Extinction risk of a density-dependent population estimated from a time series of population size

Environmental threats, such as habitat size reduction or environmental pollution, may not cause immediate extinction of a population but shorten the expected time to extinction. We develop a method to estimate the mean time to extinction for a density-dependent population with environmental fluctuation. We first derive a formula for a stochastic differential equation model (canonical model) of a population with logistic growth with environmental and demographic stochasticities. We then study an approximate maximum likelihood (AML) estimate of three parameters (intrinsic growth rate r, carrying capacity K, and environmental stochasticity sigma(2)(e)) from a time series of population size. The AML estimate of r has a significant bias, but by adopting the Monte Carlo method, we can remove the bias very effectively (bias-corrected estimate). We can also determine the confidence interval of the parameter based on the Monte Carlo method. If the length of the time series is moderately long (with 40-50 data points), parameter estimation with the Monte Carlo sampling bias correction has a relatively small variance. However, if the time series is short (less than or equal to 10 data points), the estimate has a large variance and is not reliable. If we know the intrinsic growth rate r, however, the estimate of K and sigma(2)(e)and the mean extinction time T are reliable even if only a short time series is available. We illustrate the method using data for a freshwater fish, Japanese crucian carp (Carassius auratus subsp.) in Lake Biwa, in which the growth rate and environmental noise of crucian carp are estimated using fishery records.     

Analyses of the age of genes and the first arrival times in a finite population

The age of a mutant gene is studied using the infinite allele model in which every mutant is new and selectively neutral. Based on a time reversal theory of Markov processes, we develop a method of mathematical analysis that is considerably simpler for calculating the various statistics of the age than previous methods. Formulas for the mean and variance and for the distribution of age are presented together with some examples of relevance to cases in natural populations.—Theoretical studies of the first arrival time of an allele to a specified frequency, given an initially monomorphic condition of the locus, are presented. It is shown that, beginning with an allele that has frequency p = 1 or an allele with frequency p = 1/2N, there is an initial lag phase in which there is virtually no chance of an allele with a specified intermediate frequency appearing in the population. The distribution of the first arrival time is also presented. The distribution shows several characteristics that are not immediately obvious from a consideration of only the mean and variance of first arrival time. Especially noteworthy is the existence of a very long tail to the distribution. We have also studied the distribution of the age of an allele in the population. Again, the distribution of this measure is shown to be more informative for several questions than are the mean and variance alone.     

Times on trees, and the age of an allele

In this paper we consider the genealogy of a random sample of n chromosomes from a panmictic population which has evolved with constant size N over many generations. We address two related problems. First we describe how genealogical information may be usefully partitioned into information on the events (mutations and coalescences) which occur in the genealogy, and the times between these events. We show that the distribution of the times given information on the events is particularly simple and describe how this can considerably reduce the computational burden when performing inference for these times. Second we investigate the effect on the genealogy of conditioning on a single mutation having occurred during the ancestry of the sample. In particular we use results from the first part of the paper to derive explicit formulae for the density of the age of a mutant allele, conditional on its frequency in either a sample or the population.     

DAT1 VNTR polymorphisms in a European and an African population: identification of a new allele

Polymorphism frequencies of the dopamine transporter gene (DAT1) hypervariable region have been analyzed in a sample of Italian and Ivory Coast individuals. The 3' untranslated region (UTR) of DAT1 includes a variable number of tandem repeats (VNTR) of a 40-bp monomer, ranging from 3 to 13 repeats in Caucasian and African populations. In our sample we found alleles with 3 to 16 repeats, and the most common alleles were the 10-repeat (DAT1*10) and the 9-repeat (DAT1*9) alleles. We also found two rare alleles in the Italian population and four in the Ivory Coast population. For the first time the new allele DAT1*16 is described in the Ivorians. The Ivory Coast population was not in Hardy-Weinberg equilibrium for the DAT1 locus because of a deficit of heterozygote genotypes. The observed heterozygosity of the Ivorian population was half that of the Italians. The lower observed heterozygosity and deviation from Hardy-Weinberg equilibrium could be the result of microevolutionary trends, such as genetic drift and/or inbreeding, acting on the relatively small and isolated population sampled for this study, although some sort of selective pressures acting against the shorter alleles cannot be excluded. This evidence, in association with the reduced polymorphism shown by the DAT1 VNTR compared to other VNTRs, seems to indicate that the DAT1 locus may be under some selective pressure.     

