Additive genetic variance in relative fitness (σA2(w)) is arguably the most important evolutionary parameter in a population because, by Fisher's fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σA2(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. "Generalized linear animal models" (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed ("latent") scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σA2(l)) equals (σA2(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σA2(l) and equals (exp⁡(σA2(l))-1). We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.

中文翻译：

---

当适应度服从对数正态分布时，适应度中遗传变异的估计和适应的推断

相对适应度中的加性遗传方差 (σA2(w)) 可以说是种群中最重要的进化参数，因为根据 Fisher 的自然选择基本定理 (FTNS；Fisher RA. 1930。自然选择的遗传理论。第一版。牛津: Clarendon Press)，它代表了适应性进化的速度。然而，迄今为止，对自然种群中 σA2(w) 的估计很少。此外，大多数可用的估计都依赖于不适合健身数据的高斯假设，结果不明确。“广义线性动物模型”(GLAM) 往往更适合健身数据，但它们估计转换（“潜在”）尺度上的参数，该尺度不能直接解释数据尺度上的推断。在这里，我们利用最新的理论发展来阐明如何最好地估计健康的定量遗传参数。具体来说，当预期适应度遵循对数正态分布时，我们使用计算机模拟来确认最近开发的 FTNS 模拟。在这种情况下，潜在对数尺度 (σA2(l)) 上绝对适应度的加性遗传方差等于数据尺度上的 (σA2(w))，这是一代内的适应率。然而，由于遗传失真，世代之间平均相对适应度的变化超过σA2(l)并等于(exp⁡(σA2(l))-1)。我们说明了为什么适应度的遗传力通常较低并且不是适应率的良好衡量标准。最后，我们探讨了动物模型对相关参数的估计效果如何，将高斯模型与泊松 GLAM 进行比较。我们的结果说明了 1) FTNS 中封装的数量遗传学和种群动态及其对数正态模拟之间的对应关系，以及 2) GLAM 参数估计的适当解释。