Fuzzy ecospace modelling

Abstract

Quantitative ecospace models are a numerical approach to comparing the functional structure of different ecosystems on macroevolutionary time-scales, by quantifying the distribution of functional ecological traits. Ecospace modelling has historically been restricted to a combination of visual interpretation and quantification via metrics such as mean sum of ranges. We argue that comparing ecosystem function in this way overlooks critical information about degrees of overlap and redundancy, and potentially misrepresents the role of “empty ecospace” in driving macroevolution. Fuzzy ecospace modelling (FEM) places conventional ecospace modelling within a fuzzy set-theoretic framework, wherein functional groups are learned from the dataset, creating models which are sensitive to overlap and the role of empty ecospace. Fuzzy ecospace modelling is a machine learning program which quantifies functional ecological similarity, and uses this information to classify new taxa. It creates functional groups using a Gower dissimilarity coefficient-based approach to the k-medoids algorithm, and uses fuzzy discriminant analysis to classify the taxa present in another ecosystem into these clusters, based on minimal Gower dissimilarity with a fuzzy threshold. This has the effect of quantifying the similarity between these ecosystems in terms of their functional groups, accounting for total redundancy, partial redundancy/novelty and total novelty. By using fuzzy membership functions, FEM can classify taxa which are highly ecologically dissimilar (outliers with respect to all functional groups), taxa which are fully redundant (100% similarity to those in a given functional group) and taxa in-between, which represent degrees of niche overlap. This can be used to compare the functional groups present in different ecosystems (as well as their degrees of overlap), and as a metric approach to comparing total ecological disparity. These results can be used to test models of the role of empty ecospace in macroevolutionary trends, or to investigate how ecosystems respond to global perturbations. Furthermore, it allows us to define numerically the concept of empty ecospace for n-dimensional datasets. A cluster-based approach to the quantification of ecospace allows for a numerical estimate of niche overlap, a value particularly difficult to quantify in fossil contexts.