Feasibility and coexistence of large ecological communities

The role of species interactions in controlling the interplay between the stability of ecosystems and their biodiversity is still not well understood. The ability of ecological communities to recover after small perturbations of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the conditions change (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strengths and ecological network structure on the volume of parameter space leading to feasible equilibria. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence. We show that feasibility is determined by few quantities describing the interactions, yielding a nontrivial complexity–feasibility relationship. Analysing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions

Towards an Evolutionary Interpretation of Aggregate Labor Market Regularities

Three well-known aggregate regularities (i.e. Beveridge, Wage, and Okun's curves) seem to provide a quite complete picture of the interplay between labor market macro-dynamics and business cycle. Nevertheless, existing theoretical literature still lacks micro-founded models which are able to jointly account for these three crucial stylized facts. In this paper, we present an agent-based, evolutionary, model trying to formalize from the bottom up individual behaviors and interactions in both product and labor markets. We describe as endogenous processes both vacancy and wage setting, as well as matching and bargaining, demand and price formation. Firms enjoy labor productivity improvements (technological progress) and are selected on the base of their revealed competitiveness (which is also affected by their hiring- and wage-setting behaviors). Simulations show that the model is able to robustly reproduce Beveridge, Wage and Okun's curves under quite broad behavioral and institutional settings. Moreover, the system generates endogenously an Okun's coefficient greater than one even if individual firms employ production functions exhibiting constant returns to labor. Montecarlo simulations also indicate that statistically detectable shifts in Okun's and Beveridge curves emerge as the result of changes in institutional, behavioral, and technological parameters. Finally, the model generates quite sharp predictions about how system parameters affect aggregate performance (i.e. average GDP growth) and its volatility.Labor Markets, Dynamics, Aggregate Regularities, Beveridge Curve, Okun Curve, Wage Curve, Matching Models

How Much is the Whole Really More than the Sum of its Parts? 1 + 1 = 2.5: Superlinear Productivity in Collective Group Actions

In a variety of open source software projects, we document a superlinear growth of production ($R \sim c^\beta$) as a function of the number of active developers $c$, with $\beta \simeq 4/3$ with large dispersions. For a typical project in this class, doubling of the group size multiplies typically the output by a factor $2^\beta=2.5$, explaining the title. This superlinear law is found to hold for group sizes ranging from 5 to a few hundred developers. We propose two classes of mechanisms, {\it interaction-based} and {\it large deviation}, along with a cascade model of productive activity, which unifies them. In this common framework, superlinear productivity requires that the involved social groups function at or close to criticality, in the sense of a subtle balance between order and disorder. We report the first empirical test of the renormalization of the exponent of the distribution of the sizes of first generation events into the renormalized exponent of the distribution of clusters resulting from the cascade of triggering over all generation in a critical branching process in the non-meanfield regime. Finally, we document a size effect in the strength and variability of the superlinear effect, with smaller groups exhibiting widely distributed superlinear exponents, some of them characterizing highly productive teams. In contrast, large groups tend to have a smaller superlinearity and less variability.Comment: 29 pages, 8 figure

Beyond a Company of Soldiers: Exploring Phenotypic Integration across the Multivariate Human Growth and Development Phenotype

Traditional studies exploring the interrelationships between growth and development traits have lacked the data necessary to fully describe the multivariate growth and development phenotype and the statistical methodology to quantify the complex interrelationships between varied trait types. Subsequently, human growth and development are often defined by a series of contrasts via the juxtaposition of seemingly disjoint processes in skeletal diaphyseal growth, skeletal ossification and fusion, and development of the dentition. In conjunction with robust data sources from the Subadult Virtual Anthropology Databases (SVAD), this work introduces a Mixed Discrete-Continuous Gaussian copula to explore the multivariate human growth and development phenotype. A copula is a probabilistic function that explicitly models the interrelationships between traits and describes the joint structure of the multivariate relationships.Fifty-four growth traits are collected from the United States sample in SVAD (n = 1,316). These traits include 18 measurements associated with diaphyseal dimensions collected from six long bones, 20 scores of both epiphyseal fusion and primary ossification centers, and 16 scores of dental development across the left-sided mandibular and maxillary dentition. All data are collected from computed tomography (CT) images and includes demographic information such as an individual’s chronological age and biological sex. The joint probability distribution of the 54 growth traits and the underlying dependency structure are fit to a Mixed Discrete-Continuous Gaussian copula using the gradient-based Markov Chain Monte Carlo algorithm known as Hamiltonian Monte Carlo within the Stan probabilistic programming environment. Six total copula models are fit: the first model utilizes the full dataset, the next three models use subsets of the full dataset representing the individual developmental stages of infancy, childhood, and juvenile/adolescence, and the last two models use subset of the full dataset representing biological males and females.Results from the full model show that relationships are strongest within each growth module. Further, traits that develop across similar developmental windows show stronger positive correlations as compared to traits that grow and develop during separate periods. These relationships are similar between males and females suggesting that, independent of age, multivariate growth and development processes are the same across the sexes. When considering developmental stages, the results show that the multivariate phenotype presents with different relationships between variables across ontogeny with the strongest relationships between growth and development modules tied to active growth and development periods. Importantly, the skeletal growth, skeletal development, and dental development modules can be further divided into additional units that themselves have various levels of dependence.The copula demonstrates that the relationships between broad growth modules cannot be summarized via a few pairwise correlations taken at one point during ontogeny. Instead, analyses should be conducted with as much trait information as possible and at various points throughout ontogeny. In the future, copulas could also be extended to additional applications in biological anthropology including research in bioarchaeology and paleoanthropology, method formation in forensic anthropology, and the estimation and imputation of missing data. In sum, the Mixed Discrete-Continuous Gaussian copula provides the most comprehensive analysis to date of the multivariate human growth and development phenotype and lays the groundwork for future research into the growing, developing, multivariate human

Covariate-assisted ranking and screening for large-scale two-sample inference

Two-sample multiple testing has a wide range of applications. The conventionalpractice first reduces the original observations to a vector of p-values and then chooses a cutoffto adjust for multiplicity. However, this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures.We introduce a new framework fortwo-sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power. A data-driven multiple-testing procedure is developed by employinga covariate-assisted ranking and screening (CARS) approach that optimally combines the informationfrom both the primary and the auxiliary variables. The proposed CARS procedureis shown to be asymptotically valid and optimal for false discovery rate control. The procedureis implemented in the R package CARS. Numerical results confirm the effectiveness of CARSin false discovery rate control and show that it achieves substantial power gain over existingmethods. CARS is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection