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.