Prediction of rates of inbreeding in populations undergoing index selection

For populations undergoing mass selection, previous studies have shown that the rate of inbreeding is directly related to the mean and variance of long-term contributions from ancestors to descendants, and thus prediction of the rate of inbreeding can be achieved via the prediction of long-term contributions. In this paper, it is shown that the same relationship between the rate of inbreeding and long-term contributions is found when selection is based on an index of individual and sib records (index selection) and where sib records may be influenced by a common environment. In these situations, rates of inbreeding may be considerably higher than under mass selection. An expression for the rate of inbreeding is derived for populations undergoing index selection based on variances of (one-generation) family size and incorporating the concept of long-term selective advantage. When the mating structure is hierarchical, and when half-sib records are included in the index, the correlation between parental breeding values and the index values of their offspring is higher for male parents than female parents. This introduces an important asymmetry between the contributions of male and female ancestors to the evolution of inbreeding which is not present when selection is based on individual and/or full-sib records alone. The prediction equation for index selection accounts for this asymmetry. The prediction is compared to rates of inbreeding calculated from simulation. The prediction is good when family size is small relative to the number selected. The reasons for overprediction in other situations are discussed.     

Close‐kin mating,but not inbred parents,reduces hatching rates and offspring quality in a threatened tortoise

Inbreeding depression, the reduction in fitness due to mating of related individuals, is of particular conservation concern in species with small, isolated populations. Although inbreeding depression is widespread in natural populations, long‐lived species may be buffered from its effects during population declines due to long generation times and thus are less likely to have evolved mechanisms of inbreeding avoidance than species with shorter generation times. However, empirical evidence of the consequences of inbreeding in threatened, long‐lived species is limited. In this study, we leverage a well‐studied population of gopher tortoises, Gopherus polyphemus, to examine the role of inbreeding depression and the potential for behavioural inbreeding avoidance in a natural population of a long‐lived species. We tested the hypothesis that increased parental inbreeding leads to reduced hatching rates and offspring quality. Additionally, we tested for evidence of inbreeding avoidance. We found that high parental relatedness results in offspring with lower quality and that high parental relatedness is correlated with reduced hatching success. However, we found that hatching success and offspring quality increase with maternal inbreeding, likely due to highly inbred females mating with more distantly related males. We did not find evidence for inbreeding avoidance in males and outbred females, suggesting sex‐specific evolutionary trade‐offs may have driven the evolution of mating behaviour. Our results demonstrate inbreeding depression in a long‐lived species and that the evolution of inbreeding avoidance is shaped by multiple selective forces.     

FEMALE FREQUENCIES IN GYNODIOECIOUS POPULATIONS CORRELATED WITH SELFING RATES IN HERMAPHRODITES

Gynodioecious populations consist of separate hermaphroditic and female individuals. Females are at a selective disadvantage because they contribute genes to the next generation only through ovules, while hermaphrodites contribute genes through ovules and pollen. For females to be maintained in populations they must have some compensating selective advantage. The outcrossing hypothesis postulates that females are maintained because their progeny result from obligate outcrossing, whereas some of the progeny of hermaphrodites result from self-fertilization and are less fit because of inbreeding depression. If correct, the frequency of females should be positively correlated with selfing rates of hermaphrodites in populations. We found a strong positive correlation between female frequency and selfing rates of hermaphrodites (r = 0.91, P < 0.01) in eight gynodioecious populations of Hawaiian species of Bidens. Our results confirm that the obligate outcrossing of females is a major factor maintaining females in gynodioecious populations. However, the observed selfing rates are insufficient by themselves to account for the frequency of females in these populations.     

