GENETIC VARIATION FOR PREADULT VIABILITY IN DROSOPHILA MELANOGASTER

1609

q 2001 The Society for the Study of Evolution. All rights reserved.

Evolution, 55(8), 2001, pp. 1609–1620

GENETIC VARIATION FOR PREADULT VIABILITY IN DROSOPHILA MELANOGASTER

MICHAEL GARDNER,1 KEVIN FOWLER,1 LINDA PARTRIDGE,1 AND NICK BARTON2,3

1Galton Laboratory, Department of Biology, University College London, Wolfson House, 4 Stephenson Way,London NW1 2HE, United Kingdom

2Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road,Edinburgh EH9 3JT, United Kingdom

3E-mail: [email protected]

Abstract. The extent of genetic variation in fitness and its components and genetic variation’s dependence on en-vironmental conditions remain key issues in evolutionary biology. We present measurements of genetic variation inpreadult viability in a laboratory-adapted population of Drosophila melanogaster, made at four different densities. Bycrossing flies heterozygous for a wild-type chromosome and one of two different balancers (TM1, TM2), we measureboth heterozygous (TM1/1, TM2/1) and homozygous (1/1) viability relative to a standard genotype (TM1/TM2).Forty wild-type chromosomes were tested, of which 10 were chosen to be homozygous viable. The mean numbersproduced varied significantly between chromosome lines, with an estimated between-line variance in loge numbers of0.013. Relative viabilities also varied significantly across chromosome lines, with a variance in loge homozygousviability of 1.76 and of loge heterozygous viability of 0.165. The between-line variance for numbers emerging increasedwith density, from 0.009 at lowest density to 0.079 at highest. The genetic variance in relative viability increaseswith density, but not significantly. Overall, the effects of different chromosomes on relative viability were remarkablyconsistent across densities and across the two heterozygous genotypes (TM1, TM2). The 10 lines that carried ho-mozygous viable wild-type chromosomes produced significantly more adults than the 30 lethal lines at low densityand significantly fewer adults at the highest density. Similarly, there was a positive correlation between heterozygousviability and mean numbers at low density, but a negative correlation at high density.

Key words. Density-dependent viability, Drosophila melanogaster, genetic variation, heterozygous viability, homo-zygous viability, stress.

Received September 26, 2000. Accepted April 13, 2001.

Although the additive genetic variance in net fitness is thequantity that determines the rate at which populations adapt(Fisher 1930), this value is not known to within even an orderof magnitude for any organism (Charlesworth 1987; Burt1995). Moreover, fundamental features of the living worlddepend on the patterns of genetic correlations underlyingfitness variation; for example, the evolution of life histories,rates of sex and recombination, and mate preferences. It isthus important to estimate the additive genetic variance infitness, the contribution to it of different components of fit-ness (such as viability), and the genetic correlations betweenthem.

We present measurements of the effects of a sample ofwild-type chromosomes on preadult viability. These weremade with three sets of questions in mind. First, what is therelation between effects on preadult viability and on net fit-ness? What proportion of the variance in net fitness is con-tributed by viability, and to what extent are fitness and vi-ability correlated? Net fitness has been measured in a separateexperiment, and its relation with preadult viability will bereported elsewhere. Second, how consistent are effects onviability across environments? We report measurementsmade at four different densities, which can be seen as im-posing an increasing degree of competitive stress. Third, howconsistent are effects on viability across genotypes? We in-troduce a novel method that yields independent estimates ofheterozygous and homozygous effects and that allows com-parison between two different heterozygous genotypes.

The method is described in detail by Fowler et al. (1997)and by Barton and Partridge (2000). Wild-type third chro-mosomes (constituting about 40% of the total genome) areextracted from the target population and competed against

two balancer chromosomes (TM1 and TM2). These balancerscarry a dominant marker that is lethal when homozygous;they also carry multiple inversions, which prevent recom-bination, and thus keep wild-type chromosomes intact. Theeffect on heterozygote and homozygote fitness of the wild-type chromosome is estimated from the dynamics of the in-vasion of a population of genotype TM1/1 (where 1 is thewild-type chromosome) by the TM2 chromosome (see Fowleret al. 1997; Barton and Partridge 2000). One advantage overearlier methods is that the performance of the variable ge-notypes (TM1/1, TM2/1, 1/1) can be measured against thestandard genotype (TM1/TM2). Here, we present a parallelmeasurement of preadult viability, which shares this advan-tage.

Previous studies with Drosophila have used segregationtests to examine the effects on preadult viability of homo-zygous wild-type chromosomes. One approach has been tomeasure the viability of wild-type flies made homozygousfor one autosome relative that of flies heterozygous for abalancer and the same wild-type autosome (e.g., Sved 1971;Mukai et al. 1972; Mackay 1986). These studies have shownthat the viability of wild-type chromosome homozygotes ishighly variable and usually lower (often substantially lower)than that of heterozygotes with the balancer. If the chro-mosomal effects on viability are partially dominant, then var-iation in homozygous effects on viability will be underesti-mated because there will be a positive correlation betweenthe fitness of a particular wild-type chromosome heterozygoteand the balancer heterozygote with which it is compared.

The technique has been extended to measure the hetero-zygous effects on viability of individual wild-type autosomesby making them heterozygous with a series of randomly cho-

1610 MICHAEL GARDNER ET AL.

sen wild-type autosomes from the same population (e.g., Wal-lace 1952; Mukai and Yamaguchi 1974; Mukai and Nagano1983; summarized in Mackay 1986). In these studies viabilityof the wild-type chromosome heterozygotes was assessed incompetition with chromosome heterozygotes between eachof the two wild-type chromosomes and a single balancer chro-mosome. This approach indicated that most variation in het-erozygous viability was additive. Although this approach tosome extent avoids the potential bias caused by correlationbetween heterozygous and homozygous effects, there is stillno standard genotype against which viability can be assessed.

