A method to predict the response to directional selection using a Kalman filter

Abstract

Predicting evolution remains challenging. The field of quantitative genetics provides predictions for the response to directional selection through the breeder’s equation, but these predictions can have errors. The sources of these errors include omission of traits under selection, inaccurate estimates of genetic variance, and nonlinearities in the relationship between genetic and phenotypic variation. Previous research showed that the expected value of these prediction errors is often not zero, so predictions are systematically biased. Here, we propose that this bias, rather than being a nuisance, can be used to improve the predictions. We use this to develop a method to predict evolution, which is built on three key innovations. First, the method predicts change as the breeder’s equation plus a bias term. Second, the method combines information from the breeder’s equation and from the record of past changes in the mean to predict change using a Kalman filter. Third, the parameters of the filter are fitted in each generation using a learning algorithm on the record of past changes. We compare the method to the breeder’s equation in two artificial selection experiments, one using the wing of the fruit fly and another using simulations that include a complex mapping of genotypes to phenotypes. The proposed method outperforms the breeder’s equation, particularly when traits under selection are omitted from the analysis, when data are noisy, and when additive genetic variance is estimated inaccurately or not estimated at all. The proposed method is easy to apply, requiring only the trait means over past generations.

Towards evolutionary predictions: Current promises and challenges

“…Limitations of these approaches are the inability to account for drift effects (Pélabon et al, 2021) and the assumption of linear genotype‐phenotype mapping (Milocco & Salazar‐Ciudad, 2020). A formidable challenge is thus to integrate stochasticity and nonlinearities in frameworks that are amenable to forecasting polygenic evolution (Milocco & Salazar‐Ciudad, 2022).…”

A quantitative genetics framework for understanding the selection response of microbial communities

“…If one does drop the infidelity and nonlinearity terms, the Price equation reduces to the breeder’s equation (Figure 1D; see also [17]). Conversely, some authors argue that such a simple linear relationship between heritability and selection efficacy is often an inaccurate description of biological reality [18, 19, 20]. Regardless, even if infidelity and nonlinearity are present, as long as they are uncorrelated with h 2 , we may still safely say that greater heritability is associated with more efficient selection.…”

A data‐driven framework to model the organism–environment system

“…These aspects may have important implications for development and evolution, but such implications cannot be studied with representations of the organism–environment system that do not explicitly incorporate developmental time. Indeed, because organism and environment interact dynamically in time, statistical measures of covariance and regression can also change through ontogeny, and a single value at a fixed developmental time could be a misleading representation of the system (Milocco & Salazar‐Ciudad, 2022; Sugihara et al, 2012). Furthermore, while it is commonly observed that reaction norms or trait integration indeed change over ontogeny (Mitteroecker & Bookstein, 2009; Nilsson‐Örtman et al, 2015; Pottier et al, 2022), there remains substantial ambiguity and controversy over what such patterns imply about development and evolution (e.g., Armbruster et al, 2014; Hubbe et al, 2023; Pigliucci et al, 1996).…”