Comparison of ancestral and current-generation inbreeding in an experimental strawberry breeding population

Progenies from first-generation self, half-sib, full-sib, and cross fertilizations were generated to evaluate the magnitude of inbreeding depression for vegetative and production traits in strawberry. Tests were conducted to determine the linearity of trait mean depression with inbreeding rate (F) over this range of inbreeding values, as an indication of the presence of non-additive epistasis. A control population, for which a similar range of coancestry had accumulated over several cycles of breeding and selection, was also generated to compare the consequences of ancestral and current-generation inbreeding. Trait means for crosses among current-generation half-sibs, full-sibs, and selfs were 2–17%, 3–12%, and 14–45% lower than for unrelated crosses among the same set of parents, respectively. Linear regression of progeny means on current generation F was significantly negative for all traits and explained 17–44% of the variance among progeny means. Mean depression was largely linear over the range of inbreeding rates tested in this population, indicating the absence of epistasis for the traits evaluated. Conversely, (F) regressions of progeny means on pedigree inbreeding coefficients, where coancestry had accumulated over several cycles of breeding and selection, were uniformly non-significant and explained 0–10% of the variance among cross means. Further, multiple regression of progeny means for current-generation relatives on pedigree F failed to improve fit significantly over regression on current-generation F alone for all traits. Together, these results suggest that pedigree inbreeding coefficients are poor predictors of changes in homozygosity when populations are developed through multiple cycles of breeding and selection. They also imply that inbreeding depression will be of minor importance for strawberry breeding populations managed with adequate population sizes and strong directional selection.     

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.     

LIFETIME ESTIMATES OF BIPARENTAL INBREEDING DEPRESSION IN THE SELF-INCOMPATIBLE ANNUAL PLANT RAPHANUS SATIVUS

Studies of inbreeding depression in plant populations have focused primarily on comparisons of selfing versus outcrossing in self-compatible species. Here we examine the effect of five naturally occurring levels of inbreeding (f ranging from 0 to 0.25 by pedigree) on components of lifetime fitness in a field population of the self-incompatible annual, Raphanus sativus. Pre- and postgermination survival and reproductive success were examined for offspring resulting from compatible cross-pollinations. Multiple linear regression of inbreeding level on rates of fruit and seed abortion as well as seed weight and total seed weight per fruit were not significant. Inbreeding level was not found to affect seed germination, offspring survival in the field, date of first flowering, or plant biomass (dry weight minus fruit). The effect of inbreeding on seedling viability in the greenhouse and viability to flowering was significant but small and inconsistently correlated with inbreeding level. Maternal fecundity, however, a measure of seed yield, was reduced almost 60% in offspring from full-sib crosses (f = 0.25) relative to offspring resulting from experimental outcross pollinations (f = 0). Water availability, a form of physiological stress, affected plant biomass but did not affect maternal fecundity, nor did it interact with inbreeding level to influence these characters. The delayed expression of strong inbreeding depression suggests that highly deleterious recessive alleles were not a primary cause of fitness loss with inbreeding. Highly deleterious recessives may have been purged by bottlenecks in population size associated with the introduction of Raphanus and its recent range expansions. In general, reductions in total relative fitness of greater than 50% associated with full-sib crosses should be sufficient to prohibit the evolution of self-compatibility via transmission advantage in Raphanus.     

