A hierarchical set of models for species response analysis

Abstract

Variation in the abundance of species in space and/or time can be caused by a wide range of underlying processes. Before such causes can be analysed we need simple mathematical models which can describe the observed response patterns. For this purpose a hierarchical set of models is presented. These models are applicable to positive data with an upper bound, like relative frequencies and percentages. The models are fitted to the observations by means of logistic and non‐linear regression techniques. Working with models of increasing complexity allows us to choose for the simplest possible model which sufficiently explains the observed pattern. The models are particularly suited for description of responses in time or over major environmental gradients. Deviations from these temporal or spatial trends may be statistically ascribed to, for example, climatic fluctuations or small‐scale spatial heterogeneity. The applicability of this approach is illustrated by examples from recent research. A combination of simple, descriptive models like those presented in this paper and causal models as developed by several others, is advocated as a powerful tool towards a fuller understanding of the dynamics and patterns of vegetational change.

Generalized linear and generalized additive models in studies of species distributions: setting the scene

“…Jari Oksanen and Peter Minchin expand the discussion on the shape of species response curves along continuous ecological gradients. Using data on vascular plant distribution along an elevation gradient, they test four main types of models for fitting such responses: (i) a hierarchical set of models (HOF) discussed by Huisman et al (1993); (ii) binomial GLMs (logistic link); (iii) binomial GAMs (logistic link); and (iv) beta-functions (Austin et al, 1994). HOF models are the most effective method for their data, and GAMs provide very similar results in most cases.…”

Effects of Vegetation Management and Raising the Water Table on Nutrient Dynamics and Vegetation Change in a Wet Grassland

“…To ascertain the explained variance of the response model, R2 was calculated from the observed frequency of occurrence in each year and the probability 'predicted' by the model (see Table 5). We did not use the two additional models suggested by Huisman et al (1993) because of the relatively short time span of the present study (6 years). The parameters of the response models were used to rank species in their replacement order.…”

“…However, they have been shown to be useful in various studies on vegetation succession (see Huisman et al 1993). The parameters were estimated by logistic regression, with the parameter selection based on a X2 test (Jongman, ter Braak & van Tongeren 1987;Huisman et al 1993;Olff et al 1993). To ascertain the explained variance of the response model, R2 was calculated from the observed frequency of occurrence in each year and the probability 'predicted' by the model (see Table 5).…”

“…The temporal changes in occurrence of individual species were described using a set of hierarchical models for species response analysis as proposed by Huisman, Olff & Fresco (1993) and used by Olff, Huisman & van Tooren (1993). The probability of occurrence of each species as a function of time p(t) in each combination of hydrology and grassland management was fitted to one of the following general response models: where a, b and c are the parameters to be estimated.…”

“…These curves merely describe the observed changes. However, they have been shown to be useful in various studies on vegetation succession (see Huisman et al 1993). The parameters were estimated by logistic regression, with the parameter selection based on a X2 test (Jongman, ter Braak & van Tongeren 1987;Huisman et al 1993;Olff et al 1993).…”