The distribution among populations in phenotypic variance with inbreeding.
It is often assumed that the changes in variance that follow inbreeding are constant and predictable: that the amount of additive genetic variance should decrease proportional to the inbreeding coefficient and that the amount of environmental variance should not be much affected or go up slightly by a constant amount. In fact, the change in the amount of phenotypic variance is variable; the reduction in additive genetic variance represented by (1-F) is only the mean of a distribution of possible changes (Avery and Hill 1977; Zeng and Cockerham 1991; Whitlock 1995). Unfortunately, little empirical evidence exists that can be used to quantify the distribution of changes in phenotypic variance as a result of inbreeding. These recent theoretical results demonstrate that uniform changes in variance in all bottleneck lines should not be expected, and studies on the effects of inbreeding have never been done on sufficient scale to measure accurately either the average effects of reduced population size or the distribution of variance.
The distribution of phenotypic variance in inbred populations is useful to know for several reasons. For example, one model of the probability of shifts between fitness peaks (the variance-induced peak-shift model, or VIPS) depends upon the increase in some populations of the phenotypic variance of traits under selection (Whitlock 1995). The traditional model of peak shifts, Wright's shifting balance model (Wright 1932, 1982), relies on drift in the mean phenotype of population (Rouhani and Barton 1987); the VIPS model demonstrates that drift in the variance is a more important force. When phenotypic variance increases, the mean fitness function becomes flatter, because fitness is averaged over a broader range of phenotypes, and changes in the value of the mean phenotype therefore result in smaller changes in mean fitness. As phenotypic variance increases, the mean fitness function can be smoothed sufficiently that bimodal functions can become unimodal [ILLUSTRATION FOR FIGURE 1 OMITTED]. Selection can then change the mean phenotype of the population to the domain of attraction of a new fitness peak. Whitlock (1995) has shown that such variance-mediated change is much more likely than the traditional shifting-balance process, provided that the distribution of phenotypic variance after bottlenecks includes some population that have significantly increased in phenotypic variance and that these changes persist for a few generations. There are few data at present on these questions. Models of rapid evolution, like VIPS, are potentially important in our understanding of evolution with developmental constraints (Lande 1986), speciation (Wright 1982), and patterns of macroevolution such as punctuated equilibrium (Lande 1986; Newman et al. 1985).
The distribution of phenotypic variance after inbreeding is also relevant to the interpretation of quantitative genetic experiments that seek the reasons for changes in variance due to some extrinsic factors. Selection experiments that attribute the changes in variance to limits to selection are often confounded with inbreeding effects, for example. Usually these experiments are inadequately replicated (Lynch 1988), with the presumption being that each line will accurately reflect the expected changes due to the forces under investigation. If on the other hand changes in variance due to small population sizes are extremely variable across different inbred lines, then the interpretation of these experiments becomes more difficult, and the number of degrees of freedom in an experiment becomes related to the number of lines, rather than the number of individuals measured within each line. A knowledge of the variance among lines in the amount of variance within inbred lines can help significantly in the design and interpretation of experiments (Lynch 1988).
Furthermore, inbred lines are quite often used in physiological studies with the aim of reducing the amount of noise among individuals, because inbred lines are expected to be less phenotypically variable. This expectation of reduced phenotypic variability is based on the idea that inbred lines are less genetically variable, and therefore more phenotypically uniform. It is important to know the distribution of phenotypic variance in inbred lines to assess the probability of reduced variability in inbred lines.
