Torsten Nygaard Kristensen, Department of Animal Breeding and Genetics, Danish Institute of Agricultural Sciences, PO Box 50, DK-8830 Tjele, Denmark. Tel.: +4589991339; fax: +4589991300; e-mail: firstname.lastname@example.org
Inbreeding is expected to decrease the heritability within populations. However, results from empirical studies are inconclusive. In this study, we investigated the effects of three breeding treatments (fast and slow rate of inbreeding – inbred to the same absolute level – and a control) on heritability, phenotypic, genetic and environmental variances of sternopleural bristle number in Drosophila melanogaster. Heritability, and phenotypic, genetic and environmental variances were estimated in 10 replicate lines within each of the three treatments. Standard least squares regression models and Bayesian methods were used to analyse the data. Heritability and additive genetic variance within lines were higher in the control compared with both inbreeding treatments. Heritabilities and additive genetic variances within lines were higher in slow compared with fast inbred lines, indicating that slow inbred lines retain more evolutionary potential despite the same expected absolute level of inbreeding. The between line variance was larger with inbreeding and more than twice as large in the fast than in the slow inbred lines. The different pattern of redistribution of genetic variance within and between lines in the two inbred treatments cannot be explained invoking the standard model based on selective neutrality and additive gene action. Environmental variances were higher with inbreeding, and more so with fast inbreeding, indicating that inbreeding and the rate of inbreeding affect environmental sensitivity. The phenotypic variance decreased with inbreeding, but was not affected by the rate of inbreeding. No inbreeding depression for mean sternopleural bristle number was observed in this study. Considerable variance between lines in additive genetic variance within lines was observed, illustrating between line variation in evolutionary potential.
The narrow sense heritability (h2), being a measure of evolutionary potential, is a function of genetic and environmental variance. Apart from being affected by genetic changes, h2 is sensitive to heterogeneity of environmental conditions. Lerner (1954) hypothesized that inbreeding can lead to an increase in environmental variance (VE), because inbred individuals are less stable in their development. There is some experimental evidence supporting this hypothesis, primarily for traits closely related to fitness (Whitlock & Fowler, 1999). Because the additive genetic and environmental variances can react in a variety of ways under inbreeding, the direction of change in phenotypic variance (VP) under inbreeding is difficult to predict (Fowler & Whitlock, 1999; Whitlock & Fowler, 1999).
Experimental and theoretical studies have shown that the rate of inbreeding affects the level of inbreeding depression (Ehiobu et al., 1989; Hedrick, 1994; Fu et al., 1998; Wang et al., 1999; Reed et al., 2003). For the same total amount of inbreeding slower inbreeding is often observed to cause less inbreeding depression than fast inbreeding (Ehiobu et al., 1989; Day et al., 2003; England et al., 2003; Reed et al., 2003). Apart from affecting the level of inbreeding depression, there are experimental studies indicating that the rate of inbreeding, associated with genetic drift, also affects the cumulative loss of genetic variance. At the same total level of inbreeding, slow rate of inbreeding has been shown to cause a lower reduction in evolutionary potential than fast rate of inbreeding (Tantawy, 1957; Day et al., 2003). However, in the study by Tantawy (1957) the replication was low and control lines were actually highly inbred, which makes interpretation of results difficult. Day et al. (2003) studied fitness traits, and estimated evolutionary potential from the level of genetic differentiation between fast and slow inbred lines of houseflies tested in a common environment (common garden approach). However, the results are not clear, and give only a vague indication of the effect of inbreeding and of rate of inbreeding on the evolutionary potential.
In this work, genetic and environmental parameters for the trait sternopleural bristle number were studied in D. melanogaster. The experiment comprised three treatments: fast and slow inbred lines and control lines. The objective was to test whether the trait sternopleural bristle number behaves according to expectations derived under selective neutrality and additive gene action: no inbreeding depression, and no effect of the rate of inbreeding on heritability, additive genetic, environmental, and phenotypic variances.
Materials and methods
A genetic diverse mass population of D. melanogaster was founded in August 2002 by crossing equal number of flies from four sets of pre-existing stocks (collected in Denmark, Australia and the Netherlands). The stocks were maintained at a high effective population size (n > 1000) prior to crossing. The lines used in this investigation were derived from this mass population.