Trait mean depression for second-generation inbred strawberry populations with and without parent selection

 Strawberry genotypes selected for superior fruit yield or chosen at random from first-generation self, full-sib, and half-sib populations were crossed to provide second-generation inbred progenies and composite cross-fertilized control populations. Mean yields for inbred offspring from crosses among selected parents exceeded those from the offspring of unselected parents by 87%, 23%, and 37% for self, full-sib, and half-sib populations, respectively; yields for offspring from unrelated crosses among selected parents were 54% larger than those for crosses among unselected parents. Selection for yield also resulted in significant correlated response for fruit number and plant diameter. Mean yields for second-generation half-sib and full-sib offspring from selected parents were greater than those for offspring from the unselected but non-inbred control population. This suggests that selection can be a powerful force in counteracting most of the inbreeding depression expected in cross-fertilized strawberry breeding programs. Selection treatment× inbreeding rate interactions were non-significant for all traits; thus, selection among partially inbred offspring did not have a large effect on the rate of genetic progress. Differential realized selection intensity among individuals with differing levels of homozygosity accumulated due to inbreeding is suggested as the most likely explanation for the absence of association between pedigree inbreeding coefficients and cross performance detected previously in strawberry. Received: 21 July 1996 / Accepted: 7 March 1997     

Prediction of rates of inbreeding in selected populations

A method is presented for the prediction of rate of inbreeding for populations with discrete generations. The matrix of Wright's numerator relationships is partitioned into 'contribution' matrices which describe the contribution of the Mendelian sampling of genes of ancestors in a given generation to the relationship between individuals in later generations. These contributions stabilize with time and the value to which they stabilize is shown to be related to the asymptotic rate of inbreeding and therefore also the effective population size, Ne approximately 2N/(mu 2r + sigma 2r), where N is the number of individuals per generation and mu r and sigma 2r are the mean and variance of long-term relationships or long-term contributions. These stabilized values are then predicted using a recursive equation via the concept of selective advantage for populations with hierarchical mating structures undergoing mass selection. Account is taken of the change in genetic parameters as a consequence of selection and also the increasing 'competitiveness' of contemporaries as selection proceeds. Examples are given and predicted rates of inbreeding are compared to those calculated in simulations. For populations of 20 males and 20, 40, 100 or 200 females the rate of inbreeding was found to increase by as much as 75% over the rate of inbreeding in an unselected population depending on mating ratio, selection intensity and heritability of the selected trait. The prediction presented here estimated the rate of inbreeding usually within 5% of that calculated from simulation.     

Optimal mass selection policies for schemes with overlapping generations and restricted inbreeding

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress (ΔG) are combined with expected rates of inbreeding (ΔF) in a linear objective function (Φ = ΔG - λΔF) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.     

Inbreeding under a cyclical mating system

Summary General recursion formulae for the coefficient of inbreeding under a cyclical mating system were derived in which one male and one female are selected from each of the n families per generation (population size N = 2 n). Each male is given the family number of his sire in each generation, while his mate comes from another family, varying systematically in different generations. Males of the r-th family in generations 1, 2, 3,..., t = n–1 within each cycle mate with females from families r+1, r+2, r+3,..., r+t to produce generations 2, 3, 4,..., t+1=1, respectively. The change in heterozygosity shows a cyclical pattern of rises and falls, repeating in cycles of n–1 generations. The rate of inbreeding oscillates between <-3% to >6% in different generations within each cycle, irrespective of the population size. The average rate of inbreeding per generation is approximately 1/[4 N-(Log₂N+1)], which is the rate for the maximum avoidance of inbreeding. The average inbreeding effective population size is approximately 2 N–2.     

Problems in measuring among-family variation in inbreeding depression

Understanding the sources of variation in inbreeding depression within populations is important for understanding the evolution of selfing rates. At the population level, inbreeding depression is due to decreased heterozygosity caused by inbreeding, which decreases overdominance and increases the frequency of expression of recessive deleterious alleles. However, within individual families inbreeding has two distinct consequences: it reduces heterozygosity and it restricts the alleles present in offspring to those present in the parent. Outcrossing both increases heterozygosity and brings new alleles into a family (compared to the alleles present if the plant is self-pollinated). Both consequences of inbreeding affect offspring fitness, but the most common experimental design used to measure among-family variation in inbreeding depression cannot distinguish them. The result is that variance in inbreeding depression among families is confounded by genetic variation in the traits being measured. Also, correlations (among families) between measures of inbreeding depression or between inbreeding depression and mean trait values are confounded by genetic variation in the traits being measured. I conclude that more complex crossing designs that allow estimation of breeding values for individual families are required to accurately detect and measure among-family variation in inbreeding depression.     

