Multinomial regression for analyzing macroinvertebrate assemblage composition data

Macroinvertebrate species composition data are often expressed as proportional abundances when assessing water-quality conditions or responses to disturbance. Proportional abundances represent the probability of belonging to one of many mutually exclusive and exhaustive groups (taxa). Proportional abundances have some unique properties that must be considered when analyzing these data: 1) the probabilities of group membership must sum to 1 and 2) a change in any 1 group affects all other groups. We used multinomial regressions to analyze changes in proportional abundances along gradients of urbanization in 9 metropolitan areas across the USA. Multinomial regression can be used to address multiple nonlinear responses simultaneously, whereas simple linear regressions must be used to analyze linear or polynomial responses of each group independently. We established that: 1) abundance ratios of tolerant and moderately tolerant groups responded consistently (3–5% increase in the ratios for every 1% increase in developed land cover in the watershed) across the urban gradient, 2) functional groups did not change significantly, and 3) ratios based on assemblage metrics were better indicators of environmental disturbance than ratios based on individual taxa. Multinomial regression, with its flexible model form, can capture patterns of species succession along a resource or stressor gradient. Our results also demonstrate that users of multinomial regression may encounter numerical problems with rare taxa, especially when these taxa have a complete separation along the gradient. Consequently, multinomial regressions are more suitable for analyzing aggregations of taxa or taxon traits.