Unfortunately, there is insufficient data published to allow the estimation of either the variance among lines in the variance within lines or the probability that the amount of phenotypic variance has increased. There are several unreplicated experiments that have compared the amount of phenotypic variance in extremely inbred lines to that in the [F.sub.1] between these lines (see chapter 4, Wright  for many references.). These experiments are extremely difficult to interpret, for three reasons. First, the results are very inconsistent, from species to species, or from character to character. The number of reported cases of decreased variance in the [F.sub.1] is nearly evenly matched with the number of cases finding no such decline or even an increase (Mather 1950; Rasmusen 1952; Robertson and Reeve 1952; Lewis 1953; Gruneberg 1954; McLaren and Michie 1954; Thoday 1955; Emerson and Smith 1950; Williams 1960; King 1918; Sheldon et al. 1964; see Wright  for more references). Second, in nearly every case, the experimental protocol is unreplicated. We are left not knowing whether there is anything special that separates the class of species and characters with differences from those with no changes in the variance. It is entirely possible that the differences among species and among characters simply reflect the fact that this case represents a random draw from a highly variable distribution and that the range of results among tests reflects only the distribution that would be found had all of the tests been conducted on the same species and the same characters.
The inbred lines used in these comparisons are inadequate for our purposes for a third reason: the inbred lines used are typically severely inbred, with inbreeding coefficients (F) well in excess of 0.9. In terms of interpreting the probability of peak shifts by the variance model or of interpreting changes in variance due to the inbreeding that occurs in selection experiments, we must understand the distribution of phenotypic variance in populations that are inbred to a much lower degree, that is, with F around 0.25.
Some experiments have been performed in this intermediate range of inbreeding coefficients, with replication. An analysis of the long-term effects of selection has shown significant variation among lines in the amount of phenotypic variance within lines for fly abdominal bristle counts (Clayton and Robertson 1956). Lopez-Fanjul et al. (1989) have shown significant variance among lines in the variance within lines for abdominal bristles in Drosophila melanogaster following brother-sister mating. These workers have reported increases in phenotypic variance for viability following population bottlenecks (Lopez-Fanjul and Villaverde 1989). These experiments are relevant to the problem of variance in variance, but were not designed to estimate to analyze the probability of increased variance within certain lines relative to a control outbred population. From the point of view of understanding peak shifts, it is necessary to understand the probability density in the upper tail of the distribution of variance.
In this study, we measured the phenotypic variance of thorax length and sternopleural bristle number for 30 lines of D. melanogaster inbred to a relative inbreeding coefficient of F = 0.25. These variances were compared with the corresponding values for an outbred population. The lines with the highest variance were selected for further analysis, such that degrees of freedom were not lost unnecessarily to multiple comparisons. This enabled us to measure the variance among lines in the variance within lines and to examine the tail of the distribution for increased variance.
MATERIALS AND METHODS
We used an outbred wild-type population of D. melanogaster, collected in 1970 in Dahomey (now Benin). This stock has been maintained since then at a large population size in cage culture. Throughout this experiment, all flies were kept at 25 [+ or -] 1 [degree] C with a fixed illumination cycle of 12 h light followed by 12 h dark. All handling was performed at room temperature using carbon dioxide anaesthesia.
We obtained a large sample of eggs from the Dahomey population by placing four unyeasted culture bottles in the cage for 6 h. The progeny were collected as virgins, and a random sample of 125 males and 125 females were mated in pairs. Eggs from these matings were collected by serial transfer of the adults between several culture vials. These adults constituted the parental (P) generation and after the last transfer were frozen at -20 [degrees] C for later measurement.
The [F.sub.1] progeny of the P generation were used to form 30 inbred populations and 1 outbred population. The inbred lines were produced by choosing 30 of the parental families at random and allocating 18 males and 18 females from each family to each of four culture bottles. The inbreeding coefficient of each inbred line, having gone through a single pair bottleneck, was thus approximately F = 0.25. The outbred stock was obtained by mixing together 10 flies of each of 100 parental families (including those which gave rise to the inbred lines) and allocating random samples of 18 males and 18 females to each of 28 culture bottles. The inbreeding coefficient of the controls was therefore approximately F = 0.0025 relative to the source population.
The adults ([F.sub.2] generation) that emerged from the bottles of each line were mixed randomly and manipulated to produce cultures of constant larval density. Variation in larval density can have large effects on the values of quantitative characters (for example, Spiers 1974; Caligari and Baban 1981), and we raised the [F.sub.3] generation under standard conditions of low larval density.