There has been considerable recent interest in the possi-bility that phenotypic variation is inflated under stressful con-ditions. Renewed interest in canalization, the buffering ofphenotype against genetic and environmental perturbations,has been stimulated by the discovery of extensive geneticredundancy and molecular mechanisms that protect the cellagainst various stresses (Gibson and Wagner 2000; Hoffmannand Hercus 2000; Rutherford 2000). A separate motivationstems from the realization that function can only be main-tained in the face of frequent mutations if there is both sexualreproduction and synergistic epistasis (Kondrashov 1988);that is, the effect of any one deleterious mutation must in-crease as fitness declines. In two recent studies of Drosophila,new mutations showed greater deleterious effects in harsh,high-density conditions (Kondrashov and Houle 1994; Sha-balina et al. 1997). Here, we investigate the interaction be-tween viability and both environmental and genetic differ-ences, namely, with population density and with the presenceof different balancer genotypes.

MATERIALS AND METHODS

Fly Stocks and Culture

All culture and experimental work was performed at 258Con a 12:12 L:D cycle. Population cages were maintained with12 pots of food medium, replaced on a 4-week cycle withthree fresh pots per week. The Dahomey stock was used asthe wild-type base population. This stock has been held inculture in population cages since 1970. Changes in adult life-history traits in wild flies brought into laboratory culture areminimal with this culture method, but larval competitivenessincreases in laboratory culture (Sgro and Partridge 2001). Ingeneral, evolution in response to laboratory culture is rapid(Briscoe et al. 1992; Frankham and Loebel 1992; Latter andMulley 1995), and the levels of competition encountered inpopulation cages can be regarded as natural for this stock.

The third chromosome balancers TM1 and TM2, markedrespectively with the dominant mutants Moire eye (Me) andUltrabithorax (Ubx), were used as the competitors for thewild-type third chromosomes. The TM1 and TM2 balancerchromosomes were backcrossed into the Dahomey geneticbackground, and the resulting TM1/TM2 Dahomey stock waskept in population cage culture identical to that for the Da-homey stock.

Extraction of Wild-Type Chromosomes

We extracted a total of 180 third chromosomes, using theTM1/TM2 Dahomey stock. These experimental chromosomes

were balanced independently against TM1 and TM2, and thesebalanced lines were set up as cage populations and allowedto expand in numbers to the carrying capacity of the cages.Each wild-type chromosome was represented by two replicatepopulation cages (A and B) with each balancer. Thirty of theextracted chromosomes were homozygous lethal, similar tothe frequency found previously for this stock (Fowler et al.1997) and in nature (Simmons and Crow 1977). We electedto work initially with all of the 30 homozygous lethal linesand a random sample of 10 viable and fertile lines.

Measurement of Preadult Viability

A competitive measure of larval viability is more infor-mative than survival rates in monocultures (e.g., Santos etal. 1992). To generate the larvae for the measure of preadultcompetitive ability, we made a cross between the correspond-ing TM1/1 and TM2/1 parents for each wild-type third chro-mosome, separately for the A and B replicates. This crossgenerated three genotypes (TM1/1, TM2/1, and TM1/TM2)if the wild-type chromosome was homozygous lethal and four(1/1, TM1/1, TM2/1, TM1/TM2) if it was homozygous vi-able. The TM1/TM2 acted as a standard genotype with whichthe performance of the others could be compared. We mated300 virgin TM2/1 females to 300 TM1/1 males in vials. Theflies were then set up in three egg-laying chambers per cross.After 2 days to feed and acclimate, the flies were transferredto a fresh egg-laying chamber for 2 h to minimize egg re-tention and were then transferred to fresh egg-laying cham-bers, where eggs were collected over a 3-h period. First instarlarvae were collected 26 h after the midpoint of the 3-h lay.

The larvae were reared in vials at each of four larval den-sities. Larvae were picked from the egg chambers to vials instandard densities of 30, 60, and 90, with five replicate vialsper larval density. There was some variation around thesenumbers: 6%, 1.25%, and 0.25% of vials at nominal initialnumbers 30, 60, and 90 had more than this number of adultsemerging. We also reared the products of these crosses atvery high larval densities, using two of the six replicate vialsin which the original 2-day matings occurred. Here, numbersof eggs laid in the 2 days was not controlled for; all adultprogeny emerging from the high-density treatment werescored.

Statistical Analysis

The data consist of the numbers of adults of each genotypeemerging from each replicate vial. We separate the analysisof the total number emerging from analysis of genotype fre-quencies. The distribution of total number across replicatevials is a consequence of the ecological interaction betweenlarvae of different genotypes. In our likelihood analysis, weassume that loge(numbers) are normally distributed. This isin qualitative agreement with the distribution of residuals:There are not enough data to warrant a more detailed ex-amination of the form of the distribution, beyond its first twomoments, and assuming a log-normal distribution speedscomputations. We summarize the distribution by letting themean and variance of loge(numbers) equal loge(n) and cnrespectively. Thus, n is the geometric mean number emerg-ing, and c is approximately the ratio of variance in numbers

1611GENETIC VARIATION FOR VIABILITY IN DROSOPHILA

TABLE 1. Analysis of numbers emerging at each density. n is the geometric mean number emerging, averaged across lines and replicates. n/n0 is the geometric mean viability. Vline is the variance in n between line means, corrected for between-replicate variance. Vrep is the variancebetween replicates after removing line effects. The number of 1000 datasets, randomized across replicates, which showed larger Vrep is shownin parentheses following Vrep. The next row gives the correlation in n between replicates, followed by the number of 1000 datasets, randomizedacross lines, that showed greater correlation. Values significant at P # 0.05 are shown in bold. The remaining rows give the same informationfor the variance/mean ratio, c.

