AbstractTheory is a small but critical component of the biological research process, and complements observational and experimental approaches. However, early career biologists receive little training on how to frame a theoretical question and, thus, how to evaluate when theory has successfully answered the research question. Here we develop a guide with six verbal framings for theoretical models in biology. These correspond to different roles one might play as a theorist: “Advocate”, “Explainer”, “Instigator”, “Mediator”, “Semantician”, and “Tinkerer”. These are drawn from combinations of two starting points (pattern or mechanism) and three foci (novelty, robustness, or conflict). We illustrate each of these framings with examples of specific theoretical questions, by drawing on recent theoretical papers in the fields of ecology and evolutionary biology. We show how the same research topic can be approached from slightly different perspectives, using different framings. We show how clarifying a model’s framing can debunk common misconceptions of theory: that simplifying assumptions are bad, more detail is always better, models show anything you want, and modelling requires substantial math knowledge. Finally, we provide a roadmap that early career researchers can use to identify a framing to serve as a blueprint for their own theoretical research projects.Keywords:mathematical biology, methodology, narratives, pedagogy, scientific writing, theoretical ecologyTake the theorist personality quiz here: https://z.umn.edu/theorypersonality Introduction Theory is a critical component of how biology (and science broadly) is conducted, and complements experimental and observational approaches. Theory serves many purposes, including to explore logical consistency of ideas, to identify the simplest model that can predict observed phenomena, to demonstrate the complexity of a situation, to suggest ways of looking at empirical data, to generate novel hypotheses, and to explore possible ranges of behaviour of a system [1,2]. Theory can take a range of forms including verbal, conceptual, computational, and mathematical. Broadly, theory serves as scaffolding [3] that helps us make sense of observations and experiments. Yet, papers with primarily theoretical approaches make up a small portion of the overall biological literature; only 18% of papers in the most theory-heavy journals within ecology and evolutionary biology presented primarily theoretical findings [4,5]. Perhaps due to this small representation, early career scientists in biology receive little training on how to design and interpret theory (particularly mathematical theory) [6], especially compared to the amount of training they receive on experimental approaches. Lack of training could result from an absence of conversation among biologists about best practices for designing and interpreting theory. However, this is clearly not the case; for example, people have debated how to do theory for as long as theoretical ecology has been a field. Levins’ seminal paper [7] argued that the three key aims for models are realism, precision, and generality. Since no model can accomplish all three aims simultaneously, we need different sets of models to prioritise different aims so that we can find true understanding at the point(s) where the results intersect [7]. May [8] cautioned against having an uneven balance of detail in models; including extensive detail in some model aspects while keeping others vague can convey a false sense of how much realism the model includes. In contrast to Levins and May, some researchers have called for prioritising more of one type of theoretical model over others. For example, Holling [9] argued that the field had enough of what he called ‘strategic’ models (that sacrifice precision to focus on generality), but needed more ‘tactical’ models. Evans et al. [10] similarly called for embracing complex models as a means of achieving generality through generating testable predictions. The opposite argument has also been made: Marquet et al. [11] called for the development of more ‘efficient’ theories that have fewer parameters and do not need to be precise. In addition, much has been written arguing for the value of theory in biology as a whole, drawing parallels between how theoretical and empirical studies are conducted in both ecology [1] and evolutionary biology [12]. Yet, conversations within these fields about designing and interpreting theory have not translated into guidance for newcomers on how to conduct and communicate theory. This lack of guidance creates a