Eco-evolutionary models commonly assume that traits are normally distributed in a population, and that the trait bounds do not influence the adaptation of traits. However, recent empirical evidence suggests that at least some traits are not normally distributed, and there is theoretical support for the view that trait bounds can be fundamental to trait adaptation. These attributes suggest that a beta distribution, which can accommodate unbounded (i.e. normal), singly bounded (i.e. gamma) or doubly bounded (beta) trait distributions, may be an appropriate alternative assumption for eco-evolutionary models. We develop an evolutionary model that represents how the mean values of a population’s traits change. Implementation of the model requires assumptions to be made regarding the relative fitness of the individuals in the population, and how their traits are distributed within natural bounds. We compare the numerical results of “population” models that evolve a plant population and the means of its two traits using our eco-evolutionary equations with those of “phenotype” models that evolve 10,000 phenotypes, each defined by a pair of trait values, of a plant population. The phenotype models do not assume any particular trait distribution or fitness, and allow phenotypes to wax and wane according to their ability to compete with other phenotypes in the population for a finite resource. Comparison of the trait distributions obtained by solving 3 coupled population odes with those obtained by solving 10,000 coupled phenotype odes reveals very good agreement between the approaches for each of four mortality functions. Further, it supports the ubiquity of the beta distribution in describing evolutionary processes in populations. An advantage of the simple population model is that it provides insights into why particular results are obtained, which augments the predictive power of the modelling, suggesting that in fact a simplified, abstracted modelling approach is sometimes preferable to the detailed, complicated alternative.

生态进化模型通常假设特征在人群中呈正态分布，并且特征范围不影响特征的适应性。但是，最近的经验证据表明，至少某些特征不是正态分布的，并且理论支持这种观点认为，特质界限可能是特质适应的基础。这些属性表明，可以容纳无界（即正态），单界（即γ）或双界（β）性状分布的beta分布可能是生态进化模型的适当替代假设。我们开发了一个进化模型，该模型表示人口特征的平均值如何变化。该模型的实施需要对人口中个体的相对适合度做出假设，以及它们的特征如何在自然界内分布。我们比较了使用我们的生态进化方程来进化植物种群的“种群”模型的数值结果及其两个性状的均值与进化出10,000个表型的“表型”模型的数值结果，每种表型由一对特征值定义。植物种群。表型模型不假设任何特定的性状分布或适应性，并允许表型根据其与种群中其他表型竞争有限资源的能力而起伏不定。通过解决3个耦合的人口颂歌与通过解决10,000个耦合的表型颂歌所获得的特征分布的比较，揭示了四种死亡率函数中的每一种方法之间的很好的一致性。进一步，它支持在描述种群进化过程中普遍存在的β分布。简单总体模型的优点在于，它可以洞悉为什么会获得特定结果，从而增强了建模的预测能力，这表明实际上，简化，抽象的建模方法有时比详细，复杂的替代方法更可取。