Distance-based ordinations have played a critical role in community ecology for more than half a century, but are still under active development. These methods employ a matrix of pairwise distances or dissimilarities between sample units, and map sample units from the high-dimensional distance or dissimilarity space to a low dimensional representation for analysis. Distance- or dissimilarity-based methods employ continuum or gradient ecological theory and a variety of statistical models to achieve the mapping. Recently, ecologists have developed model-based ordinations based on latent vectors and individual species response models. These methods employ the individualistic perspective of Gleason as the ecological model, and Bayesian or maximum likelihood methods to estimate the parameters for the low dimensional space represented by the latent vectors. In this research I compared two distance-based methods (NMDS and t-SNE) with two model-based methods (BORAL and REO) on five data sets to determine which methods are superior for (1) extracting meaningful ecological drivers of variability in community composition; and (2) estimating sample unit locations in ordination space that maximize the goodness-of-fit of individual species response models to the estimated sample unit locations. Environmental variables and species were fitted to the ordinations by Generalized AdditiveModels (GAMs) with Gaussian, negative binomial, or Poisson distribution models as appropriate. Across the five data sets, 22 models of environmental variability and 449 models of species distributions were calculated for each of the ordination methods. To minimize the effects of stochasticity the entire analysis was replicated three times and results averaged across the replicates. Results were evaluated by deviance explained and AIC for environmental variables and species distributions, averaged by ordination method for each data set, and ranked from best to worst. For the four assessments distance-based methods ranked 1 and 2 in three cases, and 1 and 3 in one case, significantly out-performing the model-based methods. t-SNE was the top performing method, out-performing NMDS especially on the more complex data sets. In general the gradient-based theoretical basis and data sufficiency of distance-based methods allowed distance-based methods to outperform model-based methods in every assessment.

中文翻译：

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基于距离和基于模型的排序的比较

半个多世纪以来，基于距离的排序在社区生态中发挥了关键作用，但仍在积极发展中。这些方法采用样本单元之间的成对距离或相异度矩阵，并将样本单元从高维距离或相异空间映射到低维表示进行分析。基于距离或差异的方法采用连续统或梯度生态理论和各种统计模型来实现映射。最近，生态学家开发了基于潜在向量和个体物种响应模型的基于模型的排序。这些方法采用格里森的个人主义观点作为生态模型，和贝叶斯或最大似然方法来估计由潜在向量表示的低维空间的参数。在这项研究中，我在五个数据集上比较了两种基于距离的方法（NMDS 和 t-SNE）与两种基于模型的方法（BORAL 和 REO），以确定哪种方法更适合（1）提取有意义的社区变异性生态驱动因素作品; (2) 估计排序空间中的样本单元位置，以最大化单个物种响应模型对估计样本单元位置的拟合优度。环境变量和物种通过广义加性模型 (GAM) 与高斯、负二项式或泊松分布模型适当地拟合。在五个数据集中，每种排序方法计算了 22 个环境变异模型和 449 个物种分布模型。为了尽量减少随机性的影响，整个分析重复了 3 次，结果在重复中取平均值。结果通过偏差解释和 AIC 评估环境变量和物种分布，通过排序方法对每个数据集进行平均，并从最佳到最差排名。对于四种评估，基于距离的方法在 3 种情况下排名 1 和 2，在 1 种情况下排名 1 和 3，显着优于基于模型的方法。t-SNE 是性能最好的方法，其性能优于 NMDS，尤其是在更复杂的数据集上。