Macroecological interpretation of the targeted parameters in the
neutral model
Previous studies have discussed four targeted parameters (θ, J ,d , and m ) of the neutral model in relation to geographical
and climatic contexts (Turner, 2004). Here, for each parameter, the
results of parameter dependency were interpreted from a macroecological
perspective.
First, the fundamental biodiversity number (θ) was calculated as the
product of species pool size (J M) and speciation
rate per individual in the species pool (v ); however, the
detailed equations differ among studies depending on the precision
(Hubbell, 2001; He & Hu, 2005; Etienne & Alonso, 2007). Changes in
speciation rates along geographical and climatic gradients are well
reported (Mannion, Upchurch, Benson, & Goswami, 2014; Rabosky et al.,
2018); thus, the fundamental biodiversity number should vary along
geographical and climatic gradients. Fukaya, Kusumoto, Shiono, Fujinuma,
& Kubota. (2020) recently estimated the fundamental biodiversity number
of woody plant species at regional scales and found large variations
among the four regions in Japan. In addition, speciation rates differ
among taxonomic groups (Schluter & Pennell, 2017). In the simulated
results, the upper limits (ζ) varied largely along the values of the
fundamental biodiversity number (Fig. 3i). Therefore, even if the
temporal beta-diversity values are identical, the meanings of the
changes are different; for example, 0.4 is approximately the maximum
value when the fundamental biodiversity number is 100, but that is half
of the upper limit when the number is 600 (Fig. 3i). Therefore, when
estimating the fundamental biodiversity number is difficult, considering
the differences in species pool properties due to geography, climate,
and taxonomy can be essential for future macroecological studies of
temporal beta diversity.
Second, local community size is strongly associated with the relative
influence of stochastic drift (Chave, 2004). The simulated results
showed that both the upper limit of temporal beta diversity and the
intercept increased as the size became smaller (Fig. 3j, n). These
results suggest that the probability differences in individual turnover
among the same species (i.e., apparent compositional equilibrium;
Nakadai, 2020) affect the temporal beta-diversity patterns.
Specifically, large local communities have more opportunities to obtain
individuals that are of the same species as the dead individuals in the
previous time step and cause less apparent compositional changes. In
natural situations, local community sizes are directly related to
habitat sizes, so small islands and conservation areas are likely to
have more large compositional fluctuations over time.
Third, the mortality rates are identical to the turnover rates under the
zero-sum assumption. If the contribution of individual turnover to
compositional shift is constant, a larger amount of individual turnover
causes more apparent compositional changes, and thus, larger temporal
beta diversity (Nakadai, 2022). Simulation results support this fact,
because the parameter ε, which is related to the curvature of the curve,
linearly increases as mortality rates increase; thus, the curve becomes
steeper (Fig. 3g). In contrast, the upper limits (ζ) decreased as the
mortality rates increased (Fig. 3k). This result may be attributed to
the fact that the increased mortality and turnover rates result in more
individuals being randomly selected from the species pool, keeping the
species composition of the local community close to that of the species
pool. In nature, higher temperatures facilitate faster growth and
shorter life span (Keil & de Magalhaes, 2015); therefore, mortality
rates would be higher toward the tropics, resulting in less stable
compositional dynamics.
Finally, immigration rates are the degree of habitat isolation from
species sources, which is an influential factor in island ecosystems and
both the protection and maintenance of conservation areas (MacArthur &
Wilson, 1967; Prugh, Hodges, Sinclair, & Brashares, 2008; Fahrig,
2013). The parameter dependency of temporal beta-diversity patterns
against immigration rates was similar to that against mortality rates
(Fig. 3d, h, l, p). Specifically, the parameter ε increased linearly,
and the upper limits (ζ) decreased as immigration rates increased (Fig.
3i, h). The interpretation of these results is the same as that of the
mortality rate as discussed in the above paragraph; thus, larger
immigration rates facilitate a similar community composition as that of
the species pool. This process can reduce the temporal variability of
species composition in the local community. Therefore, in nature,
isolated island ecosystems and isolated conservation areas would be more
temporally unstable.