Estimation of the rate and effects of deleterious genomic mutations in finite populations with linkage disequilibrium

Under several assumptions such as infinite population size with unlinked loci at linkage equilibrium (LD) under mutation-selection (M-S) balance, the rate (U), and the average effects (dominance and selection coefficients h and s) of deleterious genomic mutations (DGM) can be estimated by the Deng-Lynch method in some natural populations. However, all natural populations are finite in size and many of them are not large enough to be considered as approximately infinite. In the absence of an analytical estimation approach to characterize DGM in finite populations, we test the robustness and applicability of the Deng-Lynch method in finite populations with computer simulations. The results indicate that the estimation obtained by the Deng-Lynch method in finite populations with LD is generally robust when population size is greater than 400. With constant mutation effects, in outcrossing populations, the estimates U and ? are unbiased or only slightly upwardly biased, and ? is unbiased for most cases. In highly selfing populations, U and ? are upwardly biased, U is no more than 1.5U and ? is less than 1.1 h, and ? is either unbiased or slightly downwardly biased. With variable mutation effects, U ranges from 0.56 to 0.72U, and s ranges from 1.4 to 1.8s. Generally speaking, with the same finite population size, the estimation in outcrossing populations is better than in highly selfing populations. Given that even the order of the magnitude of the parameters of DMG (U in particular) is controversial, our investigation here may provide a basis for using the Deng-Lynch method to characterize DGM in finite populations of size greater than 400 in the presence of LD.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xiv. Effects of the Incomplete Dominance of the IN(2LR)SM1 (Cy) Chromosome on the Estimates of Various Genetic Parameters

Recent reports (Mukaiet al. 1974; Katz and Cardellino 1978; Cockerham and Mukai 1978) have indicated that the Cy chromosome is not always dominant over its homologous chromosome with respect to viability. Thus, the genetic parameters previously estimated using viabilities determined by the Cy method are biased. In the present paper, the biases of the estimates for the polygenic mutation rate, the degree of dominance and the homozygous load are examined. The results indicate that the biases for the mutation rate and the degree of dominance are small and that the estimate of the homozygous load relative to the average viability of the population is not biased.     

A Building Block Model for Quantitative Genetics

We introduce a quantitative genetic model for multiple alleles which permits the parameterization of the degree, D, of dominance of favorable or unfavorable alleles. We assume gene effects to be random from some distribution and independent of the D's. We then fit the usual least-squares population genetic model of additive and dominance effects in an infinite equilibrium population to determine the five genetic components--additive variance sigma 2 a, dominance variance sigma 2 d, variance of homozygous dominance effects d2, covariance of additive and homozygous dominance effects d1, and the square of the inbreeding depression h--required to treat finite populations and large populations that have been through a bottleneck or in which there is inbreeding. The effects of dominance can be summarized as functions of the average, D, and the variance, sigma 2 D. An important distinction arises between symmetrical and nonsymmetrical distributions of gene effects. With symmetrical distributions d1 = -d2/2 which is always negative, and the contribution of dominance to sigma 2 a is equal to d2/2. With nonsymmetrical distributions there is an additional contribution H to sigma 2 a and -H/2 to d1, the sign of H being determined by D and the skew of the distribution. Some numerical evaluations are presented for the normal and exponential distributions of gene effects, illustrating the effects of the number of alleles and of the variation in allelic frequencies. Random additive by additive (a*a) epistatic effects contribute to sigma 2 a and to the a*a variance, sigma 2/aa, the relative contributions depending on the number of alleles and the variation in allelic frequencies.(ABSTRACT TRUNCATED AT 250 WORDS)     

Impact of interpopulation divergence on additive and dominance variance in hybrid populations

We present a theoretical proof that the ratio of the dominance vs. the additive variance decreases with increasing genetic divergence between two populations. While the dominance variance is the major component of the variance due to specific combining ability (sigma(SCA)(2)), the additive variance is the major component of the variance due to general combining ability (sigma(GCA)(2)). Therefore, we conclude that interpopulation improvement becomes more efficient with divergent than with genetically similar heterotic groups, because performance of superior hybrids can be predicted on the basis of general combining ability effects.     

