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The study of experimental communities is fundamental to the development of ecol-1 ogy. Yet, for most ecological systems, the number of experiments required to build, 2 model, or analyze the community vastly exceeds what is feasible using current meth-3 ods. Here, we address this challenge by presenting a statistical approach that uses 4 the results of a limited number of experiments to predict the outcomes (coexistence 5 and species abundances) of all possible assemblages that can be formed from a 6 given pool of species. Using three well-studied experimental systems-encompassing 7 plants, protists, and algae with grazers-we show that this method predicts with 8 high accuracy the results of unobserved experiments, while making no assumptions 9 about the dynamics of the systems. These results suggest a fundamentally different 10 study design for building and quantifying experimental systems, requiring a small 11 number of experiments relative to traditional approaches. By providing a scalable 12 method for navigating large systems, this work provides an efficient way to study 13 highly diverse experimental communities. 14 1 Results 60 Empirical systems 61To demonstrate this method, we first analyze published data of three experimental systems. Although 62 these studies were not specifically designed to test our method, each study reports the final abundances 63 of all species in each experimental assemblage, and each contains a sufficient number of unique 64 assemblages to benchmark the method by making out-of-fit predictions. 65 First, we consider data from Kuebbing et al. 11 , who conducted growth experiments using two 66 phylogenetically paired sets of old-field plants. Both sets contain four species, drawn from the fam-67 ilies Asteraceae, Fabaceae, Lamiaceae, and Poaceae. In one set, all species are native to the study 68 site; in the other, all species are non-native. For both the native and non-native pools, experimental 69 communities were initialized with 14 out of 15 (= 2 4 − 1) possible assemblages, with each combina-70 tion replicated 10 times. Dry-weight aboveground biomass for each species in each assemblage was 71 recorded after 112 days of growth 11 . 72 Second, we analyze data from Rakowski and Cardinale 12 , who grew consumer-resource commu-73 nities consisting of five species of green algae and two herbivorous species from the family Daphni-74 idae (Ceriodaphnia dubia and Daphnia pulex). Here we focus on the four algal species that survived in 75 a sufficient number of endpoints to test our method: Chlorella sorokiniana, Scenedesmus acuminatus, 76 Monoraphidium minutum, and Monoraphidium arcuatum. The algae were grown in all four-species 77 combinations with high replication, and one of the two herbivores was added to two-thirds of the repli-78 cates. The communities were incubated for 28 days, during which time each assemblage collapsed to 79 a subset of the initial pool, generating a variety of distinct endpoints. 80 Third, we turn to time-series data published by Pennekamp et al. 13 , who stu...

Across the tree of life, organisms modify their local environment, rendering it more or less hospitable for other species. Despite the ubiquity of these processes, simple models that can be used to develop intuitions about the consequences of widespread habitat modification are lacking. Here, we extend the classic Levins metapopulation model to a setting where each of n species can colonize patches connected by dispersal, and when patches are vacated via local extinction, they retain a “memory” of the previous occupant—modeling habitat modification. While this model can exhibit a wide range of dynamics, we draw several overarching conclusions about the effects of modification and memory. In particular, we find that any number of species may potentially coexist, provided that each is at a disadvantage when colonizing patches vacated by a conspecific. This notion is made precise through a quantitative stability condition, which provides a way to unify and formalize existing conceptual models. We also show that when patch memory facilitates coexistence, it generically induces a positive relationship between diversity and robustness (tolerance of disturbance). Our simple model provides a portable, tractable framework for studying systems where species modify and react to a shared landscape.

Plant-soil feedbacks (PSFs) are considered a key mechanism generating frequencydependent dynamics in plant communities. Negative feedbacks, in particular, are often invoked to explain coexistence and the maintenance of diversity in speciesrich communities. However, the primary modelling framework used to study PSFs considers only two plant species, and we lack clear theoretical expectations for how these complex interactions play out in communities with natural levels of diversity.Here, we extend this canonical model of PSFs to include an arbitrary number of plant species and analyse the dynamics. Surprisingly, we find that coexistence of more than two species is virtually impossible, suggesting that alternative theoretical frameworks are needed to describe feedbacks observed in diverse natural communities. Drawing on our analysis, we discuss future directions for PSF models and implications for experimental study of PSF-mediated coexistence in the field.

In an experimental setting, the composition of ecological communities can be manipulated directly. Starting from a pool of n species, it is possible to co‐culture species in different combinations, ranging from monocultures, to pairs, and all the way up to the full species pool. Leveraging datasets with this experimental design, we advance methods to infer species interactions using density measurements taken at a single time point across a variety of distinct community compositions. First, we introduce a fast and robust algorithm to estimate parameters for simple statistical models describing these data, which can be combined with likelihood maximization approaches. Second, we derive from consumer–resource dynamics a family of statistical models with few parameters, which can be applied to study systems where only a small fraction of the potential community compositions have been observed. Third, we show how a Weighted Least Squares framework can be used to account for the fact that species abundances often display a strong relationship between means and variances. To illustrate our approach, we analyse datasets spanning plant, bacteria and phytoplankton communities, as well as simulations, consistently recovering a good fit to the data and demonstrating the ability of our methods to predict equilibrium densities in out‐of‐sample communities. By combining more robust model structures and fitting procedures along with a more flexible error model, we greatly extend the applicability of recently proposed methods to model community composition from experimental data, opening the door for the analysis of larger pools of species using sparser and noisier datasets than was previously possible.