Linking scaling laws across eukaryotes.

Scaling laws relating body mass to species characteristics are among the most universal quantitative patterns in biology. Within major taxonomic groups, the 4 key ecological variables of metabolism, abundance, growth, and mortality are often well described by power laws with exponents near 3/4 or related to that value, a commonality often attributed to biophysical constraints on metabolism. However, metabolic scaling theories remain widely debated, and the links among the 4 variables have never been formally tested across the full domain of eukaryote life, to which prevailing theory applies. Here we present datasets of unprecedented scope to examine these 4 scaling laws across all eukaryotes and link them to test whether their combinations support theoretical expectations. We find that metabolism and abundance scale with body size in a remarkably reciprocal fashion, with exponents near ±3/4 within groups, as expected from metabolic theory, but with exponents near ±1 across all groups. This reciprocal scaling supports "energetic equivalence" across eukaryotes, which hypothesizes that the partitioning of energy in space across species does not vary significantly with body size. In contrast, growth and mortality rates scale similarly both within and across groups, with exponents of ±1/4. These findings are inconsistent with a metabolic basis for growth and mortality scaling across eukaryotes. We propose that rather than limiting growth, metabolism adjusts to the needs of growth within major groups, and that growth dynamics may offer a viable theoretical basis to biological scaling.

A Minimal Model for the Latitudinal Diversity Gradient Suggests a Dominant Role for Ecological Limits.

The latitudinal diversity gradient (LDG) is one of Earth's most iconic biodiversity patterns and still one of the most debated. Explanations for the LDG are often categorized into three broad pathways in which the diversity gradient is created by (1) differential diversification rates, (2) differential carrying capacities (ecological limits), or (3) differential time to accumulate species across latitude. Support for these pathways has, however, been mostly verbally expressed. Here, we present a minimal model to clarify the essential assumptions of the three pathways and explore the sensitivity of diversity dynamics to these pathways. We find that an LDG arises most easily from a gradient in ecological limits compared with a gradient in the time for species accumulation or diversification rate in most modeled scenarios. Differential diversification rates create a stronger LDG than ecological limits only when speciation and dispersal rates are low, but then the predicted LDG seems weaker than the observed LDG. Moreover, range dynamics may reduce an LDG created by a gradient in diversification rates or time for species accumulation, but they cannot reduce an LDG induced by differential ecological limits. We conclude that our simple model provides a null prediction for the effectiveness of the three LDG pathways and can thus aid discussions about the causal mechanisms underlying the LDG or motivate more complex models to confirm or falsify our findings.

The more-individuals hypothesis revisited: the role of community abundance in species richness regulation and the productivity-diversity relationship.

Species richness increases with energy availability, yet there is little consensus as to the exact processes driving this species-energy relationship. The most straightforward explanation is the more-individuals hypothesis (MIH). It states that higher energy availability promotes a higher total number of individuals in a community, which consequently increases species richness by allowing for a greater number of species with viable populations. Empirical support for the MIH is mixed, partially due to the lack of proper formalisation of the MIH and consequent confusion as to its exact predictions. Here, we review the evidence of the MIH and evaluate the reliability of various predictions that have been tested. There is only limited evidence that spatial variation in species richness is driven by variation in the total number of individuals. There are also problems with measures of energy availability, with scale-dependence, and with the direction of causality, as the total number of individuals may sometimes itself be driven by the number of species. However, even in such a case the total number of individuals may be involved in diversity regulation. We propose a formal theory that encompasses these processes, clarifying how the different factors affecting diversity dynamics can be disentangled.

Equilibrium dynamics of European pre-industrial populations: the evidence of carrying capacity in human agricultural societies.

Human populations tend to grow steadily, because of the ability of people to make innovations, and thus overcome and extend the limits imposed by natural resources. It is therefore questionable whether traditional concepts of population ecology, including environmental carrying capacity, can be applied to human societies. The existence of carrying capacity cannot be simply inferred from population time-series, but it can be indicated by the tendency of populations to return to a previous state after a disturbance. So far only indirect evidence at a coarse-grained scale has indicated the historical existence of human carrying capacity. We analysed unique historical population data on 88 settlements before and after the Thirty Years War (1618-1648), one the longest and most destructive conflicts in European history, which reduced the population of Central Europe by 30-50%. The recovery rate of individual settlements after the war was positively correlated with the extent of the disturbance, so that the population size of the settlements after a period of regeneration was similar to the pre-war situation, indicating an equilibrium population size (i.e. carrying capacity). The carrying capacity of individual settlements was positively determined mostly by the fertility of the soil and the area of the cadastre, and negatively by the number of other settlements in the surroundings. Pre-industrial human population sizes were thus probably controlled by negative density dependence mediated by soil fertility, which could not increase due to limited agricultural technologies.