n0 5 30 n0 5 60 n0 5 90 n0 high

nn/n0

Vline

Vrep

Correlation between replicates

23.80.790.0086

0.0083 (6)0.522 (0)

45.40.760.0110

0.0056 (3)0.656 (0)

64.90.720.0094

0.0064 (1)0.586 (0)

306.8—

0.07900.0429 (37)0.655 (0)

cVline

Vrep

0.400.194

0.528 (317)

0.480.150

0.841 (82)

0.580.0075

0.853 (34)

5.960.407

5.844 (51)Correlation between replicates 0.286 (52) 0.140 (185) 20.002 (526) 0.053 (394)

to mean numbers. For a Poisson distribution of survival, suchas would be produced if each fly had a small density-inde-pendent viability, c ø 1. We treat n and c as properties ofthe density, wild-type chromosome, and replicate. When fit-ting models using likelihood, we assume that different effectson mean number and variance/mean ratio multiply; we there-fore work with additive models for the logarithms of thesetwo quantities, and plot them on loge scales.

The genotypic proportions are assumed to follow a bino-mial distribution, with relative viabilities depending on den-sity treatment, wild-type chromosome, and replicate. The rel-ative viabilities are summarized by the viability of the twowild-type heterozygotes relative to TM1/TM2 and by the vi-ability of TM1/1 relative to TM2/1. These are transformedto a loge scale, so that we work with the variables

1 V V VTM1/1 TM2 /1 TM1/1log and log .e e1 2 1 22 V VTM1/TM2 TM2/1

We begin analyses of total numbers and relative viabilityusing simple graphical summaries and randomization tests ofcorrelations between replicate cages, as tests of significance.For both numbers and relative viability, we also carry out astructured log-likelihood analysis (McCullagh and Nelder1989). This fits a model that specifies parameter values thatdepend on each factor separately or on combinations of fac-tors. For example, the loge mean number emerging mightdepend on an effect of density, plus an effect of line andreplicate together: this is represented as {density, line 3 rep-licate}. This approach is more flexible than a standard anal-ysis of variance or of chi-square, because it allows for ar-bitrary distributions and allows a different model structurefor different variables (e.g., mean numbers and variance/mean ratio). Twice the difference in log-likelihood betweenmodels can be tested against a chi-square distribution withthe appropriate number of degrees of freedom; this is accuratefor large samples. By the same approximation, ratios of dif-ferences in log likelihood can be tested against an F-distri-bution, as in an analysis of variance (ANOVA) table. Theroutines used for structured log-likelihood analysis are con-tained in a set of Mathematica 4.0 packages (Wolfram 1996),which are available from NB or via http://helios.bto.ed.ac.uk/icapb/.

RESULTS

Numbers of Flies

We begin by considering how the total number of flies thatemerge from each vial depends on initial density, n0, and onwild-type chromosome. The patterns at each of the four den-sities are summarized in the first two rows of Table 1. Onaverage, viability falls with density, although not greatly: n/n0 drops from 0.79 with 30 first instar larvae per vial to 0.72with 90 per vial. As well as measuring the mean number offlies emerging from each set of vials, we consider the variancein numbers between vials, within replicates; this reflects bothrandom sampling variance and additional variance in viabilitybetween vials and may be influenced by genotype indepen-dently of the mean. At the three lower densities, the varianceis about twice as large as would be expected if larvae survivedindependently of each other, with fixed viability (c 5 vari-ance/mean 5 nv[1 2 v]/nv 5 1 2 v, where v is viability).(This comparison should be treated cautiously because therewas some variation in the initial number of first instar larvae.)At the highest density, the variance is much larger than themean (c 5 5.96; Table 1). Some of the variance at highdensity is presumably due to variation in the numbers of eggslaid (which was not controlled for in the high-density treat-ment) and some to variation in subsequent survival.

At each density, there is significant variation between chro-mosome lines in mean numbers emerging, n. This is shownby the strong correlation between the two replicates for eachline (Table 1): Correlations as large as observed were neverseen in 1000 datasets that were randomized across lines. Thevariance/mean ratio, c, is only weakly correlated across rep-licates (Table 1), and this correlation only approaches sig-nificance at the lowest density. At low density, the variancein productivity between vials is expected to decrease as meanproductivity increases, because the variance must approachzero as viability approaches one. (In the line with highestviability, 28.9/30 larvae survived at n0 5 30.) The correlationbetween loge(n) and loge(c) across lines is 20.495, 20.163,20.179, and 0.018 at n0 5 30, 60, 90, high. This fits theexpected pattern; however, only the correlation at lowest den-sity is significant (0, 131, 118, and 446 of 1000 randomizeddatasets showed a more negative correlation).


FIG. 1. Correlations across densities in chromosome effects on numbers emerging, n. For each pair of densities, a point is plottedshowing the mean n for each line at those two densities. The ellipses show the quartiles for each pair of densities. The mean numbersemerging, n, are in the same order as the initial densities, n0, which allows the pairs to be identified. There are significant correlationsin line effects among the three lower densities (lower three clusters), but not with the higher density (upper three clusters; see Table2A).

