Modelling species interactions using traits

As organism density increases, certain competitive traits become more important; in other words, the importance of some traits is density dependent. For example coral sweeper tentacles may not have much importance at low densities but at high densities they can become very important to survival (Sheppard, 1985). McGill (2006) suggested that biotic interactions such as competition are best treated as a “milieu or biotic background with which an organism interacts.” He calls this the

CH 1: Introduction

‘interaction milieu’. He goes on to suggest that competition can best be conceptualized using frequency-dependent game-theoretic models in which an invader (i.e. a coral recruit) must ‘play the field’ (Faslter and Westoby, 2003) of competition.

Langmead and Sheppard (2004) created a spatially explicit model of coral community dynamics. Their model represented a homogenous plot on a Caribbean fore-reef with 10 coral species. The model, which was based around a cellular automaton, can be conceptualized as a 300 x 300 cell chessboard. The occupancy of a cell by a ‘player’ (coral polyp) at each time-step was determined by its four immediate neighbours (Von Neuman neighbourhood) and pre-set interaction rules between species based on a competitive hierarchy. A coral polyp could only ‘grow’ into adjacent cells if that cell was either unoccupied or occupied by a coral species that was competitively subordinate. The competitive ranking of species was based on field surveys of aggressive capacity.

The construction of aggressive hierarchies in coral ecology is often based on in situ or aquarium observation of coral species’ ability to overgrow one another (Lang, 1971, 1973, Sheppard, 1980, Logan, 1984, Sheppard, 1985, 1988). Directly relating coral species-level behavioural traits (i.e. presence of sweeper tentacle, sweeper polyps, histological responses, extension of digestive mesenterial filaments) and physiological traits (cnidom complements, toxicity etc.) to overall aggressive ability would eliminate the need for extensive competitive hierarchies. This would have the advantage of transferability as traits could determine which coral will ‘win’ in any species-species interaction thereby eliminating the need to recreate a competitive hierarchy for each system studied. However, such traits are difficult to obtain and use for several reasons (discussed later) and therefore aggressive hierarchies may well be the best option.

CH 1: Introduction 1.4.4.Relating coral traits to environmental variables

1.4.4.1.Importance of linking traits to environmental variables

Relating traits to environmental variables is key to creating better predictive models of how ecosystems will respond under changing environmental scenarios. Keddy (1992) suggested general predictive models could be constructed using assembly and response rules (which could be derived from understanding how traits link to environment) in addition to the following datasets: 1) the total species pool for a region, 2) the traits of these species and 3) prevailing environmental conditions at a site. The need for the development of such predictive models has been reemphasized as the realities of rapid and major environmental changes (such as climate change) raise serious questions about how communities and ecosystem functioning will respond (i.e. Thuiller, 2007). Predictive trait-based models for how species will respond to changes in the environment have already been undertaken for British butterfly populations’ response to climate change (Diamond et al., 2011), bee population responses to environmental disturbances (Williams et al., 2010), and forest community responses to human disturbances (Mabry and Fraterrigo, 2009). An extensive framework for advancing trait-based prediction theory has recently been suggested (Webb et al., 2010).

It is generally observable in nature that organismal traits relate to the habitats in which they are commonly found. It has been suggested that habitat acts as a template upon which evolution then forges a set of characteristic traits (Southwood, 1977, 1988, Statzner and Resh, 1994). Establishing clearly the traits that individual species posses and how they relate to their fitness under particular sets of environmental conditions allows for better forecasting of extinction risk under different environmental scenarios thereby identifying species in need of priority protection. Finally, relating species traits to environment variables has proved useful for predicting the invasive potential of foreign plant species (Thuiller et al., 2006, Whitney and Gabler, 2008, Van Kleunen et al., 2010). Such methodological approaches could prove highly useful in coral reef ecology as invasive introductions increase (i.e. lionfish in the Caribbean).

CH 1: Introduction 1.4.4.2.Historical overview of methods for linking traits to environment

That organisms ‘prefer’ a particular set of environmental conditions and are therefore only found in certain locations is a central in both Grinnellian (1917) and Hutchinsonian (1957) niche theory. While niche theory provides a useful underlying theoretical framework, it falls short in answering the question: what specific species traits determine their location within an ecosystem? The problem of relating species traits to the habitat conditions in which they are found is often referred to as ‘the fourth corner problem’ referring to the matrix formulation Legendre et al. (1997) used to solve it (see Figure 1.5). Coincidentally, the test case that motivated Legendre et al.’s study was relating 5 coral reef fish traits (feeding habits, ecological category, size class of adults, egg type, and activity rhythm) to 3 reef habitat variables (distance from shore, water depth, and percent substrate cover at each site).

Figure 1.5 Graphical representation of the fourth corner problem. Ecologists often generate tables L (Species x Sampling sites), Q (Species x Traits), and R (Sampling sites x environmental variables). The challenge of relating environmental variables to traits is often referred to as the fourth corner problem due to the matrix formulation used to solve the problem (Legendre et al., 1997).

CH 1: Introduction 1.4.4.3.Statistical techniques

A number of statistical techniques have been developed to solve the ‘fourth corner problem’. Since ecological communities contain multiple species with numerous quantitative and qualitative traits distributed in habitats involving a plethora of environmental conditions, statistical techniques from the field of multivariate statistics are commonly used. Here I give a brief overview of the multivariate statistical techniques developed to solve the problem of linking traits to environment. One statistical methodology, first introduced and detailed by Dolédec et al. (1996), is a multivariate ordination method that can be used to link species traits to environmental factors and is commonly known as RLQ ordination. This type of ordination aims to investigate the relationship between table R (Sampling sites x environmental variables) and Q (Species x Traits) via a third table L (Species x Sampling sites). RLQ methodology has recently been extended to include both spatial coordinates and phylogenetic variables with script for analysis made freely available in R (Pavoine et al., 2011). Both RLQ and its recent extension are highly applicable within conservation management; both methods can be used to monitor and predict how changes in anthropogenic pressures will influence community structure in terms of traits and therefore function (see for example Ribera et al.).