Christophe Pélabon

Heritability is not Evolvability

Short-term evolutionary potential depends on the additive genetic variance in the population. The additive variance is often measured as heritability, the fraction of the total phenotypic variance that is additive. Heritability is thus a common measure of evolutionary potential. An alternative is to measure evolutionary potential as expected proportional change under a unit strength of selection. This yields the mean-scaled additive variance as a measure of evolvability. Houle in Genetics 130:195–204, (1992) showed that these two ways of scaling additive variance are often inconsistent and can lead to different conclusions as to what traits are more evolvable. Here, we explore this relation in more detail through a literature review, and through theoretical arguments. We show that the correlation between heritability and evolvability is essentially zero, and we argue that this is likely due to inherent positive correlations between the additive variance and other components of phenotypic variance. This means that heritabilities are unsuitable as measures of evolutionary potential in natural populations. More generally we argue that scaling always involves non-trivial assumptions, and that a lack of awareness of these assumptions constitutes a systemic error in the field of evolutionary biology.

Measurement and Meaning in Biology

Measurement—the assignment of numbers to attributes of the natural world—is central to all scientific inference. Measurement theory concerns the relationship between measurements and reality; its goal is ensuring that inferences about measurements reflect the underlying reality we intend to represent. The key principle of measurement theory is that theoretical context, the rationale for collecting measurements, is essential to defining appropriate measurements and interpreting their values. Theoretical context determines the scale type of measurements and which transformations of those measurements can be made without compromising their meaningfulness. Despite this central role, measurement theory is almost unknown in biology, and its principles are frequently violated. In this review, we present the basic ideas of measurement theory and show how it applies to theoretical as well as empirical work. We then consider examples of empirical and theoretical evolutionary studies whose meaningfulness have been compromised by violations of measurement-theoretic principles. Common errors include not paying attention to theoretical context, inappropriate transformations of data, and inadequate reporting of units, effect sizes, or estimation error. The frequency of such violations reveals the importance of raising awareness of measurement theory among biologists.

Evolvability and genetic constraint in Dalechampia blossoms: components of variance and measures of evolvability

Abstract Many evolutionary arguments are based on the assumption that quantitative characters are highly evolvable entities that can be rapidly moulded by changing selection pressures. The empirical evaluation of this assumption depends on having an operational measure of evolvability that reflects the ability of a trait to respond to a given external selection pressure. We suggest short‐term evolvability be measured as expected proportional response in a trait to a unit strength of directional selection, where strength of selection is defined independently of character variation and in units of the strength of selection on fitness itself. We show that the additive genetic variance scaled by the square of the trait mean, IA, is such a measure. The heritability, h2, does not measure evolvability in this sense. Based on a diallel analysis, we use IA to assess the evolvability of floral characters in a population of the neotropical vine Dalechampia scandens (Euphorbiaceae). Although we are able to demonstrate that there is additive genetic variation in a number of floral traits, we also find that most of the traits are not expected to change by more than a fraction of a percent per generation. We provide evidence that the degree of among‐population divergence of traits is related to their predicted evolvabilities, but not to their heritabilities.

PHENOTYPIC SELECTION ON DALECHAMPIA BLOSSOMS: HONEST SIGNALING AFFECTS POLLINATION SUCCESS

Pollinators may choose which flowers to visit by direct assessment of rewards or by indirect assessment of “honest” advertisements or other traits correlated with the quantity or quality of reward. We wished to know whether selection generated by pollinators acted directly or indirectly on floral rewards, on advertisement traits, and/or traits affecting pollinator efficiency (their fit with flowers) in Dalechampia vines (Euphorbiaceae) and whether the advertisement (bract size) was correlated honestly with reward amount (measured by resin-gland area). In Gabon we studied bee visitation and pollen arrival rates to blossoms of D. ipomoeifolia Benth. and found that, despite the apparent visibility of the resin reward (and its volume), the strongest bee-mediated natural selection acted directly on bract size rather than gland area. Blossoms with larger bracts were visited more often by the only pollinators, female Heriades nr. spiniscutis (Apoidea: Megachilidae), and these blossoms received more pollen on their stigmas. Blossoms with larger resin glands were also visited more often and received more pollen overall, but this effect disappeared when bract size (which was phenotypically correlated with gland size) was controlled for statistically. These observational data were confirmed by experimental reduction of bract size, which significantly decreased pollen arrival rates. Thus, the bees appear to rely on the “honest” correlation between advertisement and reward in choosing the best blossoms to visit, and this behavior generates direct selection for larger bracts and indirect selection for larger resin glands. Bees visiting blossoms with larger separation between the gland and stigmas contacted the stigmas less frequently, and such blossoms received less pollen on their stigmas. Because gland area, bract size, and gland–stigma separation are positively correlated phenotypically, response to selection for larger bracts may be limited in this population by conflicting selection against large gland–stigma separation.