Strong inbreeding depression in a Daphnia metapopulation

The deleterious effects of inbreeding have long been known, and inbreeding can increase the risk of extinction for local populations in metapopulations. However, other consequences of inbreeding in metapopulations are still not well understood. Here we show the presence of strong inbreeding depression in a rockpool metapopulation of the planktonic freshwater crustacean Daphnia magna, which reproduces by cyclical parthenogenesis. We conducted three experiments in real and artificial rockpools to quantify components of inbreeding depression in the presence and the absence of competition between clonal lines of selfed and outcrossed genotypes. In replicated asexual populations, we recorded strong selection against clones produced by selfing in competition with clones produced by outcrossing. In contrast, inbreeding depression was much weaker in single-clone populations, that is, in the absence of competition between inbred and outbred clones. The finding of a competitive advantage of the outbred genotypes in this metapopulation suggests that if rockpool populations are inbred, hybrid offspring resulting from crosses between immigrants and local genotypes might have a strong selective advantage. This would increase the effective gene flow in the metapopulation. However, the finding of low inbreeding depression in the monoclonal populations suggests that inbred and outbred genotypes might have about equal chances of establishing new populations.     

Among- and within-population variation in outcrossing rate of a mixed-mating freshwater snail

Mixed-mating animals self-fertilize a proportion of their offspring. Outcrossing rate may covary with the ecological and historical factors affecting the population. Theory predicts that outcrossing is favored when inbreeding depression is high and when individual heterozygosity is important. Self-fertilization is predicted to be favored when costs of male function, or mate finding are high, for example, when empty patches are colonized by few individuals. In this study, we assessed primary (after hatching) and secondary (after juvenile mortality) outcrossing rates of two mixed-mating snail populations. Our purpose was to assess the variation in mating-system parameters and estimate significance of inbreeding depression for secondary outcrossing rate (the realized outcrossing rate of parents that produce the next generation). Secondary outcrossing rate was higher than the primary outcrossing rate in one of the two populations, suggesting considerable inbreeding depression. In the other study population, secondary outcrossing rates were found to increase when initially low, or decrease when initially high, depending on the family. Moderate outcrossing rates were found to be more stable. Parental inbreeding coefficients were close to zero in both populations. Outcrossing rate was much more variable among families in the population with the lower average outcrossing rate, suggesting that individuals differed considerably in their mating system. Our results add to recent studies suggesting that populations of mixed-mating animals may differ in their mating system parameters and expression of inbreeding depression.     

Inbreeding and Hybridizing Cyst Nematodes on Pruned Soybeans in Petri Plates

Inbred nematodes propagated on a selecting host are likely to have homozygous genes of interest for investigating the genetics of host-parasite associations. A technique is presented to inbreed soybean cyst nematodes, by sibling matings at each generation, and to cross inbred lines. Soybean seedlings with severely trimmed cotyledons survive well on 0.8% agar. Eggs from a single female are incubated in water in a microtiter well. Virgin as well as mated females result from inoculation of two juveniles per root. Sibling males from the same source are produced by mass inoculations of eggs. Males are added individually to unmated females. Overall success for fertile females was 14% in 1,368 isolations. Three generations of inbreeding by siblings were achieved using nematodes from two populations that differ in their ability to reproduce on differential soybeans. Hybrids from crosses of the two inbred lines tested on differential hosts showed that the influence of Population 1 (selected and inbred on PI 209332) is greater than that of Population 2 (selected and inbred on PI 89772). Reciprocal crosses suggest that the influence of males is stronger than that of females in determining host specificity of F₁ offspring in these crosses. Our technique is simple and effective for inbreeding and crossing soybean cyst nematodes.     

The cost of selfing inEncyclia cochleata (Orchidaceae)

To determine whether inbreeding depression accounts for the maintenance of outcrossing in populations of the self-compatible orchidEncyclia cochleata, the estimated selective advantage of selfing was compared to a measure of inbreeding depression. Individuals from three populations ofE. cochleata and some of their progeny were phenotyped using isozyme analysis. The electrophoretic data were used to estimate the outcrossing rate and the theoretical cost of outcrossing. Inbreeding depression was estimated by comparing the fitness of the progeny resulting from both types of pollinations. The seeds from outcrossed and selfed hand-pollinations and naturally pollinated seeds from a population of the triandrous form ofE. cochleata were grown aseptically on culture media, and their development over the next three years recorded. Inbreeding was common, particularly in one population (outcrossing rate 40%). However, the level of inbreeding depression was only 1–2%, considerably less inbreeding depression than expected.     

Effects of inbreeding and interpopulation crosses on performance and plasticity of two generations of offspring of a declining grassland plant

? Premise of the study: Inbreeding depression is a major evolutionary force and an important topic in conservation genetics because habitat fragmentation leads to increased inbreeding in the populations of many species. Crosses between populations may restore heterozygosity, resulting in increased performance (heterosis), but may also lead to the disruption of coadapted gene complexes and to decreased performance (outbreeding depression). ? Methods: We investigated the effects of selfing and of within and between population crosses on reproduction and the performance of two generations of offspring of the declining grassland plant Saxifraga granulata (Saxifragaceae). We also subjected the first generation of offspring to a fertilization and two stress treatments (competition and defoliation) to investigate whether the effects of inbreeding and interpopulation gene flow depend on environmental conditions. ? Key results: Inbreeding depression affected all traits in the F(1) generation (δ = 0.07-0.55), but was stronger for traits expressed late during development and varied among families. The adaptive plasticity of offspring from selfing and from interpopulation crosses in response to nutrient addition was reduced. Outbreeding depression was also observed in response to stress. Multiplicative fitness of the F(2) generation after serial inbreeding was extremely low (δ > 0.99), but there was heterosis after crossing inbred lines. Outbreeding depression was not observed in the F(2). ? Conclusions: Continuous inbreeding may drastically reduce the fitness of plants, but effects may be environment-dependent. When assessing the genetic effects of fragmentation and interpopulation crosses, the possible effects on the mean performance of offspring and on its adaptive plasticity should be considered.     

Genetic rescue persists beyond first-generation outbreeding in small populations of a rare plant

Habitat fragmentation commonly causes genetic problems and reduced fitness when populations become small. Stocking small populations with individuals from other populations may enrich genetic variation and alleviate inbreeding, but such artificial gene flow is not commonly used in conservation owing to potential outbreeding depression. We addressed the role of long-term population size, genetic distance between populations and test environment for the performance of two generations of offspring from between-population crosses of the locally rare plant Ranunculus reptans L. Interpopulation outbreeding positively affected an aggregate measure of fitness, and the fitness superiority of interpopulation hybrids was maintained in the second offspring (F2) generation. Small populations benefited more strongly from interpopulation outbreeding. Genetic distance between crossed populations in neutral markers or quantitative characters was not important. These results were consistent under near-natural competition-free and competitive conditions. We conclude that the benefits of interpopulation outbreeding are likely to outweigh potential drawbacks, especially for populations that suffer from inbreeding.     