barrier for scientists new to theoretical research. In response, there have been a number of recent ‘how-to’ guides aimed at breaking down this barrier for early career researchers. For example, recent guides on how to communicate theory to broad audiences include suggestions like clearly stating context and assumptions, reducing irrelevant complexities (adjusting math to the target audience), using clear and standardised mathematical notation, and using analogies and narratives to facilitate links between new and existing information [13,14]. In another how-to guide, Edwards and Auger-Méthé [15] provide advice for choosing mathematical notation. There have also been recent guides on how to read and use mathematical theory in ecology. Shoemaker et al. [13] suggest that readers spend extra time engaging with the math, including breaking down equations into components and working through them with peers, connecting specific equations to a general class of models, and reconstructing models or exploring parameter space to get a better handle on them. Other guides show how to use theoretical frameworks to guide empirical lab and field work, use mathematical equations to make empirically-based calculations, and test either the assumptions or predictions of theory [16,17]. Overall, these suggestions provide guidance for researchers who are either reading broadly before they start a project, or have completed a theoretical research project and want to communicate it clearly. In contrast, there is less guidance for the middle stage in the theory development process: how to choose – and frame – a theoretical research question. This is a critical gap. Even researchers who never pose theoretical research questions themselves will use and evaluate theory (e.g., as guides for experimental or observational work). Thus, we all benefit from understanding how theory is framed in order to help evaluate when theory has been successful. Here, we fill this gap by providing guidance for how to frame theoretical research in biology. Theoretical research often starts out as a verbal model, using reasoning to set up an argument about what is expected to occur. Verbal arguments can only get us so far, and relying on common sense and intuition often leads us astray [18]. It is at these points that turning the verbal (or narrative-based) argument into a mathematical (or computational) form can provide clarity and help extend a verbal argument [19]. Here, we argue that the converse is also true: a clear verbal framing can help improve the usefulness of a mathematical or computational model. Below, we present six ways to frame theoretical research, describing each as a ‘personality type’ or a specific role one might play as a theorist: the “Advocate”, “Explainer”, “Instigator”, “Mediator”, “Semantician”, and “Tinkerer”. We show that these roles are not mutually exclusive; the same question or idea can be framed using multiple roles. Finally, we demonstrate how the ways of thinking that we present can be used to address common misconceptions about theory. Framing theory Theoretical models (also called proof-of-concept models; [12]) are fundamentally about understanding the link between assumptions and outcomes. Another way to view this is that models are about linking ‘patterns’ (outcomes of interest) to ‘mechanisms’ (processes that can generate those outcomes) (Figure 1). When a researcher starts developing a theoretical model, they typically have a sense of both what mechanism(s) they want to include and what pattern(s) to expect. The core part of the modelling process is concretely stating the specifics of patterns and mechanisms and determining the conditions under which mechanisms and patterns are linked. Here, we propose that when writing about theory for general readers (e.g., in grant proposals or manuscripts), it can help to focus on either the pattern or mechanism as a starting point and then connect it to the other. For example, a theoretical project could start by describing a pattern and develop theory to better understand the mechanisms that cause it (i.e., exploring causes). Alternatively, a theoretical project could start by considering a mechanism and use theory to better understand the patterns it can generate (i.e., exploring consequences). In addition to these two starting points, we suggest that the goal of theory can be pitched with a specific focus: novelty, robustness, or conflict. Taken together, these two starting points and three foci lead to six different ways to frame theory, or six different roles one might play as a theorist (Table 1).