TABLE 2. Correlations in mean and variance of numbers emerging across densities. The left half of the table gives correlations in loge(n),and the right half correlations in loge(c). The upper half gives correlations in line means, and the lower half gives the correlations in residualeffects of replicate cage. The number of 100 datasets, randomized across lines/replicates, that gave a higher correlation than was observed isgiven in parentheses after each correlation coefficient. Correlations significant at P # 0.05 are in bold.

loge(n)

n0 5 30 n0 5 60 n0 5 90

loge(c)

n0 5 30 n0 5 60 n0 5 90

Linesn0 5 60n0 5 90n0 high

0.871 (0)0.693 (0)0.098 (185)

0.829 (0)20.132 (628) 20.180 (692)

0.093 (287)0.302 (26)0.191 (266)

0.418 (17)20.366 (931) 20.045 (674)

Replicatesn0 5 60n0 5 90n0 high

0.493 (1)0.445 (18)0.082 (693)

0.570 (4)0.105 (300) 20.048 (584)

20.077 (562)0.265 (28)0.058 (368)

0.038 (356)0.082 (296) 0.063 (402)

Relative to the 30 lethal lines, the 10 lines carrying wild-type chromosomes without recessive lethals had significantlyhigher numbers emerging at the three lower densities, andsignificantly fewer at the highest density. The ratios of nbetween nonlethals and lethals were 1.073, 1.119, 1.097, and0.582 for initial densities n0 5 30, 60, 90, and high. In 1000datasets, arbitrarily partitioned into sets of 10 and 30 lines,ratios this extreme were found in 14 cases for n0 5 30 andnever at higher n0. We discuss the relation between relativeviability and total numbers below.

The variance in n between replicate cages is considerablysmaller than that between chromosomes (Vline vs. Vrep; Table1). Nevertheless, between-replicate variation is statisticallysignificant. If vials are randomized across replicates, be-tween-replicate variances as large as observed are rarely seen

(number following Vrep in Table 1). The between-replicatevariance for c is about the same as the between-line varianceand is only marginally significant at the higher densities (lastrow in Table 1). Differences between replicate cages may bedue to both genetic divergence and environmental differencesbetween replicates.

The effects of both chromosome and replicate cage onmean numbers are consistent across densities. Figure 1 plotsn at one density against n at another, for each pair of densitiesand for each chromosome line. There are strong and signif-icant correlations in line effects across the three lower den-sities, but not with effects at high density (upper left of Table2). Effects of replicate cage are also consistent across thethree lower-density treatments, but not with high density(lower left of Table 2); however, the correlations are not as


TABLE 3. Fitting structured models for numbers emerging by maximum likelihood. Each row tests for the presence of some effect by givingthe difference in log likelihood between two models, together with the difference in number of degrees of freedom (Dlog(L), df ). P is thesignificance level of Dlog(L), assuming the asymptotic x2-distribution. P* is a significance level allowing for between-replicate variance; it iscalculated by assuming that the ratio between Dlog(L) for the effect and that for the residual component d 3 l 3 r, follows an F-distribution.(A) Fitting models for the loge mean number, loge(n), with loge(c) fitted separately for each density, chromosome line, and replicate (d 3 l 3r). The variance components Vd, Vl, Vd3l, Vl3r, Vd3l3r are the components of variance in loge(n); these are calculated directly from the mostlikely fit to model 1. (B) Fitting models for loge(c), assuming that the mean, n, is determined by an interaction between density, line, andreplicate (d 3 l 3 r).

Effect df Dlog(L) P P* Model 1 Model 2 Vd Vl Vd3l Vl3r Vd3l3r

(A)

dld 3 ll 3 rd 3 l 3 r

439

11740

160

1180.60296.22215.39

81.10162.81

00000

000.00030.0014

dd, ld 3 ld, l 3 rd 3 l 3 r

dd, ld, ld 3 l

1.1201.2021.2111.1381.179

0.0130.0130.0110.012

0.025

0.0230.00250.0026 0.0053

(B)

dld 3 ll 3 rd 3 l 3 r

339

11740

160

218.1379.81

131.3152.24

158.26

00000

00.00090.2280.117

dd, ld 3 ld, l 3 rd 3 l 3 r

dd, ld, ld 3 l

2.1232.2601.5602.1660.815

0.2720.2430.2390.308

0.626

0.8730.1800.291 0.723

strong as for line effects. The variance/mean ratio does notshow such consistent variation across density treatments(lower right of Table 2).

The magnitude of variation associated with density, line,and replicate cage and their interactions is quantified in Table3. All effects on the mean are statistically significant (Table3A), which is consistent with the randomization tests dis-cussed above. (Significance levels are higher, as expectedfrom a parametric test.) In particular, there are significanteffects of line and replicate cage, which are consistent acrossdensities (l, l 3 r), as well as effects of line and replicatecage peculiar to each density (d 3 l, d 3 l 3 r). When allfour densities are considered, there is significant variation inline effects across densities (d 3 l). When the analysis isrestricted to the three lowest densities, this component is notsignificant; all other components remain significant. The var-iance between lines in mean loge numbers, averaged overreplicates, is 0.012; correcting for the variance between rep-licate cages (Vl3r) gives an estimate of Vl 5 0.010. Thus,lines vary in total productivity by a standard deviation ofabout 10%.

A similar analysis of effects on the variance/mean ratioshows significant variation between replicate cages, peculiarto each density (d 3 l 3 r). Given this variation, there aresignificant line and density effects but no significant variationin line effects across densities (d 3 l) and no significantreplicate cage effects, consistent across densities (l 3 r) (col-umn P* in Table 3B). This pattern is similar to that from therandomization tests but, as for the mean, significance levelsare higher. For example, effects of replicate cage peculiar toeach density (d 3 l 3 r) can be tested by randomizing vialsacross replicate cages. This gave between-replicate variancegreater than that observed in 317, 82, 34, and 51 of 1000cases for the four initial densities (row Vrep in lower half ofTable 1). For comparison, fitting a different variance/meanratio for every cage and initial density increased log likeli-hood by 158.26, at the expense of 160 degrees of freedom,which is highly significant when compared with the asymp-

totic ½x2 distribution. Similarly, the highly significant lineeffects seen in Table 4B correspond to the weak correlationsin c across densities (upper right of Table 2).