The adaptive accuracy of flowers: measurement and microevolutionary patterns

BACKGROUND AND AIMS From Darwins time onward, biologists have thought about adaptation as evolution toward optimal trait values, but they have not usually assessed the relative importance of the distinct causes of deviations from optima. This problem is investigated here by measuring adaptive inaccuracy (phenotypic deviation from the optimum), using flower pollination as an adaptive system. METHODS Adaptive accuracy is shown to have at least three distinct components, two of which are optimality (deviation of the mean from the optimum) and precision (trait variance). We then describe adaptive accuracy of both individuals and populations. Individual inaccuracy comprises the deviation of the genotypic target (the mean phenotype of a genotype grown in a range of environments) from the optimum and the phenotypic variation around that genotypic target (phenotypic imprecision). Population inaccuracy has three basic components: deviation of the population mean from the optimum, variance in the genotypic targets and phenotypic imprecision. In addition, a fourth component is proposed, namely within-population variation in the optimum. These components are directly estimable, have additive relationships, and allow exploration of the causes of adaptive inaccuracy of both individuals and populations. Adaptive accuracy of a sample of flowers is estimated, relating floral phenotypes controlling pollen deposition on pollinators to adaptive optima defined as the site most likely to get pollen onto stigmas (male inaccuracy). Female inaccuracy is defined as the deviation of the position of stigma contact from the expected location of pollen on pollinators. KEY RESULTS A surprising amount of variation in estimated accuracy within and among similar species is found. Some of this variation is generated by developmental changes in positions of stigmas or anthers during anthesis (the floral receptive period), which can cause dramatic change in accuracy estimates. There seem to be trends for higher precision and accuracy in flowers with higher levels of integration and dichogamy (temporal separation of sexual functions), and in those that have pollinators that are immobile (or immobilized) during pollen transfer. Large deviations from putative adaptive optima were observed, and these may be related to the effects of conflicting selective pressures on flowers, such as selection against self-pollination promoting herkogamy (spatial separation of pollen and stigmas). CONCLUSIONS Adaptive accuracy is a useful concept for understanding the adaptive significance of phenotypic means and variances of floral morphology within and among populations and species. Estimating and comparing the various components of adaptive accuracy can be particularly helpful for identifying the causes of inaccuracy, such as conflicting selective pressures, low environmental canalization and developmental instability.

Integrated phenotypes: understanding trait covariation in plants and animals.

Integration and modularity refer to the patterns and processes of trait interaction and independence. Both terms have complex histories with respect to both conceptualization and quantification, resulting in a plethora of integration indices in use. We review briefly the divergent definitions, uses and measures of integration and modularity and make conceptual links to allometry. We also discuss how integration and modularity might evolve. Although integration is generally thought to be generated and maintained by correlational selection, theoretical considerations suggest the relationship is not straightforward. We caution here against uncontrolled comparisons of indices across studies. In the absence of controls for trait number, dimensionality, homology, development and function, it is difficult, or even impossible, to compare integration indices across organisms or traits. We suggest that care be invested in relating measurement to underlying theory or hypotheses, and that summative, theory-free descriptors of integration generally be avoided. The papers that follow in this Theme Issue illustrate the diversity of approaches to studying integration and modularity, highlighting strengths and pitfalls that await researchers investigating integration in plants and animals.

