Genetic Variance for Body Size in a Natural Population of Drosophila buzzatii

Transcription

1 Copyright by the Genetics Society of America Genetic Variance for Body Size in a Natural Population of Drosophila buzzatii Alfredo Ruiz,* Mauro Santos,* Antonio Barbadilla, Jorge E. Quezada-Diaz,* Esteban Hasson? and Antonio Fontdevila* *Departament de Genitica i de Microbiologia, Universitat Autonoma de Barcelona, Bellaterra (Barcelona), Spain, and?g.i.b.e. Departamento de Ciencias Bioldgicas, F.C.E. y N., Ciudad Universitaria Nuriez, 1428 Buenos Aires, Argentina Manuscript received June 8, 1990 Accepted for publication April 1 1, ABSTRACT Previous work has shown thorax length to be under directional selection in the Drosophila buzzatii population of Carboneras. In order to predict the genetic consequences of natural selection, genetic variation for this trait was investigated in two ways. First, narrow sense heritability was estimated in the laboratory Fn generation of a sample of wild flies by means of the offspring-parent regression. A relatively high value, 0.59, was obtained. Because the phenotypic variance of wild flies was 7-9 times that of the flies raised in the laboratory, natural heritability may be estimated as one-seventh to oneninth that value, Second, the contribution of the second and fourth chromosomes, which are polymorphic for paracentric inversions, to the genetic variance of thorax length was estimated in the field and in the laboratory. This was done with the assistance of a simple genetic model which shows that the variance among chromosome arrangements and the variance among karyotypes provide minimum estimates of the chromosome s contribution to the additive and genetic variances of the trait, respectively. In males raised under optimal conditions in the laboratory, the variance among second-chromosome karyotypes accounted for 11.43% of the total phenotypic variance and most of this variance was additive; by contrast, the contribution of the fourth chromosome was nonsignificant. The variance among second-chromosome karyotypes accounted for % of the total phenotypic variance inwildmales and was nonsignificant inwild females. The variance among fourth chromosome karyotypes accounted for % of the total phenotypic variance in wild flies. At both chromosomes, the proportion of additive variance was higher in mating flies than in nonmating flies. B ODY size is the most obvious and easily observable phenotypic trait in most animals and there is compelling evidence indicating that it is directly related to fitness. In Drosophila, evidence on the adaptive nature of body size comes from the observation of latitudinal and altitudinal clines and cyclic seasonal changes in several species (PREVOSTI 1955; DAVID and BOCQUET 1975; PARSONS 1983, pp ; LEMEU- NIER et al. 1986; COYNE and BEECHAM 1987) and from laboratory experiments with population cages (ANDERSON 1966,1973; POWELL 1974; LANDE 1977). Selection is apparently directional since body size is positively correlated with mating success (MONCL~~S and PREVOSTI ; PARTRIDGE and FARQUHAR 1983; PARTRIDGE, HOFFMAN and JONES 1987; TAY- LOR and KEKI~ 1988), ovariole number and daily fecundity (ROBERTSON 1957; HEED and MANGAN 1986), longevity (PARTRIDGE and FARQUHAR 1983) and dispersal ability (ROFF 1977). In addition, larger flies withstand better a number of ecologically relevant environmental stresses such as desiccation or anoxia (PARSONS 1973). Whether body size is nega- This paper is No. XVIII of the series The Evolutionary History of Drosophila buzzatii. tively correlated with other components of fitness (e.g., development speed) is not known with certainty at the moment. ROBERTSON (1963) observed a correlation between body size and development time in the laboratory but it was dependent on the diet. Thus, it is not clear how this observation applies to natural populations. Recent work carried out in the cactophilic fly Drosophila buzzatii (SANTOS et al. 1988; RUIZ and SANTOS 1989; M. SANTOS, A. RUIZ, J. E. QUEZADA-D~Az, A. BARBADILLA and A. FONTDEVILA, unpublished) has provided evidence for a positive correlation between thorax length and the three major adult fitness components, namely longevity, mating success and fecundity, in the natural population of Carboneras (S.E. Spain). Because selection is directional, it is of considerable interest to assess the proportion of genetic variance and the heritability of this trait in the same population in order to ascertain the genetic consequences of the observed phenotypic selection. In particular, knowledge of the heritability of thorax length would allow a prediction of the response to selection that we would expect, if selection were not acting on other correlated characters (FALCONER 1981 ; LANDE Genetics 128: (August, 1991)

2 740 A. Ruiz et al. 1979, 1982). A nonzero heritability in the field would imply either conclusion: (1) the population is not at equilibrium or (2) if it is at equilibrium, thorax length must be negatively correlated with other selected traits. The estimation of heritability entails no special problems in the laboratory (FALCONER 1981) but is a difficult task in natural populations of Drosophila because relatives cannot be identified in the field. Several indirect methods are now available, although all of them require various assumptions, sometimes impossible to verify (COYNE and BEECHAM 1987; RISKA, PROUT and TURELLI, 1989). Using these methods, PROUT and BARKER (1989) have estimated the heritability of thorax length in a natural population of D. buzzatii from Australia. In this work, we provide comparable information for the population of Carboneras obtained using two different approaches. First, we have estimated the narrow sense heritability of thorax length by means of the offspring-parent regression in the laboratory F2 of a moderately large sample of wild females collected in Carboneras. This provides, under certain assumptions (see DISCUSSION), an estimate of the heritability in the natural population. Second, we have obtained a minimum estimate of the portion of genetic variance contributed by the second and fourth chromosomes, both in the field and in the laboratory. This was done by relating body size to the karyotype of the flies at these two chromosomes, which are known to be polymorphic for paracentric