Relative Viability

Beginning at the lowest level, we observed slight but sig-nificant variation in relative viability between vials. The re-duction in log likelihood when the proportions of the threeheterozygous genotypes are constrained to be the same in allvials from the same cage, rather than varying across vials,is Dlog(L) 5 346.43, 385.47, 377.75, and 294.63 at initialdensities n0 5 30, 60, 90, and high (df 5 640, 640, 640, and160, respectively). At all but the lowest density, these valuesare significant at P # 0.01 when tested either against theasymptotic ½x2 distribution or against randomized datasetsmade by shuffling individuals across vials, keeping totals asobserved. At the three lowest densities, the magnitude ofvariation is not much greater than would be expected bychance: The observed values exceed their expectation onlyby 16%. However, at high density, Dloge(L) is 3.7 timesgreater than expected, indicating substantial variation in rel-ative viability between vials. This pattern corresponds to thatseen for total numbers, with the variance in numbers acrossvials being close to the binomial expectation at low densities,but substantially in excess at high densities. Presumably, rel-ative as well as absolute viabilities differ among vials undercompetitive conditions. However, in view of the weak pat-terns in variance of numbers seen in the previous section, wedo not consider further the variance in relative viability acrossvials.

Henceforth, we consider only total numbers of each ge-notype counted for each replicate cage and initial density.The proportions of the four genotypes are represented bythree quantities: the average viability of wild-type hetero-zygotes (1/TM2, 1/TM1) relative to the standard genotypeTM1/TM2; the relative viability of the two different wild-type heterozygotes [(1/TM2)/(1/TM1)]; and the viability of


TABLE 4. Relative viabilities at each density. (A) The geometric mean of the heterozygous viabilities (TM*/1)/(TM1/TM2), averaged acrosslines and replicates. Vline is the estimated variance between line means, corrected for between-replicate variance. Vrep is the variance betweenreplicates after removing line effects. The number of 1000 datasets, randomized across replicates, that showed larger Vrep is shown in parenthesesfollowing Vrep. The next row gives the correlation in loge heterozygous viabilities between replicates, followed by the number of 1000 datasets,randomized across lines, that showed a greater correlation. Values significant at P # 0.05 are shown in bold. The remaining sections give thesame information for the loge viability of TM2/1 relative to TM1/1 (B); of 1/1 relative to TM1/TM2 (C); and of TM*/1 relative to 1/1 (D).Sections (C) and (D) use only data from the 10 lines in which 1/1 is viable.

n0 5 30 n0 5 60 n0 5 90 n0 high

(A)

(TM*/1)/(TM1/TM2)Vline

Vrep


1.450.133

0.180 (0)0.418 (12)

1.510.151

0.100 (0)0.594 (0)

1.610.204

0.076 (0)0.729 (0)

1.760.172

0.451 (0)0.331 (64)

(B)

(TM2/1)/(TM1/1)Vline

Vrep


1.240.056

0.060 (469)0.471 (1)

1.230.049

0.063 (48)0.466 (0)

1.270.065

0.040 (22)0.650 (0)

1.260.002

0.163 (2)0.004 (570)

(C)

(1/1)/(TM1/TM2)Vline

Vrep

1.861.356

0.133 (251)

2.151.646

0.507 (21)

2.482.129

0.173 (365)

2.551.917

1.289 (21)Correlation between replicates

(D)

(TM*/1)/(1/1)Vline

Vrep


0.907 (0)

1.060.810

0.108 (249)0.921 (4)

0.789 (7)

1.041.388

0.141 (1)0.953 (11)

0.922 (0)

1.041.777

0.087 (8)0.956 (4)

0.620 (55)

1.281.893

0.248 (134)0.889 (37)

TABLE 5. Relative viabilities of the 30 lethal and 10 nonlethal lines.Values are geometric means over all cages.

n0

(TM*/1)/(TM1/TM2)

Lethal Nonlethal

(TM2/1)/(TM1/1)

Lethal Nonlethal

(1/1)/(TM1/TM2)

nonlethal

(TM*/1)/

(1/1)nonlethal

306090high

1.311.311.371.41

1.962.312.573.41

1.231.281.341.30

1.271.081.101.15

1.862.152.482.56

1.061.041.041.28

wild-type homozygotes relative to TM1/TM2. Throughout,we work with natural logarithms of these ratios. We refer tothem as heterozygous viability [(TM*/1)/(TM1/TM2)]; rel-ative viability [(TM2/1)/(TM1/1)]; and homozygous viabil-ity [(1/1)/(TM1/TM2)].

First, consider the average properties of the genotypes. Onaverage, wild-type heterozygotes have 1.58 times greater vi-ability than TM1/TM2; this ratio increases with density (Table4A, first row). The TM2/1 heterozygote is about 25% moreviable than TM1/1 across all densities (Table 4B). The geo-metric mean viability of the 1/1 homozygote relative toTM1/TM2, across the 10 lines in which it was viable, in-creased with density, and averaged 2.24 (Table 4C). Thecomparison between heterozygous and homozygous viabilitycan be made in several ways. The viability of 1/1 relativeto TM1/TM2 in the 10 nonlethal lines is 1.41 times the vi-ability of the wild-type heterozygote relative to TM1/TM2 inall 40 lines. However, if the viability of 1/1 homozygotesis compared directly with that of wild-type heterozygotes in

the same lines, homozygous viability is 10% below that ofTM*/1 heterozygotes. This is because lines carrying a wild-type chromosome that is recessive lethal have substantiallylower TM*/1 viability than lines carrying homozygous viable1 chromosomes (Table 5). This difference is highly signif-icant at all densities, although greater at high density (fourof 1000 randomly chosen sets of 10 and 30 lines exceededthe observed viability difference at low density, and zero of1000 at higher densities).