Divergent estimates of herd‐wide caribou calf survival: Ecological factors and methodological biases

Population monitoring is a critical part of effective wildlife management, but methods are prone to biases that can hinder our ability to accurately track changes in populations through time. Calf survival plays an important role in ungulate population dynamics and can be monitored using telemetry and herd composition surveys. These methods, however, are susceptible to unrepresentative sampling and violations of the assumption of equal detectability, respectively. Here, we capitalized on 55 herd‐wide estimates of woodland caribou (Rangifer tarandus caribou) calf survival in Newfoundland, Canada, using telemetry (n = 1,175 calves) and 249 herd‐wide estimates of calf:cow ratios (C:C) using herd composition surveys to investigate these potential biases. These data included 17 herd‐wide estimates replicated from both methods concurrently (n = 448 calves and n = 17 surveys) which we used to understand which processes and sampling biases contributed to disagreement between estimates of herd‐wide calf survival. We used Cox proportional hazards models to determine whether estimates of calf mortality risk were biased by the date a calf was collared. We also used linear mixed‐effects models to determine whether estimates of C:C ratios were biased by survey date and herd size. We found that calves collared later in the calving season had a higher mortality risk and that C:C tended to be higher for surveys conducted later in the autumn. When we used these relationships to modify estimates of herd‐wide calf survival derived from telemetry and herd composition surveys concurrently, we found that formerly disparate estimates of woodland caribou calf survival now overlapped (within a 95% confidence interval) in a majority of cases. Our case study highlights the potential of under‐appreciated biases to impact our understanding of population dynamics and suggests ways that managers can limit the influence of these biases in the two widely applied methods for estimating herd‐wide survival.     

On the average coefficient of dominance of deleterious spontaneous mutations

T. Mukai and co-workers in the late 1960s and O. Ohnishi in the 1970s carried out a series of experiments to obtain direct estimates of the average coefficient of dominance (h) of minor viability mutations in Drosophila melanogaster. The results of these experiments, although inconsistent, have been interpreted as indicating slight recessivity of deleterious mutations, with h approximately 0.4. Mukai obtained conflicting results depending on the type of heterozygotes used, some estimates suggesting overdominance and others partial dominance. Ohnishi's estimates, based on the ratio of heterozygous to homozygous viability declines, were more consistent, pointing to the above value. However, we have reanalyzed Ohnishi's data, estimating h by the regression method, and obtained a much smaller estimate of approximately 0.1. This significant difference can be due partly to the different weighting implicit in the estimates, but we suggest that this is not the only explanation. We propose as a plausible hypothesis that a putative nonmutational decline in viability occurring in the first half of Ohnishi's experiment (affecting both homozygotes and heterozygotes) has biased upward the estimates from the ratio, while it would not bias the regression estimates. This hypothesis also explains the very high h approximately 0.7 observed in Ohnishi's high-viability chromosomes. By constructing a model of spontaneous mutations using parameters in the literature, we investigate the above possibility. The results indicate that a model of few mutations with moderately large effects and h approximately 0.2 is able to explain the observed estimates and the distributions of homozygous and heterozygous viabilities. Accounting for an expression of mutations in genotypes with the balancer chromosome Cy does not alter the conclusions qualitatively.     

Statewide and local recruitment of mourning doves in Missouri

Intensive harvests have the potential to greatly affect local mourning dove (Zenaida macroura) populations, a popular gamebird and songbird. To evaluate if recruitment was commensurate with harvest, we applied a ratio-based method to estimate local and statewide mourning dove recruitment across 7 public hunting areas in Missouri from 2005 to 2011. We estimated recruitment from preharvest adult sex ratios and harvest age ratios that incorporated various methods to address potential inherent biases (e.g., bias in the adults of unknown sex in preharvest samples, bias in unknown age wings, and local differential vulnerability; DV). Data from 356 radio-marked doves revealed a DV rate, where hatch year doves were, on average 2.7× more likely to be harvested than adult doves. Recruitment estimates for local areas were highly variable and in some cases, biologically unrealistic (e.g., >10 offspring/female), because of small preharvest sample sizes. However, data pooled statewide provided recruitment estimates of 3.1 offspring/female (±0.3 SE) or 4.1 offspring/female (±0.3 SE), assuming samples of unknown sex doves were female biased or male biased, respectively. Although statewide estimates agree with directly observed rates, the sex ratios and differential vulnerability comprising them vary considerably from what has been previously assumed. Whether preharvest sex ratios are biased from trapping methods has 2 important implications; either regional approaches have overestimated recruitment or the number of females in Missouri's population is much less than originally thought. Because each of these scenarios are important to understanding the effects of regional harvest management on Missouri's dove population, they highlight the importance of a better understanding of biases involved in estimating recruitment. © 2012 The Wildlife Society.     

Effects of sample size on estimates of population growth rates calculated with matrix models

Background

Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen''s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ.

Methodology/Principal Findings

Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography.

Conclusions/Significance

We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.     

Variance component analysis of bristle characters in local populations of Drosophila melanogaster.

