National Institute of Aquatic Resources, Technical University of Denmark, Lyngby, 2800, Denmark.
Greenpeace Brazil, Avenida Joaquim Nabuco, 2367, Centro, Manaus, Amazonas, 6902-031, Brazil.
Ecology. 2019 Jul;100(7):e02706. doi: 10.1002/ecy.2706. Epub 2019 May 21.
Reproduction by individuals is typically recorded as count data (e.g., number of fledglings from a nest or inflorescences on a plant) and commonly modeled using Poisson or negative binomial distributions, which assume that variance is greater than or equal to the mean. However, distributions of reproductive effort are often underdispersed (i.e., variance < mean). When used in hypothesis tests, models that ignore underdispersion will be overly conservative and may fail to detect significant patterns. Here we show that generalized Poisson (GP) and Conway-Maxwell-Poisson (CMP) distributions are better choices for modeling reproductive effort because they can handle both overdispersion and underdispersion; we provide examples of how ecologists can use GP and CMP distributions in generalized linear models (GLMs) and generalized linear mixed models (GLMMs) to quantify patterns in reproduction. Using a new R package, glmmTMB, we construct GLMMs to investigate how rainfall and population density influence the number of fledglings in the warbler Oreothlypis celata and how flowering rate of Heliconia acuminata differs between fragmented and continuous forest. We also demonstrate how to deal with zero-inflation, which occurs when there are more zeros than expected in the distribution, e.g., due to complete reproductive failure by some individuals.
个体繁殖通常记录为计数数据（例如，一个巢中的雏鸟数量或植物上的花序数量），通常使用泊松分布或负二项分布进行建模，这两种分布都假设方差大于等于均值。然而，生殖力的分布通常是过离散的（即方差<均值）。在进行假设检验时，忽略过离散的模型将过于保守，可能无法检测到显著的模式。在这里，我们表明广义泊松（GP）和康威-马克斯韦尔-泊松（CMP）分布是建模生殖力的更好选择，因为它们可以处理过度离散和过离散；我们提供了一些示例，说明生态学家如何在广义线性模型（GLMs）和广义线性混合模型（GLMMs）中使用 GP 和 CMP 分布来量化生殖力的模式。使用新的 R 包 glmmTMB，我们构建 GLMM 来研究降雨量和种群密度如何影响莺 Oreothlypis celata 的雏鸟数量，以及 Heliconia acuminata 的开花率在破碎和连续森林之间有何不同。我们还演示了如何处理零膨胀，即分布中的零值多于预期，例如由于某些个体的完全生殖失败。