Universal species-area and endemics-area relationships at continental scales.

Despite the broad conceptual and applied relevance of how the number of species or endemics changes with area (the species-area and endemics-area relationships (SAR and EAR)), our understanding of universality and pervasiveness of these patterns across taxa and regions has remained limited. The SAR has traditionally been approximated by a power law, but recent theories predict a triphasic SAR in logarithmic space, characterized by steeper increases in species richness at both small and large spatial scales. Here we uncover such universally upward accelerating SARs for amphibians, birds and mammals across the world's major landmasses. Although apparently taxon-specific and continent-specific, all curves collapse into one universal function after the area is rescaled by using the mean range sizes of taxa within continents. In addition, all EARs approximately follow a power law with a slope close to 1, indicating that for most spatial scales there is roughly proportional species extinction with area loss. These patterns can be predicted by a simulation model based on the random placement of contiguous ranges within a domain. The universality of SARs and EARs after rescaling implies that both total and endemic species richness within an area, and also their rate of change with area, can be estimated by using only the knowledge of mean geographic range size in the region and mean species richness at one spatial scale.

Niche and metabolic principles explain patterns of diversity and distribution: theory and a case study with soil bacterial communities.

The causes of biodiversity patterns are controversial and elusive due to complex environmental variation, covarying changes in communities, and lack of baseline and null theories to differentiate straightforward causes from more complex mechanisms. To address these limitations, we developed general diversity theory integrating metabolic principles with niche-based community assembly. We evaluated this theory by investigating patterns in the diversity and distribution of soil bacteria taxa across four orders of magnitude variation in spatial scale on an Antarctic mountainside in low complexity, highly oligotrophic soils. Our theory predicts that lower temperatures should reduce taxon niche widths along environmental gradients due to decreasing growth rates, and the changing niche widths should lead to contrasting α- and ß-diversity patterns. In accord with the predictions, α-diversity, niche widths and occupancies decreased while ß-diversity increased with increasing elevation and decreasing temperature. The theory also successfully predicts a hump-shaped relationship between α-diversity and pH and a negative relationship between α-diversity and salinity. Thus, a few simple principles explained systematic microbial diversity variation along multiple gradients. Such general theory can be used to disentangle baseline effects from more complex effects of temperature and other variables on biodiversity patterns in a variety of ecosystems and organisms.

Differential effects of temperature change and human impact on European Late Quaternary mammalian extinctions.

Species that inhabited Europe during the Late Quaternary were impacted by temperature changes and early humans, resulting in the disappearance of half of the European large mammals. However, quantifying the relative importance that each factor had in the extinction risk of species has been challenging, mostly due to the spatio-temporal biases of fossil records, which complicate the calibration of realistic and accurate ecological niche modeling. Here, we overcome this problem by using ecotypes, and not real species, to run our models. We created 40 ecotypes with different temperature requirements (mean temperature from -20 °C to 25 °C and temperature range from 10 °C to 40 °C) and used them to quantify the effect of climate change and human impact. Our results show that cold-adapted ecotypes would have been highly affected by past temperature changes in Europe, whereas temperate and warm-adapted ecotypes would have been positively affected by temperature change. Human impact affected all ecotypes negatively, and temperate ecotypes suffered the greatest impacts. Based on these results, the extinction of cold-adapted species like Mammuthus primigenius may be related to temperature change, while the extinction of temperate species, like Crocuta crocuta, may be related to human impact. Our results suggest that temperature change and human impact affected different ecotypes in distinct ways, and that the interaction of both impacts may have shaped species extinctions in Europe.

Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline.

