity. These results are consistent with observations that many cultures of ciliated protozoans and vertebrate fibroblasts have characteristic extinction times. The model also predicts that clonal lineages are unlikely to survive more than 10⁴ to 10⁵ generations, which is consistent with existing data on parthenogenetic animals. Contrary to the usual view that Muller's ratchet does more damage when selection is weak, we show that the mean extinction time declines as mutations become more deleterious. Although very small sexual populations, such as self-fertilized lines, are subject to mutational meltdowns, recombination effectively eliminates the process when the effective population size exceeds a dozen or so. The concept of the effective mutation load is developed, and several procedures for estimating it are described. It is shown that this load can be reduced substantially when mutational effects are highly variable.     

The effect of differential reproductive success on population genetic structure: correlations of life history with matrilines in humpback whales of the gulf of maine

To examine whether demographic and life-history traits are correlated with genetic structure, we contrasted mtDNA lineages of individual humpback whales (Megaptera novaeangliae) with sighting and reproductive histories of female humpback whales between 1979 and 1995. Maternal lineage haplotypes were obtained for 323 whales, either from direct sequencing of the mtDNA control region (n = 159) or inferred from known relationships along matrilines from the sequenced sample of individuals (n = 164). Sequence variation in the 550 bp of the control region defined a total of 19 maternal lineage haplotypes that formed two main clades. Fecundity increased significantly over the study period among females of several lineages among the two clades. Individual maternal lineages and other clades were characterized by significant variation in fecundity. The detected heterogeneity of reproductive success has the potential to substantially affect the frequency and distribution of maternal lineages found in this population over time. There were significant yearly effects on adult resighting rates and calf survivorship based on examination of sighting histories with varying capture-recapture probability models. These results indicate that population structure can be influenced by interactions or associations between reproductive success, genetic structure, and environmental factors in a natural population of long-lived mammals.     

Time to extinction in deteriorating environments

Habitat degradation and destruction are the predominant drivers of population extinction, but there is little theory to guide the analysis of population viability in deteriorating environments. To address this gap, we investigated extinction times in time-varying, demographically stochastic versions of the logistic model for population dynamics. A property of these models is the “extinction delay,” a quantitative measure of the time lag in extinction created by species-specific extinction debt. For completeness, three models were constructed to represent the different demographic routes by which deterioration may affect population dynamics. Numerical analysis for two notional life histories indicated that the demographic response to environmental deterioration had a large effect on extinction delay, but a third analysis showed that the trajectory of the decline in carrying capacity ultimately characterized its magnitude. A concave decline in carrying capacity produced a large extinction delay while a small delay occurred with a convex decline. Furthermore, our results explore the non-monotonicity of extinction debt with respect to the speed of deterioration. A peak is present at low levels of deterioration, and the height of the peak and the asymptote of delay are affected by both life history parameterizations and the rate of change of the carrying capacity. The results suggest that population viability analyses must consider not only environmental deterioration, but also the effects of deterioration on the trajectory of the decline in carrying capacity.     

Does an ecological advantage produce the asymmetric lineage ratio in a harvester ant population?

In dependent-lineage harvester ant populations, two lineages interbreed but are genetically distinct. The offspring of a male and queen of the same lineage are female reproductives; the offspring of a male and queen of different lineages are workers. Geographic surveys have shown asymmetries in the ratio of the two lineages in many harvester ant populations, which may be maintained by an ecological advantage to one of the lineages. Using census data from a long-term study of a dependent-lineage population of the red harvester ant, Pogonomyrmex barbatus, we identified the lineage of 130 colonies sampled in 1997–1999, ranging in age from 1 to 19 years when collected, and 268 colonies sampled in 2010, ranging in age from 1 to 28 years when collected. The ratio of lineages in the study population is similar across an 11-year interval, 0.59 J2 in 1999 and 0.66 J2 in 2010. The rare lineage, J1, had a slightly but significantly higher number of mates of the opposite lineage than the common lineage, J2, and, using data from previous work on reproductive output, higher male production. Mature colonies of the two lineages did not differ in nest mound size, foraging activity, or the propensity to relocate their nests. There were no strong differences in the relative recruitment or survivorship of the two lineages. Our results show no ecological advantage for either lineage, indicating that differences between the lineages in sex ratio allocation may be sufficient to maintain the current asymmetry of the lineage ratio in this population.     