inversions in D. buzzatii (RUIZ, NAVEIRA and FONT- DEVILA 1984; RUIZ et al. 1986). A GENETIC MODEL FOR THE BIOMETRICAL EFFECT OF INVERSIONS In species polymorphic for chromosomal arrangements, different karyotypes from natural populations have been sometimes found to differ in their mean value for one or more metrical characters (WHITE and ANDREW 1960, 1962; WHITE, LEWONTIN and AN- DREW 1963; PREVOSTI 1966; KRIMBAS 1967; KRIMBAS and LOUKAS 1980; STALKER 1976; BUTLIN, READ and DAY 1982) and, in some cases, this correlation between karyotype and metrical characters has been shown to have a genetic basis (PREVOSTI 1960, 1967; see also RUIZ and SANTOS 1989). The biometrical effect of inversions is thought to be caused by the association of different arrangements with particular -1leles at loci which influence the trait under consideration. Thus, it may be possible to relate the variation observed among karyotypes with the genetic variance of the trait itself. Consider a very large and panmictic population polymorphic for two chromosome arrangements, ST and IN, in a given pair of autosomes. Let u and v stand for the relative frequencies of the two arrangements. The three karyotypes STIST, STIIN and IN/IN will occur in the population in Hardy-Weinberg proportions, u2, 2uv and v2, respectively. An arbitrary number of loci (n) affecting the phenotypic trait will be considered. They may be located inside the inverted chromosome segment or close to it. The population frequencies of the two alleles at the i locus, Ai and ai, are represented by pi and qi, respectively. This locus is associated with the inversion-polymorphic chromosome and the corresponding gametic association measured by the determinant of the gamete frequency matrix Di (LEWONTIN and KOJIMA 1960) or by the correlation of gene frequencies pi (HILL and ROBERTSON 1968). Thus, the frequencies of alleles Ai and ai are, respectively, pi + (D,/u) and q, - (D,/u) within arrangement ST, and p, - (Di/v) and qz + (Di/v) within arrangement IN. In addition, any pair of loci ij may be associated within each of the two chromosome arrangements, the association being measured by DV(m and DV([N for chromosomes ST and IN, respectively. The gametic association between the two loci in the total population (09) can be derived using NEI and LI (1973, p. 214) as equal to: If the n loci act additively on the measured phenotypic trait (i.e., no epistasis) and there are neither genotype-environment interaction nor genotype-environment covariance, the contributions of the n loci to the mean (P), genetic additive variance (VA) and dominance variance (VD) of the phenotypic trait in the population, are given by known expressions (AVERY and HILL 1978; EWENS 1979; WEIR, COCKERHAM and REYNOLDS 1980). Also, the mean value of each n-locus genotype is the sum of the contributions of the n onelocus genotypes. Using this principle and the appropriate gene frequencies given above, the mean phenotypic value of each karyotype can be derived as: where ai is the average effect of a gene substitution at the i locus (FALCONER 1981). From these expressions, the variance among karyotypes (ui) can be readily calculated: This variance can be partitioned into two components, the variance explained by the linear regression on the chromosome dose (uz) and the unexplained or deviation variance (a;), which are analogous to the familiar additive and dominance components of the

3 Variance Genetic genetic variance (KEMPTHORNE 1957; FALCONER 1981). From standard statistical theory (SOKAL and ROHLF 1981), the slope of the regression on the chromosome (ST) dose will be: and the average effects of the two chromosome arrangements: ast = Dj ai/u; (YIN = Di ai/v. (7) 1 i The portion of the variance among karyotypes explained by the linear regression on the chromosome dose is: a: = p2& = 2(C Di (Y,)*/uv, (8) which is equivalent to twice the variance of the arrangement average effects. Expression (8) is the first term on the right side of expression (5). It follows that the second term must correspond to the variance unexplained by the linear regression, i.e. the deviation variance: 1 a; = 4(C D?d1)2/U2V*. (9) i The regression variance u: given by (8) can be written as a function of the correlations of gene frequencies as follows: a: = c 2 fiqia?p? + 4 cc a:ajj~ipj- (10) i i<j It can be clearly seen from this expression that in order to get a statistically significant contribution of the regression variance (u:) two conditions have to be fulfilled. First, at least one of the n loci must have a non zero contribution to the additive variance of the population. Second, there must be a gametic association between those loci contributing to the additive variance and the inversion, which means a differential accumulation of alleles plus and minus in the two chromosome arrangements. When both conditions are met and since pi always lies between -1 and +1, a: provides a minimum estimate of the contribution of the n loci to the additive variance of the population (VAL A simple and explicit relationship between u: and V, can be derived under some simplifying assumptions. If the n loci (i) are not associated within the two chromosome arrangements; (ii) have the same degree of association with the inversion (p); and (iii) contribute equally to the additive variance; then: 2 Qa "- n'p2 VA 1 + (n' - l)p2 ' where n' = (m - rn')'/n and m(m') stands for the number of loci showing a positive (negative) gametic Size for Body 741 association with the inversion; thus, n' may be termed the net number of loci. Figure 1 shows some numerical examples. It is worth noting that if n' is large, the variance ratio d/va is close to unity even for moderate values of p. Similarly, the deviation variance u; given by expression (9) can be put in terms of the correlation between gene frequencies as follows: The structure of this expression is very similar to that of the regression variance (10) and the conditions for a significant contribution of the deviation variance (u:) are also analogous, namely, that the loci must contribute to the dominance variance of the trait and there must be gametic associations between the loci and the inversion. Once again, r; provides a minimum estimate of the dominance variance in the population (VD). It should be noted, though, that in expression (12) the