The Living Planet Index (LPI) measures the average change in population size of vertebrate species over recent decades and has been repeatedly used to assess the changing state of nature. The LPI indicates that vertebrate populations have decreased by almost 70% over the last 50 years. This is in striking contrast with current studies based on the same population time series data that show that increasing and decreasing populations are balanced on average. Here, we examine the methodological pipeline of calculating the LPI to search for the source of this discrepancy. We find that the calculation of the LPI is biased by several mathematical issues which impose an imbalance between detected increasing and decreasing trends and overestimate population declines. Rather than indicating that vertebrate populations do not substantially change, our findings imply that we need better measures for providing a balanced picture of current biodiversity changes. We also show some modifications to improve the reliability of the LPI.

Habitat modifies the relationship between grass and herbivore species richness in a South African savanna.

The savanna ecosystem is dominated by grasses, which are a key food source for many species of grazing animals. This relationship creates a diverse mosaic of habitats and contributes to the high grass species richness of savannas. However, how grazing interacts with environmental conditions in determining grass species richness and abundance in savannas is still insufficiently understood. In the Kruger National Park, South Africa, we recorded grass species and estimated their covers in 60 plots 50 × 50 m in size, accounting for varying proximity to water and different bedrocks. To achieve this, we located plots (i) near perennial rivers, near seasonal rivers, and on crests that are distant from all water sources and (ii) on nutrient-rich basaltic and nutrient-poor granitic bedrock. The presence and abundance of large herbivores were recorded by 60 camera traps located in the same plots. Grass cover was higher at crests and seasonal rivers than at perennial rivers and on basalts than on granites. The relationship between grass species richness and herbivore abundance or species richness was positive at crests, while that between grass species richness and herbivore species richness was negative at seasonal rivers. We found no support for controlling the dominance of grasses by herbivores in crests, but herbivore-induced microsite heterogeneity may account for high grass species richness there. In contrast, the decrease in grass species richness with herbivore species richness at seasonal rivers indicates that the strong grazing pressure over-rides the resistance of some species to grazing and trampling. We suggest that the relationships between grasses and herbivores may work in both directions, but the relationship is habitat-dependent, so that in less productive environments, the effect of herbivores on vegetation prevails, while in more productive environments along rivers the effect of vegetation and water supply on herbivores is more important.

Hot spring oases in the periglacial desert as the Last Glacial Maximum refugia for temperate trees in Central Europe.

Northern glacial refugia are a hotly debated concept. The idea that many temperate organisms survived the Last Glacial Maximum (LGM; ~26.5 to 19 thousand years) in several sites across central and northern Europe stems from phylogeographic analyses, yet direct fossil evidence has thus far been missing. Here, we present the first unequivocal proof that thermophilous trees such as oak (Quercus), linden (Tilia), and common ash (Fraxinus excelsior) survived the LGM in Central Europe. The persistence of the refugium was promoted by a steady influx of hydrothermal waters that locally maintained a humid and warm microclimate. We reconstructed the geological and palaeohydrological factors responsible for the emergence of hot springs during the LGM and argue that refugia of this type, allowing the long-term survival and rapid post-LGM dispersal of temperate elements, were not exceptional in the European periglacial zone.

The relationship between geographic range size and rates of species diversification.

Range size is a universal characteristic of every biological species, and is often assumed to affect diversification rate. There are strong theoretical arguments that large-ranged species should have higher rates of diversification. On the other hand, the observation that small-ranged species are often phylogenetically clustered might indicate high diversification of small-ranged species. This discrepancy between theory and the data may be caused by the fact that typical methods of data analysis do not account for range size changes during speciation. Here we use a cladogenetic state-dependent diversification model applied to mammals to show that range size changes during speciation are ubiquitous and small-ranged species indeed diversify generally slower, as theoretically expected. However, both range size and diversification are strongly influenced by idiosyncratic and spatially localized events, such as colonization of an archipelago or a mountain system, which often override the general pattern of range size evolution.

Species abundance distribution results from a spatial analogy of central limit theorem.

The frequency distribution of species abundances [the species abundance distribution (SAD)] is considered to be a fundamental characteristic of community structure. It is almost invariably strongly right-skewed, with most species being rare. There has been much debate as to its exact properties and the processes from which it results. Here, we contend that an SAD for a study plot must be viewed as spliced from the SADs of many smaller nonoverlapping subplots covering that plot. We show that this splicing, if applied repeatedly to produce subplots of progressively larger size, leads to the observed shape of the SAD for the whole plot regardless of that of the SADs of those subplots. The widely reported shape of an SAD is thus likely to be driven by a spatial parallel of the central limit theorem, a statistically convergent process through which the SAD arises from small to large scales. Exact properties of the SAD are driven by species spatial turnover and the spatial autocorrelation of abundances, and can be predicted using this information. The theory therefore provides a direct link between SADs and the spatial correlation structure of species distributions, and thus between several fundamental descriptors of community structure. Moreover, the statistical process described may lie behind similar frequency distributions observed in many other scientific fields.

