Graduate Program in Operations Research Industrial Engineering, The University of Texas at Austin, Austin, Texas, United States of America.
Department of Integrative Biology, The University of Texas at Austin, Austin, Texas, United States of America.
PLoS One. 2019 May 23;14(5):e0214190. doi: 10.1371/journal.pone.0214190. eCollection 2019.
The maximum entropy model, a commonly used species distribution model (SDM) normally combines observations of the species occurrence with environmental information to predict the geographic distributions of animal or plant species. However, it only produces point estimates for the probability of species existence. To understand the uncertainty of the point estimates, we analytically derived the variance of the outputs of the maximum entropy model from the variance of the input. We applied the analytic method to obtain the standard deviation of dengue importation probability and Aedes aegypti suitability. Dengue occurrence data and Aedes aegypti mosquito abundance data, combined with demographic and environmental data, were applied to obtain point estimates and the corresponding variance. To address the issue of not having the true distributions for comparison, we compared and contrasted the performance of the analytical expression with the bootstrap method and Poisson point process model which proved of equivalence of maximum entropy model with the assumption of independent point locations. Both Dengue importation probability and Aedes aegypti mosquito suitability examples show that the methods generate comparatively the same results and the analytic method we introduced is dramatically faster than the bootstrap method and directly apply to maximum entropy model.
最大熵模型是一种常用的物种分布模型 (SDM)，通常将物种出现的观测值与环境信息相结合，以预测动物或植物物种的地理分布。然而，它只能对物种存在的概率进行点估计。为了理解点估计的不确定性，我们从输入的方差中推导出最大熵模型输出的方差。我们应用分析方法获得登革热输入概率和埃及伊蚊适宜性的标准偏差。应用登革热发生数据和埃及伊蚊蚊虫丰度数据，结合人口和环境数据，获得点估计值和相应的方差。为了解决没有真实分布进行比较的问题，我们比较和对比了分析表达式与自举法和泊松点过程模型的性能，证明了最大熵模型与独立点位置假设的等效性。登革热输入概率和埃及伊蚊适宜性的例子都表明，这些方法产生了相似的结果，并且我们引入的分析方法比自举法快得多，并且可以直接应用于最大熵模型。
