Predicting subgroup treatment effects for a new study: Motivations, results and learnings from running a data challenge in a pharmaceutical corporation.

We present the motivation, experience, and learnings from a data challenge conducted at a large pharmaceutical corporation on the topic of subgroup identification. The data challenge aimed at exploring approaches to subgroup identification for future clinical trials. To mimic a realistic setting, participants had access to 4 Phase III clinical trials to derive a subgroup and predict its treatment effect on a future study not accessible to challenge participants. A total of 30 teams registered for the challenge with around 100 participants, primarily from Biostatistics organization. We outline the motivation for running the challenge, the challenge rules, and logistics. Finally, we present the results of the challenge, the participant feedback as well as the learnings. We also present our view on the implications of the results on exploratory analyses related to treatment effect heterogeneity.

The stochastic logistic model with correlated carrying capacities reproduces beta-diversity metrics of microbial communities.

The large taxonomic variability of microbial community composition is a consequence of the combination of environmental variability, mediated through ecological interactions, and stochasticity. Most of the analysis aiming to infer the biological factors determining this difference in community structure start by quantifying how much communities are similar in their composition, trough beta-diversity metrics. The central role that these metrics play in microbial ecology does not parallel with a quantitative understanding of their relationships and statistical properties. In particular, we lack a framework that reproduces the empirical statistical properties of beta-diversity metrics. Here we take a macroecological approach and introduce a model to reproduce the statistical properties of community similarity. The model is based on the statistical properties of individual communities and on a single tunable parameter, the correlation of species' carrying capacities across communities, which sets the difference of two communities. The model reproduces quantitatively the empirical values of several commonly-used beta-diversity metrics, as well as the relationships between them. In particular, this modeling framework naturally reproduces the negative correlation between overlap and dissimilarity, which has been observed in both empirical and experimental communities and previously related to the existence of universal features of community dynamics. In this framework, such correlation naturally emerges due to the effect of random sampling.

Generalized size scaling of metabolic rates based on single-cell measurements with freshwater phytoplankton.

Kleiber's law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber's law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber's law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber's law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

Covariations in ecological scaling laws fostered by community dynamics.

Scaling laws in ecology, intended both as functional relationships among ecologically relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances, and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked has been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply, and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations.

On the probabilistic nature of the species-area relation.

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR.

A macroecological description of alternative stable states reproduces intra- and inter-host variability of gut microbiome.

The most fundamental questions in microbial ecology concern the diversity and variability of communities. Their composition varies widely across space and time, as a result of a nontrivial combination of stochastic and deterministic processes. The interplay between nonlinear community dynamics and environmental fluctuations determines the rich statistical structure of community variability. We analyze long time series of individual human gut microbiomes and compare intra- and intercommunity dissimilarity under a macroecological framework. We show that most taxa have large but stationary fluctuations over time, while a minority of taxa display rapid changes in average abundance that cluster in time, suggesting the presence of alternative stable states. We disentangle interindividual variability in a stochastic component and a deterministic one, the latter recapitulated by differences in carrying capacities. Last, by combining environmental fluctuations and alternative stable states, we introduce a model that quantitatively predicts the statistical properties of both intra- and interindividual community variability, therefore summarizing variation in a unique macroecological framework.

Betweenness centrality for temporal multiplexes.

Betweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of [Formula: see text]k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.

Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time.

In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the walks that can be travelled according to the network temporal structure, i.e. "trips", while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports' centrality losses due to delays in the flight network.