correlation parameters are raised to a higher power than in (10). A simple and explicit relationship between a; and VD can be found if conditions (i) and (ii) above hold, and (iii) the n loci contribute equally to the dominance variance: Figure 1 shows some numerical examples. In this case, the variance ratio U;/VD increases with the actual number of loci, i.e. the sign of their association with the inversion does not make any difference. Since a: d VA and a; d VD, it follows that ai = uf + u; d Vc = V A + VD. Therefore, the variance among karyotypes provides a minimum estimate of the genetic variance due to the underlying n loci. MATERIALS AND METHODS Natural population: All Drosophila buzzetii adults used in this study were collected in, or derived from, the population of Carboneras (Almeria, SE Spain). This population is a semiabandoned Opuntiaficus-indica (prickly pear) plantation which was described in detail by RUIZ et al. (1986). D. buzzatii is polymorphic there for four arrangements on the second chromosome, namely 2 standard (2st), Zj, 2jz' and 2jq7, and two arrangements on the fourth chromosome, namely 4st and 4s. A description of these inversions and their population frequencies can be found in FONTDEVILA et al. (198 1) and RUIZ, NAVEIRA and FONTDEVILA (1984) and RUIZ et al. (1986). Flies were handled using carbon dioxide as an anesthetic through the experiments. Crosses involving wild flies were carried out at room temperature for the first 5 days and in a walk-in incubator at 23 O thereafter. Laboratory flies were always kept at 23". A modified formula of David's killedyeast Drosophila medium (DAVID 1962) was used as food. Phenotypic character: Thorax length, from the anterior margin of thorax to posterior tip of scutellum as viewed laterally, was used as an indication of adult body size. All measurements were carried out on live individuals using a

4 742 A. Ruiz et al.? c:.o I SO Gene-inversion association (p) FIGURE 1.-Graphic representation of the variance ratios U:/VA (left) and u&/vd (right) as a function of the gene-inversion association. The curves shown assume that the n loci are (1) not associated between them within the two chromosome arrangements (DB(sT) = D,,(IN) = 0); (2) equally associated with the inversion (pa = = p); and (3) contributing equally to the additive and dominance variances of the character. n is the net number of loci. See text for more information. binocular microscope fitted with an ocular micrometer (1 mm = 75 ocular units in the laboratory tests and 1 mm = 40 ocular units in the field study) and are given here in mm. Data analysis was carried out always with the untransformed measurements. The BIOM package of statistical programs (ROHLF 1982) and the BMDP Statistical Software (1988) were used. A complete description of all statistical tests employed can be found in SOKAL and ROHLF (1981) and RAWLINGS (1 988). Heritability estimation: Narrow sense heritability was estimated in the laboratory by means of the parent-offspring regression using the following experimental procedure. Fifty-three wild females were collected in Carboneras on March 1989 and set individually in shell vials with fresh culture medium. Seven males and seven females from each of 35 progenies (490 flies in total) were placed in an eggcollecting chamber. Eggs were then taken from the chamber daily and allowed to hatch. Batches of 80 first-instar larvae were transferred to 20 vials containing 20 ml of fresh food for optimal growth. The adults emerging from these vials were pair-mated using a balanced 20 X 20 factorial design. Each of the resulting 400 pairs was aged for 4-5 days and then allowed to lay eggs for 24 hr in a shell vial with fresh food. Replica vials for each family were not necessary since only offspring-parent regression was used and not covariance of siblings. Both parents and four offspring (two males and two females) from each of 302 families were measured. This experimental procedure resulted in an effective random mating for thorax size (father-mother correlation coefficient , d.f. = 300, P > 0.05). Body size and inversions, laboratory test: The effect of karyotype on thorax length was tested in the laboratory with a sample of 287 males derived from the same wild flies and in exactly the same way as the parents used for the estimation of heritability (see above). Thus, the results of both analyses pertain to the same population (the laboratory F2 of the wild flies collected in Carboneras) and are strictly comparable. In order to determine the karyotypes, each male was mated with two virgin females from a homokaryotypic laboratory stock (the BU-51 stock, see below) and ten larvae from its progeny dissected for cytological inspection. Afterwards, the male s thorax length was measured in the usual manner. Body size and inversions, field study: The correlation between body size and inversions was also investigated in wild flies collected in June For the purpose of sampling, the population was divided in nine sections of roughly the same area with one collecting site in each. A few decaying Opuntia cladodes per section were found and moved a short distance to the collecting site. Every evening for 5 consecutive days (June 25 through 29) a sample of mating and nonmating adults was taken from each site using an insect aspirator. In total, we collected 396 mating pairs, 357 nonmating females and 335 nonmating males. Further details about the mating behavior of D. buzzatzi and the sampling procedure are given in SANTOS et al. (1988). Within the next 3 hr after collection, mating and nonmating flies were separated by sex and placed individually in shell vials with fresh culture medium. Males were immediately provided with two virgin females from the BU-SI stock. After 60 hr approximately, each male and the two females were transferred into a new vial with fresh food. This operation was repeated 2 days later and, for some males, once more 2 days afterward. About 90% of all males gave offspring. Eight to twelve larvae from each progeny were dissected and their salivary gland chromosomes examined to ascertain the male karyotype. Females, on the other hand, were kept in the original vials for 36 hr and then transferred to a new vial with fresh food. The transfer was repeated again the next day. About 62% of the mating females and 48% of the nonmating females produced offspring in these no-male vials. Twenty- four hours after the last transfer, each female was transferred again into a new vial with fresh food and provided with two males from the BU-51 stock. Two days later, each female and the two males were transferred to another vial and this operation was repeated again 2 days afterward. Thus, three male vials per female were obtained in this way. About 86% of the mating females and 79% of the nonmating females gave offspring in this case. Eight to twelve larvae from the progeny of each female were dissected for cytolog-

