On estimating the exponent of power-law frequency distributions

Power-law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power-laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning-based methods traditionally utilized in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation out-performs other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Evolving ecological networks and the emergence of biodiversity patterns across temperature gradients

In ectothermic organisms, it is hypothesized that metabolic rates mediate influences of temperature on the ecological and evolutionary processes governing biodiversity. However, it is unclear how and to what extent the influence of temperature on metabolism scales up to shape large-scale diversity patterns. In order to clarify the roles of temperature and metabolism, new theory is needed. Here, we establish such theory and model eco-evolutionary dynamics of trophic networks along a broad temperature gradient. In the model temperature can influence, via metabolism, resource supply, consumers' vital rates and mutation rate. Mutation causes heritable variation in consumer body size, which diversifies and governs consumer function in the ecological network. The model predicts diversity to increase with temperature if resource supply is temperature-dependent, whereas temperature-dependent consumer vital rates cause diversity to decrease with increasing temperature. When combining both thermal dependencies, a unimodal temperature–diversity pattern evolves, which is reinforced by temperature-dependent mutation rate. Studying coexistence criteria for two consumers showed that these outcomes are owing to temperature effects on mutual invasibility and facilitation. Our theory shows how and why metabolism can influence diversity, generates predictions useful for understanding biodiversity gradients and represents an extendable framework that could include factors such as colonization history and niche conservatism

Signature of relic heavy stable neutrinos in underground experiments

Considering heavy stable neutrinos of 4th generation we calculate the relic density of such neutrinos in the Universe. Taking into account the condensation of heavy neutrinos in the Galaxy and applying the results of calculations to experimental data from underground experiments on search for WIMPs in elastic neutral current scattering on nuclei we found an exclusion region of neutrino mass 60 GeV < m < 290 GeV. The bounds obtained from present underground experiments while confirming the previous bounds derived from analysis of cosmic ray spectra are more relible ones. We discuss also the first indication of elastic scattering induced by WIMP in DAMA experiment finding a very narrow window of neutrino mass 45 GeV < m < 50 GeV compatible with the possible signal rate in the detector.Comment: 12 pages, 3 figure

Drought survival is positively associated with high turgor loss points in temperate perennial grassland species

1. Turgor loss point (πtlp) has been suggested to be a key trait for drought resistance in woody species. In herbaceous grassland species the role of πtlp for species drought survival has not yet been tested, although grasslands are projected to experience more frequent and intense droughts with climate change. 2. To gain insights into the role of πtlp for drought resistance of temperate perennial grassland species, we assessed πtlp of 41 species common in Germany (20 forbs, 21 grasses). We directly related them to the species' comparative whole-plant drought survival and midday leaf water potentials under drought (ΨMD) assessed in a common garden drought experiment, and to species moisture association. 3. Species drought survival increased with increasing πtlp across all species as well as within forbs or grasses separately. ΨMD was positively related to πtlp and drought survival. Our results imply that high πtlp promotes drought survival of common perennial European temperate mesic grassland species by enabling them to maintain high leaf water potentials under drought, i.e., a desiccation avoidance strategy. However, πtlp was not related to species moisture association. 4. The positive relationship between πtlp and drought survival in herbaceous grassland species was opposite to the negative relationship previously established in woody plants, implying that mechanisms of drought resistance differ between woody and herbaceous species. Our results highlight the necessity of directly testing the relationship of functional traits to whole-plant drought survival in different plant life forms, before using trait assessments for predicting plant responses to drought.Funding provided by: DFG Priority Program 1374Crossref Funder Registry ID: Award Number: Infrastructure-Biodiversity-Exploratorie

The ghosts of forests past and future : deforestation and botanical sampling in the Brazilian Amazon

The remarkable biodiversity of the Brazilian Amazon is poorly documented and threatened by deforestation. When undocumented areas become deforested, in addition to losing the fauna and flora, we lose the opportunity to know which unique species had occupied a habitat. Here we quantify such knowledge loss by calculating how much of the Brazilian Amazon has been deforested and will likely be deforested until 2050 without having its tree flora sufficiently documented. To this end, we analysed 399 147 digital specimens of nearly 6000 tree species in relation to official deforestation statistics and future deforestation scenarios. We find that by 2017, 30% of all the localities where tree specimens had been collected were mostly deforested. Some 300 000 km(2)(12%; 485 25 x 25 km grid cells) of the Brazilian Amazon had been deforested by 2017, without having a single tree specimen recorded. An additional 250 000-900 000 km(2)of severely under-collected rainforest will likely become deforested by 2050. If future tree sampling is to cover this area, sampling effort has to increase two- to six-fold. Nearly 255 000 km(2)or 7% of rainforest in the Brazilian Amazon is easily accessible but does yet but remain under-collected. Our study highlights how progressing deforestation increases the risk of losing undocumented species of a hyper-diverse tree flora.Peer reviewe

The Plant Diversity Sampling Design for The National Ecological Observatory Network

The National Ecological Observatory Network (NEON) is designed to facilitate an understanding of the impact of environmental change on ecological systems. Observations of plant diversity—responsive to changes in climate, disturbance, and land use, and ecologically linked to soil, biogeochemistry, and organisms—result in NEON data products that cross a range of organizational levels. Collections include samples of plant tissue to enable investigations of genetics, plot-based observations of incidence and cover of native and non-native species, observations of plant functional traits, archived vouchers of plants, and remote sensing airborne observations. Spatially integrating many ecological observations allows a description of the relationship of plant diversity to climate, land use, organisms, and substrates. Repeating the observations over decades and across the United States will iteratively improve our understanding of those relationships and allow for the testing of system-level hypotheses as well as the development of predictions of future conditions

A Dual Infection Pseudorabies Virus Conditional Reporter Approach to Identify Projections to Collateralized Neurons in Complex Neural Circuits

Replication and transneuronal transport of pseudorabies virus (PRV) are widely used to define the organization of neural circuits in rodent brain. Here we report a dual infection approach that highlights connections to neurons that collateralize within complex networks. The method combines Cre recombinase (Cre) expression from a PRV recombinant (PRV-267) and Cre-dependent reporter gene expression from a second infecting strain of PRV (PRV-263). PRV-267 expresses both Cre and a monomeric red fluorescent protein (mRFP) fused to viral capsid protein VP26 (VP26-mRFP) that accumulates in infected cell nuclei. PRV-263 carries a Brainbow cassette and expresses a red (dTomato) reporter that fills the cytoplasm. However, in the presence of Cre, the dTomato gene is recombined from the cassette, eliminating expression of the red reporter and liberating expression of either yellow (EYFP) or cyan (mCerulean) cytoplasmic reporters. We conducted proof-of-principle experiments using a well-characterized model in which separate injection of recombinant viruses into the left and right kidneys produces infection of neurons in the renal preautonomic network. Neurons dedicated to one kidney expressed the unique reporters characteristic of PRV-263 (cytoplasmic dTomato) or PRV-267 (nuclear VP26-mRFP). Dual infected neurons expressed VP26-mRFP and the cyan or yellow cytoplasmic reporters activated by Cre-mediated recombination of the Brainbow cassette. Differential expression of cyan or yellow reporters in neurons lacking VP26-mRFP provided a unique marker of neurons synaptically connected to dual infected neurons, a synaptic relationship that cannot be distinguished using other dual infection tracing approaches. These data demonstrate Cre-enabled conditional reporter expression in polysynaptic circuits that permits the identification of collateralized neurons and their presynaptic partners