For each inbred population, approximately 100 inseminated females were transferred to an egg-laying vial. For the outbred line, six such vials were established. These 65 x 35 mm vials carried an egg-laying medium containing grape juice (Fowler and Partridge 1986). After 12 h on fresh medium (to prevent egg retention), eggs were collected over two successive 2-h lay periods. The adults were discarded and after 25 h from the midpoint of the lay period, 50 first-instar larvae were picked from the medium with a small paintbrush. The larvae were set up in standard food vials (75 x 25 mm diameter) with 7 ml of medium. Four vials of this type were produced for each of the inbred lines, and 26 vials were made for the outbred line. After emergence of all flies, these [F.sub.3] adults were frozen at -20 [degrees] C for later measurement.
Two morphological characters of the [F.sub.3] adults were measured; thorax length (TL) and sternopleural bristle number (SBN). Flies were assayed for TL by being laid on their side under a binocular microscope, and the distance from the base of the most anterior humeral bristle to the posterior tip of the scutellum was measured. Individuals were assayed for SBN by adding together the count for the left and right sides.
Flies were measured in two batches. First, 16 of each sex were measured for each inbred line, and 96 of each sex were measured for the outbred line. There was significant heterogeneity among lines in the amount of phenotypic variance for both sexes and for both characters (see below for statistical details). Therefore, five lines were chosen for each sex and each character for further analysis. The five lines with the highest variance for each character and for each sex were then measured for all remaining individuals of that sex for that character. This selection allowed us to ask if there were specific lines that had increased variance relative to the outbred line, while allowing an independent analysis of new flies on a smaller number of lines and therefore with fewer degrees of freedom lost to multiple comparisons. To investigate the amount of variance among lines in the variance within lines, a further 16 individuals per sex were measured for both characters for all lines, for a total of 32 individuals measured per sex per line. A total of 351 males and 352 females were measured for both characters in the outbred lines.
An analysis of variance (ANOVA) was performed across all inbred populations to give an estimate of the amount of genetic variance in the stock population, by using the variance among full-sib group means (Falconer 1981). Variance components were calculated by standard techniques (Sokal and Rohlf 1981; Becker 1992).
The analysis was aimed at asking two questions: first, is there significant variance among lines in the amount of phenotypic variance for these characters within lines, and second, are there specific lines in which the amount of phenotypic variance has increased? To answer the first question, a bootstrap analysis of the homogeneity of variance was performed on the data for each character and each sex separately on the data from the inbred lines.
A nested ANOVA showed significant vial effects and line effects in the inbred flies. In order to not include effects due to differences in the microconditions of each experimental vial and to the differences in means among lines, an analysis of variance was performed on each line, and the variance components among vials and among lines were discarded. The residuals were then resampled from inbred lines without respect to line or vial, in sample sizes equivalent to the sample sizes of the real data. The variance of these residuals is not equal to the error variance, because the number of degrees of freedom for the residuals has been reduced by the number of degrees of freedom of the model. To measure the pseudovalues from the bootstrap on the same scale as the real data, it is necessary to multiply the bootstrapped variance values by the square of the ratio of the denominators of the mean square calculations, that is, the number of degrees of freedom of the error term over the number of degrees of freedom of the residuals. For these analyses, the bootstrapped variances must be multiplied by 1.16.
TABLE 1. Summary statistics for all inbred and outbred flies by character and sex. Outbred Inbred Mean Variance Mean Variance Sternople ural bristles: Males 20.16 7.79 20.54 10.11 Females 21.45 6.80 21.57 10.13 Thorax length: Males 0.930 5.7 x [10.sup.-4] 0.920 6.8 x [10.sup.-4] Females 1.06 6.7 x [10.sup.-4] 1.05 8.6 x [10.sup.-4]
To ask whether there were specific lines in which the amount of phenotypic variance increased relative to the out-bred line requires adjusting for the number of multiple comparisons that are made for each character. To avoid losing degrees of freedom to unpromising lines and to reduce unnecessary measurements, a preliminary screening of 16 individuals was used to select lines for later analysis (see above). All of the remaining individuals of both sexes were measured for each trait in each of these selected lines. Only the flies measured in this second round were included in this subsequent analysis. The variance component among individuals was determined as above with a nested ANOVA for each inbred line and for the control line. The phenotypic variance within each inbred line was then compared with the outbred line by a bootstrap of the control lines, as above. Here the correction term for the variance of the residuals is 1.19. The tests on each character and sex were performed independently of each other character. Multiple comparisons were accounted for by the sequential Bonferroni method (Rice 1989).
