MATERIALS AND METHODS

Selection lines were developed from a D. melanogaster laboratory population taken from the wild in Santiago de Compostela in 1992 and kept since then at 25° in a culture medium made up of 250 g whole corn flour, 180 g live baker’s yeast, 18 g agar, 3 g ClNa, 3 g Nipagin, 33.3 ml ethanol, and 9.4 ml propionic acid in 2.2 liters water. The same conditions were used in this experiment. Every female in the selection lines laid eggs in a 23.7-cm³ plastic vial.

The experiment had three nonsimultaneous replicates. Each one was started with 64 virgin pairs sampled from the base population. Two sets of four males and four females were taken from the progeny of every pair, and each set was used to start one selection line. The mate selection method was applied in one of them (OPT line), and a standard selection plan was applied in the other (REF line). We made six generations of selection in each line. The selected trait was pupa length, measured in arbitrary micrometer length units (mlu) by means of a micrometer introduced in one of the oculars of a binocular microscope. The females’ fecundity was also measured, as the number of eggs laid by every selected female in its culture vial after 24 hr in replicates 1 and 2. In replicate 3, every selected female laid eggs on a black plastic rectangle that was covered on one of its sides by a layer of medium and introduced into the vial. After 48 hr, the eggs were counted and the layer of medium was divided in two pieces containing similar numbers of eggs, and each one was introduced in a different vial already containing 3 ml culture medium. Having two different vial effects for every female, we intended to measure better the variation between vials. The selection procedures used in each line were as follows:

REF selection line: The 256 (64 × 4) male and 256 female pupae assigned to this line were measured, and the longest 8 males and 64 females were selected. Each selected male was mated to a random sample of 8 selected females. The mating took place in two steps, each step comprising 4 adult females introduced into the male’s vial for 24 hr. They were kept identified by clipping different combinations of their two posterior scutellar bristles. We measured 4 males and 4 females from every female’s progeny and used these measures, along with all their ancestors’ information, to obtain their BLUP genetic evaluations. Using this as a criterion, 8 males and 64 females were selected and the next generation established. The same procedure was followed for the remaining selection generations.

OPT selection line: In the same way as in the REF line, 4 males and 4 females from the progeny of 64 females were measured in every generation, but the selection procedure was different. In this line, we searched for the set of matings between the selection candidates that maximized the expected selection response in the following generation, under a restriction on the inbreeding increase. The allocation of matings can be treated as a linear programming problem (Jansen and Wilton 1985; Kinghorn 1987) by using an X matrix, where x_ij {i = 1, 256, j = 1, 256} is a decision variable indicating whether male i and female j are (x_ij = 1) or are not (x_ij = 0) to be mated. Following the mate selection method, we tried to find, among all possible X mating matrices, the maximizing objective function, ∑∑xij(a^i+a^j)∕2, that is, the expected genetic gain in the next generation, in which â_i and â_j are the BLUPs for the breeding values of male i and female j. In this experiment, to save computational resources, we did not apply the method to the whole array of 256 × 256 possible matings, but made a preselection of the 32 males and 64 females having the highest genetic evaluation and selected a set of matings between them. The objective function was subjected to the following restrictions:

1. ΣΣx_ij = 64

2. Σx_ij = 0 or 1 (for every j)

3. Σx_ij ≤ 12 (for every i)

4. ΣΣx_ij f_ij/64 < (F + ∂F),

where F and f_ij are the average population inbreeding in the previous generation and the coancestry coefficient between the ith male and the jth female, and ∂F is the maximum additive increase in inbreeding allowed per generation. We used an additive increase in F as the restriction because we wanted a criterion that was simple and did not depend on the changes in inbreeding in the previous generations. Thus, mate selection maximized the expected response while respecting some reproductive restrictions (1 to 3) and a restriction (4) on the inbreeding increase, and did it by using nonrandom mating, a variable number of sires, and a variable mating ratio. In all replicates, the solution matrix X was obtained with linear programming computer programs that were written in the computer center of the Instituto Nacional de Investigaciones Agrarias (Madrid) following the algorithms given by Land and Powell (1979).