Evolution of morphological allometry

Morphological allometry refers to patterns of covariance between body parts resulting from variation in body size. Whether measured during growth (ontogenetic allometry), among individuals at similar developmental stage (static allometry), or among populations or species (evolutionary allometry), allometric relationships are often tight and relatively invariant. Consequently, it has been suggested that allometries have low evolvability and could constrain phenotypic evolution by forcing evolving species along fixed trajectories. Alternatively, allometric relationships may result from natural selection for functional optimization. Despite nearly a century of active research, distinguishing between these alternatives remains difficult, partly due to wide differences in the meaning assigned to the term allometry. In particular, a broad use of the term, encompassing any monotonic relationship between body parts, has become common. This usage breaks the connection to the proportional growth regulation that motivated Huxleys original narrow‐sense use of allometry to refer to power–law relationships between traits. Focusing on the narrow‐sense definition of allometry, we review here evidence for and against the allometry‐as‐a‐constraint hypothesis. Although the low evolvability and the evolutionary invariance of the static allometric slope observed in some studies suggest a possible constraining effect of this parameter on phenotypic evolution, the lack of knowledge about selection on allometry prevents firm conclusions.

ALLOMETRIC CONSTRAINTS AND THE EVOLUTION OF ALLOMETRY

Morphological traits often covary within and among species according to simple power laws referred to as allometry. Such allometric relationships may result from common growth regulation, and this has given rise to the hypothesis that allometric exponents may have low evolvability and constrain trait evolution. We formalize hypotheses for how allometry may constrain morphological trait evolution across taxa, and test these using more than 300 empirical estimates of static (within‐species) allometric relations of animal morphological traits. Although we find evidence for evolutionary changes in allometric parameters on million‐year, cross‐species time scales, there is limited evidence for microevolutionary changes in allometric slopes. Accordingly, we find that static allometries often predict evolutionary allometries on the subspecies level, but less so across species. Although there is a large body of work on allometry in a broad sense that includes all kinds of morphological trait–size relationships, we found relatively little information about the evolution of allometry in the narrow sense of a power relationship. Despite the many claims of microevolutionary changes of static allometries in the literature, hardly any of these apply to narrow‐sense allometry, and we argue that the hypothesis of strongly constrained static allometric slopes remains viable.

On Adaptive Accuracy and Precision in Natural Populations

Adaptation is usually conceived as the fit of a population mean to a fitness optimum. Natural selection, however, does not act only to optimize the population mean. Rather, selection normally acts on the fitness of individual organisms in the population. Furthermore, individual genotypes do not produce invariant phenotypes, and their fitness depends on how precisely they are able to realize their target phenotypes. For these reasons we suggest that it is better to conceptualize adaptation as accuracy rather than as optimality. The adaptive inaccuracy of a genotype can be measured as a function of the expected distance of its associated phenotype from a fitness optimum. The less the distance, the more accurate is the adaptation. Adaptive accuracy has two components: the deviance of the genotypically set target phenotype from the optimum and the precision with which this target phenotype can be realized. The second component, the adaptive precision, has rarely been quantified as such. We survey the literature to quantify how much of the phenotypic variation in wild populations is due to imprecise development. We find that this component is often substantial and highly variable across traits. We suggest that selection for improved precision may be important for many traits.

Artificial selection on allometry: change in elevation but not slope.

To what extent within‐species (static) allometries constitute a constraint on evolution is the subject of a long‐standing debate in evolutionary biology. A prerequisite for the constraint hypothesis is that static allometries are hard to change. Several studies have attempted to test this hypothesis with artificial‐selection experiments, but their results remain inconclusive due to various methodological issues. Here, we present results from an experiment in which we selected independently on the slope and the elevation of the allometric relationship between caudal‐fin size and body size in male guppies (Poecilia reticulata). After three episodes of selection, the allometric elevation (i.e. intercept at constant slope) had diverged markedly between the lines selected to increase or decrease it, and showed a realized heritability of 50%. In contrast, the allometric slope remained unaffected by selection. These results suggest that the allometric elevation is more evolvable than the allometric slope, this latter representing a potential constraint on adaptive trait evolution. To our knowledge, this study is the first artificial‐selection experiment that directly tests the evolvability of static allometric slopes.