The lines (slow and fast, and ‘noninbred’ treatments) were founded in December 2002 (eight generations after the mass population was founded). Ten lines with expected equivalent levels of inbreeding (F ≈ 0.67) were obtained either by five generations of full-sib mating (fast rate) or by maintaining a population size of four pairs during 18 generations (slow rate). For the inbreeding procedures, offspring of each line from each consecutive generation were collected as virgins, and four ‘replicates’ of full sib pairs (fast inbreeding) or two replicates of four males and four females (slow inbreeding) were randomly chosen as parents for the next generation and set up in individual vials. Offspring from only one of these ‘replicates’ were randomly chosen to establish the next generation of inbreeding. A number of lines went extinct through the process of inbreeding. Therefore, extra lines were set up to ensure that enough reached the expected level of inbreeding. Twenty and 15 independent lines were started to constitute the fast and slow inbred lines, respectively. Twenty per cent of the fast inbred lines went extinct whereas none of the slow inbred lines went extinct before reaching F ≈ 0.67. After reaching the desired level of inbreeding, lines were flushed to sizes of approximately 500 breeding individuals. Ten ‘noninbred’ control lines, each founded by approximately 500 breeding individuals were also established. The major features of the design used to generate the experimental lines are summarized in Table 1.
Table 1. Expected effective population sizes (Ne) in each of the 30 lines being either inbred or control.
t (Ne > 500)
t(Ne) is the number of generations populations were held at the Ne specified in the Ne column.
t(Ne > 500) specifies the number of generations where all populations were held at a Ne > 500 prior to the experiment.
E(Ft) is the expected inbreeding coefficient within the three treatments following the bottleneck.
Assuming that the inbreeding level of the base population from which all lines were sampled is equal to zero, and that Ne is equal to the census size (N), the expected inbreeding coefficient (F) in a given generation (t) was calculated from the expression Ft = (1 + 2Ft−1 + Ft−2)/4 (Falconer & Mackay, 1996), for the fast inbred treatment, and from the expression Ft = Ft-1 + (1 – 2Ft−1 + Ft−2)/2Ne (Crow & Kimura, 1970), for the slow inbred treatment.
Throughout the duration of the experiment flies were maintained in standard laboratory conditions (25 ± 0.2 °C, 50% RH, 12/12 hours light/dark cycle).
Flies were sampled from the 10 lines within each treatment in October 2003. A total of 200 vials in total with one virgin male and female were set up per line, even though only 104 vials were used per line (each vial constituting a family). Mating and egg-laying were allowed to proceed during 48 h. Thereafter, parents were removed and stored in Eppendorf tubes in a solution of alcohol and glycerol. After emergence offspring were collected and kept under the same experimental conditions as their parents.
Sternopleural bristle number was counted on male parents and on two male offspring in each family. In total, sternopleural bristles were counted on 9360 flies (104 male parents + 208 male offspring from each of 10 lines in each of the three treatments).
Test for inbreeding depression
The effect of treatment and line on mean sternopleural bristle number (the mean of the two male offspring within each family was used to represent family mean sternopleural bristle number) was tested fitting a model with treatment as fixed factor, and line nested within treatment as a random effect.
Least squares regression analysis
The linear mean square regression model (Bulmer, 1980) does not (in principle) assume any specific form of gene action affecting the trait in question. It constitutes, therefore, a robust and simple tool for inferences about genetic parameters. However, it has the disadvantage that it makes less efficient use of information in the data, relative to a full likelihood or a Bayesian approach.
Heritability was estimated in each of the 30 lines, as twice the least squares regression of the average sternopleural bristle number of the two male offspring on sternopleural bristle number of their father. Deviation from linearity was not observed in any of the lines (results not shown). The phenotypic variance for sternopleural bristle number was estimated by averaging squared deviations from the mean in the parental and offspring generation. The estimate of the additive genetic variance () was obtained as the product of the estimates of heritability and phenotypic variance (). Assuming that nonadditive gene action is negligible, that there is no interaction between genotype and environment and no covariance between genotype and environment, the estimated residual variance , was calculated as and is interpreted as environmental variance.