Variance among Populations in Means
The mean scores for each sex and each character were compared between all inbred and outbred flies (see Table 1). For sternopleural bristle counts, there was no significant difference between inbred and outbred flies for either sex. For thorax length, the inbred flies were about 1% smaller than the outbred flies for both sexes, although the difference is marginally not significant (P = 0.060 for males, P = 0.078 for females). An inbreeding depression for thorax length of 1% for F = 0.25 is consistent with the 4% reduction in thorax length observed with completely inbred lines (Robertson and Reeve 1955).
The data from the flies of the outbred line was analyzed by a nested ANOVA to determine whether the differences between vials contributed significantly to the variance within lines. For both sexes, thorax length had a significant vial effect in the outbred line, but for neither sex was there evidence of significant variance caused by any difference among vials for sternopleural bristle counts. Therefore, the variance component among vials was removed from the total variance for thorax length for both sexes, but not for the sternopleural bristle counts. The estimated variance among individuals for the control line is shown for each character in Table 1. The revised measure of variance for thorax length for the control individuals, adjusted for vial effects, is 5.4 x [10.sup.-4] and 6.4 x [10.sup.-4], for males and females, respectively.
TABLE 2. Analysis of variance among the inbred lines. Sum of Mean Source df squares square F P Sternopleural bristle counts - males Line 29 6683.9 230.5 36.0 0.0000 Vial 90 574.9 6.4 1.02 0.4222 Error 1563 9757.3 6.2 Total 1682 17016.1 Sternopleural bristle counts - females Line 29 6801.8 234.5 30.1 0.0000 Vial 90 703.8 7.8 1.29 0.0402 Error 1555 9455.1 6.1 Total 1674 16960.6 Thorax length - males Line 29 0.272 0.0094 10.5 0.0000 Vial 90 0.080 0.0009 1.74 0.0001 Error 1562 0.798 0.0005 Total 1681 1.150 Thorax length - females Line 29 0.326 0.0112 8.8 0.0000 Vial 90 0.111 0.0013 1.92 0.0001 Error 1554 0.998 0.0006 Total 1673 1.435
For each of the characters and for each sex, there is a highly significant variance among inbred lines for their mean values, as shown by a nested ANOVA on all of the available data for the inbred lines. Table 2 shows the ANOVA tables for these analyses. This variance among lines indicates the presence of genetic variance for the characters. Because these lines are the products of full-sib mating, twice the variance among lines is a good approximation for the amount of additive variance for each trait. The heritability estimates for each trait are shown in Table 3, where the standard errors are calculated as recommended by Becker (1992). These estimates are in general accord with previous estimates for the same stock population (Wilkinson et al. 1990).
Variance among Populations in Phenotypic Variance
The among line distribution of variance within lines (calculated from 32 individuals of each sex per line) is shown in Figures 2A-C. The basic statistics and analyses of the heterogeneity of variances are presented in Table 4. In both sexes, the phenotypic variance within lines for sternopleural bristle counts are significantly more variable than expected. In females, the variance for thorax length is more heterogeneous across lines than expected from the sampling scheme. In males, however, the analysis does not find any more variance among lines in the variance within lines than expected by the size of the samples.