The magnitude of the restriction on the inbreeding increase was not constant throughout the experiment. In replicate 1 and in generations 1-4 of replicate 2, the limit value for ∂F was 0.03 per generation, which was fixed by using as reference the increase in F per generation that was predicted for the REF line by the Robertson (1961) effective population number expression. This value of 0.03 is higher than those typically used in large populations of livestock, which are ∼0.01 (Wray and Goddard 1994), but was appropriate for a smaller and intensively selected population as was used in this experiment. From generation 5 of replicate 2, we changed our procedure to fix the maximum F increase allowed in the OPT line, because in that generation the observed F in the REF line was not only less than the average value predicted with the Robertson (1961) expression, but even less than that observed in the OPT line, which was respecting the restriction fixed on its F increase. This can happen in practice, as a particular population can be above or below its expected F value. To avoid this, we first set up the random matings in the REF line, and then calculated the expected F increase for these particular matings. This value was used as a reference to fix the maximum increase in F that was allowed in the OPT line in that generation. We kept using this new procedure in the rest of the experiment (i.e., in generations 5 and 6 of replicate 2 and in all of replicate 3). Thus, we made sure from that moment that the OPT line had lower inbreeding than its corresponding REF line.

Data analysis: We obtained two genetic evaluations for every individual. The first, EBV1, was an animal-model BLUP based on all the information available on every animal at the time of making selection decisions, and included its phenotypic value and that of its sibs and ancestors. It was used as a selection criterion. The second, EBV2, was the BLUP evaluation used in the final analysis of the results, and was obtained by using all the information available at the end of the experiment, which included all the individual’s descendants in addition to the information used for EBV1. The genetic evaluations for the OPT and REF lines in a given replicate of the experiment were obtained with a single execution of the corresponding program as both lines descended from the same set of founders, and it was possible to include them in a single genealogical file.

As the experiment advanced, we used more complete theoretical models and more recent computer programs to obtain the EBV1s. In replicates 1 and 2 we used JAA, the univariate BLUP program by Misztal and Gianola (1987), and in replicate 3 we obtained these EBV1s with DFREML(UNI), the univariate version of the derivative-free program for BLUP genetic evaluation and variance component estimation by Meyer (1991, 1993). This was also used to obtain the EBV2s in all replicates.

We obtained additional estimates for the EBV2 and variance components using a Bayesian approach. There are multiple advantages to this approach: use of prior information (when available), elimination of nuisance parameters, exact finite sample analyisis and integrated estimation, prediction, and decision (Gianolaet al. 1989). Markov chain Monte Carlo methods such as Gibbs sampling allow us to draw Bayesian inferences about genetic parameters and responses (Wanget al. 1994). The MTGSAM set of programs by Van Tassell and Van Vleck (1996) accomplished Gibbs sampling analysis for multitrait models. In our case the model included pupa length and fecundity. We assumed flat prior distributions for fixed effects and normal distributions for all random effects in the model, including residuals. For the genetic effects it is additionally assumed that there is a known covariance structure corresponding to the numerator relationship matrix. Finally, we also assigned flat prior distributions for all (co)variance components. The Gibbs sampler was run once for every replicate in the experiment, with 500,000 iterations in each run, the first 2000 iterations being discarded (“burn in”). As a consequence of the use of conditional probabilities in each step of Markov chains, there is an autocorrelation between their successive elements, so that an original chain can be reduced to a shorter one having lower autocorrelation without loss of information. We saved a sample of the parameters of interest every 500 iterations, so that we had 1000 saved samples per replicate. We obtained Gibbs samples for (co)variance components, breeding values, and inbreeding depression effects for both characters, while samples for the slope of the regression of the mean EBV on generation number were obtained for pupa length only.

A summary of the computer programs and theoretical models used in the data analysis can be seen in Table 1. We used a heritability of 0.3 for pupa length in the analyses made in replicate 1 with JAA. The programs DFREML and MTGSAM use the actual data set to estimate the parameters required to obtain the genetic evaluations.