Mating system contributes only slightly to female maintenance in gynodioecious Geranium maculatum (Geraniaceae)

Gynodioecy, the co-occurrence of female and hermaphroditic individuals within a population, is an important intermediate in the evolution of separate sexes. The first step, female maintenance, requires females to have higher seed fitness compared with hermaphrodites. A common mechanism thought to increase relative female fitness is inbreeding depression avoidance, the magnitude of which depends on hermaphroditic selfing rates and the strength of inbreeding depression. Less well studied is the effect of biparental inbreeding on female fitness. Biparental inbreeding can affect relative female fitness only if its consequence or frequency differs between sexes, which could occur if sex structure and genetic structure both occur within populations. To determine whether inbreeding avoidance and/or biparental inbreeding can account for female persistence in Geranium maculatum, we measured selfing and biparental inbreeding rates in four populations and the spatial genetic structure in six populations. Selfing rates of hermaphrodites were low and did not differ significantly from zero in any population, leading to females gaining at most a 1–14% increase in seed fitness from inbreeding avoidance. Additionally, although significant spatial genetic structure was found in all populations, biparental inbreeding rates were low and only differed between sexes in one population, thereby having little influence on female fitness. A review of the literature revealed few sexual differences in biparental inbreeding among other gynodioecious species. Our results show that mating system differences may not fully account for female maintenance in this species, suggesting other mechanisms may be involved.     

Population Genetics and the Effects of a Severe Bottleneck in an Ex Situ Population of Critically Endangered Hawaiian Tree Snails

As wild populations decline, ex situ propagation provides a potential bank of genetic diversity and a hedge against extinction. These programs are unlikely to succeed if captive populations do not recover from the severe bottleneck imposed when they are founded with a limited number of individuals from remnant populations. In small captive populations allelic richness may be lost due to genetic drift, leading to a decline in fitness. Wild populations of the Hawaiian tree snail Achatinella lila, a hermaphroditic snail with a long life history, have declined precipitously due to introduced predators and other human impacts. A captive population initially thrived after its founding with seven snails, exceeding 600 captive individuals in 2009, but drastically declined in the last five years. Measures of fitness were examined from 2,018 captive snails that died between 1998 and 2012, and compared with genotypic data for six microsatellite loci from a subset of these deceased snails (N = 335), as well as live captive snails (N = 198) and wild snails (N = 92). Surprisingly, the inbreeding coefficient (F_is) declined over time in the captive population, and is now approaching values observed in the 2013 wild population, despite a significant decrease in allelic richness. However, adult annual survival and fecundity significantly declined in the second generation. These measures of fitness were positively correlated with heterozygosity. Snails with higher measures of heterozygosity had more offspring, and third generation offspring with higher measures of heterozygosity were more likely to reach maturity. These results highlight the importance of maintaining genetic diversity in captive populations, particularly those initiated with a small number of individuals from wild remnant populations. Genetic rescue may allow for an increase in genetic diversity in the captive population, as measures of heterozygosity and rarified allelic richness were higher in wild tree snails.     

Inbreeding depression for various traits in two cultured populations of the American bay scallop, Argopecten irradians irradians Lamarck (1819) introduced into China

This paper examines the effect of inbreeding level of population on the magnitude of inbreeding depression expressed by comparing them between two cultured populations (A and B) in the hermaphroditic animal of the bay scallop Argopecten irradians irradians. Population A is expected to have less genetic variations and higher inbreeding level due to longer cultured history (20 generations) and less “ancestral” individuals (26 individuals) than population B due to shorter cultured history (4 generations) and more “ancestral” individuals (406 individuals). Two groups within each population were produced, one using self-fertilization and one using mass-mating within the same population. Selfed offspring (AS and BS) from two populations both had lower fitness components than their mass-mated counterparts (AM and BM) and exhibited inbreeding depression for all examined traits, e.g. lower hatching, less viability and slower growth, indicating that inbreeding depression is a common feature in this animal. Fitness components in all traits of offspring from population A significantly differed those from population B and the magnitude of inbreeding depression for all traits in population A with higher inbreeding level was significantly smaller than that in population B with lower inbreeding level, indicating that both fitness components and magnitude of inbreeding depression were significantly affected by inbreeding level of populations and genetic load harbored in population A may be partially purged through inbreeding. Moreover, the magnitude of inbreeding depression in the two populations both varied among traits and life history stages. The present results support the partial-dominance hypothesis of inbreeding depression.     

