Estimates of the Average Strength of Natural Selection Are Not Inflated by Sampling Error or Publication Bias

Most published selection gradients are underestimated: Why this is and how to fix it

Ecologists and evolutionary biologists routinely estimate selection gradients. Most researchers seek to quantify selection on individual phenotypes, regardless of whether fixed or repeatedly expressed traits are studied. Selection gradients estimated to address such questions are attenuated unless analyses account for measurement error and biological sources of within-individual variation. Estimates of standardized selection gradients published in Evolution between 2010 and 2019 were primarily based on traits measured once (59% of 325 estimates). We show that those are attenuated: bias increases with decreasing repeatability but differently for linear versus nonlinear gradients. Others derived individual-mean trait values prior to analyses (41%), typically using few repeats per individual, which does not remove bias. We evaluated three solutions, all requiring repeated measures: (i) correcting gradients derived from classic models using estimates of trait correlations and repeatabilities, (ii) multivariate mixed-effects models, previously used for estimating linear gradients (seven estimates, 2%), which we expand to nonlinear analyses, and (iii) errors-in-variables models that account for within-individual variance, and are rarely used in selection studies. All approaches produced accurate estimates regardless of repeatability and type of gradient, however, errors-in-variables models produced more precise estimates and may thus be preferable.

Meta-analysis of magnitudes, differences and variation in evolutionary parameters

Meta-analysis is increasingly used to synthesize major patterns in the large literatures within ecology and evolution. Meta-analytic methods that do not account for the process of observing data, which we may refer to as 'informal meta-analyses', may have undesirable properties. In some cases, informal meta-analyses may produce results that are unbiased, but do not necessarily make the best possible use of available data. In other cases, unbiased statistical noise in individual reports in the literature can potentially be converted into severe systematic biases in informal meta-analyses. I first present a general description of how failure to account for noise in individual inferences should be expected to lead to biases in some kinds of meta-analysis. In particular, informal meta-analyses of quantities that reflect the dispersion of parameters in nature, for example, the mean absolute value of a quantity, are likely to be generally highly misleading. I then re-analyse three previously published informal meta-analyses, where key inferences were of aspects of the dispersion of values in nature, for example, the mean absolute value of selection gradients. Major biological conclusions in each original informal meta-analysis closely match those that could arise as artefacts due to statistical noise. I present alternative mixed-model-based analyses that are specifically tailored to each situation, but where all analyses may be implemented with widely available open-source software. In each example meta-re-analysis, major conclusions change substantially.

Interspecific patterns of phenotypic selection do not predict intraspecific patterns

We estimated linear (β) and nonlinear (γ) selection gradients to quantify host plant-mediated selection on the trait gall size in each of 22 unequally sampled subpopulations of the cynipid gall wasp Belonocnema treatae. We characterized the relationship between variation in subpopulation sample size and the magnitude of and the variance among selection gradients. We then tested the hypothesis that the intraspecific patterns we observed would follow two patterns that have emerged from published estimates of linear and nonlinear selection gradients compiled across species, namely that the average magnitude of β and γ and the variance among estimated β and γ decrease with increasing sample size. For both β and γ, intraspecific patterns of phenotypic selection in relation to sample size were not predicted by interspecific patterns. Thus, our results suggest that when selection is heterogeneous among subpopulations, variation in the biological basis for selection is more important in influencing estimates of selection than is variation in study size. Our study highlights the value of inspecting selection in relation to sampling effort at the level at which understanding the sources of variation in selection is most important, among populations within species.

Pollinators exert natural selection on flower size and floral display in Penstemon digitalis

• A major gap in our understanding of floral evolution, especially micro-evolutionary processes, is the role of pollinators in generating patterns of natural selection on floral traits. Here we explicitly tested the role of pollinators in selecting floral traits in a herbaceous perennial, Penstemon digitalis. • We manipulated the effect of pollinators on fitness through hand pollinations and compared phenotypic selection in open- and hand-pollinated plants. • Despite the lack of pollen limitation in our population, pollinators mediated selection on floral size and floral display. Hand pollinations removed directional selection for larger flowers and stabilizing selection on flower number, suggesting that pollinators were the agents of selection on both of these traits. • We reviewed studies that measured natural selection on floral traits by biotic agents and generally found stronger signatures of selection imposed by pollinators than by herbivores and co-flowering plant species.