The genetic variabilities of sternopleural and abdominal bristle numbers existing in local natural populations were assessed. Using second chromosome lines of Drosophila melanogaster extracted from three natural populations in Japan (the Ishigakijima, Ogasawara and Aomori populations), experiments were conducted to estimate the components of genetic variances, additive and dominance variances. The following results were obtained: For both sternopleural and abdominal bristle numbers, the additive genetic variances (sigma 2A) were much larger than the dominance variances (sigma 2D) especially in the southern populations. For example, in the Ishigakijima population, for females sternopleural bristle numbers of the inversion-free chromosome group, the additive and dominance variances were estimated to be 1.255 +/- 0.2034 and 0.0552 +/- 0.0180, respectively. The magnitudes of the estimates of additive genetic variances were nearly equal from north to south. By comparing the additive genetic variances of the inversion-free chromosome group with those of the In(2L)t-carrying chromosome group, it was inferred that sufficient number of generations to achieve the equilibrium state has not passed since the introduction of a single or a small number of the In(2L)t-carrying chromosomes to the Ishigakijima population.     

Estimates of the average strength of natural selection are not inflated by sampling error or publication bias

Kingsolver et al.'s review of phenotypic selection gradients from natural populations provided a glimpse of the form and strength of selection in nature and how selection on different organisms and traits varies. Because this review's underlying database could be a key tool for answering fundamental questions concerning natural selection, it has spawned discussion of potential biases inherent in the review process. Here, we explicitly test for two commonly discussed sources of bias: sampling error and publication bias. We model the relationship between variance among selection gradients and sample size that sampling error produces by subsampling large empirical data sets containing measurements of traits and fitness. We find that this relationship was not mimicked by the review data set and therefore conclude that sampling error does not bias estimations of the average strength of selection. Using graphical tests, we find evidence for bias against publishing weak estimates of selection only among very small studies (N<38). However, this evidence is counteracted by excess weak estimates in larger studies. Thus, estimates of average strength of selection from the review are less biased than is often assumed. Devising and conducting straightforward tests for different biases allows concern to be focused on the most troublesome factors.     

Estimation of deleterious genomic mutation parameters in natural populations by accounting for variable mutation effects across loci

The genomes of all organisms are subject to continuous bombardment of deleterious genomic mutations (DGM). Our ability to accurately estimate various parameters of DGM has profound significance in population and evolutionary genetics. The Deng-Lynch method can estimate the parameters of DGM in natural selfing and outcrossing populations. This method assumes constant fitness effects of DGM and hence is biased under variable fitness effects of DGM. Here, we develop a statistical method to estimate DGM parameters by considering variable mutation effects across loci. Under variable mutation effects, the mean fitness and genetic variance for fitness of parental and progeny generations across selfing/outcrossing in outcrossing/selfing populations and the covariance between mean fitness of parents and that of their progeny are functions of DGM parameters: the genomic mutation rate U, average homozygous effect s, average dominance coefficient h, and covariance of selection and dominance coefficients cov(h, s). The DGM parameters can be estimated by the algorithms we developed herein, which may yield improved estimation of DGM parameters over the Deng-Lynch method as demonstrated by our simulation studies. Importantly, this method is the first one to characterize cov(h, s) for DGM.     

Analysis of the estimators of the average coefficient of dominance of deleterious mutations

We investigate the sources of bias that affect the most commonly used methods of estimation of the average degree of dominance (h) of deleterious mutations, focusing on estimates from segregating populations. The main emphasis is on the effect of the finite size of the populations, but other sources of bias are also considered. Using diffusion approximations to the distribution of gene frequencies in finite populations as well as stochastic simulations, we assess the behavior of the estimators obtained from populations at mutation-selection-drift balance under different mutational scenarios and compare averages of h for newly arisen and segregating mutations. Because of genetic drift, the inferences concerning newly arisen mutations based on the mutation-selection balance theory can have substantial upward bias depending upon the distribution of h. In addition, estimates usually refer to h weighted by the homozygous deleterious effect in different ways, so that inferences are complicated when these two variables are negatively correlated. Due to both sources of bias, the widely used regression of heterozygous on homozygous means underestimates the arithmetic mean of h for segregating mutations, in contrast to their repeatedly assumed equality in the literature. We conclude that none of the estimators from segregating populations provides, under general conditions, a useful tool to ascertain the properties of the degree of dominance, either for segregating or for newly arisen deleterious mutations. Direct estimates of the average h from mutation-accumulation experiments are shown to suffer some bias caused by purging selection but, because they do not require assumptions on the causes maintaining segregating variation, they appear to give a more reliable average dominance for newly arisen mutations.     

