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Defining mathematical terms and objects is a constant issue in ecology; often definitions are absent, erroneous, or imprecise. Through a bibliographic prospection, we show that this problem appears in macro-ecology (biogeography and community ecology) where the lack of definition for the sigmoid class of functions results in difficulties of interpretation and communication. In order to solve this problem and to help harmonize papers that use sigmoid functions in ecology, herein we propose a comprehensive definition of these mathematical objects. In addition, to facilitate their use, we classified the functions often used in the ecological literature, specifying the constraints on the parameters for the function to be defined and the curve shape to be sigmoidal. Finally, we interpreted the different properties of the functions induced by the definition through ecological hypotheses in order to support and explain the interest of such functions in ecology and more precisely in biogeography.

Although patterns of biodiversity across the globe are well studied, there is still a controversial debate about the underlying mechanisms and their generality across biogeographic scales. In particular, it is unclear to what extent diversity patterns along environmental gradients are directly driven by abiotic factors, such as climate, or indirectly mediated through biotic factors, such as resource effects on consumers.

Andes, Southern Ecuador; Mt. Kilimanjaro, Tanzania.

We studied the diversity of fleshy-fruited plants and avian frugivores at the taxonomic level, that is, species richness and abundance, as well as at the level of functional traits, that is, functional richness and functional dispersion. We compared two important biodiversity hotspots in mountain systems of the Neotropics and Afrotropics. We used field data of plant and bird communities, including trait measurements of 367 plant and bird species. Using structural equation modeling, we disentangled direct and indirect effects of climatemportance of bottom-up mechanisms for the taxonomic diversity of consumers, suggesting the importance of active resource tracking. Our results also suggest that it might be difficult to identify signals of ecological fitting between functional plant and animal traits across biogeographic regions, since different species groups may respond to different climatic drivers. This decoupling between resource and consumer communities could increase under future climate change if plant and animal communities are consistently related to distinct climatic drivers.Whether or not biogeographic rules dealing with spatial patterns of animal body sizes are valid for ectotherms is controversial. Motolimod As the ectotherms grow all their lives, we explored the role of age and annual growth rate in body size variation in Phrynocephalus przewalskii in northern China. Morphological data were collected from 11 populations across a broad geographic gradient. Correlations between age, sex, climatic factors, and body size were analyzed using generalized linear model (GLM) and generalized linear mixed model (GLMM). GLM analysis indicated that the general body size of both sexes and the appendage size of females increased significantly with increasing temperature; however, the coefficient of determination was very small. GLMM analysis indicated that body size only correlated with age, whereas appendage size was affected by age, temperature, rainfall, and sunshine. Annual growth rates were positively correlated with temperature. We concluded that body size variation was mainly caused by age structure and plasticity of the growth rate in P. przewalskii and did not follow Bergmann's rule; however, females followed Allen's rule. Future studies to investigate the effect of energy restriction are needed to further understand the relationship between growth rate and body size. We also suggest that further studies on thermal advantage and sexual selection may be helpful to understand appendage size variation in P. przewalskii.Climate and environmental condition drive biodiversity at many levels of biological organization, from populations to ecosystems. Combined with paleoecological reconstructions, palaeogenetic information on resident populations provides novel insights into evolutionary trajectories and genetic diversity driven by environmental variability. While temporal observations of changing genetic structure are often made of sexual populations, little is known about how environmental change affects the long-term fate of asexual lineages. Here, we provide information on obligately asexual, triploid Daphnia populations from three Arctic lakes in West Greenland through the past 200-300 years to test the impact of environmental change on the temporal and spatial population genetic structure. The contrasting ecological state of the lakes, specifically regarding salinity and habitat structure may explain the observed lake-specific clonal composition over time. Palaeolimnological reconstructions show considerable regional environmental fluctuations since 1,700 (the end of the Little Ice Age), but the population genetic structure in two lakes was almost unchanged with at most two clones per time period. Their local populations were strongly dominated by a single clone that has persisted for 250-300 years. We discuss possible explanations for the apparent population genetic stability (a) persistent clones are general-purpose genotypes that thrive under broad environmental conditions, (b) clonal lineages evolved subtle genotypic differences unresolved by microsatellite markers, or (c) epigenetic modifications allow for clonal adaptation to changing environmental conditions. Our results motivate research into the mechanisms of adaptation in these populations, as well as their evolutionary fate in the light of accelerating climate change in the polar regions.

As global climate change alters drought regimes, rapid evolution of traits that facilitate adaptation to drought can rescue populations in decline. The evolution of phenological advancement can allow plant populations to escape drought, but evolutionary responses in phenology can vary across a species' range due to differences in drought intensity and standing genetic variation.

, a perennial herb spanning a broad climatic gradient, recently experienced a period of record drought. Here, we used a resurrection study comparing flowering time and stem height at first flower of pre-drought ancestors and post-drought descendants from northern-edge, central, and southern-edge populations in a common environment to examine the evolution of drought escape across the latitudinal range.

Contrary to the hypothesis of the evolution of advanced phenology in response to recent drought, flowering time did not advance between ancestors and descendants in any population, though storage condition and maternal effects could have impacted these results.

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