5 Genetic Variance Size for Body 743 ical analysis. All sampled larvae were taken from the second and third male vials of each female to increase the probability of them being fathered by the laboratory stock males. The first vial which might contain larvae of mixed paternity was discarded at once. We have previously shown that sperm predominance occurs in D. buzzatii and that in the laboratory the proportion of progeny fathered by the second male mating a female, increases almost to nearly 100% in 2 days (BARBADILLA et al. 1991). The results of the present study further corroborated this point. Cytological analysis: Males and females were crossed with adults from the BU-51 stock in order to ascertain their karyotype. The BU-51 stock is homokaryotypic for arrangements Zj, #st and 5Z. Thus, the cytologicalanalysisof a number of larvae from the progeny of these crosses allowed to infer the karyotype at the second and fourth chromosomes of their parent. Salivary gland chromosomes were prepared as in FONTDEVILA et al. (1981). Although larvae per progeny were dissected, not all the slides could be read under the microscope. The finding of two different karyotypes among the sibsof a progeny is sufficient to correctly classify their parent as heterozygous. On the other hand, when all the examined larvae have the same karyotype there exist the possibility of mistakenly classifying their heterozygous parent as homozygous. Consequently, in this second case, we read a minimum of 5 and usually 6-8 larvae per progeny (7 larvae on the average). With 7 larvae, the probability ofmisclassifying a heterozygous individual is I.56%. Therefore, since the maximum frequency of heterozygotes observed was about 65% (for the second chromosome), our experimental error in assigning the karyotypes was about 1% on the average in the worst case. The 51 inversion is not a naturally occurring one. It appeared in a genetically unstable line produced by introgressive hybridization and its complete denomination in Zn(5)FZb; F2e (NAVEIRA and FONTDEVILA 1985). Hence, inversion 51 is not present at the Carboneras population and was used here as a marker to distinguish, among the progeny of the wild females, the larvae fathered by the BU-51 stock males from those fathered by wild males. Aswe expected, sperm displacement was almost complete and 98% of the progenies we analyzed cytologically had the correct parentage. The remaining progenies, which contained larvae of mixed paternity, were omitted from the analysis. Biometrical effect of inversions; statistical analysis: The five population samples (laboratory males, nonmating males, mating males, nonmating females and mating females) were analyzed separately for each polymorphic chromosome. In order to test for an effect of the karyotype on thorax length, the individuals in each sample were arranged according to a single classification criterion and a one-way ANOVA was carried out. According to the underlying model, each observation can be written as: X, = ~t + etj, where /.ti represents the mean thorax length of individuals with the i karyotype (see above) and e,, is a random deviation of the j individual from its expectation p,. The error term e, is assumed to be an independent, normally distributed variable with expectation E(e,,) = 0 and variance E(& = 2. The variance among karyotypes (u;) was estimated from the formulae for the expected mean squares shown in Table 1. The method is formally identical to that devised by BOER- WINKLE and SING (1 986) to estimate the contribution of a singlelocus to the phenotypic variance of a quantitative trait. Prior to the ANOVAs, each sample was tested for homoscedasticity by means of the F,,,, and Bartlett s tests (SOKAL and ROHLF 198 1, p. 403). Only one case out of ten showed TABLE 1 Analysis of variance performed to test for a biometrical effect of the karyotype Source of variation d.f. MS Expected MS Among karyotypes k - 1 MSPoupa 6 + N d/(k - 1) Regression a - 1 MS,., 6 + N u!/(a - 1) Deviations k -a MSd,, u2 + N&(k - a) Within karyotypes N - k ML,,,, u2 Total N- 1 N = total number of individuals in the sample; k = number of different karyotypes; a = number of chromosome arrangements; MS = mean square. an indication of heteroscedasticity. This was the sample of nonmating males which for the fourth chromosome gave a significant result on Bartlett s test (adjusted x 7.16, d.f. = 2, P < 0.05) but a nonsignificant result on the F,,, test (F,,, = 3.35 with parameters 3 and 7, P > 0.05). In all cases, including this one (see RESULTS), the nonparametric Kruskall-Wallis test (SOKAL and ROHLF 1981, p. 430) corroborated the results of the ANOVA. In addition, the data in each sample were fitted to the linear regression on the number of arrangements of a given type carried by each individual, i.e., the chromosome dose. With only two chromosome arrangements (a = 2) this regression has a single degree of freedom and in the general case (a > 2) a multiple regression with a - 1 degrees of freedom is appropriate. Following RAWLINGS (1988, pp ) the regression sum of squares and the deviations sum of squares were tested against the error variance (2). The variance due to the additive effects of the chromosome arrangements (u:) and that due to the deviations from additivity (ui) were estimated from the formulas for the expected mean squares given in Table 1. The average effect on the character of each chromosome arrangement was deduced from the prediction equation. The frequencies of arrangements Zjz and Zjq7 were quite lowin all samples. Consequently, some of the karyotypes carrying these arrangements, such as the Zjz ljz and Zjq7/ jq homokaryotypes and the 2jq7/jr3 heterokaryotype, were always very