1. It is common practice for ecologists to examine species niches in the study of community composition. The response curve of a species in the fundamental niche is usually assumed to be quadratic. The centre of a quadratic curve represents a species' optimal environmental conditions, and the width its ability to tolerate deviations from the optimum.
2. Most multivariate methods assume species respond linearly to niche axes, or with a quadratic curve that is of equal width for all species. However, it is widely understood that some species have the ability to better tolerate deviations from their optimal environment (generalists) compared to other (specialist) species. Rare species often tolerate a smaller range of environments than more common species, corresponding to a narrow niche.
3. We propose a new method, for ordination and fitting Joint Species Distribution Models, based on Generalized Linear Mixed-effects Models, which relaxes the assumptions of equal tolerances.
4. By explicitly estimating species maxima, and species optima and tolerances per ecological gradient, we can better explore how species relate to each other.

中文翻译：

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具有不等生态位宽度的物种的基于模型的排序

1. 生态学家在群落组成研究中检查物种生态位是一种常见的做法。基本生态位中物种的响应曲线通常被假定为二次曲线。二次曲线的中心代表物种的最佳环境条件，以及其容忍偏离最佳环境的能力的宽度。
2. 大多数多元方法假设物种对生态位轴呈线性响应，或对所有物种具有相同宽度的二次曲线。然而，人们普遍认为，与其他（专业）物种相比，某些物种能够更好地容忍偏离其最佳环境（通才）的情况。与更常见的物种相比，稀有物种通常能忍受的环境范围更小，对应于一个狭窄的生态位。
3. 我们提出了一种基于广义线性混合效应模型的排序和拟合联合物种分布模型的新方法，它放宽了相等容差的假设。
4. 通过明确估计物种最大值、物种最优值和每个生态梯度的耐受性，我们可以更好地探索物种之间的关系。