Spontaneous symmetry breaking in ride-sharing adoption dynamics.

Symmetry breaking ubiquitously occurs across complex systems, from phase transition in statistical physics to self-organized lane formation in pedestrian dynamics. Here, we uncover spontaneous symmetry breaking in a simple model of ride-sharing adoption. We analyze how collective interactions among ride-sharing users to avoid detours in shared rides give rise to spontaneous symmetry breaking and pattern formation in the adoption dynamics. These dynamics result in bistability of high homogeneous and partial heterogeneous adoption states, potentially limiting the population-wide adoption of ride sharing. Our results provide a framework to understand real-world adoption patterns of ride sharing in complex urban settings and support the (re)design of ride-sharing services and incentives for sustainable shared mobility.

Diversity dependence is a ubiquitous phenomenon across Phanerozoic oceans.

Biodiversity on Earth is shaped by abiotic perturbations and rapid diversifications. At the same time, there are arguments that biodiversity is bounded and regulated via biotic interactions. Evaluating the role and relative strength of diversity regulation is crucial for interpreting the ongoing biodiversity changes. We have analyzed Phanerozoic fossil record using public databases and new approaches for identifying the causal dependence of origination and extinction rates on environmental variables and standing diversity. While the effect of environmental factors on origination and extinction rates is variable and taxon specific, the diversity dependence of the rates is almost universal across the studied taxa. Origination rates are dependent on instantaneous diversity levels, while extinction rates reveal delayed diversity dependence. Although precise mechanisms of diversity dependence may be complex and difficult to recover, global regulation of diversity via negative diversity dependence of lineage diversification seems to be a common feature of the biosphere, with profound consequences for understanding current biodiversity crisis.

Demand-driven design of bicycle infrastructure networks for improved urban bikeability.

Cycling is crucial for sustainable urban transportation. Promoting cycling critically relies on sufficiently developed infrastructure; however, designing efficient bike path networks constitutes a complex problem that requires balancing multiple constraints. Here we propose a framework for generating efficient bike path networks, explicitly taking into account cyclists' demand distribution and route choices based on safety preferences. By reversing the network formation, we iteratively remove bike paths from an initially complete bike path network and continually update cyclists' route choices to create a sequence of networks adapted to the cycling demand. We illustrate the applicability of this demand-driven approach for two cities. A comparison of the resulting bike path networks with those created for homogenized demand enables us to quantify the importance of the demand distribution for network planning. The proposed framework may thus enable quantitative evaluation of the structure of current and planned cycling networks, and support the demand-driven design of efficient infrastructures.

Moth Diversity Increases along a Continent-Wide Gradient of Environmental Productivity in South African Savannahs.

Environmental productivity, i.e., the amount of biomass produced by primary producers, belongs among the key factors for the biodiversity patterns. Although the relationship of diversity to environmental productivity differs among studied taxa, detailed data are largely missing for most groups, including insects. Here, we present a study of moth diversity patterns at local and regional scales along a continent-wide gradient of environmental productivity in southern African savannah ecosystems. We sampled diversity of moths (Lepidoptera: Heterocera) at 120 local plots along a gradient of normalized difference vegetation index (NDVI) from the Namib Desert to woodland savannahs along the Zambezi River. By standardized light trapping, we collected 12,372 specimens belonging to 487 moth species. The relationship between species richness for most analyzed moth groups and environmental productivity was significantly positively linear at the local and regional scales. The absence of a significant relationship of most moth groups' abundance to environmental productivity did not support the role of the number of individuals in the diversity-productivity relationship for south African moths. We hypothesize the effects of water availability, habitat complexity, and plant diversity drive the observed moth diversity patterns.

Water availability, bedrock, disturbance by herbivores, and climate determine plant diversity in South-African savanna.

