DOI: 10.5061/dryad.jdfn2z3m6
title: Linking genomic offset statistics to the shape of selection gradients

description: 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.
description: The ⍺<em>-</em>GO<em> </em>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,
 (x<sub>1</sub>, x<sub>2</sub>). Two traits,
 (z<sub>1</sub>, z<sub>2</sub>), 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(z<sub>1</sub>, z<sub>2
 </sub>|<sub>  </sub>x) = exp( –1/2<em> *
 </em>((|z<sub>1</sub> – x<sub>1</sub>|
 /σ<sub>K</sub>)<sup>⍺ </sup> +
 (|z<sub>2</sub> –
 x<sub>2</sub>|/σ<sub>K</sub>)<sup>⍺
 </sup>))) where x<sub>1 </sub>and
 x<sub>2 </sub>are the local environmental values corresponding
 to the optimal trait values in that local environment, z<sub>1
 </sub>and z<sub>2 </sub>are the individual trait values
 estimated from the 120 adaptive mutations, and σ<sub>K</sub>
 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.” <em>Molecular Biology and
 Evolution</em> 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. <em>Molecular
 Biology and Evolution</em> 36 (3): 632–37.
 https://doi.org/10.1093/molbev/msy228.
description: # GENERAL INFORMATION This README.txt file was updated on May 12th 2025 by
 Thibaut Capblancq ### Paper associated with this archive This repository
 contains the data necessary to reproduce the results of the article
 "Linking genomic offset statistics to the shape of selection
 gradients", written by Thibaut Capblancq, Aurlien Tauzin, Yves
 Vigouroux, Philippe Cubry and Olivier Franois and published in 2025 in the
 journal*The American Naturalist* for a special feature on Genomic
 Forecasting. ### Originators Thibaut CAPBLANCQ (1), Aurélien TAUZIN (1),
 Yves VIGOUROUX (2), Philippe CUBRY (2) and Olivier FRANÇOIS (1) (1) *TIMC,
 Centre National de la Recherche Scientifique, Université
 Grenoble-Alpes, Grenoble INP, Grenoble, France* (2) *DIADE, Université de
 Montpellier, Institut de Recherche pour le
 Développement, Montpellier, France* ### Contact information Capblancq
 Thibaut:
 [thibaut.capblancq@univ-grenoble-alpes.fr](mailto:thibaut.capblancq@univ-grenoble-alpes.fr) Olivier FRANÇOIS: [olivier.francois@univ-grenoble-alpes.fr](mailto:olivier.francois@univ-grenoble-alpes.fr) ### Funding Sources This project was supported by the French National Research Agency ([ANR-22-CE45-0033](https://anr.fr/Projet-ANR-22-CE45-0033) and [ANR-22-CE32-0008](https://anr.fr/Projet-ANR-22-CE32-0008)) # ACCESS INFORMATION ### Licenses/restrictions placed on the data or code CC0 1.0 Universal (CC0 1.0) Public Domain Dedication ### Data derived from other sources Empirical data were retrieved from the following sources: * Gain et al., (2023). [https://doi.org/10.1093/molbev/msad140](https://doi.org/10.1093/molbev/msad140) * Rhone et al., (2020). [https://doi.org/10.1038/s41467-020-19066-4](https://doi.org/10.1038/s41467-020-19066-4) * Fitzpatrick et al., (2021). [https://doi.org/10.1111/1755-0998.13374](https://doi.org/10.1111/1755-0998.13374) * Capblancq et al., (2023). [https://doi.org/10.1111/nph.18465](https://doi.org/10.1111/nph.18465) ### Recommended citation for this data/code archive Data from: Linking genomic offset statistics to the shape of selection gradients. DOI: 10.5061/dryad.jdfn2z3m6 # DATA & CODE FILE OVERVIEW This data repository consists of 1015 data files, 6 code scripts, and this README document, with the following data and code filenames and variables ### Data files and variables ###### File: data_poplar.zip A zipped folder containing genomic, climatic and phenotypic data for 41 sampled localities of balsam poplar: * data_poplar_accessions.csv: A list of names for the 41 accessions * data_poplar_climate.csv: A table of five climate predictors (bio2: Mean Temperature Diurnal Range in celsius, bio10: Mean Temperature of Warmest Quarter in celsius, bio11: Mean Temperature of Coldest Quarter in celsius, bio18: Precipitation of Warmest Quarter in mm and bio19: Precipitation of Coldest Quarter in mm) for the source locality of each accession. * data_poplar_climate.cg.csv: A table of five climate predictors (bio2: Mean Temperature Diurnal Range in celsius, bio10: Mean Temperature of Warmest Quarter in celsius, bio11: Mean Temperature of Coldest Quarter in celsius, bio18: Precipitation of Warmest Quarter in mm and bio19: Precipitation of Coldest Quarter in mm) for a common garden site in Vermont (USA). * data_poplar_trait.csv: Height increment data for each accession in centimetres, measured in a common garden in Vermont (USA). * data_poplar_genotype.csv: genotypes for 9,100 loci. These data have been extracted from Fitzpatrick *et al.