The Genetic Structure of Natural Populations of Drosophila Melanogaster. Xxiv. Effects of Hybrid Dysgenesis on the Components of Genetic Variance of Viability

Eight hundred second chromosomes were extracted from the Ishigakijima population, one of the southernmost populations of Drosophila melanogaster in Japan. Half of them were extracted in Native cytoplasm (P-type), and half in Foreign cytoplasm (M-type). Various population-genetic parameters, including the frequency of lethal-carrying second chromosomes (Q = 0.235 for the Native; 0.218 for the Foreign), the allelism rate of lethal second chromosome (Ic = 0.0217 for the Native; 0.0134 for the Foreign), the homozygous detrimental and lethal loads (D = 0.179 for the Native; 0.270 for the Foreign; L = 0.262 for the Native; 0.240 for the Foreign), the average degree of dominance of mildly deleterious mutations (?E = 0.244 for the Native; 0.208 for the Foreign), and the components of genetic variance for viability [additive (sigma A2) and dominance (sigma D2)](?igma A2 = 0.0187 for the Native; 0.0172 for the Foreign; ?igma D2 = 0.0005 for the Native; 0.0009 for the Foreign) were estimated. The data indicate that D was significantly larger and hE was significantly smaller in the Foreign cytoplasm. However, the estimates of additive and dominance variances were not significantly different between the two cytoplasms. The additive genetic variance for viability in the Ishigakijima population was greater than expected on the basis of mutation-selection balance confirming previous studies on papers of D. melanogaster in warm climates.     

Within-generation mutation variance for litter size in inbred mice

The mutational input of genetic variance per generation (sigma(m)(2)) is the lower limit of the genetic variability in inbred strains of mice, although greater values could be expected due to the accumulation of new mutations in successive generations. A mixed-model analysis using Bayesian methods was applied to estimate sigma(m)(2) and the across-generation accumulated genetic variability on litter size in 46 generations of a C57BL/6J inbred strain. This allowed for a separate inference on sigma(m)(2) and on the additive genetic variance in the base population (sigma(a)(2)). The additive genetic variance in the base generation was 0.151 and quickly decreased to almost null estimates in generation 10. On the other hand, sigma(m)(2) was moderate (0.035) and the within-generation mutational variance increased up to generation 14, then oscillating between 0.102 and 0.234 in remaining generations. This pattern suggested the existence of a continuous uploading of genetic variability for litter size (h(2)=0.045). Relevant genetic drift was not detected in this population. In conclusion, our approach allowed for separate estimation of sigma(a)(2) and sigma(m)(2) within the mixed-model framework, and the heritability obtained highlighted the significant and continuous influence of new genetic variability affecting the genetic stability of inbred strains.     

The quantitative genetics of maximal and basal rates of oxygen consumption in mice

A positive genetic correlation between basal metabolic rate (BMR) and maximal (VO(2)max) rate of oxygen consumption is a key assumption of the aerobic capacity model for the evolution of endothermy. We estimated the genetic (V(A), additive, and V(D), dominance), prenatal (V(N)), and postnatal common environmental (V(C)) contributions to individual differences in metabolic rates and body mass for a genetically heterogeneous laboratory strain of house mice (Mus domesticus). Our breeding design did not allow the simultaneous estimation of V(D) and V(N). Regardless of whether V(D) or V(N) was assumed, estimates of V(A) were negative under the full models. Hence, we fitted reduced models (e.g., V(A) + V(N) + V(E) or V(A) + V(E)) and obtained new variance estimates. For reduced models, narrow-sense heritability (h(2)(N)) for BMR was <0.1, but estimates of h(2)(N) for VO(2)max were higher. When estimated with the V(A) + V(E) model, the additive genetic covariance between VO(2)max and BMR was positive and statistically different from zero. This result offers tentative support for the aerobic capacity model for the evolution of vertebrate energetics. However, constraints imposed on the genetic model may cause our estimates of additive variance and covariance to be biased, so our results should be interpreted with caution and tested via selection experiments.     

Prediction of additive and dominance effects in selected or unselected populations with inbreeding