scarce. In order to avoid the low numbers in these classes, the three arrangementse Zj, 2jz3 and Zjq7 were sometimes pooled into a single class (henceforth denoted as 2j). These three arrangements share inversion Zj and are thus cytologically derived compared to the 2st arrangement which is the species ancestral chromosome (Rurz, FONTDEV- ILA and WASSERMAN 1982). Theoretically, the pooling of several arrangements into a single class cannot increase the among-karyotype variance (u;) nor the regression variance (u. ). Hence, the values obtained by pooling will still be minimum estimates of the chromosome s contribution to the variance of the trait. RESULTS Heritability: Narrow sense heritability (f SE) estimated as the slope of the offspring-midparent regression was _ which is highly significant (P < 0.001). This estimate, however, assumes equal variances in the two sexes. In our population, females were more variable than males (F = 1.23, d.f. = 301/ 301, P < 0.01). Thus, the regression coefficients were calculated separately for each sex and corrected for

6 ~~ 744 A. Ruiz et al. TABLE 2 Offspring-parent regression coefficients ( ~se) for thorax length in D. buuatii, broken down by sex and corrected for unequal variances in the two sexes Offspring Parent Mean Variance Son Daughter Sire f f Dam f f All regression coefficients significant at the level. the difference in variance between sexes (FALCONER 198 1, pp ). The results are given in Table 2 and heritability estimates can be obtained from this table as twice the slopes of the offspring-single parent regressions. An analysis of covariance showed that the four slopes were significantly different but only barely SO ( F = 2.70, d.f. = , P < 0.05). Furthermore, none of the slopes was significantly different from the others in the a posteriori tests. Therefore, sex-linkage and/or maternal effects are not apparent and the four heritability values can be averaged to give as a better estimate of the heritability of thorax length. Biometrical effect of inversions, laboratory test: Nearly 300 males raised in the laboratory under homogeneous, near optimal conditions were karyotyped and scored for thorax length. Arrangement frequencies in this sample were: 2st , 2j , 2jz and 2jq ; 4st and 4s These values are very similar to those in the wild flies from which the sample was derived. In addition, karyotype frequencies did not depart from the expected Hardy-Weinberg proportions at either chromosome (x2 = 8.75, d.f. = 6, P > 0.05 for the second chro- mosome and x' = 0.00, d.f. = 1, P > 0.05 for the fourth chromosome). Thorax length means of the ten second-chromosome karyotypes (Table 3) differed significantly as shown by the results of the ANOVA (Table 4). The chief difference was that between the karyotypes carrying the 2j inversion and those with the 2st arrangement. This became altogether clear when arrangements 2j, 2jz3 and 2jq7 were pooled into a single class (denoted 2j.; see MATERIALS AND METHODS). Mean thorax lengths of the three resulting karyotypes Bstlst, 2j.lst and 2j./j. were , 1.IO36 and , respectively; the difference being highly significant (Table 4). When all four second-chromosome arrangements were considered, the regression on the chromosome dose was statistically highly significant (Table 4) and the average effect on the character of each chromosome arrangement was: 2st -O.O052,2j , 2jz and 2jq' The regression was also highly significant when the three arrangements sharing inversion 2j were pooled (Table 4) showing again that the divergence between arrangements 2st and 2j. accounts for the major part of the total variance among arrangements. The average effects of the two resulting chromosome arrangements 2st and 2j. were, respectively, and Thus, in the laboratory the 2st arrangement has a decreasing effect on male body size while the 2j inversion has, on the average, an increasing effect. The three fourth-chromosome karyotypes did not differ significantly in mean thorax length (Tables 5 and 6) and the linear regression on the chromosome dose was also nonsignificant (Table 6). Therefore, there seems to be no effect of the fourth chromosome inversions on thorax length under laboratory conditions. Biometrical effect of inversions, field study: More than one thousand wild D. buzzatii adults collected at Carboneras were karyotyped and scored for thorax size. This total number comprises four independent samples (nonmating males, mating males, nonmating females and mating females) which were analyzed separately due to the previously detected differences among them in mean body size (SANTOS et al. 1988). Chromosome frequencies in these four samples (to be dealt with fully elsewhere) did not differ grossly from those in the laboratory males. For the total sample of wild flies, they were: 2st , 2j , 2jz and 2jq ; 4st and 4s Besides, none of the samples showed a significant departure of the karyotype frequencies from the Hardy-Weinberg expectations at either chromosome. It is worth noting, though, that there may be a real tendency for the 4slst heterokaryotype to be in excess since this was observed in all four samples (see RUIZ and SANTOS 1989). Wild males were smaller than those raised in the laboratory, nonmating males by about 13% and mating males by about 11%, and more variable, nonmating males 9.3 times and mating males 7.9 times (Table 3, rightmost column). Likewise, wild females were smaller and more variable than laboratory females (nonmating females 9 times and mating females 5.7 times more variable; cf: Tables 2 and 3). These results are similar to those previously reported for D. buzzatii (ROBERTSON 1987; SANTOS et al. 1988; PROUT and BARKER 1989). The increased variance of wild flies is very relevant here for the difference can be attrib-