Effects of inbreeding on economic traits of channel catfish

Summary Inbred channel catfish (Ictalurus punctatus) were produced from two generations of full-sib matings to study the effect of inbreeding on reproduction, growth and survival. A randomly mated control line was propagated from the same base population to be used for the evaluation of the inbred fish. First generation inbred (I1) and control (C1) lines comprised five full-sib families each. Second generation inbred (I2) and control (C2) lines were produced by mating each male catfish from the I1 or C1 line to two females in sequence, one from the I1 and one from the C1 line. The design also produced two reciprocal outcross lines to be compared to their contemporary inbred and control lines. The coefficient of inbreeding for the inbred line increased from 0.25 in generation 1 to 0.375 in generation 2. The inbreeding coefficient was zero for all other lines. The resulting fish were performance tested in two locations, Tifton, Georgia and Auburn, Alabama and no genotype-environment interactions occurred. Results indicated that one generation of inbreeding increased number of days required for eggs to hatch by 21%, but did not significantly influence spawn weight or hatchability score. However, inbred females produced more eggs/kg body weight than control females. Two generations of full-sib mating in Georgia did not depress weight when expressed as a deviation to random controls but was depressed 13–16% when expressed as a deviation to half-sib out-crosses. Second generation inbreds produced in Alabama exhibited a 19% depression for growth rate when compared to either random or half-sib outcross controls. Survival rates at various age intervals was not decreased by inbreeding. The amount of inbreeding depression varied among families and between sexes.This study was supported by State and Hatch Funds allocated to the Georgia and Alabama Agricultural Experiment Stations     

Inbreeding depression and mating-distance dependent offspring fitness in large and small populations of Lychnis flos-cuculi (Caryophyllaceae)

The spatial structure of four Lychnis flos-cuculi populations, varying in size and degree of isolation, was studied by comparing the fitness of offspring resulting from self-pollination and pollinations by neighbouring plants, plants within the same population, and plants from other populations. Selfed offspring had the lowest fitness of the four offspring groups. No significant difference was found between the performance of offspring from pollinations by neighbouring plants and offspring pollinated by plants further apart but within the same population. A lower fitness of offspring from pollinations between neighbours would be expected if these matings, on average, yielded inbred offspring which suffered from inbreeding depression. These results imply that either a tight neighbourhood structuring is not present, or that the inbreeding depression for offspring by neighbours is too low to detect, although these are inbred. Crossings between populations produced offspring with a significantly higher fitness than offspring sired within populations. There were no significant differences in response to inbreeding among the populations, and differences in mean fitness among populations had no clear relation to the population size or degree of isolation. A reduced fitness of small populations due to inbreeding depression or a less severe response to experimental inbreeding due to purging of deleterious alleles is therefore not supported by our results.     

A Test of the 'Genetic Rescue' Technique Using Bottlenecked Donor Populations of Drosophila melanogaster

We produced replicated experimental lines of inbred fruit flies Drosophila melanogaster to test the effects of crossing different bottlenecked populations as a method of 'genetic rescue' for endangered species lacking outbred donor populations. Two strains differing in the origin of the founders were maintained as isolated populations in a laboratory environment. After two generations of controlled full-sib matings, the resulting inbred fruit flies had significantly reduced breeding success and survival rates. However, crosses between the two bottlenecked strains reversed the effects of inbreeding and led to increases in breeding success and survival that persisted into the second generation of hybrid offspring. In contrast, crosses within each strain (but between different replicate lines) resulted in only slight improvements in some fitness components, and this positive trend was reversed in the second generation. This experiment highlights the potential value of translocations between different inbred populations of endangered species as a tool to mitigate the negative effects of inbreeding, but this benefit may depend upon the origin of the populations. Our results also confirm the importance of maintaining adequate levels of genetic variation within populations and that severely bottlenecked populations should not be discounted as possible donors in genetic rescue programs for endangered species.     

Methods for predicting rates of inbreeding in selected populations

Summary In selected populations, families superior for the selected trait are likely to contribute more offspring to the next generation than inferior families and, as a consequence, the rate of inbreeding is likely to be higher in selected populations than in randomly mated populations of the same structure. Methods to predict rates of inbreeding in selected populations are discussed. The method of Burrows based on probabilities of coselection is reappraised in conjunction with the transition matrix method of Woolliams. The method of Latter based on variances and covariances of family size is also examined. These methods are one-generation approaches in the sense that they only account for selective advantage over a single generation, from parents to offspring. Two-generation methods are developed that account for selective advantage over two generations, from grandparent to grandoffspring as well as from parent to offspring. Predictions are compared to results from simulation. The best one-generation method was found to underpredict rates of inbreeding by 10–25%, and the two-generation methods were found to underpredict rates of inbreeding by 9–18%.     