Considering threats to population viability of the endangered Korean long-tailed goral (Naemorhedus caudatus) using VORTEX

Population viability analysis (PVA) has frequently been used in conservation biology to predict extinction rates for threatened or endangered species. In this study, we used VORTEX to model Korean long-tailed goral (Naemorhedus caudatus) using previously collected ecological data. We focused on modelling population extinction, mean population size and heterozygosity. The minimum viable population size was found to be at least 50 gorals for 100 years, regardless of carrying capacity. However, populations with fewer than 50 gorals could not remain successful in the model. Inbreeding depression, catastrophes and supplementation also affected patterns of population extinction, mean population size and heterozygosity. Supplementation with new individuals had the strongest effect on extinction, mean population size and heterozygosity, followed by initial population size, inbreeding, catastrophes and carrying capacity. These results suggest that a supplementation by extra goral individuals from goral proliferation facilities would be the most helpful means for the restoration programme. More Korean goral-specific information regarding demographic and habitat parameters is needed for further PVA of the species.     

Population viability analysis predicts decreasing genetic diversity in <Emphasis Type="Italic">ex situ</Emphasis> populations of the Itasenpara bitterling <Emphasis Type="Italic">Acheilognathus longipinnis</Emphasis> from the Kiso River,Japan

To conserve endangered species, the maintenance of ex situ captive populations with sustainable genetic diversity is often required, in combination with population viability analysis (PVA). Since 2010, the threatened Itasenpara bitterling Acheilognathus longipinnis lineages in the Kiso region, Japan, have been maintained in ex situ rearing facilities to allow for conservation efforts. In this study, we obtained microsatellite data from DNA extracted from these captive populations to elucidate their genetic diversity and effective population size. The populations of several initial generations indicated a deviation from Hardy–Weinberg equilibrium, probably due to the limited number of extracted founder individuals analyzed. The effective population size of the captive population tended to increase over the course of generations, although the degree of genetic diversity tended to decrease highlighting the concern for the progression of inbreeding. Our prediction based on the PVA suggests that the maintenance of the captive population under the current conditions could lead to extinction of the Itasenpara bitterling in 50 years. In contrast, simultaneously increasing the carrying capacity and individual exchange among populations appears to enhance the effective management of captive Itasenpara bitterling populations.     

Demographic factors and genetic variation influence population persistence under environmental change

Population persistence has been studied in a conservation context to predict the fate of small or declining populations. Persistence models have explored effects on extinction of random demographic and environmental fluctuations, but in the face of directional environmental change they should also integrate factors affecting whether a population can adapt. Here, we examine the population‐size dependence of demographic and genetic factors and their likely contributions to extinction time under scenarios of environmental change. Parameter estimates were derived from experimental populations of the rainforest species, Drosophila birchii, held in the lab for 10 generations at census sizes of 20, 100 and 1000, and later exposed to five generations of heat‐knockdown selection. Under a model of directional change in the thermal environment, rapid extinction of populations of size 20 was caused by a combination of low growth rate (r) and high stochasticity in r. Populations of 100 had significantly higher reproductive output, lower stochasticity in r and more additive genetic variance (V_A) than populations of 20, but they were predicted to persist less well than the largest size class. Even populations of 1000 persisted only a few hundred generations under realistic estimates of environmental change because of low V_A for heat‐knockdown resistance. The experimental results document population‐size dependence of demographic and adaptability factors. The simulations illustrate a threshold influence of demographic factors on population persistence, while genetic variance has a more elastic impact on persistence under environmental change.     

Predicting the time to quasi-extinction for populations far below their carrying capacity

Populations threatened by extinction are often far below their carrying capacity. A population collapse or quasi-extinction is defined to occur when the population size reaches some given lower density. If this density is chosen to be large enough for the demographic stochasticity to be ignored compared to environmental stochasticity, then the logarithm of the population size may be modelled by a Brownian motion until quasi-extinction occurs. The normal-gamma mixture of inverse Gaussian distributions can then be applied to define prediction intervals for the time to quasi-extinction in such processes. A similar mixture is used to predict the population size at a finite time for the same process provided that quasi-extinction has not occurred before that time. Stochastic simulations indicate that the coverage of the prediction interval is very close to the probability calculated theoretically. As an illustration, the method is applied to predict the time to extinction of a declining population of white stork in southwestern Germany.     

