Linking genomic offset statistics to the shape of selection gradients

Genomic offset metrics are increasingly used to predict population maladaptation under changing climates, based on the assumption of a negative statistical relationship between offset measures and local relative fitness. Recent theoretical advances have confirmed this relationship by relating genomic offset to phenotypic trait distances along selection gradients. However, these metrics typically rely on the assumption that stabilizing selection, which maintains local adaptive optima, operates on fitness-related traits through Gaussian-shaped selection gradients. In this study, we extend the theory to accommodate more diverse forms of selection gradients and introduce more general genomic offset measures that preserve the fitness-offset relationship. We validate this generalization through simulations and demonstrate the utility of these new measures in predicting relative fitness in common garden experiments involving three plant species: pearl millet, a vital staple cereal grown in arid soils, and two emblematic North American tree species, balsam poplar and red spruce. Our findings indicate that assuming a local Gaussian-shaped selection gradient for climate adaptation is a robust approximation for these species. These results have important implications for validating genomic offset predictions using fitness proxies and for studies that aim to predict fitness loss based on genomic offset metrics.

Methods
The ⍺-GO statistics and their relationship with the geometric GO were first tested using simulations. Spatially explicit individual-based simulations were performed using SLiM 3.7 (Haller and Messer 2019), as described for the highly polygenic scenario in Gain and colleagues (2023). Briefly, each individual genome contained both neutral and adaptive mutations, the latter ones being under local stabilizing selection from a 2D environment (12x12 grid) with two orthogonal environmental gradients, (x1, x2). Two traits, (z1, z2), controlled by 120 adaptive mutations with additive effects, were matched to each causal environmental variable by local stabilizing selection. The probability of survival of an individual genome in the next generation was calculated as the product of density regulation and fitness. The density of individuals was regulated by spatial competition depending on the number of individuals within a circle with radius S = 0.8 (Haller and Messer 2019). Individual fitness was calculated according to the following formula:

ω(z1, z2 |  x) = exp( –1/2 * ((|z1 – x1| /σK)⍺  + (|z2 – x2|/σK)⍺ )))

where x1 and x2 are the local environmental values corresponding to the optimal trait values in that local environment, z1 and z2 are the individual trait values estimated from the 120 adaptive mutations, and σK is a selection coefficient. The parameter ⍺ depends on the shape of the stabilizing selection gradient considered, with ⍺ = 0.5 giving a strict exponential shape, ⍺ = 1 a Laplacian shape, ⍺ = 2 a Gaussian shape and ⍺ = 3 giving a more tolerant shape (Figure 1). For each scenario, 100 replicates were run with different seed values of the random generator for 2,000 generations before an instantaneous environmental change. At the end of a simulation, individual geographic coordinates, environmental variables and individual fitness values before and after the instantaneous environmental change were recorded.

Gain, Clément, Bénédicte Rhoné, Philippe Cubry, Israfel Salazar, Florence Forbes, Yves Vigouroux, Flora Jay, and Olivier François. 2023. “A Quantitative Theory for Genomic Offset Statistics.” Molecular Biology and Evolution 40 (6): msad140.

Haller, Benjamin C, and Philipp W Messer. 2019. “SLiM 3: Forward Genetic Simulations Beyond the Wright–Fisher Model.” Edited by Ryan Hernandez. Molecular Biology and Evolution 36 (3): 632–37. https://doi.org/10.1093/molbev/msy228.