Average estimates of heritability, phenotypic, genetic and environmental variance for each treatment were obtained as weighted averages (weighted by the inverse of the squared standard errors) of the 10 line estimates within treatment. Standard errors for estimates of heritability were calculated as twice the standard errors of the respective regression estimates. The variance of the estimate of the phenotypic variance was obtained from . Standard errors for were approximated from the estimated standard errors of with treated as a constant. Estimated standard errors for were approximated from the estimated standard errors of and assuming these to be independent.
The Bayesian analysis
It was assumed that the sampling distribution of data y (vector of order n), given parameters β, r, a and VE, is the multivariate normal process
Here β is a vector that contains effects of generation (two levels), r is a vector of line effects (10 levels), a is a vector of additive genetic effects of order q, X, W and Z are known incidence matrices associating β, r and a with y and VE is the variance of the conditional distribution, which, given the model, is interpreted as the environmental variance. The vector r is assumed to follow the normal process
where Vr is the variance between lines and I in eqns (1) and (2) is the identity matrix of appropriate order. The variance between lines can be interpreted as the variance of line means assuming many observations within lines. Additive genetic values are assumed to result from the sum of many independently segregating loci, each with small effect. Therefore, invoking the central limit theorem, the distribution of additive genetic values is
Above, A is the additive genetic relationship matrix (of dimension q × q) and VA is the additive genetic variance within lines. The parameters which are the focus of inference are Vr, VA, and VE and possible functions thereof, such as the heritability within lines VA/(VA + VE) and the phenotypic variance within lines (VP = VA + VE).
The prior distribution assigned to β, Vr, VA, and VE is the improper uniform prior
Then the joint posterior density of all unknown quantities is
This model was fitted using a Gibbs sampler. All the fully conditional posterior distributions are of standard form; that is, normal for (β,a) and scaled inverted chi-squares for the variance components. Details of the algorithm can be found, for example, in Sorensen & Gianola (2002).
Differences between treatments were studied via the Monte Carlo estimates of the posterior probabilities (Xcontrol–Xslow > 0|y), (Xcontrol–Xfast > 0|y), and (Xslow–Xfast > 0|y), for X = h2, VA, VE and VP.
Relative to the least squares model, the Bayesian model is more heavily parameterized. However, it has the advantage that it extracts more information from the data (among other things, it makes use of the within family variation), and in contrast to the least squares approach, avoids the use of approximations, and inferences of all relevant parameters are carried out simultaneously. As shown below, the patterns emerging from both methods of inference are in agreement. Therefore, conclusions will be mainly drawn from the Bayesian analysis, since it leads to sharper inferences. In this analysis, in contrast to the least squares approach, data from all lines within a treatment were analysed jointly.
Least squares regression analysis
Estimated heritabilities are presented for each line and as a weighted within treatment average in Table 2. Estimates of phenotypic variance, additive genetic variance within lines, and environmental variance are presented for each line and as a weighted within treatment average in Table 3. The phenotypic variance, the additive genetic variance within lines and the heritability are larger in control than in inbred lines, and slightly larger in slow inbred lines than in fast inbred lines. The environmental variance is larger in the inbred lines, especially in the fast inbred lines. The results in Tables 2 and 3 show considerable variation between lines in the within line additive genetic variance.
Table 2. Estimated heritability () and corresponding standard errors (SE) for all lines and for the overall mean within each treatment obtained from the least squares analysis.
The values are expressed as (SE).
Table 3. Estimates of phenotypic variance (), additive genetic variance () and environmental variance () with corresponding standard errors (SE) for each line within the three treatments obtained from least squares analysis
Additionally, a weighted average for each treatment is presented.
Heritability within lines and confidence intervals are shown in Table 4. The inference from this analysis is that heritabilities differ in all three contrasts tested (Fig. 1a). Heritability was higher in the control than in inbred lines, and higher in slow than in fast inbred lines.
Table 4. Monte Carlo estimates of marginal posterior means for the three treatments (control, slow inbred, fast inbred) of heritability h2, phenotypic variance VP, additive genetic variance VA and environmental variance VE.
Monte Carlo estimates of 95% posterior probability intervals in brackets.