Genomic Predictability of Interconnected Biparental Maize Populations

Intense structuring of plant breeding populations challenges the design of the training set (TS) in genomic selection (GS). An important open question is how the TS should be constructed from multiple related or unrelated small biparental families to predict progeny from individual crosses. Here, we used a set of five interconnected maize (Zea mays L.) populations of doubled-haploid (DH) lines derived from four parents to systematically investigate how the composition of the TS affects the prediction accuracy for lines from individual crosses. A total of 635 DH lines genotyped with 16,741 polymorphic SNPs were evaluated for five traits including Gibberella ear rot severity and three kernel yield component traits. The populations showed a genomic similarity pattern, which reflects the crossing scheme with a clear separation of full sibs, half sibs, and unrelated groups. Prediction accuracies within full-sib families of DH lines followed closely theoretical expectations, accounting for the influence of sample size and heritability of the trait. Prediction accuracies declined by 42% if full-sib DH lines were replaced by half-sib DH lines, but statistically significantly better results could be achieved if half-sib DH lines were available from both instead of only one parent of the validation population. Once both parents of the validation population were represented in the TS, including more crosses with a constant TS size did not increase accuracies. Unrelated crosses showing opposite linkage phases with the validation population resulted in negative or reduced prediction accuracies, if used alone or in combination with related families, respectively. We suggest identifying and excluding such crosses from the TS. Moreover, the observed variability among populations and traits suggests that these uncertainties must be taken into account in models optimizing the allocation of resources in GS.     

Effect of inbreeding on production of filled seed in Pinus radiata — experimental results and a model of gene action

Summary Pinus radiata D. Don was inbred to different degrees, commencing with a founder population of 8 clones. Yield of filled seed was determined for each mating type. Mean yields (%), relative to outcrossing, were: half-sib 102; full-sib 97; S₁ 43; S₂ 42. An epistatic model was developed to predict the empty seed yield following selfing, assuming that homozygosity for several recessive co-lethals is necessary to kill an embryo. Calculations were then extended to predict the yields following different degrees of inbreeding. The proposed model gave a better fit to present results, and to other published results of similar investigations, than did an alternative based on action of independent recessive lethals. Implications for breeding and seed production strategy are discussed.     

Inbreeding in Pinus radiata. I. The effect of inbreeding on growth, survival and variance

 The effects of inbreeding on growth, survival and variance in a 12-year-old radiata pine trial were studied in five populations each inbred to one of five different levels: outcross (F=0), half-sib (F=0.125), full-sib (F=0.25), selfing (S₁, F=0.5), and two-generations of selfing (S₂, F=0.75). These five populations were derived from a founder population of eight clones. Inbreeding reduced diameter, growth, and survival but increased the variance for diameter. Inbreeding depression at F=0.125, 0.25, 0.5, and 0.75 was 5%, 6%, 15%, and 19% respectively for DBH; −3%, 1%, 7%, and 11% respectively, for survival. The standard deviation for diameter increased by 10%, 10%, 30%, and 25% respectively for F=0.125, 0.25, 0.5, and 0.75 and, similarly, the coefficient of variation increased by 17%, 16%, 53%, and 55% respectively. There were significant differences among the eight founder clones in their response to inbreeding. The best clone in the trial showed no inbreeding depression. Overall, inbreeding depression was found to be linearly related to the inbreeding coefficient F with no significant quadratic effects for any trait at any population level. However, two individual clones had a quadratic relationship with F for DBH and one clone had a similar relationship for survival. A significant correlation (r=0.96) between S₂ and the breeding values of founder clones was observed while the correlation (r=0.58) between S₁ and breeding values was insignificant. The low inbreeding depression in radiata pine relative to other conifers may indicate that historical purging of detrimental alleles through small geographic populations, a higher degree of population subdivision, and the relative high fecundity of inbred progenies has rendered radiata pine an ideal species to use inbreeding as a breeding tool. Received: 10 March 1998 / Accepted: 19 May 1998     

