Quantifying Variation In The Strengths Of Species Interactions

INTRODUCTION

Understanding how the strengths of species interactions are distributed among species is critical for developing both predictive models of natural food webs (Hall and Raffaelli 1993, Wootton 1997) and management and conservation strategies (Mills et al. 1993, Power et al. 1996). Species interaction strength (i.e., the magnitude of the effect of one species on the abundance of another) is a key parameter in most dynamic food web models. Due to a lack of empirical data on interaction strengths, theorists have generally assumed that they are drawn from a uniform or symmetrical distribution (Lawton 1992, Hall and Rafaelli 1993). In four recent empirical studies, estimated interaction strengths among a suite of species have all had highly skewed distributions (Paine 1992, Fagan and Hurd [TABULAR DATA FOR TABLE 1 OMITTED] 1994, Raffaelli and Hall 1996, Wootton 1997). Most species had weak or no detectable effects on the abundances of other species, while a few had strong effects. These patterns are consistent with the observations and intuition of many ecologists that the structure of many communities is likely to be determined by a small subset of species that exert disproportionately strong effects (e.g., Paine 1980, Power et al. 1996). These four recent studies (Paine 1992, Fagan and Hurd 1994, Raffaelli and Hall 1996, Wootton 1997) are unique and valuable contributions for two reasons: (1) some of them use indices of "interaction strength" that can be derived from explicit models of species interaction, and thus could be estimates of parameters describing interaction strength used in these models; and (2) they measure a suite of interactions in an assemblage with a common metric, so that the relative importance of many interactions can be compared.

Using interaction strength indices derived from theoretical models is extremely important, because communication between empiricists and theoreticians has historically been impeded by confusion over the definition of interaction strength and by a discordance between what theoreticians model and what empiricists actually measure (MacArthur 1972, Laska and Wootton 1998). In fact, the empirical studies were partly motivated by recent efforts by ecologists to clarify the concepts of "strong-" and "weak-interactors" in a community and to derive techniques for quantifying interaction strengths in the field that are consistent, comparable, and of relevance to theoreticians (e.g., Paine 1992, Wootton 1994, 1997, Power and Mills 1995, Osenberg and Mittelbach 1996, Power et al. 1996, Ruesink 1998).

Laska and Wootton (1998) reviewed and clarified alternative theoretical concepts of interaction strength, and they evaluated different approaches for empirically estimating the per capita interaction strength coefficients in dynamic models of species interactions. In this paper, we focus on the more empirical problem of finding a common metric to quantify variation in species interactions in natural communities. Using a common metric in measuring interaction strength has important practical implications, independent of how a given system is modeled, because this practice allows characterization of (1) the patterns of variation in interaction strength among species within a community (i.e., the distribution of interaction strengths among species), (2) the identity of which species, if any, play disproportionately strong roles, and (3) how these vary over space and time. Thus, it is important to understand how our perception of the patterns of interaction strengths is influenced by the inherent mathematical behavior of the index used, including the index's response in prey or predator density to natural variation among species or among sites.

Using both simulated and published data, we explore the behavior of four commonly used or formally proposed indices for quantifying the relative importance of consumer-prey interactions (Table 1): (1) the raw, arithmetic difference in prey abundance in treatments, with and without predators; (2) an index proposed by Paine (1992) and used by Fagan and Hurd (1994) and Raffaelli and Hall (1996) (hereafter "Paine's Index, PI"); (3) an index proposed by Osenberg and Mittelbach (1996) and Wootton (1997) (hereafter "Dynamic Index, DI"); and (4) an index of "community importance" (CI) proposed by Power et al. (1996) to quantify the degree to which a community or ecosystem trait is altered by a species deletion. Since CI exhibited similar behavior to PI, it is not included in all of our analyses. All the indices have the potential to provide useful information about the relative importance of interactions among species. They must be used, however, with a clear understanding of what they actually measure and of the conditions under which one can expect them to be most revealing.

EMPIRICAL ESTIMATES OF INTERACTION STRenGTH

In this study, we focus on consumer-prey interactions to explore the behavior of the different empirical indices of interaction strength. Many field ecologists have historically quantified the strength of consumer impacts by the raw, arithmetic difference in prey abundance between treatments with and without predators (N - D), or as the per capita effect ((N - D)/Y); where N (normal condition) is prey abundance in the presence of predators, D (deleted) is prey abundance in the absence of predators, and Y is predator abundance (Table 1; e.g., Connell 1961, Dayton 1971, Menge 1976, 1978).