Mutation and selection in a large population

In this paper we study a large, but finite population, in which mutation and selection occur at a single genetic locus in a diploid organism. We provide theoretical results for the equilibrium allele frequencies, their variances and covariances and their equilibrium distribution, when the population size is larger than the reciprocal of the mean allelic mutation rate. We are also able to infer that the equilibrium distribution of allele frequencies takes the form of a constrained multivariate Gaussian distribution. Our results provide a rapid way of obtaining useful information in the case of complex mutation and selection schemes when the population size is large. We present numerical simulations to test the applicability of our theoretical formulations. The results of these simulations are in very reasonable agreement with the theoretical predictions.     

Host mating system and the spread of a disease-resistant allele in a population

The model presented here modifies a susceptible-infected (SI) host–pathogen model to determine the influence of mating system on the outcome of a host–pathogen interaction. Both deterministic and stochastic (individual-based) versions of the model were used. This model considers the potential consequences of varying mating systems on the rate of spread of both the pathogen and resistance alleles within the population. We assumed that a single allele for disease resistance was sufficient to confer complete resistance in an individual, and that both homozygote and heterozygote resistant individuals had the same mean birth and death rates. When disease invaded a population with only an initial small fraction of resistant genes, inbreeding (selfing) tended to increase the probability that the disease would soon be eliminated from a small population rather than become endemic, while outcrossing greatly increased the probability that the population would become extinct due to the disease.     

Electrophoretically silent alleles in a finite population

Summary The expected number of silent alleles in an electromorph is computed for various values of population size (N), mutation rate (u), and sample size (s) under the assumption of no selection. The proportion of alleles undetectable by electrophoresis is higher when Nu is large than when this is small. It is shown that an electromorph of high population frequency has more silent alleles than an electromorph of low frequency if the sample size is the same.     

Extinction dynamics,population growth and seed banks

The goal of this paper is to test theoretical predictions about the effects of seed banks on population dynamics and extinction rates in variable environments using simulations based on data from a natural population of the winter annual Collinsia verna. In the simulations, we varied the frequency of demographically good and bad years and the autocorrelation between conditions in consecutive years to examine the impact of seed dormancy on population growth rate, extinction rate and time to extinction. The existence of a seed bank enhanced population growth rates under all environmental regimes except when good years were very frequent, but this enhancement was minimal. In addition, the presence of the seed bank decreased the likelihood of extinctions and increased the time to extinction. The time to extinction was longest when the environmental conditions were most unpredictable.     

The effects of season,daylight saving and time of sunrise on serum cortisol in a large population

Cortisol is critical for maintenance of health and homeostasis and factors affecting cortisol levels are of clinical importance. There is conflicting information about the effects of season on morning cortisol and little information on the effects of sunlight on population cortisol assessment. The aim of this study was to assess whether changes in median serum cortisol occurred in a population in conjunction with changing seasons, daylight saving time (DST) or time of sunrise. We analysed serum cortisol results (n?=?27 569) from a single large laboratory over a 13-year period. Subjects with confounding medications or medical conditions were excluded and data analysed in 15-minute intervals. We assessed the influence of traditional seasons, seasons determined by equinox/solstice, DST and time of sunrise on median cortisol. The median time of cortisol collection did not vary significantly between seasons. Using traditional seasons, median cortisol was lowest in summer (386?nmol/L) and spring (384?nmol/L) with higher cortisol in autumn (406?nmol/L) and winter (414?nmol/L). Median cortisol was lowest in the summer solstice quarter with significant comparative increases in the spring equinox quarter (3.1%), the autumn equinox quarter (4.5%) and the winter solstice quarter (8.6%). When cortisol was modelled against time, with adjustment for actual sunrise time on day of collection, for each hour delay in sunrise there was a 4.8% increase in median cortisol (95% CI: 3.9–5.7%). In modelling to explain the variation in cortisol over the morning, sunrise time was better than season in explaining seasonal effects. A subtle cyclic pattern in median cortisol also occurred throughout the months of the year. A 3-year trial of DST allowed comparison of cortisol in DST and non DST periods, when clock time differed by one hour. There was modest evidence of a difference in acrophase between DST and non DST cortisol (p?=?0.038), with DST peak cortisol estimated to occur 58?minutes later than non-DST peak. In summary, we found that time of sunrise and time of cortisol collection were the most important factors influencing median cortisol. For each hour later that the sun rose there was an almost 5% increase in median cortisol. There was significant seasonal variability with lowest cortisol noted in summer coinciding with the earliest sunrise time. This is an important finding which is consistent with the understanding that light is the major zeitgeber in entrainment of the human circadian cortisol rhythm. Our data suggest this rhythm is resistant to the arbitrary changes in clock time with daylight saving.