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Konon Eagles
Konon Eagles

The Dynamics Swiss, Part 6 Of 6 15:51

Ecological theory has advanced our understanding of how diversity patterns are shaped by the joint influence of coexistence mechanisms and spatial structure. In particular, the paradigm of a metacommunity, defined as a set of local communities connected by dispersal (Leibold et al. 2004), has evolved into one of the most successful approaches for describing spatial ecosystems. According to the metacommunity paradigm, patterns of species coexistence and diversity are governed by four major archetypes: species sorting, patch dynamics, mass effects, and neutral dynamics (Leibold et al. 2004). These mechanisms rarely act in isolation, and some advances have been made towards synthesizing their effects (Leibold 2011; Fournier et al. 2017; Thompson et al. 2020; Bauer et al. 2021). A recently proposed metacommunity framework (Thompson et al. 2020) reduced the number of factors that are shaping ecological communities to the interplay of three fundamental processes: (i) density-independent growth rates that are based on abiotic conditions and vary in space, (ii) density-dependent biotic interactions, and (iii) dispersal. Thereby, dispersal generates source-sink effects: emigration locally reduces population size in sites where conditions are more favorable, whereas immigration increases population size in less favorable sites and introduces species that interact with local biota, thus altering density-dependent processes and competition.

The Dynamics Swiss, Part 6 of 6 15:51

We remark that our results are based on numerical observations, and, in particular, for large dispersal rates, we observed increasingly long transient times until the system fully equilibrated. Thus, we cannot completely rule out that our observations in the large dispersal limit are just transients. To validate our results, we have confirmed our results with various numerical ODE-solving schemes, including root-solving algorithms for equilibrium states which should be independent of transient dynamics. All these different algorithms yielded very similar outcomes, making the possibility of numerical artifacts rather unlikely. A more rigorous analysis would require analytical calculations in the limit of infinite dispersal in which spatial structure of consumers can be neglected.

RP definition A gave more consistent percentages than RP definition B, where the percentage considered as RPs varied from 0.4% to 4.5%, as shown in Figure 3, depending on the length of follow-up and number of measurements per year considered. Furthermore, a higher percentage of those with RP under definition A progressed to CKD compared to definition B. As RP definition A combines absolute and average renal function decline, it is based on all available eGFR and is less restrictive (in particular for longer follow-up) and therefore may better reflect the dynamics of RP than definition B. One potential limitation of our RP definition is that we did not base our definitions on relative (percentage) changes. There have been suggestions that a 25% decline from baseline in eGFR levels may be an appropriate definition for RP [12]. 041b061a72


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