TABLE 3. Heritability and standard error of heritability of sternopleural bristle count and thorax length for separate sexes. Character Heritability Standard error Sternopleural bristles Males 0.79 0.13 Females 0.80 0.13 Thorax length Males 0.39 0.097 Females 0.35 0.094
The Increase of Variance
The five lines with the highest phenotypic variance for each of the four combinations of sex and character were measured for that sex and character for all additional flies in the [F.sub.3], which resulted in 51 to 94 flies per line in the second data set for each character and each sex. For thorax length in both sexes, the ANOVA for the control outbred individuals revealed a significant vial effect, which was removed. The variance among vials was estimated for each inbred line separately with a nested ANOVA. For sternopleural bristle counts, the variance among vials was not significant in the controls or in any of the individual inbred lines chosen for further study; thus, the total variance within a line was used to characterize the variance among individuals.
The corrected variance components for each selected line are shown in Table 5. None of the lines selected for high sternopleural bristle counts have a significant increase in the amount of phenotypic variance relative to the outbred controls, using the conservative test with corrections for multiple comparisons. Two of the lines have significantly increased variance in male thorax length (at the P = 0.004 and P = 0.005 levels), both of which are significant at P = 0.025, accounting for five multiple comparisons. The probability of getting two results so extreme out of the 20 is less than 0.005. (On a testwise alpha value of 0.05, line 98 is significantly increased for bristle number variance in females. Line 1 is significantly increased in variance at the level of a single test for female thorax length.) Coupled with the analysis above showing significant variance among lines in the amount of phenotypic variance within lines, this result demonstrates that the tail of the distribution of the phenotypic variance extends above the original value in control populations.
Inbreeding changes the distribution and partitioning of variance within and among lines. According to standard theory, the amount of additive genetic variance within lines should be equivalent to the amount of additive genetic variance in the outbred population times the inbreeding coefficient of the inbred line relative to that outbred population (Falconer 1981). This result is true, but only for traits affected by purely additive genetic interactions (Robertson 1952; Bryant et al. 1986; Goodnight 1988) and only as an expectation (Avery and Hill 1977; Whitlock 1995). Similarly, the amount of environmental variance within lines is subject to change with inbreeding, as higher levels of homozygosity can be associated with developmental instability (Lerner 1954; Mitton and Grant 1986). We know little about the distribution of phenotypic variance following population bottlenecks, including the level of variance among populations in variance within populations and how many populations might in fact increase in the amount of phenotypic variability.
These parameters are essential to our understanding in several contexts. One motivation for this study has been a new view of rapid morphological evolution from one adaptive peak to another, which requires an increase in phenotypic variance in some populations as a result of population size bottlenecks, the VIPS model (Whitlock 1995). Phenotypic versions of Wright's shifting balance theory (Wright 1932, 1940, 1977) [TABULAR DATA FOR TABLE 4 OMITTED] have examined the role of genetic drift in changing the mean phenotype of a population from the domain of attraction of one fitness peak to another (Rouhani and Barton 1987). The variance-induced peak-shifts model postulates that in some populations the amount of phenotypic variance will increase as a result of inbreeding, which in turn changes the adaptive landscape such that selection can deterministically move a population from one peak on the adaptive landscape to another. As it turns out, this variance-driven model of peak shifts is much more likely to produce peak shifts than the more traditional shifting-balance models that involve genetic drift of the mean phenotype, assuming certain conditions are met about the distribution of phenotypic variance after bottlenecks. From this perspective, it is essential to know whether there is a tail of the distribution of phenotypic variance in which the amount of phenotypic variance is increased significantly from the outbred source population. This study has shown that there are populations, at least for one of the two characters, which can show a significant increase in the amount of phenotypic variance relative to the outbred population. An essential condition for evolution by variance-mediated mechanisms is met.
There are other reasons to study the distribution of phenotypic variance. Primarily, the distribution of variance is useful in the context of understanding quantitative genetic studies and other studies of the relationship between genotype and morphology (Lynch 1988). Quantitative genetic studies of the changes in heritability or phenotypic variation as a function of selection must be replicated sufficiently, because the real level of replication will be the line, not individuals within lines. A simple comparison of the variances of a selected and an unselected population will not suffice to demonstrate changes in variance associated with selection, because selection experiments inevitably involve inbreeding, and as the results of this study have shown, inbreeding effects are not consistent, even if the amount of inbreeding has been held constant.