Gender-specific inbreeding depression in a gynodioecious plant, Geranium maculatum (Geraniaceae)

In gynodioecious species, females coexist with hermaphrodites in natural populations even though hermaphrodites attract more pollinators, are capable of reproducing through pollen, and can self-fertilize. This study tests the hypothesis that inbreeding depression helps to maintain females in natural populations. It also examines whether gender lineages that differ in selfing rates might experience different levels of inbreeding depression. Female and hermaphroditic lineages of the gynodioecious species Geranium maculatum were used in self, sib-cross and outcross experiments to examine inbreeding depression levels and to determine whether these levels differ between hermaphroditic and female lineages. Six fitness correlates were measured in the greenhouse and compared among pollination types and between genders. Severe inbreeding depression was found for both individual fitness traits and cumulative fitness in early life history stages. Inbreeding depression levels were slightly higher in hermaphroditic than in female lineages, but this difference was not statistically significant. Because females are unable to self-pollinate and are less likely to experience inbreeding than hermaphrodites under natural conditions, these results suggest that severe inbreeding depression could confer a selective advantage for females that could help to maintain females in natural populations.     

Variation in inbreeding depression among populations of the seed beetle, Stator limbatus

Inbreeding depression has been documented in many insect species, but the degree to which it varies among traits within populations and among populations within species is poorly understood. We used a single‐generation factorial breeding design to examine variation in inbreeding depression among three populations of the seed‐feeding beetle, Stator limbatus Horn (Coleoptera: Chrysomelidae: Bruchinae), from the southwestern USA. Eggs from sib matings were less likely to develop and hatch, and larval hatch‐to‐adult mortality was higher for offspring of sib matings. Overall, inbreeding resulted in a reduction in the proportion of eggs that produced an adult from >80% for outbred matings in all three populations to an average of only 54% for inbred matings. Of those larvae that survived to adult, inbred beetles took ～1.5 days (>5%) longer to reach adult. The only measured trait not affected by inbreeding was adult body mass. The degree to which inbreeding increased mortality varied among the populations – inbreeding depression was lowest in the population that is most isolated. Although populations of S. limbatus are generally large in nature our results suggest that increased inbreeding associated with population fragmentation can have substantial effects on fitness of S. limbatus.     

Mating patterns and demography in the tristylous daffodil Narcissus triandrus

Mating patterns in plant populations are influenced by interactions between reproductive traits and ecological conditions, both factors that are likely to vary geographically. Narcissus triandrus, a wide-ranging heterostylous herb, exhibits populations with either two (dimorphic) or three (trimorphic) style morphs and displays substantial geographical variation in demographic attributes and floral morphology. Here, we investigate this variation to determine if demography, morphology, and mating system differ between the two sexual systems. Our surveys in Portugal and NW Spain indicated that dimorphic populations were less dense, of smaller size, and had larger plants and flowers compared to trimorphic populations. Outcrossing rates estimated using allozyme markers revealed similar outcrossing rates in dimorphic and trimorphic populations (t(m) dimorphic=0.759; t(m) trimorphic=0.710). All populations experienced significant inbreeding in progeny (mean F=0.143). In contrast, parental estimates of inbreeding were not significantly different from zero (mean F=0.062), implying that few inbred offspring survive to reproductive maturity due to inbreeding depression. Although the majority of inbreeding results from selfing, significant levels of biparental inbreeding were also detected in eight of the nine populations (mean s(s)-s(m)=0.081). Density was negatively associated with levels of selfing but positively associated with biparental inbreeding. Population size was positively associated with outcrossing but not biparental inbreeding. There were no consistent differences among the style morphs in outcrossing or biparental inbreeding indicating that the maintenance of trimorphism vs dimorphism is unlikely to be associated with inbreeding of maternal parents.