Except at high density, chromosome lines differ signifi-cantly in heterozygous viability, relative viability, and ho-mozygous viability (see randomization tests in Table 4). Thebetween-line variance in loge homozygous viability (calcu-lated for the 10 nonlethal lines) is highest. Averaged overdensities, this variance is 1.76 on a loge scale, which cor-responds to a typical ratio of about Exp ø 3.8 betweenÏ1.76lines (Table 4C, second row). The average variance betweenlines in heterozygous viability of 0.165 corresponds to a typ-ical ratio of about 1.5 between lines. The variance in viabilityof TM1/1 relative to TM2/1 is only 0.043, corresponding toratios of about 1.2 between lines. Thus, there is significantbut weak interaction between the wild-type chromosome andthe two balancers. (This interaction reflects dominance whenwhole chromosomes are viewed as alternative alleles, butmay be due to epistasis between the constituent genes.)

At high density, the correlation between replicates in bothheterozygous and homozygous viability is only marginallysignificant (Table 4A, C, last column). This is surprisingbecause there are highly significant differences between linesin the total number of flies produced and the between-line


FIG. 2. Variation in chromosome effects on relative viability across densities. (A) Heterozygous viabilities (i.e., TM*/1 relative to TM1/TM2) of the nonlethal lines are plotted in the upper panel, and for the lethal lines in the lower panel. (B) Viabilities of TM2/1 relativeto TM1/1, as in (A). (C) 1/1 viability relative to TM1/TM2 for the 10 nonlethal lines.

variance in total numbers, heterozygous viability, and ho-mozygous viability increases with density (Table 1). The lowsignificance at high density may be because TM1/TM2 thenhas very low viability, averaging only about 5% of the prog-

eny. Therefore, measures of viability made relative to thisgenotype are subject to much error at high density. However,this does not explain why between-line variation in the rel-ative advantage of TM2/1 over TM1/1 is also insignificant


TABLE 6. Correlations across densities in effects on relative viability. The left columns show line effects, and the right columns replicateeffects. The upper, middle, and lower sections of the table give correlations in loge[(TM*/1)/(TM1/TM2)], loge[(TM2/1)/(TM1/1)] and loge[(1/1)/(TM1/TM2)]. The number of 1000 datasets, randomized across lines/replicates, that gave a higher correlation than was observed is givenin parentheses after each correlation coefficient. Correlations significant at P # 0.05 are in bold.

n0

Line effects

n0 5 30 n0 5 60 n0 5 90

Replicate effects

n0 5 30 n0 5 60 n0 5 90

(TM*/1)/(TM1/TM2)

(TM2/1)/(TM1/1)

6090

high6090

0.848 (0)0.871 (0)0.825 (0)0.565 (0)0.645 (0)

0.949 (0)0.805 (0)

0.838 (0)

0.812 (0)

0.611 (0)0.525 (58)0.348 (158)0.384 (61)0.375 (48)

0.663 (1)0.339 (25)

0.580 (2)

0.050 (418)

(1/1)/(TM1/TM2)high6090

high

0.188 (176)0.966 (0)0.976 (0)0.803 (9)

0.417 (17)

0.977 (0)0.893 (4)

0.440 (8)

0.828 (6)

0.378 (24)20.260 (678)

0.105 (382)20.135 (695)

0.349 (128)

0.505 (20)0.533 (126)

0.355 (69)

0.323 (73)

at high density (Table 4D). The explanation may be that thereis greater random variation in viability at high density. Thisis shown by the high between-replicate variances (Vrep inTable 4) and the high between-vial variance in total numbers(c in Table 1) and in relative viabilities (see above).

There are significant differences in all measures of relativeviability between replicate cages, as well as between chro-mosome lines, at least at some densities (Vrep in Table 4).The between-replicate variance in loge heterozygous viabilityis of the same order as the between-line variance for (TM*/1)/(TM1/TM2) and (TM2/1)/(TM1/1), but much smaller forcomparisons involving the wild-type homozygotes. Between-line differences are strongly correlated across densities (Table6, left; Fig. 2). In contrast, between-replicate differences areless consistent (Table 6, right).

We next consider the relation between the viabilities ofdifferent genotypes. Across all 40 lines, there is a weak pos-itive correlation between the advantage of TM2/1 over TM1/1, and the average advantage of wild-type heterozygotes overthe double balancer heterozygote (r 5 0.22, line means av-eraged over densities). However, this is not significant (P 50.096), and although correlations at each density are all pos-itive, only that at the lowest density is significant (r 5 0.31at n0 5 30; P 5 0.019). The most interesting correlation isbetween heterozygous and homozygous effects of the wild-type chromosome. As discussed above, the 30 1 chromo-somes that carry recessive lethals have substantially lowerheterozygous viability than the 10 that are homozygous vi-able. Within the latter 10 lines, there is a surprisingly closerelation between heterozygous and homozygous viability,apart from one outlier that has exceptionally low homozygousviability. The same pattern is seen at all four densities, eventhough the points are ranked quite differently (Fig. 3). Forthose nonlethal lines with low viability (upper left of Fig.3), heterozygous and homozygous viabilities are almostequal, whereas for those lines with high viability, homozy-gous viability tends to be greater (except the one outlier).