All interactions between multiple species invading together (coinvasion) must be accounted for to predict species coexistence patterns across space. Mutualisms, particularly, are known to influence species’ population dynamics and their invasive ability (e.g. mycorrhizal fungi with partner plants). Yet, while modelling coinvasion, their role in mediating coexistence is overlooked. We build a spatial model of coinvasion of two competing plant species with a shared fungal mutualist to study how mutualism and competition shape the spatial coexistence of competitors. We find that mutualist presence engenders regional (spatial) coexistence between competitors even when local coexistence between them is impossible. Further, increasing mutualist dispersal results in sharp transitions in competitor coexistence outcomes. Finally, differences in mutualist partner dependence and competitive ability interact to produce a variety of local and regional coexistence outcomes. Thus, incorporating mutualism dependence and dispersal behaviour into coinvasion models offers new insights into spatial coexistence and invasive species distributions.

Animal migration impacts organismal health and disease transmission: migrants are simultaneously exposed to parasites and able to reduce infection at the population and individual levels. However, these dynamics are difficult to study; empirical studies reveal disparate results while existing theory makes assumptions that simplify natural complexity. Here, we systematically review empirical studies of migration and infection across taxa, highlighting key gaps in our understanding. Next, we develop a unified evolutionary framework incorporating different mechanisms of parasite-migration interactions while accounting for ecological complexity that goes beyond previous theory. Our framework generates diverse migration-infection patterns paralleling those seen in empirical systems, including partial and differential migration. Finally, we generate predictions about which mechanisms dominate which empirical systems to guide future studies. Our framework provides an overarching understanding of selective pressures shaping migration patterns in the context of animal health and disease, which is critical for predicting how environmental change may threaten migration.

Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly-dispersive individuals may arrive at the population edge than less-dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.

Several racial and ethnic identities are widely understood to be under-represented within academia, however, actual quantification of this under-representation is surprisingly limited. Challenges include data availability, demographic inertia and identifying comparison points. We use de-aggregated data from the U.S. National Science Foundation to construct a null model of ethnic and racial representation in one of the world’s largest academic communities. Making comparisons between our model and actual representation in academia allows us to measure the effects of retention (while controlling for recruitment) at different academic stages. We find that, regardless of recruitment, failed retention contributes to mis-representation across academia and that the stages responsible for the largest disparities differ by race and ethnicity: for Black and Hispanic scholars this occurs at the transition from graduate student to postdoctoral researcher whereas for Native American/Alaskan Native and Native Hawaiian/Pacific Islander scholars this occurs at transitions to and within faculty stages. Even for Asian and Asian-Americans, often perceived as well represented, circumstances are complex and depend on choice of baseline. Our findings demonstrate that while recruitment continues to be important, retention is also a pervasive barrier to proportional representation.

Interspecific interactions shape how and when species (and population) ranges change. Natural enemies (like parasites) can slow population spread, or, conversely, a population can ‘outrun’ its enemies and spread uninhibited. Yet, less is know about how mutualistic interactions shape population spread, and what role ‘outrunning’ mutualistic partners plays. Here, I examine host-symbiont interactions specifically (where a symbiont species lives in/on a host species); common across animals and plants, and spanning the spectrum from parasitism to mutualism. I develop a model to determine when a symbiont shapes its host’s population spread versus when the host outruns its symbiont. I find that symbiont transmission mode is key. For density-dependent transmission, symbionts cannot be sustained at the low-density population edge and the host outruns its symbiont, whereas frequency-dependent transmission leads to symbionts affecting host spread. However, this pattern breaks down in the presence of a host Allee effect; spread dynamics switch from ‘pulled’ to ‘pushed’, enabling a symbiont to influence population spread from behind the range edge. Overall, mutualistic symbionts speed up (and parasitic symbionts slow down) host population spread. These findings indicate that contact structures within a population (which shape symbiont transmission) are critical for determining whether host-symbiont interactions influence population spread.

Research has conclusively demonstrated the potential for dispersal evolution in range expansions and shifts through a process termed spatial sorting. However, the degree of dispersal evolution observed has varied substantially among organisms. Further, it is unknown how the factors influencing dispersal evolution might impact other ecological processes at play. We use an individual-based model to investigate the effects of the underlying genetics of dispersal and mode of reproduction in range expansions and shifts. Spatial sorting behaves similarly to natural selection in that dispersal evolution increases with sexual selection and loci number. Contrary to our predictions, however, increased dispersal does not always improve a population's ability to track changing conditions. The mate finding Allee effect inherent to sexual reproduction increases extinction risk during range shifts, counteracting the beneficial effect of increased dispersal evolution. Our results demonstrate the importance of considering both ecological and evolutionary processes for understanding range expansions and shifts.