Statistical analysis
Posterior medians were used as appropriate point estimates in the
following statistical analysis. To examine how the strengths of intra-
and interspecific density dependence of C. dalli and G.
furcata change depending on intrinsic growth rates, the posterior
median of each parameter obtained from the state-space model was used
for regression analysis. We used the intrinsic growth rates of the two
species as explanatory variables, and the parameters of the four
strengths of density dependence were treated as response variables.
Without knowing whether the strength of density dependence changes
linearly or nonlinearly with environmental suitability, we used a
generalized linear model (GLM) and a generalized additive model (GAM)
simultaneously and selected the optimal model based on the Akaike
information criterion (AIC).
Model selection. To determine how the environmental suitability
of C. dalli (rsC ) and G. furcata(rsG ) affect the strength of density dependence
and whether the effect is linear or nonlinear, we started by modelling
all possible covariate combinations and specifications for the
relationship between strength of density dependence and environmental
suitability. For each of αii ,
αjj , αij , and
αji , a total of four candidate GLMs and six
candidate GAMs were defined (Table 1). Then, we screened for optimal
models based on AIC.
All GLMs were fitted with the R function lm (R Core Team 2013),
and all GAMs were fitted with the function gam in the R packagemgcv v1.8 (Wood 2017) in R v3.6.2. Model selection was conducted
using the R function AIC in R v3.6.2 (R Core Team 2013).