The breeder's equation, which predicts evolutionary change when a phenotypic covariance exists between a heritable trait and fitness, has provided a key conceptual framework for studies of adaptive microevolution in nature. However, its application requires strong assumptions to be made about the causation of fitness variation. In its univariate form, the breeder's equation assumes that the trait of interest is not correlated with other traits having causal effects on fitness. In its multivariate form, the validity of predicted change rests on the assumption that all such correlated traits have been measured and incorporated into the analysis. Here, we (i) highlight why these assumptions are likely to be seriously violated in studies of natural, rather than artificial, selection and (ii) advocate wider use of the Robertson–Price identity as a more robust, and less assumption‐laden, alternative to the breeder's equation for applications in evolutionary ecology.

Climate change has the potential to affect the ecology and evolution of every species on Earth. Although the ecological consequences of climate change are increasingly well documented, the effects of climate on the key evolutionary process driving adaptationnatural selection-are largely unknown. We report that aspects of precipitation and potential evapotranspiration, along with the North Atlantic Oscillation, predicted variation in selection across plant and animal populations throughout many terrestrial biomes, whereas temperature explained little variation. By showing that selection was influenced by climate variation, our results indicate that climate change may cause widespread alterations in selection regimes, potentially shifting evolutionary trajectories at a global scale.C limate affects organisms in ways that ultimately shape patterns of biodiversity (1). Consequently, the rapid changes in Earth's recent climate impose challenges for many organisms, often reducing population fitness (2-4). Although some species may migrate and undergo range shifts to avoid climate-induced declines and potential extinction (5), an alternative outcome is adaptive evolution in response to selection imposed by climate (6). However, we lack a general understanding of whether local and global climatic factors such as temperature, precipitation, and water availability influence selection (2, 7). Understanding these effects is critical for predicting the consequences of increasing droughts, heat waves, and extreme precipitation events that are expected in many regions (8, 9).To quantify how climate variation influences selection, we assembled a large database of standardized directional selection gradients and differentials from spatially [mean = 4.6 ± 5.4 (SD) populations, range = 2 to 59 populations] and temporally [mean = 5.2 ± 6.8 (SD) years, range = 2 to 45 years] replicated selection studies (N = 168) in plant and animal populations (Table 1 and database S1). We focused on directional selection that can generate increases or decreases in trait values because it is well characterized and is likely to drive rapid evolution (10) in response to variation in climatic factors. However, selection acting on trait combinations and trait variance may also be affected by climate (7). Selection gradients estimate the strength and direction of selection acting directly on a trait, whereas differentials estimate "total selection" on a trait via both direct and indirect selection because of trait correlations (11). These standardized selection coefficients describe selection in terms of the relationship between relative fitness and quantitative traits measured in standard deviations, thus facilitating cross-study comparisons (11,12).Geographically, the database contains many estimates of selection from temperate, mid-latitude regions centered at 40°N (Fig. 1A). The populations in this database span many terrestrial biomes on Earth, with the exception of tundra and tropical rainforests where selection has rarely been quantified (Fig. 1B...

Temporal variation in selection is a fundamental determinant of evolutionary outcomes. A recent paper presented a synthetic analysis of temporal variation in selection in natural populations. The authors concluded that there is substantial variation in the strength and direction of selection over time, but acknowledged that sampling error would result in estimates of selection that were more variable than the true values. We reanalyze their dataset using techniques that account for the necessary effect of sampling error to inflate apparent levels of variation and show that directional selection is remarkably constant over time, both in magnitude and direction. Thus we cannot claim that the available data support the existence of substantial temporal heterogeneity in selection. Nonetheless, we conject that temporal variation in selection could be important, but that there are good reasons why it may not appear in the available data. These new analyses highlight the importance of applying techniques that estimate parameters of the distribution of selection, rather than parameters of the distribution of estimated selection (which will reflect both sampling error and "real" variation in selection); indeed, despite availability of methods for the former, focus on the latter has been common in synthetic reviews of the aspects of selection in nature, and can lead to serious misinterpretations. K E Y W O R D S :Directional selection, meta-analysis, repeatability, selection, temporal variation.

Local adaptation, adaptive population divergence and speciation are often expected to result from populations evolving in response to spatial variation in selection. Yet, we lack a comprehensive understanding of the major features that characterise the spatial patterns of selection, namely the extent of variation among populations in the strength and direction of selection. Here, we analyse a data set of spatially replicated studies of directional phenotypic selection from natural populations. The data set includes 60 studies, consisting of 3937 estimates of selection across an average of five populations. We performed meta-analyses to explore features characterising spatial variation in directional selection. We found that selection tends to vary mainly in strength and less in direction among populations. Although differences in the direction of selection occur among populations they do so where selection is often weakest, which may limit the potential for ongoing adaptive population divergence. Overall, we also found that spatial variation in selection appears comparable to temporal (annual) variation in selection within populations; however, several deficiencies in available data currently complicate this comparison. We discuss future research needs to further advance our understanding of spatial variation in selection.