* (2021), [https://doi.org/10.1111/1755-0998.13374](https://doi.org/10.1111/1755-0998.13374). ###### File: data_redspruce.zip A zipped folder containing genomic, climatic and phenotypic data for 63 sampled localities of balsam poplar: * data_redspruce_accessions.csv: A list of names for the 63 accessions * data_redspruce_climate.csv: A table of eleven climate predictors (DD_0: degree-days below 0°C, DD18: degree-days above 18°C, MAR: mean annual solar radiation (MJ m‐2 d‐1), PAS: precipitation as snow (mm) between August in previous year and July in current year, MSP: May to September precipitation (mm), RH: mean annual relative humidity (%), EXT: extreme maximum temperature over 30 years, CMD: Hargreaves climatic moisture deficit (mm), TD: temperature difference between MWMT and MCMT, or continentality (°C), eFFP: the day of the year on which FFP ends and PET: Potential evapotranspiration) for the source locality of each accession. * data_redspruce_climate.cg.csv: A table of eleven climate predictors (DD_0: degree-days below 0°C, DD18: degree-days above 18°C, MAR: mean annual solar radiation (MJ m‐2 d‐1), PAS: precipitation as snow (mm) between August in previous year and July in current year, MSP: May to September precipitation (mm), RH: mean annual relative humidity (%), EXT: extreme maximum temperature over 30 years, CMD: Hargreaves climatic moisture deficit (mm), TD: temperature difference between MWMT and MCMT, or continentality (°C), eFFP: the day of the year on which FFP ends and PET: Potential evapotranspiration) for a common garden site in Burlington (USA). * data_redspruce_trait.csv: Height increment data for each accession in centimetres, measured in a common garden in Burlington (USA). * data_redspruce_genotype.csv: genotypes for 176,716 loci. These data have been extracted from Capblancq *et al.*(2023), [https://doi.org/10.1111/nph.18465](https://doi.org/10.1111/nph.18465). ###### File: data_millet.zip A zipped folder containing genomic and climatic and phenotypic data for 154 sampled localities of pearl millet. * data_millet_accessions.csv: A list of names for the 154 accessions * data_millet_climate.csv: A table of five climate predictors (PREC1: first axis of a pca with only precipitation variables, TEMP1: first axis of a pca with only temperature variables, TEMP2: second axis of a pca with only temperature variables, TEMP8: eigth axis of a pca with only temperature variables and TEMP14: fourteenth axis of a pca with only temperature variables, see Gain et al., (2023). [https://doi.org/10.1093/molbev/msad140](https://doi.org/10.1093/molbev/msad140) for details) for the source locality of each accession. * data_millet_climate.cg.csv: A table of five climate predictors (PREC1: first axis of a pca with only precipitation variables, TEMP1: first axis of a pca with only temperature variables, TEMP2: second axis of a pca with only temperature variables, TEMP8: eigth axis of a pca with only temperature variables and TEMP14: fourteenth axis of a pca with only temperature variables, see Gain et al., (2023). [https://doi.org/10.1093/molbev/msad140](https://doi.org/10.1093/molbev/msad140) for details) for a common garden site in Sadoré (Niger). * data_millet_trait.csv: Total seed weight data for each accession in grams, measured in a common garden in Sadoré (Niger). * data_millet_genotype.csv: genotypes for 16,632 loci. These data have been extracted from Rhone *et al.* (2020), [https://doi.org/10.1038/s41467-020-19066-4](https://doi.org/10.1038/s41467-020-19066-4). ###### File: sims_slim.zip A zipped folder containing 100 simulations used to confirm the validity of the alpha-GO statistic and its relationship with the geometric genomic offset. 10 files are associated with each simulation including: * environmental values for the two causal variables var1 and var2 before (*var1_step1*and* **var2_step1*) and after (var1_pred1) a brutal environmental change, * the position of each sampled individual on the simulated grid (*position_ind_step1*) * individuals' fitness before (*fitness_step1*) and after (*fitness_pred1*) the environmental change, * individuals' trait value for the two simulated traits (*trait1* and *trait2*) * individuals' genotypes (*genome_step1.vcf*) * positions of the 120 causal mutations associated with QTL1 (*mutationm2_step1.txt*) and QTL2 (*mutationm3_step1.txt*) ### Code scripts and workflow ###### File: scripts_slim.zip A zipped folder containing the scripts used to produce the simulations with four different alpha values with SLiM (version 3.7). ###### File: GO-selection-gradient_S3.Rmd R markdown script file describing all the analyses conducted on the simulated datasets ###### File: GO-selection-gradient_S4.Rmd R markdown script file describing all the analyses conducted on the empirical datasets # SOFTWARE VERSIONS The only software required to reproduce our results is the software R (version 4.3.1) and the R-packages LEA (version 3.19), reshape2 (version 1.4.4), ggplot2 (version 3.5.1) and ggpubr (version 0.6.0). If one wants to reproduce the simulations, the software SLiM (version 3.7) will be needed as well.