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.