Navarro and Manly (Popul Ecol 51:505–512, 2009) (NM) have proposed a randomization protocol for null model analysis of species occurrences at discrete locations based on probability distributions and generalized linear models. In the NM method, presences-absences are governed by independent Bernoulli random variables. In addition, a non-observable non-negative random variable (“quasi-abundance”) from either Poisson, Binomial or Negative Binomial distributions are log-linearly related to the qualitative effects of species and location. By connecting the probability of occurrence of each species on each location and the quasi-abundance distributions, one generalized linear model for the observed presences-absences is selected by profile deviance, and the resulting fitted probabilities of the null model with minimum deviance is used to generate random matrices via parametric bootstrap. This work contributes with a unified theoretical formulation of the NM method, based on Faddy distributions, to allow general distributions of over-dispersed and under-dispersed discrete random variables. For a subset of the Faddy models, the log concave property of the inverse link function guarantees convergence to a global minimum deviance thus providing unique estimates for the linear parameters of the models. The method is illustrated using presence-absence data of island lizard communities. Interpretations of this combined GLM-parametric bootstrap protocol are discussed, highlighting the way fitted probabilities under the chosen null model are related to the row and column totals of the observed table. Additional properties of the probabilistic NM protocol, with possible avenues of future research, are also discussed.

Navarro 和 Manly (Popul Ecol 51:505–512, 2009) (NM) 提出了一种随机化协议，用于基于概率分布和广义线性模型对离散位置的物种发生进行零模型分析。在 NM 方法中，存在-不存在由独立的伯努利随机变量控制。此外，来自泊松、二项式或负二项式分布的不可观察的非负随机变量（“准丰度”）与物种和位置的定性影响呈对数线性相关。通过连接每个物种在每个位置的出现概率和准丰度分布，通过轮廓偏差选择观察到的存在-不存在的一个广义线性模型，并且得到的具有最小偏差的空模型的拟合概率用于通过参数引导生成随机矩阵。这项工作有助于基于 Faddy 分布的 NM 方法的统一理论公式，以允许过度分散和分散不足的离散随机变量的一般分布。对于 Faddy 模型的一个子集，反向链接函数的对数凹属性保证收敛到全局最小偏差，从而为模型的线性参数提供唯一估计。该方法使用岛屿蜥蜴群落的存在与否数据来说明。讨论了对这种组合 GLM 参数引导协议的解释，强调了所选空模型下的拟合概率与观察表的行和列总数相关的方式。