Unifying ecosystem ecology and evolutionary biology promises a more complete understanding of the processes that link different levels of biological organization across space and time. Feedbacks across levels of organization link theory associated with eco‐evolutionary dynamics, niche construction and the geographic mosaic theory of co‐evolution. We describe a conceptual model, which builds upon previous work that shows how feedback among different levels of biological organization can link ecosystem and evolutionary processes over space and time. We provide empirical examples across terrestrial and aquatic systems that indicate broad generality of the conceptual framework and discuss its macroevolutionary consequences. Our conceptual model is based on three premises: genetically based species interactions can vary spatially and temporally from positive to neutral (i.e. no net feedback) to negative and drive evolutionary change; this evolutionary change can drive divergence in niche construction and ecosystem function; and lastly, such ecosystem‐level effects can reinforce spatiotemporal variation in evolutionary dynamics. Just as evolution can alter ecosystem function locally and across the landscape differently, variation in ecosystem processes can drive evolution locally and across the landscape differently. By highlighting our current knowledge of eco‐evolutionary feedbacks in ecosystems, as well as information gaps, we provide a foundation for understanding the interplay between biodiversity and ecosystem function through an eco‐evolutionary lens. A http://onlinelibrary.wiley.com/doi/10.1111/1365-2435.13267/suppinfo is available for this article.

A scientific understanding of the biological world arises when ideas about how nature works are formalized, tested, refined, and then tested again. Although the benefits of feedback between theoretical and empirical research are widely acknowledged by ecologists, this link is still not as strong as it could be in ecological research. This is in part because theory, particularly when expressed mathematically, can feel inaccessible to empiricists who may have little formal training in advanced math. To address this persistent barrier, we provide a general and accessible guide that covers the basic, step-by-step process of how to approach, understand, and use ecological theory in empirical work. We first give an overview of how and why mathematical theory is created, then outline four specific ways to use both mathematical and verbal theory to motivate empirical work, and finally present a practical tool kit for reading and understanding the mathematical aspects of ecological theory. We hope that empowering empiricists to embrace theory in their work will help move the field closer to a full integration of theoretical and empirical research.

The patterns and outcomes of coevolution are expected to depend on intraspecific trait variation.Various evolutionary factors can change this variation in time. As a result, modeling coevolu-3 tionary processes solely in terms of mean trait values may not be sufficient; one may need to study the dynamics of the whole trait distribution. Here, we develop a theoretical framework for studying the effects of evolving intraspecific variation in two-species coevolutionary systems. 6In particular, we build and study mathematical models of competition, exploiter-victim interactions, and mutualism in which the strength of within-and between-species interactions depends on the difference in continuously varying traits. We use analytical approximations based on the 9 invasion analysis and supplement it with a numerical method. We find that intraspecific variation can be maintained if stabilizing selection is weak in at least one species. When intraspecific variation is maintained, stable coexistence is promoted by small ranges of interspecific interac-12 tion in two-species competition and mutualism, and large ranges in exploiter-victim interactions.We show that trait distributions can become multimodal. Our approach and results contribute to the understanding of the ecological consequences of intraspecific variation in coevolutionary 15 systems by exploring its effects on population densities and trait distributions. 2. CC-BY-NC-ND 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is madeThe copyright holder for this preprint this version posted March 10, 2020. ;

Theories underpin science. In biology, theories are often formalized in the form of mathematical models, which may render them inaccessible to those lacking mathematical training. In the present article, we consider how theories could be presented to better aid understanding. We provide concrete recommendations inspired by cognitive load theory, a branch of psychology that addresses impediments to knowledge acquisition. We classify these recommendations into two classes: those that increase the links between new and existing information and those that reduce unnecessary or irrelevant complexities. For each, we provide concrete examples to illustrate the scenarios in which they apply. By enhancing a reader's familiarity with the material, these recommendations lower the mental capacity required to learn new information. Our hope is that these recommendations can provide a pathway for theoreticians to increase the accessibility of their work and for empiricists to engage with theory, strengthening the feedback between theory and experimentation.