7 ~~~~ ~~ ~~~~ ~~ ~ Variance Genetic for Body Size 745 TABLE 3 Mean thorax size (in mm), standard deviation (SD) and sample size (A ) for the ten second chromosome karyotypes in laboratory males and in wild males and females of D. buuatii collected at Carboneras (Spain) Sample SI/Sl jlst j/j jz3/st jz3/jz3 jz3/j jq7/st jq7/j jq ljz jq7/jq7 Total Laboratorymales F SD N Nonmatingmales y SD N Mating males SD N Nonmating females F SD N Matingfemales SD N TABLE 4 Results (in mm* X lo ) of the one-way ANOVAS performed to test for mean thorax length differences among second-chromosome karyotypes in males of D. buuatti Laboratory males Nonmating males Mating males Source of variation d.f. MS F d.f. MS F d.f. MS F Among karyotypes *** Regression *** * Deviations stlst, jqst, jqp *** * 3.80* Regression *** ** Deviations Amongj-1st ** Amongj-ljn Within karyotypes a P < 0.10; * P < 0.05; ** P < 0.01; *** P < MS = mean square. j* stands for arrangementsj, jr and jq pooled. uted, in principle, to the heterogeneity of the natural environment [see SANTOS et al. (1988) for a discussion]. Consequently, even if the variance among karyotypes is the same in the field as it wasin the laboratory, we would expect that the environmental variance will augment the error component of the phenotypic variance and will lessen accordingly the possibilities of detecting statistically significant differences among karyotypes. In the samples of wild flies, none of the F values among the ten second-chromosome karyotypes was significant at the usual 0.05 level but a significant variation among karyotype means was observed in the two samples of males when arrangements 2j, 2jr3 and 2jq were pooled (Tables 3 and 4). Moreover, the pattern was similar in the two samples to that observed in the laboratory: mean values for the three karyotypes 2st/st, 29lst and were, respectively; , and in nonmating males, and , and in mating males. A similar trend was observed for females yet without reaching statistical signification (ANOVA results not shown). Mean values for these three karyotypes were in nonmating females , and , respectively, and in mating females , and The multiple regression of thorax length on chromosome dose, taking into consideration all four second-chromosome arrangements, was statistically significant in mating males but nonsignificant in nonmating males (Table 4). When the three chromosome arrangements sharing inversion 2j were pooled, similar results were obtained. In both male samples, however, the average effect of the two chromosome arrangements was very similar: 2st and in nonmating males, and 2st and in mating males. These values are identical in sign and comparable in magnitude with those observed in the laboratory. Therefore, the secondchromosome arrangements exhibit in the field a sim-

8 746 A. Ruiz et al. TABLE 5 Mean thorax size (in mm), standard deviation (SD) and sample size (A') for the three fourth-chromosome karyotypes in laboratory males and in wild males and females of D. buzratii collected at Carboneras (Spain) Sample stlst sfst SIS Total Lab males F SD N Nonmating males F SD N Mating males SD N Nonmating females SD N Matingfemales F SD N ilar effect to that observed in the laboratory: 29 increases body size whereas 2st decreases it. A slight but consistent difference in size among the three fourth-chromosome karyotypes was observed in all samples (Table 5). This difference was statistically significant in nonmating males and marginally significant in mating females (Table 6). For the sample of nonmating males, which was not clearly homoscedastic (see MATERIALS AND METHODS), a nonparametric Kruskal-Wallis test confirmed the results of the AN- OVA (H = 7.67, d.f. = 2, P < 0.05). In all samples, the 4s/st heterokaryotype was larger than the 4st/st homokaryotype. On the other hand, mean thorax length of the 4s/s homokaryotype was more variable, perhaps due to its small sample size, but in general it was also lower than that of the heterokaryotype. Thus, the data suggest that the heterokaryotype for the fourth chromosome is the largest karyotype in the field, a result not observed in the laboratory. The regression ofsize on chromosome dose was nonsignificant in nonmating males and nonmating females but marginally significant in mating males and mating females (Table 6). In addition, the average effects of the two arrangements in the various samples were quite similar: nonmating males, 4st and 4s ; mating males, 4st and 4s ; nonmating females, 4st and 4s ; and mating females, 4st and 4s Therefore, although the regression was not statistically significant at the usual 5% level in any of the individual samples, the pattern seems consistent. Wild flies carrying the 4s inversion are on the average larger than those bearing the 4st arrangement. Contribution of the second and fourth chromosomes to the phenotypic variance: In the laboratory males, the variance among the second chromosome karyotypes accounted for 11.43% (when all four arrangements were considered) and 8.35% (pooling arrangements 2j, 2jr3 and Zjq') of the total phenotypic variance for thorax length. Most of this variance was due to the linear regression on the chromosome dose (Table 7). As shown above (see description of the genetic model above), this provides a minimum estimate of the contribution of the second chromosome to the additive variance of the trait. On the other hand, in the laboratory the fourth chromosome karyotypes did not contribute significantly to the phenotypic variance of male thorax length. As pointed out above, the total phenotypic variance for thorax length in wild males was considerably larger than in laboratory males and most of the difference was due, as expected, to the error component (Table 7). Consequently, yet the variance among the secondchromosome karyotypes in nonmating males and mating males was comparable in magnitude to that found in the laboratory, it only accounted for 1.56% and 1.78%, respectively, of the total phenotypic variance (arrangements 2j, 2jr3 and 2jq7 pooled; Table 7). In addition, an interesting difference was observed between the two samples of males. In mating males, as observed in the laboratory males, most of the amongkaryotype variance was explained by the linear regression on the chromosome dose whereas in nonmating males this proportion was much lower (Table 7). A similar situation was found for the fourth chromosome. In this case, the among-karyotype variance accounted for % of the total phenotypic var- TABLE 6 Results (in mm' X lo') of the one-way ANOVAS performed to test for mean thorax size differences among fourthchromosome karyotypes in males and females of D. buuatii Laboratory Nonmating females Mating ofvariation Source d.f. MS F d.f. MS F d.f. MS F d.f. MS F d.f. MS F Amongkaryotypes ** " Regression " " Deviations ** Within karyotypes a 0.05 < P < 0.10; ** P < MS = mean square.