Additive genetic variance within lines and posterior confidence intervals are shown in Table 4. The inference from the analysis is that additive genetic variances differs in all three contrasts tested (Fig. 1b), showing the same pattern as the heritabilities. The expected additive genetic variance in both inbred treatments, based on additive gene action and selective neutrality, is 0.25. The estimated additive genetic variance (estimated posterior mean) is 0.18 and 0.29 within the fast and slow inbred treatments, respectively (Table 4). The posterior probability that the additive genetic variance in the fast inbred treatment is smaller than 0.25, is 88%. On the other hand, the posterior probability that VA in the slow inbred treatment is smaller than 0.25, is 25%. This indicates a larger departure from expectation in the fast than in the slow inbred treatment.
A word of caution concerning the way the Bayesian model was implemented is in order. The present Bayesian model postulates a common additive genetic variance for all the 10 lines within a treatment. A more refined analysis would fit one additive genetic variance for each of the 10 lines. However, it is unlikely that inferences concerning the ‘effect of the three treatments’ on the within line additive genetic variance would change much, especially if the 10 variances were to be averaged over lines, in order to arrive at an overall additive genetic variance within each treatment. Otherwise, inferences would need to be based on the pattern emerging from thirty, partly overlapping posterior distributions.
Environmental variance within treatments and posterior confidence intervals are shown in Table 4. The inference from the analysis is that VE differs in all three contrasts tested (Fig. 1c).
Phenotypic variance within lines within treatments and posterior confidence intervals are shown in Table 4. The inference from the analysis is that the variance was higher in the control than in the inbred treatments, and that there is no difference between phenotypic variance in the two inbred treatments (Fig. 1d).
Additive genetic variance between lines: the Monte Carlo estimates of the posterior mean of the between line variance Vr, and 95% posterior intervals (in brackets) are 2.42 (0.79–6.99), 0.90 (0.29–2.58), and 0.19 (0.05–0.56), for the fast inbred treatment, the slow inbred treatment and the control treatment, respectively. The estimate of the posterior mean of the difference between variances in the fast and slow inbred treatments is 1.52 (0.48–4.44). The Monte Carlo estimates of the posterior modes are 1.38, 0.53, and 0.14 for the fast inbred treatment, the slow inbred treatment and the control treatment, respectively. The Bayesian model captures correctly the small sample properties of the posterior distributions of the variance between lines, which display a heavy tail to the right (Fig. 2).
Mean sternopleural bristle number
The means for sternopleural bristle number over lines within treatments were 9.80 for control, 9.75 for slow inbred and 9.98 for fast inbred. The statistical test (not shown) indicates that inbreeding did not affect mean sternopleural bristle number.
This study shows that inbreeding reduces the within line additive genetic variance and increases the environmental variance of sternopleural bristle number in D. melanogaster. However, the effects of inbreeding are more pronounced with a high rate of inbreeding than with a lower rate, when compared at equal expected cumulative amounts of inbreeding. The between line variance is also differentially affected by the rate of inbreeding. The variance between lines was more than twice as large in the fast rate treatment relative to the slow rate treatment. This difference in the redistribution of variance between rates of inbreeding contradicts the expectation based on selective neutrality and additive gene action.
The behaviour of the redistribution of the variance within and between lines can be explained invoking the interaction between selection operating on genes of large effect, and genetic drift. As for many other quantitative traits, natural selection appears to favour individuals with sternopleural bristle number in the middle of the phenotypic range. Further, stabilizing selection has been shown to operate on sternopleural bristle number and on other correlated traits in D. melanogaster (López-Fanjul & Hill, 1973; Gibson & Bradley, 1974). The presence of alleles of large effect affecting sternopleural bristle number has been documented by Dilda & Mackay (2002). In the fast inbred treatment, selection has relatively less opportunity to operate than random drift, thereby resulting in more or less random fixation of alleles conferring very small or very large number of bristles. This results in a relatively large variance between lines. On the other hand, selection is likely to be more effective in the slow inbred lines. This favours the heterozygote genotype which restrains the fixation process leading to a relatively larger variance within lines and smaller variance between lines. Evidence for a larger amount of heterozygosity at the same level of inbreeding, in slow inbred lines compared with fast inbred lines, has been provided in a simulation study by Wang et al. (1999).
The heritability, as a measure of evolutionary potential, decreased with inbreeding both, due to reduced additive genetic variance, and due to increased environmental variance. Hence, inbred populations are less capable to adapt and are more sensitive to environmental changes, and more so at higher rates of inbreeding.