Implications of a long-term, pollinator-mediated selection on floral traits in a generalist herb

BACKGROUND AND AIMS

The phenotypic selection of a diverse insect assemblage was studied on a generalist plant species (Paeonia broteroi) in ten flowering seasons, with tests for whether visitor preferences for plants with larger flowers eventually translated into significant differences among plants in visitation rates, seed production, seed mass, seed germination and seedling survival.

METHODS

Selection gradients were used to assess if selection on flower size contributed to explain differences in visitation rates, seed production and seed mass. First, independent analyses were carried out for each season; then for the ten season as a whole. Seedling emergence and survival were assessed by generalized linear models.

KEY RESULTS

Directional selection was found on flower size through visitation rates and seed production, and stabilizing selection through seed mass. Thus, larger flowers were more visited, and produced more, but lighter seeds, than smaller flowers. The results suggest a conflicting selection on flower size through seed number and size. Floral integration found in the study populations was larger than that in populations of a distant region. Finally, seed size did not influence seedling emergence and survival; thus, any advantages of seed size may be constrained under natural conditions before plants become reproductive individuals.

CONCLUSIONS

Plants with larger flowers may be benefited by producing more lighter seeds than fewer heavier ones, as they may contribute disproportionately to the seed bank, and have better chances that any descendant could eventually recruit. However, it seems unlikely that differences in flower size and integration found among populations in different regions could have been originated by rapid evolutionary change. First, because of the conflicting selection described; second, because of the remarkably low seedling survival found under natural conditions. Consequently, the influence of pollinator selection alone does not seem to explain differences in flower size and integration.

Asymmetry of genetic variation in fitness-related traits: apparent stabilizing selection on g(max)

The maintenance of genetic variation in traits closely associated with fitness remains a key unresolved issue in evolutionary genetics. One important qualification on the observation of genetic variation in fitness-related traits is that such traits respond asymmetrically to selection, evolving to a greater extent in the direction of lower fitness. Here we test the hypothesis that standing genetic variation in fitness-related traits is principally maintained for unfit phenotypes. Male Drosophila bunnanda vary in mating success (the primary determinant of male fitness) due to female mate choice. We used competitive mating success to partitioning males into two groups: successful (high fitness) and unsuccessful (low fitness). Relative to successful males, unsuccessful males harbored considerably greater levels of additive genetic variation for sexual signaling traits. This genetic asymmetry was detected for a multivariate trait that we demonstrated was not directly under stabilizing sexual selection, leading us to conclude the trait was under apparent stabilizing selection. Consequently, our results suggest genetic variance might be biased toward low fitness even for traits that are not themselves the direct targets of selection. Simple metrics of genetic variance are unlikely to be adequate descriptors of the complex nature of the genetic basis of traits under selection.

The fitness costs of developmental canalization and plasticity

Organisms are capable of an astonishing repertoire of phenotypic responses to the environment, and these often define important adaptive solutions to heterogeneous and unpredictable conditions. The terms 'phenotypic plasticity' and 'canalization' indicate whether environmental variation has a large or small effect on the phenotype. The evolution of canalization and plasticity is influenced by optimizing selection-targeting traits within environments, but inherent fitness costs of plasticity may also be important. We present a meta-analysis of 27 studies (of 16 species of plant and 7 animals) that have measured selection on the degree of plasticity independent of the characters expressed within environments. Costs of plasticity and canalization were equally frequent and usually mild; large costs were observed only in studies with low sample size. We tested the importance of several covariates, but only the degree of environmental stress was marginally positively related to the cost of plasticity. These findings suggest that costs of plasticity are often weak, and may influence phenotypic evolution only under stressful conditions.

Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.