REVIEW AND SYNTHESIS Evolutionarily stable communities: a framework for understanding the role of trait evolution in the maintenance of diversity Kyle F. Edwards, 1, * Colin T. Kremer, 2,3,4 Elizabeth T. Miller, 5 Matthew M. Osmond, 6 Elena Litchman, 3,4,7 and Christopher A. Klausmeier 3,4,8 Abstract Biological diversity depends on the interplay between evolutionary diversification and ecological mechanisms allowing species to coexist. Current research increasingly integrates ecology and evo- lution over a range of timescales, but our common conceptual framework for understanding spe- cies coexistence requires better incorporation of evolutionary processes. Here, we focus on the idea of evolutionarily stable communities (ESCs), which are theoretical endpoints of evolution in a community context. We use ESCs as a unifying framework to highlight some important but under-appreciated theoretical results, and we review empirical research relevant to these theoreti- cal predictions. We explain how, in addition to generating diversity, evolution can also limit diver- sity by reducing the effectiveness of coexistence mechanisms. The coevolving traits of competing species may either diverge or converge, depending on whether the number of species in the com- munity is low (undersaturated) or high (oversaturated) relative to the ESC. Competition in over- saturated communities can lead to extinction or neutrally coexisting, ecologically equivalent species. It is critical to consider trait evolution when investigating fundamental ecological ques- tions like the strength of different coexistence mechanisms, the feasibility of ecologically equiva- lent species, and the interpretation of different patterns of trait dispersion. Keywords Adaptive dynamics, adaptive landscape, character displacement, coexistence, eco-evolutionary dynamics, ecological equivalence, ESS. Ecology Letters (2018) 21: 1853–1868 INTRODUCTION To understand the origin and maintenance of biological diver- sity, it is necessary to dissect the integrated effects of evolu- tionary and ecological processes. Genetic diversity is ultimately generated by mutation, and the fate of new muta- tions is determined by a combination of drift and selection. Selection takes many forms and is often driven by ecological interactions such as competition, predation and mutualism. These interactions therefore influence how species evolve and can thereby enhance or diminish the diversity (species rich- ness) of communities. Meanwhile, ecological interactions themselves are affected by the (co-)evolutionary change of species. Although these general principles have been long understood (Darwin 1859; Brown & Wilson 1956; Hutchinson 1965), disentangling the interplay of ecological and evolutionary processes in natural communities remains a diffi- cult challenge. A greater appreciation of the possibility of rapid evolution (Reznick et al. 1990; Hairston et al. 1999; Grant & Grant 2002) has invigorated the study of eco-evolutionary dynamics, or the interplay of ecological and evolutionary processes on similar timescales (Fussmann et al. 2007; Lankau 2011; Scho- ener 2011). The reciprocal effects of environmental conditions on trait evolution, and of trait change on environmental con- ditions, can lead to eco-evolutionary feedbacks that are essen- tial for understanding the outcome of species interactions (Yoshida et al. 2003; Bull et al. 2006; Post & Palkovacs 2009, Hanski 2011). Ecological theory has increasingly included evo- lutionary processes by assuming that the parameters repre- senting species’ traits are not constant over time, but rather evolve in response to selection caused by abiotic and biotic 1 Department of Oceanography, University of Hawai’i at Manoa, Honolulu, HI 96822, USA 2 Department of Ecology & Evolutionary Biology, Yale University, New Haven, CT 06520, USA 3 Kellogg Biological Station, Michigan State University, Hickory Corners, MI 49060, USA 4 Program in Ecology, Evolutionary Biology, & Behavior, Michigan State University, East Lansing, MI 48824, USA 5 Institute of Ecology and Evolution, University of Oregon, Eugene, OR 97403, USA 6 Department of Zoology, University of British Columbia, Vancouver, BC V6T 1Z4, USA 7 Department of Integrative Biology, Michigan State University, East Lansing, MI 48824, USA 8 Department of Plant Biology, Michigan State University, East Lansing, MI 48824, USA *Correspondence: E-mail: kfe@hawaii.edu © 2018 John Wiley & Sons Ltd/CNRS Ecology Letters, (2018) 21: 1853–1868 doi: 10.1111/ele.13142