In the present experiment, the true inbreeding level in the two treatments cannot be estimated. It is likely that the effective population size in the slow rate treatment is smaller than expected (see for example, Frankham et al., 1993; Rumball et al., 1994; McGoldrick & Hedgecock, 1997). This should result in a higher than expected level of inbreeding. On the other hand, selection can be imagined to favour individuals with smaller than expected inbreeding level. Selection could operate between matings, or among offspring within a mating. This should result in a lower than expected level of inbreeding. Overall it is therefore unlikely that deviations of inbreeding coefficients from expectations could explain the differences between variances observed in the two inbred treatments.
No inbreeding depression for sternopleural bristle number was observed in this study. This observation is in agreement with the literature on sternopleural bristle number supporting the hypothesis that either this trait is primarily under additive genetic control, or that directional dominance is absent (Clayton et al., 1957; Falconer & Mackay, 1996).
The environmental variance can be interpreted as a measure of environmental sensitivity. Our analysis indicates that inbred lines are more sensitive than noninbred lines, and that environmental sensitivity increases with the rate of inbreeding. This result is in agreement with Lerner's (1954) hypothesis of genetic homeostasis, but this presupposes that the trait is related to fitness. The higher environmental variance in the fast inbred treatment (Fig. 1) could be due to fixation of conditionally expressed mutants (Vermeulen & Bijlsma, 2004).
The phenotypic variance was reduced by inbreeding. This result is in agreement with most other studies on the redistribution of phenotypic variance with inbreeding for morphological characters (Fowler & Whitlock, 1999 and references therein). However, we also found that the rate of inbreeding did not affect VP (Fig. 1). That is, even though both VA and VE differed between the two inbreeding treatments, their sum, VP, was the same. This is an interesting result in connection with the concept of environmental and genetic stress, as increased VP estimates often have been used as an indicator of stressful conditions. Assuming that the slow inbred lines retain higher fitness than the fast inbred (as expected from theory) the results here suggest that in sexually reproducing species VE is a more suitable indicator of genetic stress, as e.g. inbreeding, than VP.
The magnitude of the variance between lines of the within line additive genetic variance (see Tables 2 and 3) illustrates that some lines retain more potential for evolution than others despite the same expected level of inbreeding. This is important to take into account in relation to decision making in, for example, conservation biology and animal breeding.
The overall objective of this study was to test whether inbreeding and the rate of inbreeding impacts on heritabilities and variance components for sternopleural bristle number according to expectations based on selective neutrality and additive gene action. This does not seem to be the case. A number of conclusions can be drawn from this study on sternopleural bristle numbers in D. melanogaster. (1) On average, inbreeding reduces the heritability and additive genetic variance within lines and thereby the potential for within line evolution and genetic gain. However, considerable variance between lines in within line additive genetic variance is observed in the three treatments, illustrating variation in evolutionary potential. (2) In disagreement with the postulate of selective neutrality and additive gene action fast inbreeding reduces the additive genetic variance and the heritability within lines more than slow inbreeding, in lines inbred to the same absolute level of inbreeding. (3) Considerable variation between lines (parameter Vr) is observed. This variation is larger with inbreeding, according to theory, but in disagreement with the postulate of selective neutrality and additive gene action, it is larger in fast inbred lines than in slow inbred lines. (4) The phenotypic variance within lines decreases with inbreeding but is not affected by the rate of inbreeding. (5) Environmental sensitivity increases with inbreeding and is higher in fast compared to slow inbred lines. (6) Inbreeding depression was not observed for sternopleural bristle number, so the trait is not likely affected by directional dominance.
Drosophila has been used as a model organism for investigations on quantitative traits for more than half a century, and in no case have experimental results been misleading when generalized to equivalent traits in other species (Clayton et al., 1957; Frankham et al., 2002; Mackay, 2004). We advocate that in relation to animal breeding, evolutionary biology and conservation genetics, quantitative genetic studies on model organisms are ideal to fill the gap between theoretical work and computer simulations on the one side, and studies on domesticated and wild populations on the other.
We are grateful to Stuart Barker and Armando Caballero for fruitful discussions on the design of this experiment and interpretation of the results, to Tatyana A. Rakitskaya for performing the sternopleural bristle counting, to Doth Andersen for excellent technical assistance and to the Danish Natural Science Research Council (centre grant and frame grant) for financial support.