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The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory, and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated. Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer–resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density‐regulation functions are usually non‐linear and may exhibit convex or concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. We show how population‐level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. We propose simple relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer–resource systems. Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time‐series from microbial food chains to fit population growth models as a test case for our theoretical predictions. Our results show that density‐regulation functions need to be chosen carefully as their shapes will depend on the study system's biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions. [ABSTRACT FROM AUTHOR]

Numerous biodiversity–ecosystem functioning (BEF) experiments have shown that plant community productivity typically increases with species diversity. In these studies, diversity is generally quantified using metrics of taxonomic, phylogenetic, or functional differences among community members. Research has also shown that the relationships between species diversity and functioning depends on the spatial scale considered, primarily because larger areas may contain different ecosystem types and span gradients in environmental conditions, which result in a turnover of the species set present locally. A fact that has received little attention, however, is that ecological systems are hierarchically structured, from genes to individuals to communities to entire landscapes, and that additional biological variation occurs at levels of organization above and below those typically considered in BEF research. Here, we present cases of diversity effects at different hierarchical levels of organization and compare these to the species‐diversity effects traditionally studied. We argue that when this evidence is combined across levels, a general framework emerges that allows the transfer of insights and concepts between traditionally disparate disciplines. Such a framework presents an important step towards a better understanding of the functional importance of diversity in complex, real‐world systems. [ABSTRACT FROM AUTHOR]

Biological invasions are globally affecting ecosystems, causing local species loss and altering ecosystem functioning. Understanding how such biological invasions occur and succeed is thus of high priority. Both local properties and the spatial network structure have been shown to be determinants of invasion success, and the identification of spatial invasion hubs directly promoting invasion dynamics is gaining attention. Spatial dynamics, however, could also indirectly alter invasion success by shaping pre‐invasion local community structure: in many ecosystems, such as riverine networks, regional properties such as patch size distribution are known drivers of local community structures, which themselves may affect the establishment success of invading species. Using microcosm experiments in dendritic networks, we disentangled how inherent patch size distribution and dispersal along specific network topologies shaped local resident communities, and, subsequently, affected the establishment success of invading species. After controlling for regional scale effects of connectivity on pre‐invasion diversity, we find that patch size distributions independently shaped pre‐invasion community diversity and invasion success, with no direct effect of pre‐invasion diversity on invasion success. Our results suggest that 1) landscape configuration plays an underestimated role in invasion success and that 2) invasion success should follow predictable landscape‐scale patterns in riverine networks given non‐random patch‐size distribution. [ABSTRACT FROM AUTHOR]

Cross‐ecosystem subsidies are studied with a focus on resource exchange at local ecosystem boundaries. This perspective ignores regional dynamics that can emerge via constraints imposed by the landscape, potentially leading to spatially‐dependent effects of subsidies and spatial feedbacks. Using miniaturized landscape analogues of river dendritic and terrestrial lattice spatial networks, we manipulated and studied resource exchange between the two whole networks. We found community composition in dendritic networks depended on the resource pulse from the lattice network, with the strength of this effect declining in larger downstream patches. In turn, this spatially‐dependent effect imposed constraints on the lattice network with populations in that network reaching higher densities when connected to more central patches in the dendritic network. Consequently, localized cross‐ecosystem fluxes, and their respective effects on recipient ecosystems, must be studied in a perspective taking into account the explicit spatial configuration of the landscape. [ABSTRACT FROM AUTHOR]