The loge mean number of flies emerging from each vial ispositively correlated with the loge heterozygous viability atthe lowest three densities (r 5 0.19, 0.45, 0.52 at n0 5 30,60, 90) but negatively correlated at the highest density (r 520.50; Fig. 4). All except the correlation at the lowest densityare statistically significant (P 5 0). The obvious explanationis that when competition is negligible, the numbers emerging

are proportional to viability, whereas when competition issevere, a greater number surviving early larval stages maygenerate fewer successful pupae. However, competition mustbe strong even at the lowest densities, because the regressionsof loge mean numbers against loge heterozygous viability aresmall: 0.049, 0.118, 0.118, and 20.252 at n0 5 30, 60, 90high. Because the wild-type heterozygotes make up at leasthalf the population (and at least two-thirds in the 30 lethallines), the regression would be at least 0.5 if larvae survivedindependently of each other.

Table 7 summarizes the variation in segregation ratios byfitting a series of nested models. For simplicity, we presenta single table, in which the same model is fitted to bothloge[(TM*/1)/(TM1/TM2)] and loge[(TM2/1)/(TM1/1)].There is significant variation between replicate cages, pe-culiar to each density (d 3 l 3 r; last row of Table 7). Thiscage- and density-specific variation in segregation ratios isdue, at least in part, to the excess variation between vialsnoted above. It corresponds to the significant between-rep-licate variance seen at each density in Table 4 (Vrep), whichis not consistent across densities (Table 6, right). This var-iation is taken into account when testing the significance ofother components (column P* in Table 7).

There is highly significant variation between lines and be-tween replicates of the same lines (l, l 3 r; first two rows ofTable 7). The line differences do not vary significantly acrossdensities (d 3 l; fourth row of Table 7), which is consistentwith the high correlations in line effects seen across densities(Fig. 2, Table 6). Furthermore, there is no significant variationin segregation ratios across densities (d; third row of Table7). However, there is a suggestion that the mean heterozygousviability [(TM*/1)/(TM1/TM2)] increases with density, asdoes the between-line variance in loge heterozygous viability(Table 4). The estimated variance components in Table 7differ somewhat from the averages of the density-specificestimates given in Table 4; because the former are calculatedfrom maximum-likelihood estimates based on the whole da-taset, they are preferred.

DISCUSSION

We have assessed the effects of different wild-type chro-mosomes on both the numbers of adult flies emerging andon the relative preadult viability of different genotypes over


FIG. 3. Relation between heterozygous and homozygous viabilities (i.e., of TM*/1 relative to TM1/TM2 and 1/1 relative to TM1/TM2).From top left to bottom right, initial densities are n0 5 30, 60, 90, high. The 30 lethal lines are plotted at an arbitrary low value on thevertical axis. The line shows equal viabilities for the heterozygotes and homozygotes.

FIG. 4. Relation between mean numbers emerging, n, and viability of TM*/1 relative to TM1/TM2. There are four clusters of points,showing variation across lines for the four initial densities (n0 5 30, 60, 90, and high, from bottom to top). Ellipses show quartiles ofbetween-line variation at each initial density.

a range of larval densities. Our method is novel, in that astandard genotype was present against which the others couldbe compared. We also had two different balancer chromo-somes present in our cultures, so that any nonadditive effectsdue to interaction between the wild-type chromosomes andthe balancers could be detected. Finally, we examined theeffects both of wild-type chromosomes that were carrying arecessive lethal and chromosomes that produced homozygous

viable and fertile flies. This allowed us to examine the re-lationship between independently measured homozygous andheterozygous effects on preadult viability.

The main finding of the study was that there were strongeffects of the wild-type chromosome both on the total num-bers of adults emerging and on the relative viability of dif-ferent genotypes. Mean numbers produced varied signifi-cantly between chromosome lines across all densities, with


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0.013 (Table 3). Both heterozygous and homozygous via-bility, relative to the standard TM1/TM2 genotype, also variedsignificantly between chromosome lines: On a loge scale andaveraged over densities, the variances were 0.165 and 1.76,respectively (Tables 4A, C). In contrast to the effects onaverage productivity and viability, genetic effects on the var-iance in productivity and viability between replicate vialswere weak and inconsistent.

These data are consistent with previous studies that haveshown that homozygous effects are much more variable thanheterozygous effects (e.g., Mukai and Yamaguchi 1974; Mu-kai and Nagano 1983; Mackay 1986). However, our exper-iment gave substantially higher estimates of the genetic var-iance in heterozygous viability. For example, Mackay (1986,table 2) measured a between-line variance in loge viabilityof 1/1 homozygotes relative to TM3/1 of 0.25. The com-parable figure in our experiment varies between 0.81 at lowdensity and 1.89 at high density (Table 4D); this is necessarilybased on only the 10 nonlethal lines. Mukai and Nagano(1983) estimated the additive variance in heterozygous fitnessusing 12 sets of 7 3 7 diallel crosses and a large sample ofsecond chromosomes; the additive variance in loge viabilitywas 0.023, much lower than our estimate of 0.165 (Table4A). One explanation is that we compared the viability ofTM*/1 relative to TM1/TM2, whereas Mukai and Nagano(1983) compared wild-type 1i/1j heterozygotes, relative toCy/1i heterozygotes. The effects of wild-type chromosomesmay be greater when competed against a relatively unfit ge-notype such as TM1/TM2.

The variance in loge viability of TM1/1 relative to TM2/1 is only about 0.043, corresponding to ratios in viability ofabout 1.2 between lines. Thus, there is significant but weakinteraction between the wild-type chromosome and the twobalancers. This interaction reflects dominance when wholechromosomes are viewed as alternative alleles, but may bedue to epistasis between the constituent genes. However, notethat these net interactions are averaged over interactions be-tween all the genes on the third chromosome; the underlyinginteractions might be much stronger than their net conse-quence suggests.

