Optimal entropic properties of SARS-CoV-2 RNA sequences.

The reaction of the scientific community against the COVID-19 pandemic has generated a huge (approx. 106 entries) dataset of genome sequences collected worldwide and spanning a relatively short time window. These unprecedented conditions together with the certain identification of the reference viral genome sequence allow for an original statistical study of mutations in the virus genome. In this paper, we compute the Shannon entropy of every sequence in the dataset as well as the relative entropy and the mutual information between the reference sequence and the mutated ones. These functions, originally developed in information theory, measure the information content of a sequence and allows us to study the random character of mutation mechanism in terms of its entropy and information gain or loss. We show that this approach allows us to set in new format known features of the SARS-CoV-2 mutation mechanism like the CT bias, but also to discover new optimal entropic properties of the mutation process in the sense that the virus mutation mechanism track closely theoretically computable lower bounds for the entropy decrease and the information transfer.

Upscaling human activity data: A statistical ecology approach.

Big data require new techniques to handle the information they come with. Here we consider four datasets (email communication, Twitter posts, Wikipedia articles and Gutenberg books) and propose a novel statistical framework to predict global statistics from random samples. More precisely, we infer the number of senders, hashtags and words of the whole dataset and how their abundances (i.e. the popularity of a hashtag) change through scales from a small sample of sent emails per sender, posts per hashtag and word occurrences. Our approach is grounded on statistical ecology as we map inference of human activities into the unseen species problem in biodiversity. Our findings may have applications to resource management in emails, collective attention monitoring in Twitter and language learning process in word databases.

Reconciling cooperation, biodiversity and stability in complex ecological communities.

Empirical evidences show that ecosystems with high biodiversity can persist in time even in the presence of few types of resources and are more stable than low biodiverse communities. This evidence is contrasted by the conventional mathematical modeling, which predicts that the presence of many species and/or cooperative interactions are detrimental for ecological stability and persistence. Here we propose a modelling framework for population dynamics, which also include indirect cooperative interactions mediated by other species (e.g. habitat modification). We show that in the large system size limit, any number of species can coexist and stability increases as the number of species grows, if mediated cooperation is present, even in presence of exploitative or harmful interactions (e.g. antibiotics). Our theoretical approach thus shows that appropriate models of mediated cooperation naturally lead to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.

Upscaling species richness and abundances in tropical forests.

The quantification of tropical tree biodiversity worldwide remains an open and challenging problem. More than two-fifths of the number of worldwide trees can be found either in tropical or in subtropical forests, but only ≈0.000067% of species identities are known. We introduce an analytical framework that provides robust and accurate estimates of species richness and abundances in biodiversity-rich ecosystems, as confirmed by tests performed on both in silico-generated and real forests. Our analysis shows that the approach outperforms other methods. In particular, we find that upscaling methods based on the log-series species distribution systematically overestimate the number of species and abundances of the rare species. We finally apply our new framework on 15 empirical tropical forest plots and quantify the minimum percentage cover that should be sampled to achieve a given average confidence interval in the upscaled estimate of biodiversity. Our theoretical framework confirms that the forests studied are comprised of a large number of rare or hyper-rare species. This is a signature of critical-like behavior of species-rich ecosystems and can provide a buffer against extinction.

Rhythmic behavior in a two-population mean-field Ising model.

Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.

Neutral dynamics with environmental noise: Age-size statistics and species lifetimes.

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic [O√N)] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems--age-size relationships and species extinction time--in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of "zero mean" environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics, and discuss their relevance to realistic models of community dynamics.

Sample and population exponents of generalized Taylor's law.

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.