9 Genetic Variance for Body Size 747 TABLE 7 Estimated contribution of the second and fourth chromosomes to the phenotypic variance of thorax length (in mm' X lo') in laboratory males and wild males and females of D. buuatii Sample Arrangements Components of phenotypic variance A A A A A aza UZd up* 2 &OTAL Second chromosome Laboratory males All four st, j Nonmating males All four st, j Mating males All four st, j Fourth chromosome Nonmating males Mating males Nonmating females Mating females Data from Tables 4 and 6. For estimation procedures see Table 1. j* stands for arrangementsj,jr3 and jq' pooled. iance in the various samples. Whereas in mating males and mating females most of the among-karyotype variance was attributable to the linear regression, in nonmating males and nonmating females the linear regression explained none of it (Table 7). DISCUSSION The heritability of D. buzzatii thorax length estimated in the laboratory by means of the offspringparent regression was This figure is somewhat higher than those reported in the literature for other Drosophila (1 5-50%; ROFF and MOUSSEAU 1987) but comparable to the relatively large values obtained by ROBERTSON (1987) and PROUT and BARKER (1989) for D. buzzatii populations from Australia. The observed heritability can be taken, with certain caveats [see CHARLESWORTH (1 987) and references therein], as the ratio of additive genetic to phenotypic variance for thorax length, under the uniform, near optimal laboratory conditions, i.e., h2 = &/& in the notation of LANDE (1987). Of course, we are most interested in the value that this ratio has in fact in the natural population, ie., h$ = &/u?n in the same notation. There are three main methods to indirectly estimate heritabilities in nature. (1) The regression coefficient of laboratory progeny on midparent from nature, /3(oL.pN)(LANDE 1987); (2) the ratio,8tol.pn) = y2 hi, where is the additive genetic correlation of the character across environments (RISKA, PROUT and TURELLI 1989, p. 865); and (3) the ratio of additive genetic variance in the laboratory to the phenotypic variance in nature, &/un (RISKA, PROUT and TUR- ELLI 1989, p. 866). We know the phenotypic variance of the trait in wild flies and also its heritability in a sample of flies derived from the same population and grown under optimal conditions in the laboratory. With these data we can only use the third method, which will produce a biassed estimate whenever the additive variance in the laboratory differs from that in nature, i.e. if & # uin. Since I y I d 1, the second method will always yield downwards biassed estimates and would be in principle preferable, whereas LANDE'S method is affected by both types of bias (RISKA, PROUT and TURELLI 1989). For the population of Carboneras, and averaged over the two sexes, the phenotypic variance in nature was about for nonmating flies and for mating flies. The additive variance in the labora- tory can be calculated multiplying the phenotypic variance in the laboratory by the heritability as Therefore, the heritability of thorax length in this natural population may be estimated as and in nonmating and mating flies, respectively. PROUT and BARKER (1 989) obtained estimates of heritability of the same trait at three different levels (within Opuntia rots, between rots and across rots) in a natural population from Australia. Their value for the heritability across rots, which is the one comparable to our estimates, was Thus, our values and that of PROUT and BARKER are surprisingly close, if one takes into account that different populations were studied and that different estimation methods were used. In our D. buzzatii population, the phenotypic variance of thorax length in males was not larger than in females neither in the field nor in the laboratory. In addition, the slopes of the offspring-parent regressions broken down by sex were also roughly similar (Table 1). Thus, there is no evidence of a significant contribution of the X chromosome to the genetic variance of thorax length. These observations agree well with those made by ROBERTSON (1987) who did not find differences in additive genetic variance between the

10 748 Ruiz A. sexes in the Australian populations studied by him. A note of caution should be made however. KEARSEY and KOJIMA (1967) found a significant contribution of the X chromosome to the additive variance of body weight in D. melanogaster, and COWLEY and ATCHLEY (1988) also detected significant additive X-linked variance in many morphometric traits (yet not in scutellum length) in the same species. Thus, a more thorough study might reveal eventually a contribution of the X chromosome also in D. buzzatii. What our present data imply, however, is that this contribution is not very large in comparison with that of the autosomes in the population of Carboneras. Since the interpretation of our results on the biometrical effect of inversions is based in the proposed genetic model, we will discuss briefly the assumptions on which the model rests. The D. buzzatii population at Carboneras is most likely a very large and panmictic one [see SANTOS, RUIZ and FONTDEVILA (1989) for a discussion of this point based on previous data]. In the laboratory study, matings were arranged so as to produce an effectively panmictic population. In addition, since near-optimal growth conditions were used to raise the experimental males, no frequency changes probably occurred between the zygote and the adult phases. As expected, Hardy-Weinberg proportions were observed at the two polymorphic chromosomes in the laboratory male sample. In the field study, no significant correlation between the body sizes of the mating partners was detected (SANTOS et al. 1988) and the karyotype frequencies of the mating pairs did not depart significantly from the random combinations of the marginal karyotype frequencies in any of the two chromosomes (unpublished results). Thus, mating seems to occur approximately at random in the natural population also. In addition, none of the samples of wildflies showed a significant departure of the karyotype frequencies from the Hardy-Weinberg expectations. Our genetic model is based on the supposition, advanced by other authors (WHITE and ANDREW 1960; PREVOSTI 1967), that chromosomal arrangements exert their biometricai effect because they are predominantly associated with particular alleles at loci influencing the quantitative trait under consideration. From the genetic point of view, however, this is not the only way to explain such an effect. The different character means of the various karyotypes might be the result of a position effect of the inversions (SPER- LICH and PFRIEM 1986). But while the evidence favoring this possibility is quite meagre, that showing gametic associations between inversions and the loci included within, or closely adjacent to them, is overwhelming (see reviews by HEDRICK, JAIN and HOLDEN 1978; BARKER 1979; ZAPATA