Initial larval density had a significant effect on both num-bers emerging and relative viabilities. On average, the pro-portion of larvae that gave rise to adults fell with densityover the three lower larval densities, although not greatly.However, the viability of wild-type heterozygotes and ho-mozygotes relative to TM1/TM2 increased substantially withdensity (Table 4A, 4C). The obvious explanation is that theviability of TM1/TM2 was particularly density dependent.This view is supported by the data in Table 4D), which showthat the viability of wild-type homozygote relative to theheterozygote changed rather little with density; this com-parison does not involve TM1/TM2. Thus, those genotypesthat, on average, had the lowest larval viability were also themost sensitive to increasing density, in accordance with thefindings of Kondrashov and Houle (1994) and Shabalina etal. (1997) for the effects of new mutations.

Overall, the effects of wild-type chromosomes on relativeviability and on numbers emerging were consistent acrossdensities (Tables 2, 6; Fig. 2). There is no significant inter-


action between the effects of chromosome line and densityon relative viabilities (Table 7); for numbers emerging, theinteraction is only insignificant if the highest density is in-cluded (Table 3). The variance among lines in relative via-bility does increase with density; for example, the variancein viability of TM*/1 relative to TM1/TM2 increases from0.13 to 0.17 across the range of densities (Table 4A). How-ever, the increases are not large and are not significant ac-cording to F-ratio tests. The variance between lines in num-bers emerging is significantly greater at high density, butvaries little between the three lower densities (0.08 vs. 0.01;Table 1). Thus, although the weaker genotypes (TM1/TM2,TM1/1) are, on average, relatively less viable at higher den-sity, variation in effects on relative viability of different wild-type chromosomes increases less markedly with density.

There are counter-examples in the literature in which fit-ness differences are greatest in benign conditions (see Hoff-mann and Hercus 2000). For example, Mueller and Ayala(1981) found that the difference between homozygous linesand the random heterozygous standard was largest at thelowest initial density. However, this study did not use a com-petitive measure of fitness. Clark and Feldman (1981) lookedfor an interaction between culture population density andpreadult viability, albeit using artificial genotypes; they foundno significant gene-environment interaction. Marks (1982)made pure cultures at different densities of homozygotes andheterozygotes, using chromosomes extracted from a naturalpopulation. Preadult survival decreased with increasing larvaldensity for all genotypes, but the extent to which it did sovaried significantly between genotypes. The studies of Clarkand Feldman (1981) and Marks (1982) are also limited be-cause they did not use a reference genotype. Indeed, becausethere are few studies of these types, we cannot make thegeneralization that genetic effects on viability are necessarilymagnified in more stringent conditions (Kondrashov andHoule 1994; Shabalina et al. 1997). Moreover, Shabalina etal. (1997) did not use a reference genotype and, althoughKondrashov and Houle (1994) did, they made no commenton whether its viability was affected by density.

We found a strong positive correlation between the ho-mozygous and heterozygous effects of the nonlethal chro-mosomes on preadult viability at all four larval densities,apart from one outlier that had exceptionally low homozy-gous viability (Fig. 3). A formal estimate of dominance isnot warranted, given that we only measured 10 lines. Usinga different method that did not permit the heterozygous ef-fects of individual chromosomes to be assessed, Mukai andYamaguchi (1974), Mukai and Nagano (1983), and Mackay(1986) also found a correlation between homozygous andheterozygous viability for nonlethal lines. We also found thatthose chromosomes carrying recessive lethals had signifi-cantly lower viability when heterozygous with a balancerchromosome. Mukai and Yamaguchi (1974) found such adifference in viability between lethal and nonlethal lines,albeit much smaller in magnitude.

Such correlations between homozygous and heterozygouseffects could arise through ecological interactions betweengenotypes, if the survival of the unfit TM1/TM2 genotype isparticularly sensitive to the presence of a competitive ge-notype in the cultures. If 1/1 is particularly competitive and

this competitiveness has a larger impact on TM1/TM2 thanon TM*/1, the apparent viability of the latter would be el-evated. This could also explain why we found that TM*/1had a greater viability advantage over TM1/TM2 in the non-lethal lines.

Our results give some insight into the relation betweengenetic and ecological processes. The 10 lines that carriedhomozygous viable wild-type chromosomes produced about10% more adults than the 30 lethal lines at low density, butapproximately 40% fewer adults at the higher density. Sim-ilarly, there was a significant positive correlation betweenheterozygous viability and numbers emerging at low densi-ties, but a negative correlation at the highest density. Thisindicates that increased survival in the early instars leadsdirectly to more adults when competition is weak, but reduceslater survival, and thus numbers emerging, when competitionis intense.

The ecological complexity of even an artificial Drosophilaculture makes the measurement of fitness and its componentsdifficult both in practice and in principle. For example, ourhigh estimates of the variance in effects of heterozygous wild-type chromosomes may be due, in part, to the sensitivity tocompetition of the TM1/TM2 reference genotype. On a morepositive note, much more can be gleaned from straightfor-ward counts of genotypes than one simple measure of via-bility. Each wild-type chromosome may in principle haveeffects not just on mean viability, but rather on the distri-bution of viabilities across environments that arises from theecological interactions among competing individuals. Nev-ertheless, our study reveals remarkably high and consistenteffects of a random sample of wild-type chromosomes onrelative viability and on net productivity.

ACKNOWLEDGMENTS

We thank SERC and BBSRC for financial support and R.Miah, G. Geddes, and E. Garcia for technical assistance.

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Corresponding Editor: T. Kawecki

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GENETIC VARIATION FOR PREADULT VIABILITY IN DROSOPHILA MELANOGASTER