Effect of rate of inbreeding on inbreeding depression in Drosophila melanogaster

Summary This experiment was designed to study the relationship between rate of inbreeding and observed inbreeding depression of larval viability, adult fecundity and cold shock mortality in Drosophila melanogaster. Rates of inbreeding used were full-sib mating and closed lines of N=4 and N=20. Eight generations of mating in the N=20 lines, three generations in the N=4 lines and one generation of full-sib mating were synchronised to simultaneously produce individuals with an expected level of inbreeding coefficient (F) of approximately 0.25. Inbreeding depression for the three traits was significant at F=0.25. N=20 lines showed significantly less inbreeding depression than full-sib mated lines for larval viability at approximately the same level of F. A similar trend was observed for fecundity. No effect of rate of inbreeding depression was found for cold shock mortality, but this trait was measured with less precision than the other two. Natural selection acting on loci influencing larval viability and fecundity during the process of inbreeding could explain these results. Selection is expected to be more effective with slow rates of inbreeding because there are more generations and greater opportunity for selection to act before F=0.25 is reached. Selection intensities seem to have been different in the three traits measured. Selection was most intense for larval viability, less intense for fecundity and, perhaps, negligible at loci influencing cold shock mortality.     

INBREEDING AND ITS FITNESS EFFECTS IN AN INSULAR POPULATION OF SONG SPARROWS (MELOSPIZA MELODIA)

Inbreeding depression is thought to be a major factor affecting the evolution of mating systems and dispersal. While there is ample evidence for inbreeding depression in captivity, it has rarely been documented in natural populations. In this study, I examine data from a long-term demographic study of an insular population of song sparrows (Melospiza melodia) and present evidence for inbreeding depression. Forty-four percent of all matings on Mandarte Island, British Columbia, were among known relatives. Offspring of a full-sib mating (f = 0.25) experienced a reduction in annual survival rate of 17.5% on average. Over their lifetime, females with f = 0.25 produced 48% fewer young that reached independence from parental care. In contrast, male lifetime reproductive success was not affected by inbreeding. Reduced female lifetime reproductive success was mostly due to reduced hatching rates of the eggs of inbred females. Relatedness among the parents did not affect their reproductive success. Using data on survival from egg stage to breeding age, I estimated the average song sparrow egg on Mandarte Island to carry a minimum of 5.38 lethal equivalents (the number of deleterious genes whose cumulative effect is equivalent to one lethal); 2.88 of these lethal equivalents were expressed from egg stage to independence of parental care. This estimate is higher than most estimates reported for laboratory populations and lower than those reported for zoo populations. Hence, the costs of inbreeding in this population were substantial and slightly above those expected from laboratory studies. Variability in estimates of lethal equivalents among years showed that costs of inbreeding were not constant across years.     

Inbreeding in three captive groups of rhesus monkeys

Using electrophoretic and serological genetic markers each of 17 potentially inbred matings in three groups of rhesus monkeys could be classified as either inbred or noninbred matings. Although nine of these 17 matings involved either father-daughter or paternal half-sib matings, only 7.4 were expected by chance alone. At least two, and possibly as many as three, of the nine cases of inbreeding involved father-daughter matings. Thus, no evidence of avoidance of inbreeding was observed in the closed captive groups of rhesus monkeys studied. Colony management policies must be developed to minimize the opportunity for or the deleterious effects of both father-daughter and half-sib matings. Furthermore, kin selection theory should consider why kin recognition, if it occurs, does not lead to avoidance of inbreeding.     

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.     