The route to extinction in variable environments

Estimating the extinction risk of natural populations is not only an urgent problem in conservation biology but also involves some profound aspects of population dynamics. Apart from the obvious case of a continuous decrease in a population's carrying capacity, understanding the extinction process necessarily includes environmental and demographic stochasticity. Here, we build from first principles two stochastic, single-population models that can account for various routes to extinction via demographic and environmental variability. The Ricker model of population dynamics generates extinctions from either low or high (around or above carrying capacity) population densities, primarily depending on the growth parameter r . Since extinctions from high densities seem 'unnatural', there is either something wrong with the model or with our intuition. Suitable data are scarce. Environmental variability has its strongest influence on extinction risk via per capita birth rates and is only marginally influencing that risk via per capita death rates if the growth parameter is high. The distribution of the environmental noise and the stochastic structure of the model have quantitative, but not qualitative effects on the estimates of extinction risks. We conclude that to determine the route to extinction and to estimate the extinction risk require a careful choice of both the deterministic component of the population model (e.g., under- or over-compensation) and the structure of the demographic and environmental variabilities.     

The Effective Size of a Subdivided Population

This paper derives the long-term effective size, N(e), for a general model of population subdivision, allowing for differential deme fitness, variable emigration and immigration rates, extinction, colonization, and correlations across generations in these processes. We show that various long-term measures of N(e) are equivalent. The effective size of a metapopulation can be expressed in a variety of ways. At a demographic equilibrium, N(e) can be derived from the demography by combining information about the ultimate contribution of each deme to the future genetic make-up of the population and Wright's F(ST)'s. The effective size is given by N(e) = 1/(1 + var ( &))<(1 - f(STi))/N(i)n>, where n is the number of demes, &(i) is the eventual contribution of individuals in deme i to the whole population (scaled such that σ(i) &(i) = n), and < > denotes an average weighted by &(i)(2). This formula is applied to a catastrophic extinction model (where sites are either empty or at carrying capacity) and to a metapopulation model with explicit dynamics, where extinction is caused by demographic stochasticity and by chaos. Contrary to the expectation from the standard island model, the usual effect of population subdivision is to decrease the effective size relative to a panmictic population living on the same resource.     

Prior adaptation,diversity, and introduction frequency mediate the positive relationship between propagule pressure and the initial success of founding populations

Propagule pressure is often considered the most consistent predictor of the success of founding populations. This relationship could be mediated by the composition of the founding group (e.g. level of prior adaptation to the recipient environment or its diversity) as well as the introduction scenario (i.e. the frequency, size and timing of discrete introduction events). We introduced groups of Tribolium castaneum (red flour beetle) eggs across three levels of propagule pressure (n?=?15, 30, 60), of three possible compositions (single, adapted lineage; single, unadapted lineage; mixed lineages) to a novel environment using six unique introduction scenarios, in a fully factorial design to evaluate the importance of composition and introduction scenario in influencing the relationship between propagule pressure and establishment. In our system, prior adaptation to the environment, including having some adapted individuals in mixed groups, rivaled the importance of propagule pressure in determining the establishment success and size of founding populations. More frequent introduction events resulted in fewer individuals that initially survived founding, but introduction scenario did not significantly influence establishment success or population size. This experimental evidence demonstrates the importance of context, both of the founding group and the recipient environment, in understanding how propagule pressure influences the success of founding populations.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