To identify factors that drive plant species richness in South-African savanna and explore their relative importance, we sampled plant communities across habitats differing in water availability, disturbance, and bedrock, using the Kruger National Park as a model system. We made plant inventories in 60 plots of 50 × 50 m, located in three distinct habitats: (i) at perennial rivers, (ii) at seasonal rivers with water available only during the rainy season, and (iii) on crests, at least ~ 5 km away from any water source. We predicted that large herbivores would utilise seasonal rivers' habitats less intensely than those along perennial rivers where water is available throughout the year, including dry periods. Plots on granite harboured more herbaceous and shrub species than plots on basalt. The dry crests were poorer in herb species than both seasonal and perennial rivers. Seasonal rivers harboured the highest numbers of shrub species, in accordance with the prediction of the highest species richness at relatively low levels of disturbance and low stress from the lack of water. The crests, exposed to relatively low pressure from grazing but stressed by the lack of water, are important from the conservation perspective because they harbour typical, sometimes rare savanna species, and so are seasonal rivers whose shrub richness is stimulated and maintained by the combination of moderate disturbance imposed by herbivores and position in the middle of the water availability gradient. To capture the complexity of determinants of species richness in KNP, we complemented the analysis of the above local factors by exploring large-scale factors related to climate, vegetation productivity, the character of dominant vegetation, and landscape features. The strongest factor was temperature; areas with the highest temperatures reveal lower species richness. Our results also suggest that Colophospermum mopane, a dominant woody species in the north of KNP is not the ultimate cause of the lower plant diversity in this part of the park.

Thirteen moth species (Lepidoptera, Erebidae, Noctuidae) newly recorded in South Africa, with comments on their distribution.

Background: Thanks to the high diversity of ecosystems and habitats, South Africa harbours tremendous diversity of insects. The Kruger National Park, due to its position close to the border between two biogeographic regions and high heterogeneity of environmental conditions, represents an insufficiently studied hotspot of lepidopteran diversity. During our ecological research in the Kruger National Park, we collected abundant moth material, including several interesting faunistic records reported in this study. New information: We reported 13 species of moths which had not yet been recorded in South Africa. In many cases, our records represented an important extension of the species' known distribution, including two species (Ozarbagaedei and O.persinua) whose distribution ranges extended into the Zambezian biogeographic region. Such findings confirmed the poor regional knowledge of lepidopteran diversity.

Range size heritability in Carnivora is driven by geographic constraints.

Range size heritability refers to an intriguing pattern where closely related species occupy geographic ranges of similar extent. Its existence may indicate selection on traits emergent only at the species level, with interesting consequences for evolutionary processes. We explore whether range size heritability may be attributable to the fact that range size is largely driven by the size of geographic domains (i.e., continents, biomes, areas given by species' climatic tolerance) that tend to be similar in phylogenetically related species. Using a well-resolved phylogeny of Carnivora, we show that range sizes are indeed constrained by geographic domains and that the phylogenetic signal in range sizes diminishes if the domain sizes are accounted for. Moreover, more detailed delimitation of species' geographic domain leads to a weaker signal in range size heritability, indicating the importance of definition of the null model against which the pattern is tested. Our findings do not reject the hypothesis of range size heritability but rather unravel its underlying mechanisms. Additional analyses imply that evolutionary conservatism in niche breadth delimits the species' geographic domain, which in turn shapes the species' range size. Range size heritability patterns thus emerge as a consequence of this interplay between evolutionary and geographic constraints.

Between geometry and biology: the problem of universality of the species-area relationship.

The species-area relationship (SAR) is considered to be one of a few generalities in ecology, yet a universal model of its shape and slope has remained elusive. Recently, Harte et al. argued that the slope of the SAR for a given area is driven by a single parameter, the ratio between total number of individuals and number of species (i.e., the mean population size across species at a given scale). We provide a geometric interpretation of this dependence. At the same time, however, we show that this dependence cannot be universal across taxa: if it holds for a taxon composed from two subsets of species and also for one of its subsets, it cannot simultaneously hold for the other subset. Using three data sets, we show that the slope of the SAR considerably varies around the prediction. We estimate the limits of this variation by using geometric considerations, providing a theory based on species spatial turnover at different scales. We argue that the SAR cannot be strictly universal, but its slope at each particular scale varies within the constraints given by species' spatial turnover at finer spatial scales, and this variation is biologically informative.