INTRODUCTION
Both theoretical and empirical studies have pointed out that environmental factors can regulate population dynamics (Menge & Sutherland 1987; Cantrell & Cosner 1991), thus how population dynamics depends on environmental changes has attracted extensive attention of ecologists. To answer this question, many studies have examined how population parameters, such as intrinsic growth rate and strength of density dependence, vary spatially within a single species between the center and the margins of the species’ range (e.g., Fukaya et al. 2014; Nielsen et al. 2014) and at different positions along a single environmental gradient (e.g., Agrawal et al. 2004; Jenkins et al. 2008; Armas et al. 2011; Street et al. 2015). These comparative studies revealed that population parameters may be interdependent: populations with higher intrinsic growth rates tend to exhibit stronger negative density dependence (Underwood 2007). This finding suggests that increasing environmental suitability (i.e., higher intrinsic growth rate) often increases the strength of density dependence (Maguire 1973; Weber et al. 2017). Unlike at the single population level, however, the context dependence of population dynamics is harder to predict at the community level, owing to the scarcity of empirical studies on the topic and the lack of a study framework to quantify the context dependence of the dynamics of multiple species.
Similar to single population dynamics, the dynamics of multiple species can be described by mathematical population models; therefore, context dependence might be clarified by examining how population parameters of all members of a community vary depending on the environment. To investigate this question, a two-species system is the most convenient, because mathematical population models of two-species systems (e.g., species i and j ) consist of the smallest possible set of population parameters: intrinsic growth rates (ri , rj ), strengths of intraspecific density dependence (αii , αjj ), and strengths of interspecific density dependence (αij , αji ). Although most natural communities consist of more than two species and the behavior of systems comprising three or more species can rarely be predicted from parameters obtained from two-species systems (Levine et al. 2017; Grilli et al. 2017; Broekman et al. 2019), such concision of parameters assures several advantages, such as ease of estimating population parameters from empirical data, simplicity of hypotheses, and ease of predicting the context dependence of population parameters. Indeed, both theoretical and empirical studies using two-species systems have greatly contributed to the progress in understanding various types of species interactions (Wootton & Emmerson 2005; Chesson & Kuang 2008) and to linking modern coexistence theory (Chesson 2000, 2003, 2018; Chesson & Kuang 2008; Barabás et al. 2018) to empirical testing (Adler et al. 2018; Ellner et al. 2019).
An effective approach to understanding the context dependence of the mechanisms driving two-species population dynamics is to examine how six population parameters (ri ,rj , αii , αjj , αij , and αji ) vary among localities in which a certain two species co-occur. In this context, intrinsic growth rates at a certain locality might be considered as proxies of the time-averaged environmental suitability of each species at the locality, the intrinsic growth rate is the maximum instantaneous growth rate of a population under given physical and biological conditions, it can reflect the environmental suitability of the habitat in which the species resides. Here, we propose a new framework to understand the context dependence of the mechanism driving two-species population dynamics, in which we regard intrinsic growth rates as proxies for the environmental suitability of each species, and then assess how the strengths of intra- and interspecific density dependence change among localities on a coordinate plane constituted by intrinsic growth rates of the two species obtained from many localities. This study framework will provide critical information for understanding the relationship between population dynamics and environmental suitability in a two-species system.
We applied 18-year intertidal sessile assemblage census data obtained from 33 quadrats located on 4 sites along the Pacific coast of Japan, whereChthamalus dalli (a barnacle) and Gloiopeltis furcata (a perennial red alga) are the first and second most dominant species at high shore of rocky intertidal zone (Munroe et al. 2010). Rocky intertidal sessile assemblages are ideal for studying the relationship between population dynamics and environmental suitability because they share a common resource: space (Dayton 1971). They can therefore provide insight into the general processes affecting community structure and how these vary between environments. In addition, both the amount of the shared resource (space) utilized, and the population size of all species can be measured easily, precisely, and simultaneously, as coverage (Menge 2000). Furthermore, because physical environmental stress and predation pressure vary within small spatial scales (Menge & Farrell 1989), intrinsic growth rates and strengths of intra- and interspecific density dependence will vary spatially, depending on the variation of these environmental conditions.