Power of two and three-generation QTL mapping experiments in an outbred population containing full-sib or half-sib families

QTL mapping experiments involve many animals to be genotyped and performance tested. Consequently, experimental designs need to be optimized to minimize the costs of data collection and genotyping. The present study has analyzed the power and efficiency of experiments with two or three-generation family structures containing full-sib families, half-sib families, or both. The focus was on data from one outbred population because the main interest is to locate genes that can be used for within-line selection. For a two generation experiment more animals had to be typed for marker loci to obtain a certain power than for a three generation experiment. Fewer trait values, however, had to be obtained for a two-generation experiment than for a three-generation experiment. A two or three-generation family structure with full-sib offspring was more efficient than a two or three-generation family structure with half-sib offspring. A family structure with full-sib grand-offspring, however, was less efficient than a family structure with half-sib grand-offspring. For the most efficient family structure each pair of parents had full-sib offspring that were genotyped for the marker. For the most-efficient family structure each full-sib offspring had half-sib grand-offspring for which trait values were obtained. For equal power with a heritability of 0.1 and 100 grand-offspring per full-sib offspring, 30-times less marker typings were required for this most efficient family structure than for a two-generation half-sib structure in which marker genotypes and trait values were obtained for half-sib offspring. The effect of heritability and the type of analysis (single marker or interval analysis) on the efficiency of a family structure is described. The results of this study should help to design QTL mapping experiments in an outbred population.     

A comparison of genetic information from open-pollinated and control-pollinated progeny tests in two eucalypt species

Genetic-parameter estimates and parental breeding-value predictions were compared from open-pollinated and control-pollinated progeny populations of Eucalyptus globulus and two populations of E. nitens. For E. globulus there were two types of open-pollinated populations (native stand open-pollinated and seed orchard open-pollinated) and two types of control-pollinated populations (intra-provenance and interprovenance full-sib families). For E. nitens there were two populations, a seed orchard open-pollinated population and intra-provenance full-sib families. Progeny tests were established across multiple sites and 2-year height and diameter were measured and volume calculated. Genetic parameters from native stand open-pollinated E. globulus were unlike the parameters from the other three E. globulus populations; heritability estimates were severely inflated, presumably due to high levels, and possibly differential levels, of inbreeding depression relative to the other populations. Estimates of dominance variance in the E. globulus full-sib populations were high, but were zero in the E. nitens population. Correlations among parental breeding values, predicted using data from the different populations, were generally low and non-significant, with two exceptions: predictions from the two E. globulus full-sib populations were significantly correlated (r=0.54, P = 0.001), as were predictions from the E. nitens seed orchard OP and full-sib population (r = 0.61, P = 0.08). There was some indication that superior parents of E. globulus native stand open-pollinated families also tended to have above-average breeding values based on the performance of intra-provenance full-sib offspring. The consequences of these results for exploitation of base-population collections from native stands are discussed.     

Effect of selection against deleterious mutations on the decline in heterozygosity at neutral loci in closely inbreeding populations.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.     

Optimised parent selection and minimum inbreeding mating in small aquaculture breeding schemes: a simulation study