and ALVAREZ 1987). Although most of the reported associations involve loci with alleles which may be nearly neutral, there et al. are instances of associations with genes affecting quantitative traits (WATANABE and YAMAZAKI 1976; Wu and BECKENBACH 1983). In fact, this is exactly what the widespread concept of coadaptation and the results of many laboratory experiments on the adaptive value of inversions imply (DOBZHANSKY 1970). It should be pointed out, on the other hand, that whereas the examples of allozyme loci-inversion associations are very abundant, the evidence of significant gametic associations between allozyme loci within chromosome arrangements is rather sparse. Thus, although the failure to detect such associations may be in part due to the usually small samples and low power of the statistical tests used (ZAPATA and AL- VAREZ 1987), the conclusion to be drawn from the available evidence in Drosophila is that their magnitude, if any, is usually rather small. This means, in terms of our genetic model, that DG(sv and DV(,N are probably negligible in comparison with D, and Dj, as Figure 1 assumes. Most of the genetic variance for body size, as indicated by such morphological traits as thorax length, wing length and body weight, seems to be additive and interactions and dominance are apparently weak or absent (KELLER and MITCHELL 1962; KEARSEY and KOJIMA 1967; ROBERTSON 1987). Although additivity of gene effects across loci is a convenient assumption to make the model mathematically tractable, it seems also admissible on empirical grounds. Nevertheless, the derived expressions (see GENETIC MODEL) should be taken only as an approximation to the true relationships. In the field study, a significant effect of the second chromosome karyotype was found for males but not for females. The cause for this difference cannot be fully elucidated at the moment, for we do not have, as yet, data on females raised under laboratory conditions to compare with. A priori, however, there is no reason to expect a sex-dependent effect of the autosomal polygenes located on the second chromosome. In general, the pattern of chromosomal effects in wild males was quite similar to that observed in the laboratory: the 2st arrangement decreased thorax length whereas those arrangements bearing the 2j inversion had, on the average, the opposite effect. Furthermore, the variance among karyotypes (d) was comparable in the three samples of males (laboratory males, nonmating males and mating males; Table 7). Thus, it would seem that the genotype-environmental interaction and covariance are unimportant for this chromosome. It is remarkable, though, that the proportion of regression variance was higher in mating males than in nonmating males. This result may be explained with the aid of observations made in Carboneras in June That summer we collected again samples of mating and nonmating flies and determined their age in addition to their thorax

11 Genetic Variance for Body Size 749 length. As might be expected, mating males were, on LITERATURE CITED the average, older and less variable than nonmating ANDERSON, W. W., 1966 Genetic divergence in M. Vetukhiv s experimental populations of Drosophila pseudoobscura. 3. Dimales. In addition, there was a very significant correvergence in body size. Genet. Res. 7: lation between body size and age in nonmating males ANDERSON, W. W., 1973 Genetic divergence in body size among (r2 = 6.2%) whereas the correlation was nonsignificant experimental populations of Drosophila pseudoobscura kept at different temperatures. Evolution 27: in mating males (M. SANTOS, A. RUE, J. E. QUEZADA- AVERY, P. J., and W. G. HILL, 1978 The effect of linkage dise- D~Az, A. BARBADILLAND A. FONTDEVILA, unpub- quilibrium on the genetic variance of a quantitative trait. Adv. lished). Thus, the lower proportion of regression var- App. Probab iance in nonmating males might be due to the fact BARBADILLA, A., J. E. QUEZADA-DiAZ, A. RUIZ, M. SANTOS and A. FONTDEVILA, 1991 The evolutionary history of Drosophila that this sample is a mixture of several cohorts and buzzatii. XVII. Double mating and sperm predominance. Gethat there are environmental differences among co- net. Sel. Evol. 23 (in press). horts and differential longevity related to body size. BARKER, J. S. F., 1979 Inter-locus interactions: a review of exper- Mating females were also older, on the average, and imental evidence. Theor. Popul. Biol. 16: BMDP STATISTICAL SOFTWARE (1988). University of California less variable than nonmating females but both female Press, Berkeley. samples showed a significant correlation between BOERWINKLE, E., and C. F. SING, 1986 Bias of the contribution of thorax length and age (r2 = 2.7% in mating females single-locus effects to the variance of a quantitative trait. Am. J. Hum. Genet and r2 = 19.7% in nonmating females). Thus, a similar BUTLIN, R. K., I. L. READ and T. H. DAY, 1982 The effects of a hypothesis could also help to explain the lack of ad- chromosomal inversion on adult size and male mating success ditive variance in wild females. An easy way to test in the seaweed fly, Coelopa frigida. Heredity 49: this hypothesis would be to study the effect of the CHARLESWORTH, B., 1987 The heritability of fitness, pp in Sexual Selection: Testing the Alternatives, edited by J. W. karyotype on the thorax length of newly emerged BRADBURY and M. B. ANDERSON. John Wiley and Sons Ltd, wild flies, which is feasible in D. buzzatii, and this is New York. obviously the next step of our work. COWLEY, D. E., and W. R. ATCHLEY, 1988 Quantitative genetics of Drosophila melanogaster. 11. Heritabilities and genetic corre- In the laboratory, no significant variance among the lations between sexes for head and thorax traits. Genetics 119: three fourth-chromosome karyotypes was found, whereas in nature the heterokaryotype seems to be COYNE, J. A., and E. 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MANGAN, 1986 Community ecology of again, further discussion must await the analysis of Sonoran Desert Drosophila, pp , in The Genetics and thorax length and karyotype in samples of newly Biology of Drosophila, Vol. 3e, edited by M. ASHBURNER, H. L. emerged wild adults. Future work in this direction CARSON and J. N. THOMPSON, JR. Academic Press, London. HILL, W. C., and A. ROBERTSON, 1968 Linkage disequilibrium in should allow the discrimination among these alternafinite populations. Theor. Appl. Genet tives. KEARSEY, M. J., and K. KOJIMA, 1967 The genetic architecture of body weight and egg hatchability in Drosophila melanogaster. Wewish to thank Dr. Francesc Peris and Esther Betran for Genetics helping us in the collection and handling of flies, and Carlos L6pez- KELLER, E. C., and D. F. MITCHELL, 1962 Interchromosomal Fanjul, Horacio Naveira and an anonymous reviewer for their genotypic interactions. I. An analysis of morphological characters. 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