Effects of habitat quality and size on extinction in experimental populations

Stochastic population theory makes clear predictions about the effects of reproductive potential and carrying capacity on characteristic time-scales of extinction. At the same time, the effects of habitat size and quality on reproduction and regulation have been hotly debated. To trace the causal relationships among these factors, we looked at the effects of habitat size and quality on extinction time in experimental populations of Daphnia magna. Replicate model systems representative of a broad-spectrum consumer foraging on a continuously supplied resource were established under crossed treatments of habitat size (two levels) and habitat quality (three levels) and monitored until eventual extinction of all populations. Using statistically derived estimates of key parameters, we related experimental treatments to persistence time through their effect on carrying capacity and the population growth rate. We found that carrying capacity and the intrinsic rate of increase were each influenced similarly by habitat size and quality, and that carrying capacity and the intrinsic rate of increase were in turn both correlated with time to population extinction. We expected habitat quality to have a greater influence on extinction. However, owing to an unexpected effect of habitat size on reproductive potential, habitat size and quality were similarly important for population persistence. These results support the idea that improving the population growth rate or carrying capacity will reduce extinction risk and demonstrate that both are possible by improving habitat quality or increasing habitat size.     

mtDNA history of the Cayapa Amerinds of Ecuador: detection of additional founding lineages for the Native American populations.

mtDNA variation in the Cayapa, an Ecuadorian Amerindian tribe belonging to the Chibcha-Paezan linguistic branch, was analyzed by use of hypervariable control regions I and II along with two linked regions undergoing insertion/deletion mutations. Three major maternal lineage clusters fit into the A, B, and C founding groups first described by Schurr and colleagues in 1990, whereas a fourth lineage, apparently unique to the Cayapa, has ambiguous affinity to known clusters. The time of divergence from a common maternal ancestor of the four lineage groups is of sufficient age that it indicates an origin in Asia and supports the hypothesis that the degree of variability carried by the Asian ancestral populations into the New World was rather high. Spatial autocorrelation analysis points out (a) statistically significant nonrandom distributions of the founding lineages in the Americas, because of north-south population movements that have occurred since the first Asian migrants spread through Beringia into the Americas, and (b) an unusual pattern associated with the D lineage cluster. The values of haplotype and nucleotide diversity that are displayed by the Cayapa appear to differ from those observed in other Chibchan populations but match those calculated for South American groups belonging to various linguistic stocks. These data, together with the results of phylogenetic analysis performed with the Amerinds of Central and South America, highlight the difficulty in the identification of clear coevolutionary patterns between linguistic and genetic relationships in particular human populations.     

On the number of New World founders: a population genetic portrait of the peopling of the Americas

The founding of New World populations by Asian peoples is the focus of considerable archaeological and genetic research, and there persist important questions on when and how these events occurred. Genetic data offer great potential for the study of human population history, but there are significant challenges in discerning distinct demographic processes. A new method for the study of diverging populations was applied to questions on the founding and history of Amerind-speaking Native American populations. The model permits estimation of founding population sizes, changes in population size, time of population formation, and gene flow. Analyses of data from nine loci are consistent with the general portrait that has emerged from archaeological and other kinds of evidence. The estimated effective size of the founding population for the New World is fewer than 80 individuals, approximately 1% of the effective size of the estimated ancestral Asian population. By adding a splitting parameter to population divergence models it becomes possible to develop detailed portraits of human demographic history. Analyses of Asian and New World data support a model of a recent founding of the New World by a population of quite small effective size.     

Consequences of insular population structure: Distribution and extinction of spruce grouse populations

Summary The population structure of the spruce grouse (Canachites canadensis) was studied in the Adirondack Mountains of New York, U.S.A. Twenty-five isolated habitat patches exist and are occupied by spruce grouse, with 7 suitable but unoccupied patches existing at the periphery of the range. The regional distribution and abundance of spruce grouse is correlated with the amount of lowland coniferous forest habitat. Unoccupied patches were significantly smaller and significantly farther from occupied patches than were other occupied patches. For all patches, as distance from the nearest occupied patch increased, the percent of occupied patches decreased linearly. I incorporated birth and death rates for spruce grouse into the MacArthur-Wilson survivorship model which closely predicted the proportion of occupied patches for an average population density (2.8 spruce grouse/100ha). For the same demographic parameters, extinction times were calculated which indicate that the 15 habitat patches of a carrying capacity of 3 female spruce grouse (100 ha) would have an average extinction time of less than 6 years. This in part accounts for the high proportion of these patches which are unoccupied. Extinctions and recolonizations of patches were observed during the study. The patterns of patch occupancy can partially be predicted based on their size, spatial arrangement, and the demographic characteristics of the spruce grouse.