The theoretical model used for the data analysis included the effect of generation and, as long as the data reflect the true genetic situation, they allow us to separate realized genetic changes from environmental changes between generations within a selection line. In any case the aim of the experiment was to compare the OPT and REF selection lines; the generation environmental effects would not affect the comparison, because the OPT and REF lines in the same replicate were maintained simultaneously and therefore shared these effects.

We measured the effect of mate selection on response as the difference in phenotypic response between the OPT and REF lines. We used the expression given by Aggrey et al. (1995) for the expected variance of this difference between two selection lines, which takes into account both drift variance and measurement error, sR2=2σA2Ne{t+4(1+β)h2[c2+βpm1+α(1−c2−h2∕2)]}, where σA2 is the additive variance, N_e the effective population size, which was calculated taking into account the different numbers of male and female parents, t is the number of generations, p_m is the proportion of males selected, α the number of females scored for every male, β the number of females selected for every male, h² the trait’s heritability, and c² the environmental correlation between full sibs. We used the estimated variance for environmental vial effects as the environmental covariance between full sibs. However, this expression is but an approximation that does not take into account all the effects of directional selection on genetic variance (Aggreyet al. 1995). To complement this test and to obtain a more empirical value for the standard deviation of selection response, we also carried out 100 runs of a computer simulation of selection lines with the features of the REF lines in our experiment.

We studied nonrandom mating in the selection lines by means of Wright’s F statistics (Wright 1969), (1−FIT)=(1−FST)(1−FIS), where F_IT is the average inbreeding of animals born in a given generation and was calculated with the genealogical information, F_ST is the average coancestry coefficient between the sires and dams of all possible mates and provides a measure of the contribution of limited population size to inbreeding, and F_IS measures that of nonrandom mating.

In addition to inbreeding coefficients, we used methods based on the genetic contributions from founders and probabilities of gene loss to study the maintenance of genetic variability in the experiment. First, we calculated the “number of founder equivalents” (Lacy 1989), which is a measure of the balancedness of the contributions from the different founders, i.e., the 64 males and 64 females used to start every replicate, fe=1∕∑i=1M+Fci2, where M and F are the numbers of male and female founders and c_i is the total contribution of founder i to the gene pool of the population or the probability that a gene randomly sampled in this population originates from founder i. It was calculated as ci=∑j=1N(aij∕N), where a(i,j) is the additive relationship coefficient between the founder i and the current animal j and N the number of animals of the current population (Σ c_i = 1). The sum of c²_i can be calculated in every generation, and after several generations, the distribution of c stabilizes, and then the sum of c²_i predicts the asymptotic rate of inbreeding as ΔF = (¼) Σ ci2 (Wray and Thompson 1990; Woolliams and Thompson 1994). We observed this stabilization at the end of our experiment, and used the sum of c²_i in the last generation to calculate the asymptotic rate of inbreeding.

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Figure 1.

—Phenotypic selection response and phenotypic cumulated selection differentials for pupa length in mlu in the OPT (continuous) and REF (broken) selection lines.

We calculated also a direct measure of the amount of genetic variability remaining in each line at the end of the experiment. This was the “founder genome equivalent” (Lacy 1989), fg=1∕∑i=1M+F(ci2∕ri), where r_i is the probability of a given gene from founder i to be retained in the population of descendants. It was calculated with the gene drop computer simulation technique (MacClueret al. 1986), which simulates the transmission of a gene from every founder parent through the genealogy, assuming that the probability of a parent’s gene being transmitted to a descendant is 50%. The value of r_i is taken as the proportion of runs in which the gene is present in the descendants’ generation. The founder genome equivalent may be defined as the number of equally contributing founders, with no random loss of founder alleles in the offspring, that would be expected to produce the same genetic diversity as in the population under study. In contrast with the founder equivalent, it takes into account the effect of genetic drift and population bottlenecks on gene loss (Lacy 1989).