Summary A genetic model with either 64 or 1,600 unlinked biallelic loci and complete dominance was used to study prediction of additive and dominance effects in selected or unselected populations with inbreeding. For each locus the initial frequency of the favourable allele was 0.2, 0.5, or 0.8 in different alternatives, while the initial narrow-sense heritability was fixed at 0.30. A population of size 40 (20 males and 20 females) was simulated 1,000 times for five generations. In each generation 5 males and 10 or 20 females were mated, with each mating producing four or two offspring, respectively. Breeding individuals were selected randomly, on own phenotypic performance or such yielding increased inbreeding levels in subsequent generations. A statistical model containing individual additive and dominance effects but ignoring changes in mean and genetic covariances associated with dominance due to inbreeding resulted in significantly biased predictions of both effects in generations with inbreeding. Bias, assessed as the average difference between predicted and simulated genetic effects in each generation, increased almost linearly with the inbreeding coefficient. In a second statistical model the average effect of inbreeding on the mean was accounted for by a regression of phenotypic value on the inbreeding coefficient. The total dominance effect of an individual in that case was the sum of the average effect of inbreeding and an individual effect of dominance. Despite a high mean inbreeding coefficient (up to 0.35), predictions of additive and dominance effects obtained with this model were empirically unbiased for each initial frequency in the absence of selection and 64 unlinked loci. With phenotypic selection of 5 males and only 10 females in each generation and 64 loci, however, predictions of additive and dominance effects were significantly biased. Observed biases disappeared with 1,600 loci for allelic frequencies at 0.2 and 0.5. Bias was due to a considerable change in allelic frequency with phenotypic selection. Ignoring both the covariance between additive and dominance effects with inbreeding and the change in dominance variance due to inbreeding did not significantly bias prediction of additive and dominance effects in selected or unselected populations with inbreeding.     

Gene flow and effective population size in two life-history types of broad whitefish Coregonus nasus from the Canadian Arctic

In this study, the magnitude and direction of gene flow and estimates of effective population sizes (N(e) ) were quantified among two life-history types (lacustrine and anadromous) of broad whitefish Coregonus nasus in the lower Mackenzie River system. The data suggest that dispersal and subsequent gene flow occurs between these groups, with the former appearing to be asymmetrical. Gene flow may potentially be directionally biased as well, a result attributed to source-sink population dynamics and the ongoing process of post-glacial colonization and contemporary range expansion. Additionally, average N(e) estimates were consistently lower for lacustrine populations of C. nasus although confidence intervals for both contemporary and historical estimates broadly overlapped. The lower average estimates of N(e) for lacustrine populations was suggested to be the result of more recent founding events following post-glacial dispersal. This study provides one of the first assessments of gene flow and N(e) in an Arctic coregonine, results that may be relevant to other freshwater and anadromous Arctic species persisting in systems near the periphery of their range.     

Biases in Visual,Auditory, and Audiovisual Perception of Space

Localization of objects and events in the environment is critical for survival, as many perceptual and motor tasks rely on estimation of spatial location. Therefore, it seems reasonable to assume that spatial localizations should generally be accurate. Curiously, some previous studies have reported biases in visual and auditory localizations, but these studies have used small sample sizes and the results have been mixed. Therefore, it is not clear (1) if the reported biases in localization responses are real (or due to outliers, sampling bias, or other factors), and (2) whether these putative biases reflect a bias in sensory representations of space or a priori expectations (which may be due to the experimental setup, instructions, or distribution of stimuli). Here, to address these questions, a dataset of unprecedented size (obtained from 384 observers) was analyzed to examine presence, direction, and magnitude of sensory biases, and quantitative computational modeling was used to probe the underlying mechanism(s) driving these effects. Data revealed that, on average, observers were biased towards the center when localizing visual stimuli, and biased towards the periphery when localizing auditory stimuli. Moreover, quantitative analysis using a Bayesian Causal Inference framework suggests that while pre-existing spatial biases for central locations exert some influence, biases in the sensory representations of both visual and auditory space are necessary to fully explain the behavioral data. How are these opposing visual and auditory biases reconciled in conditions in which both auditory and visual stimuli are produced by a single event? Potentially, the bias in one modality could dominate, or the biases could interact/cancel out. The data revealed that when integration occurred in these conditions, the visual bias dominated, but the magnitude of this bias was reduced compared to unisensory conditions. Therefore, multisensory integration not only improves the precision of perceptual estimates, but also the accuracy.     

The consequences of using inadequate testers in the simplified triple test-cross.

The genetical consequences of common alleles in the L1 and L2 testers of a simplified version of the triple test-cross which is applicable to populations of inbred lines are examined. The test for epistasis under these circumstances becomes ambiguous and can spuriously detect non-allelic interactions when they may not exist although it still provides a test for epistasis and the adequacy of the testers simultaneously. The tests of significance and the estimates of additive variation are biased to an extent related to the dominance and dominance x additive effects of the common loci while the significance and estimates of dominance variation are deflated because they reflect the dominance effects at the non-common loci only. The covariance of sums and differences is also underestimated for the same reasons. These expectations are illustrated by analysing the 190 simplified triple test-crosses that could be extracted from a 20 x 20 diallel set of crosses between pure-breeding lines of Nicotiana rustica.