Early estimates of epidemic final sizes

ABSTRACT

Early in a disease outbreak, it is important to be able to estimate the final size of the epidemic in order to assess needs for treatment and to be able to compare the effects of different treatment approaches. However, it is common for epidemics, especially of diseases considered dangerous, to grow much more slowly than expected. We suggest that by assuming behavioural changes in the face of an epidemic and heterogeneity of mixing in the population it is possible to obtain reasonable early estimates.     

Linkage and inbreeding coefficients in a finite random mating population

The notion of inbreeding coefficient associated with one single locus introduced by G. Malecot can be extended to two loci. For a panmictic model with separate generation the recurrence equations are given therein allowing to calculate the coefficients in the event of migration and mutation, or loss of kinship.Hence it is derived particularly that the limit genetic distance of two groups associated with two loci is, under specific hypotheses, little different from the sum of marginal genetic distances.For an isolat this paper studies, in terms of crossing over, mutations, and population size, the evolution of the inbreading coefficients of order 2 and especially the difference of this evolution from the evolution to independence of the two loci.     

The influence of survey frequency on population estimates of moorland breeding birds

Capsule A minimum of four constant‐effort‐search survey visits are required to generate reliable population estimates of breeding birds on moorland that are not subject to biases associated with varying levels of detectability through the season.

Aims To investigate the influence of the number and the combination of survey visits on the population estimates of breeding birds on moorland.

Methods Four constant‐effort‐search surveys (80–100 minutes per km² per visit) of moorland in southwest Scotland were undertaken in each of six years, 2003–2008. Using standard protocols, the numbers of apparent territories that would have been identified for each possible combination of survey visits were determined.glms were used to assess the influence of the frequency of survey visits, and different combination scenarios on the derived population estimates for Red Grouse, European Golden Plover, Common Snipe, Eurasian Curlew, Sky Lark, Winter Wren and Stonechat. Independent assessments of population density were made by transect sampling for Red Grouse and Sky Lark.

Results Robust population estimates were possible from three survey visits for European Golden Plover, Eurasian Curlew and Stonechat. However, there were differences between species in the seasonal variation of their detectability. Four survey visits would underestimate the populations of Red Grouse (probably by 67–91%), Sky Lark (probably by 31–61%) and Winter Wren (by an undetermined proportion). Common Snipe were also likely to be underestimated after four survey visits, but the value of the derived estimate as an index of population density deserves further investigation.

Conclusions If there is a need to carry out a multi‐species survey on moorland, we suggest that a minimum of four survey visits is required to ensure the derivation of reliable population estimates for a suite of the most readily detectable species. Population estimates derived from three or fewer survey visits risk biases through uneven sampling in periods of differing detectability. With evidence for changes in the breeding phenology of birds associated with changing climate or weather patterns, it arguably becomes more important to ensure that surveys sample an adequately broad period of the breeding season.     

Good–Turing frequency estimation in a finite population

Good–Turing frequency estimation (Good, 1953 ) is a simple, effective method for predicting detection probabilities of objects of both observed and unobserved classes based on observed frequencies of classes in a sample. The method has been used widely in several disciplines, such as information retrieval, computational linguistics, text recognition, and ecological diversity estimation. Nevertheless, existing studies assume sampling with replacement or sampling from an infinite population, which might be inappropriate for many practical applications. In light of this limitation, this article presents a modification of the Good–Turing estimation method to account for finite population sampling. We provide three practical extensions of the modified method, and we examine performance of the modified method and its extensions in simulation experiments.     

The effect of intragenic recombination on the number of alleles in a finite population

A two-site infinite allele model is constructed to study the effect of intragenic recombination on the number of neutral alleles and the distribution of their frequencies in a finite population. The results of theory and Monte Carlo simulation of the two-site model demonstrate that intragenic recombination significantly increases the mean and variance of the number of alleles when the rates of mutation and recombination are as large as the reciprocal of the population size. Data from natural populations indicate that this may be a significant process in generating variation and determining its distribution.     

Parametric and semiparametric model-based estimates of the finite population mean for two-stage cluster samples with item nonresponse

This article concerns item nonresponse adjustment for two-stage cluster samples. Specifically, we focus on two types of nonignorable nonresponse: nonresponse depending on covariates and underlying cluster characteristics, and depending on covariates and the missing outcome. In these circumstances, standard weighting and imputation adjustments are liable to be biased. To obtain consistent estimates, we extend the standard random-effects model by modeling these two types of missing data mechanism. We also propose semiparametric approaches based on fitting a spline on the propensity score, to weaken assumptions about the relationship between the outcome and covariates. These new methods are compared with existing approaches by simulation. The National Health and Nutrition Examination Survey data are used to illustrate these approaches.     

On the nonidentifiability of population sizes

Summary .   When a nonparametric mixture model is adopted to deal with the heterogeneity among individual capture probabilities, the population size is nonidentifiable ( Link, 2003 , Biometrics 59 , 1123–1130). Holzmann, Munk, and Zucchini (2006, Biometrics 62, 934–936) discussed the conditions under which a subfamily of mixing distributions is identifiable. Link (2006, Biometrics 92 , 936–939) found that the nonidentifiability occurs across identifiable subfamilies. It is shown that there is a subfamily in which each mixing distribution is determined by its mixture, and the population size admits estimable lower bounds that can be used to construct lower confidence limits.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Modelling population processes with random initial conditions

Population dynamics are almost inevitably associated with two predominant sources of variation: the first, demographic variability, a consequence of chance in progenitive and deleterious events; the second, initial state uncertainty, a consequence of partial observability and reporting delays and errors. Here we outline a general method for incorporating random initial conditions in population models where a deterministic model is sufficient to describe the dynamics of the population. Additionally, we show that for a large class of stochastic models the overall variation is the sum of variation due to random initial conditions and variation due to random dynamics, and thus we are able to quantify the variation not accounted for when random dynamics are ignored. Our results are illustrated with reference to both simulated and real data.     

Similarity in recombination rate estimates highly correlates with genetic differentiation in humans

Recombination varies greatly among species, as illustrated by the poor conservation of the recombination landscape between humans and chimpanzees. Thus, shorter evolutionary time frames are needed to understand the evolution of recombination. Here, we analyze its recent evolution in humans. We calculated the recombination rates between adjacent pairs of 636,933 common single-nucleotide polymorphism loci in 28 worldwide human populations and analyzed them in relation to genetic distances between populations. We found a strong and highly significant correlation between similarity in the recombination rates corrected for effective population size and genetic differentiation between populations. This correlation is observed at the genome-wide level, but also for each chromosome and when genetic distances and recombination similarities are calculated independently from different parts of the genome. Moreover, and more relevant, this relationship is robustly maintained when considering presence/absence of recombination hotspots. Simulations show that this correlation cannot be explained by biases in the inference of recombination rates caused by haplotype sharing among similar populations. This result indicates a rapid pace of evolution of recombination, within the time span of differentiation of modern humans.