The effectiveness of low cost breeding scheme designs for small aquaculture breeding programmes were assessed for their ability to achieve genetic gain while managing inbreeding using stochastic simulation. Individuals with trait data were simulated over 15 generations with selection on a single trait. Combinations of selection methods, mating strategies and genetic evaluation options were evaluated with and without the presence of common environmental effects. An Optimal Parent Selection (OPS) method using semi-definite programming was compared with a truncation selection (TS) method. OPS constrains the rate of inbreeding while maximising genetic gain. For either selection method, mating pairs were assigned from the selected parents by either random mating (RM) or Minimum Inbreeding Mating (MIM), which used integer programming to determine mating pairs. Offspring were simulated for each mating pair with equal numbers of offspring per pair and these offspring were the candidates for selection of parents of the next generation. Inbreeding and genetic gain for each generation were averaged over 25 replicates. Combined OPS and MIM led to a similar level of genetic gain to TS and RM, but inbreeding levels were around 75% lower than TS and RM after 15 generations. Results demonstrate that it would be possible to manage inbreeding over 15 generations within small breeding programmes comprised of 30 to 40 males and 30 to 40 females with the use of OPS and MIM. Selection on breeding values computed using Best Linear Unbiased Prediction (BLUP) with all individuals genotyped to obtain pedigree information resulted in an 11% increase in genetic merit and a 90% increase in the average inbreeding coefficient of progeny after 15 generations compared with selection on raw phenotype. Genetic evaluation strategies using BLUP wherein elite individuals by raw phenotype are genotyped to obtain parentage along with a range of different samples of remaining individuals did not increase genetic progress in comparison to selection on raw phenotype. When common environmental effects on full-sib families were simulated, performance of small breeding scheme designs was little affected. This was because the majority of selection must anyway be applied within family due to inbreeding constraints.     

Influence of parentage upon growth in Ostrea edulis: evidence for inbreeding depression

Genetic variability for growth was analysed in three populations of Ostrea edulis, selected for resistance to the protozoan parasite Bonamia ostreae. This study was undertaken first to determine the potential for selection for growth in populations that have never been selected for this character, and second to estimate heterosis versus inbreeding depression. Growth was monitored in culture for 10 months. The selected populations (namely S85-G3, S891-G2 and S89W-G2), their crossbred population and a control population were composed of full-sib families whose parents were already genotyped using five microsatellite markers. This genotyping allowed the estimation of genetic relatedness among pairs of parents. The parents' relatedness was then correlated with the growth performance of their offspring within each of the three populations, and inbreeding depression was estimated. The population effect for growth was highly significant, with the crossbred population having the highest growth rate, followed by S891-G2 and S89W-G2, S85-G3 and the control population. The within-populations family effect was also highly significant, indicating, as well as the high value for heritability at the family level (between 0.57 and 0.92), that a potential for a further selection for growth still exists within the three populations. Estimates of inbreeding depression (relative to the mean, for complete inbreeding) were high (1 for S891-G2, 0.44 for S89W-G2 and between 0.02 and 0.43 for S85-G3), which correlates with the apparent heterosis for growth observed in the crossbred population. These results are discussed in the context of the future management of the selected populations.     

MEASURES OF PHENOTYPIC SELECTION ARE BIASED BY PARTIAL INBREEDING

When populations are partially inbred due to the population structure or to a mixed mating system like partial self-fertilization, some individuals will be more inbred than others. This heterogeneity among individuals in the history of inbreeding can greatly complicate the interpretation of measures of quantitative genetic variability when the traits studied exhibit inbreeding depression. Partial inbreeding can also bias measures of phenotypic selection toward the detection of strong directional and stabilizing selection. In this paper, data are presented from several inbreeding experiments conducted on two partially selfing, annual populations of the monkeyflower Mimulus guttatus that show that the means of many of the morphological and phenological traits measured were affected by inbreeding. These findings imply that estimates of heritabilities and additive genetic covariances would not reflect the potential for these populations to respond to selection. Phenotypic selection analyses conducted on naturally occurring plants, involving linear regressions of relative seed production on the traits, revealed significant directional selection on many of the same quantitative traits measured in the inbreeding studies. However, when the same selection analyses were performed on plants with known histories of inbreeding, part of the statistical relationship between relative seed number and the traits was found to be due to the mating system: inbred individuals had both lower seed production and different mean values for the traits than outcrossed individuals. It is also shown, with a hypothetical example, that partial inbreeding can bias measures of stabilizing selection toward the detection of strong stabilizing selection. Partial inbreeding therefore tends to make directional and stabilizing selection appear stronger than it is, and it may be that natural selection in the wild is actually weaker than many studies of partially inbred species suggest.