We provide a framework to upscale biodiversity in tropical forests from local samples of species richness and abundances.

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. (1), also known as fluctuation scaling in physics, is one of the most verified patterns in both the biological (2-6) and physical (7-12) sciences. TL states that the variance of a nonnegative random variable V = Var½X is approximately related to its mean M = E½X by a power law; that is, Var½X = aE½X b , with a > 0 and b ∈ R. In ecology, the random variable of interest is generally the size or density N of a censused population and TL can arise in time (i.e., the statistics of N are computed over time) or in space (i.e., the statistics are computed over space). The widespread verification of TL has led many authors to suggest the existence of a universal mechanism for its emergence, although there is currently no consensus on what such a mechanism would be. Various approaches have been used in the attempt, ranging from the study of probability distributions compatible with the law Here, we distinguish between values of b derived from empirical fitting (sample exponents) and values obtained via theoretical models that pertain to the probability distribution of the random variable N (population exponents). We show that in a broad class of multiplicative growth models, the sample and population exponents coincide only if the number of observed samples or replicates is greater than an exponential function of the duration of observation. Among the relevant consequences, we demonstrate that the sample TL exponent robustly settles on b ' 2 for any ...

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.

We propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.