“Evolutionary and Ecological Processes Determining the Properties of the G Matrix”

Steinar Engen and Bernt-Erik Sæther: Read the article

The analyses in this paper show that Fisher's fundamental theorem of natural selection cannot be used to infer the rate of evolutionary responses to changes in the environment due to deterioration effects caused by genetic drift, mutations and environmental fluctuations

How do different evolutionary mechanisms shape phenotypes as the environment changes? Accurately predicting evolutionary responses to shifting environments has been a key challenge throughout the history of evolutionary biology. Indeed, theoretical predictions are sometimes mismatched with observed responses. Steinar Engen and Bernt-Erik Sæther of the Norwegian University of Science and Technology sought to demonstrate the importance of including non-selective processes (e.g., mutation, genetic drift, and environmental fluctuations), which affect a given population’s genetic composition. Not correcting for these processes in previous models may have caused differences between predicted and observed responses.

Engen and Sæther focus on the G matrix for a population, which is the additive genetic variance-covariance matrix for a set of phenotypes on which selection acts. They draw from Lande’s (1979) classical gradient formula and Fisher’s (1930) fundamental theorem of natural selection to decompose the G matrix and the average additive genetic variance of fitness into additive components generated by mutation, drift, and environmental fluctuations (modeled as fluctuations in fitness around a mean vector). Here, a large and stable population size is assumed, with each trait encoded at a single biallelic locus. They expand from Fisher and Lande’s seminal theories to build a model that more sufficiently accounts for the effects of selection over time while correcting for deteriorating effects.

Figure 1. “Illustration of how two stochastic effects, random genetic drift (expressed by the effective population size Ne) and environmental fluctuations in the fitness function (expressed by a factor θ increasing with increasing environmental fluctuations), affect the average additive genetic variance of fitness at stasis.” Adapted from Engen and Sæther 2024, Figure 2. For more methodological details, please see the full paper and figure caption.

The authors, therefore, formalize Frank’s (2012, p. 47) idea of an approximate conservation law stating that “an increase in the mean fitness of a population caused by natural selection must usually be balanced by an equal and opposite decrease in mean fitness caused by deterioration of the environment.” Indeed, the theory presented demonstrates how the deteriorating effects of mutation, genetic drift, and environmental fluctuations can generate selection because they “generate additive components to the additive genetic variance of fitness in populations at stasis” (Engen and Sæther 2024, p. 13; Figure 1). Interestingly, while the largest eigenvalue and associated eigenvector of the G matrix demonstrate the direction evolution is most likely to occur, the smallest eigenvalues are also revelatory. Processes other than selection produce the smallest eigenvalue greater than 0 and can add considerable additive genetic variance in traits associated with fitness. The associated eigenvector’s loading can indicate the phenotype components that most contribute to fitness.

In summary, Engen and Sæther demonstrate how the G matrix can be broken down into additive components due to selection, mutation, drift, and environmental fluctuations. Their model shows how deteriorating effects can counteract selection. Selection andthe effects of mutation, drift, and environmental fluctuations need to be accounted for together when modeling how populations respond and adapt to changing environments, both in stasis and over time. The authors discuss possible routes of further investigation.

Eleanor Diamant is a Zuckerman Post-doctoral Scholar at Ben Gurion University of the Negev, working with Profs. Uri Roll and Oded Berger-Tal. She is interested in the interaction between human-caused environmental change and wildlife response, specifically birds in the built environment. For her post-doctorate, she is developing a framework to understand how climate shapes biodiversity patterns in urban environments. She is also using fine-scale animal tracking data to determine how climate and weather impact habitat choice and behavior in birds across a landscape mosaic. Beyond the sciences, she enjoys painting, birding, hiking, and B horror movies.