Unidirectional response to bidirectional selection on body size II. Quantitative genetics

Abstract Anticipating the genetic and phenotypic changes induced by natural or artificial selection requires reliable estimates of trait evolvabilities (genetic variances and covariances). However, whether or not multivariate quantitative genetics models are able to predict precisely the evolution of traits of interest, especially fitness‐related, life history traits, remains an open empirical question. Here, we assessed to what extent the response to bivariate artificial selection on both body size and maturity in the medaka Oryzias latipes, a model fish species, fits the theoretical predictions. Three lines (Large, Small, and Control lines) were differentially selected for body length at 75 days of age, conditional on maturity. As maturity and body size were phenotypically correlated, this selection procedure generated a bi‐dimensional selection pattern on two life history traits. After removal of nonheritable trends and noise with a random effect (“animal”) model, the observed selection response did not match the expected bidirectional response. For body size, Large and Control lines responded along selection gradients (larger body size and stasis, respectively), but, surprisingly, the Small did not evolve a smaller body length and remained identical to the Control line throughout the experiment. The magnitude of the empirical response was smaller than the theoretical prediction in both selected directions. For maturity, the response was opposite to the expectation (the Large line evolved late maturity compared to the Control line, while the Small line evolved early maturity, while the opposite pattern was predicted due to the strong positive genetic correlation between both traits). The mismatch between predicted and observed response was substantial and could not be explained by usual sources of uncertainties (including sampling effects, genetic drift, and error in G matrix estimates).

Autocorrelation for the random effect parameters was assessed with the autocorr.diag() function from package coda. The effective size (sample size adjusted for autocorrelation) was evaluated with the function effectiveSize() from the same package. .

Stationarity
The vast majority of MCMC chains passed the Heidelberg stationarity test implemented in the heidel.diag() function from the coda package (null hypothesis H 0 : the chain is stationary at least over its last half, the dashed line illustrates the 5% threshold). Top: Distribution of the inbreeding coefficients (calculated from the full pedigree) across families in the course of the experiment (assuming no inbreeding in F 0 ). Middle: relationship between the inbreeding coefficient of families (normalized by the average of the line each generation) to phenotypic traits (centered on the line and generation mean). None of these regressions were statistically significant. Bottom: posterior distribution of the inbreeding effects on Sdl and maturity (vertical lines indicate 2.5%, 50%, and 97.5% quantiles).

Appendix 3 Model fitting on partial datasets
Ref The animal model estimates variance components in the starting population (F 0 ) accounting for drift and selection in subsequent generations. As a consequence, if the assumptions of the infinitesimal model hold, fitting the model on partial datasets should not affect the estimates (while the posterior distribution is expected to be wider due to the decrease in information). We split the dataset according to (i) generations (fitting the model on generations F 0 to F 3 , and from F 4 to F 7 ), and (ii) to the selected line (Large, Small, and Control lines), fitting the model excluding sequentially each line. In the figure, "Ref" stands for the posterior when including all the data, and boxplots represent the full range of the posterior distributions and their quartiles. The estimates for genetic variances and covariances increased for most sub-datasets, and residual variances and covariances decrease accordingly. The most straightforward explanation is that the parameters estimated from the full dataset result from a compromise between early/late generations and selection lines, and that the goodness of fit of the model increased when fitted on partial data. Note that most posterior distributions largely overlap (no posterior distributions differ significantly from the reference), suggesting that the estimated parameters remain meaningful. The mid-parent-offspring regression coefficient estimates trait heritability. In addition, the shape of the parent-offspring relationship is indicative of potential deviations from the infinitesimal model assumptions. Non-linear parent-offspring relationships may indicate dominance, epistasis, or genetic asymmetries.
B. However, considering each line separately, the pattern rather reflected different linear relationships in all three lines. The Large line response to selection shifted the offspring phenotype upwards, while the Small line lack of response set the average offspring at the same level as the Control. Non-linearity in this case was the consequence, rather than the cause, of the asymmetric response.
C. When considering the Control line alone, which had the most statistical power because of the large variance in parental phenotypes, the quadratic term disappeared, supporting the fact that the parent-offspring regression was linear (h 2 ≃ 0.14, Pr(h 2 = 0) = 0.00698, Pr(k 2 = 0) = 0.62) D. Running mother-offspring and father-offspring regressions independently provided very similar results. Focusing on the control line sub-dataset, the mother-offspring regression lead to h 2 = 0.089±0.031 (s.e.), while the father-offspring regression resulted in h 2 = 0.081±0.032.