TABLE 5. The variance among individuals for each of the selected lines. Thorax values are times [10.sup.-4]. Line Male [V.sub.p] Line Female [V.sub.p] Bristles Control 7.79 Control 6.80 79 8.83 4 6.36 92 7.25 94 7.96 97 9.41 97 8.73 101 7.43 98 9.49(*) 110 7.37 108 8.73 Thorax Control 5.4 Control 6.4 2 5.7 1 9.4(*) 4 8.6(**) 2 6.8 96 8.7(**) 92 6.9 102 3.9 96 7.7 106 4.3 107 5.6 * P [less than] 0.05; ** P [less than] 0.005.
Similarly, studies of the effects of enzyme heterozygosity on morphological variability must be viewed as being replicated at the level of the population, not of the individual. Because the effects of inbreeding on morphological variance are not consistent from inbred line to inbred line, we similarly expect to see much variation among populations in the correlation with heterozygosity. In fact, the results from studies on this phenomenon are widely divergent (see Mitton and Grant  for review; Mitton 1978; Eanes 1978; Fleisher et al. 1983; Leamy 1982 show increased variance with increased homozygosity; but also see negative results by Handford 1980; McAndrew et al. 1982; Zink et al. 1985; Houle 1989; Booth et al. 1990; Whitlock 1993). Most of these studies involve the comparison of a single outbred population to a single inbred population; the results reported here demonstrate that this confusion of results is likely not due to differences between species or characters studied, but rather to the expected difference among lines in the response to inbreeding.
From the data presented here, it is impossible to know the exact mechanism of the changes in the phenotypic variance. It is not possible to ascribe the variation in variance to changes in environmental or genetic variance. The average variance within lines for each character is consistent with the additive expectation of (1 - [h.sup.2]F) times the variance in the outbred population. This would indicate that the changes in variance are not due to a deterministic effect associated with the loss of heterozygosity, as has been suggested in some cases in the past. These results are more compatible with the hypothesis that either the genetic variance or the developmental sensitivity to environmental fluctuations is drifting during the episode of small population size.
The variance among lines in the phenotypic variance within lines that we have seen can also be possibly attributed to variation in linkage disequilibrium (Avery and Hill 1977). However, we have variance estimates from a single time point; thus, testing the changes in variance over time predicted by the breakdown of linkage disequilibria is not possible. This test has been performed in a similar study, and no evidence of loss of variance in variance was observed (Lopez-Fanjul et al. 1989). Even with a breakdown of the amount of the variation in phenotypic variance, it is impossible to attribute the effects of linkage disequilibrium unambiguously, because a reduction in the variance in variance would be expected by the action of stabilizing selection, for example.
After inbreeding, there can be a large variance among populations in the amount of phenotypic variance within populations. This variation in the effects of inbreeding must be taken into account in the design of experiments aimed at discovering the reasons for changes in the amount of variation, following any experimental protocol that involves even relatively mild inbreeding, such as selection experiments or analyses aimed at uncovering the developmental basis of homeostasis. Moreover, some populations exhibit phenotypic variance much larger than even control populations. These increases in the amount of phenotypic variation as a result of inbreeding give evidence for the plausibility of the assumptions the variance-induced peak shifts model (Whitlock 1995). We must understand more about the mechanisms that generate the distribution of phenotypic variation and learn more about the patterns of variance that occur in more traits and more species.
We would like to thank N. Barton, S. Otto, J. Holsinger, and anonymous reviewers for their useful comments. K.F. was supported by funds from the Royal Society (UK), and M.C.W. by Natural Environment Research Council (UK).
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|Author:||Whitlock, Michael C.; Fowler, Kevin|
|Date:||Oct 1, 1996|
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