Data from: Spatial autocorrelation in fitness affects the estimation of natural selection in the wild

1. Natural selection is typically estimated in the wild using Lande and Arnold's multiple regression approach. Despite its utility for evolutionary ecologists, this method is subject to the classical assumptions of multiple regressions, which could result in potential analytical problems. In particular, spatial autocorrelation in fitness violates the assumption of residuals independence. Although widespread in the wild, the consequences of this effect have yet to be investigated in the context of Lande and Arnold's regression and resulting selection estimation. 2. Here we first described four spatially explicit models that allow to control for spatial autocorrelation in residuals of the Lande and Arnold's regression: a generalized least square (GLS) model with a distance-based exponential covariance function, two simultaneous autoregressive models (SAR, the lagged-response model (SAR-lag) and the spatial error model (SAR-err)) and a 5-step procedure using the principal coordinates of neighbour matrices (PCNM) method based on the extraction of spatial descriptors. We then compared the four spatially explicit models of selection to non-spatial models for three life-history traits recorded over 6 years in a wild blue tit (Cyanistes caeruleus) population. We also compared the performance of the four spatially explicit models of selection using a simulation approach. 3. Our analyses revealed strong spatial autocorrelation in residuals of selection models, which was completely described by the two SAR and the PCNM models, while only partially described by the GLS model. The magnitude of selection gradients and differentials decreased systematically in the 4 spatially explicit models while the degree of fit of these models increased (except for the GLS model). Moreover, we showed using simulations that the selection coefficients extracted from the SAR-lag model were systematically biased compared to those extracted from the GLS, SAR-err and PCNM models. 4. We hereby showed that spatial autocorrelation in fitness can severely affect selection differentials and gradients, even at a relatively small spatial scale. By using geostatistical models such as PCNM or SAR-err models, it is possible to control for this spatial autocorrelation. Finally, since spatial autocorrelation is closely linked to spatial environmental variation, this approach can also be used to explore environmental components of covariance between fitness and traits.

1. 自然选择（Natural selection）通常在野生种群中采用兰德与阿诺德（Lande and Arnold）提出的多元回归（multiple regression）方法进行估算。尽管该方法对进化生态学家极具实用价值，但它必须满足多元回归的经典假设，这可能引发潜在的分析问题。具体而言，适合度（fitness）的空间自相关（spatial autocorrelation）会违背残差独立性假设。尽管这种现象在野外广泛存在，但目前尚未有研究在兰德-阿诺德回归框架及其衍生的选择估算场景中，探讨该效应的具体影响。
2. 本研究首先介绍了四种可用于校正兰德-阿诺德回归残差空间自相关的空间显式模型（spatially explicit models）：其一为采用基于距离的指数协方差函数的广义最小二乘（generalized least square, GLS）模型；其二为两种同时自回归模型（simultaneous autoregressive models, SAR），即滞后响应模型（SAR-lag）与空间误差模型（SAR-err）；其三为基于空间描述子（spatial descriptors）提取的邻域矩阵主坐标（principal coordinates of neighbour matrices, PCNM）方法构建的五步流程。随后，我们针对野生蓝山雀（Cyanistes caeruleus）种群为期6年记录的3种生活史性状（life-history traits），将四种空间显式选择模型与非空间模型进行了对比。此外，我们还通过模拟方法，对四种空间显式选择模型的性能进行了比较。
3. 分析结果显示，选择模型的残差存在显著的空间自相关，其中两种SAR模型与PCNM模型可完全解释该效应，而GLS模型仅能部分解释。在四种空间显式模型中，选择梯度（selection gradients）与选择差（selection differentials）的幅值均呈现系统性下降，而模型拟合优度则普遍提升（GLS模型除外）。此外，通过模拟分析我们发现，相较于从GLS、SAR-err及PCNM模型中提取的选择系数（selection coefficients），从SAR-lag模型中提取的选择系数存在系统性偏差。
4. 本研究证实，即便在相对较小的空间尺度下，适合度的空间自相关也会对选择差与选择梯度造成显著影响。通过采用PCNM或SAR-err等地质统计模型（geostatistical models），可有效校正该空间自相关效应。最后，由于空间自相关与空间环境变异紧密相关，该方法还可用于探究适合度与性状间协方差的环境组分。