Writing mathematical ecology: A guide for authors and readers

MacArthur's Consumer-Resource Model: A Rosetta Stone for Competitive Interactions

AbstractRecent developments in competition theory-namely, modern coexistence theory (MCT)-have aided empiricists in formulating tests of species persistence, coexistence, and evolution from simple to complex community settings. However, the parameters used to predict competitive outcomes, such as interaction coefficients, invasion growth rates, and stabilizing differences, remain biologically opaque, making findings difficult to generalize across ecological settings. This article is structured around five goals toward clarifying MCT by first making a case for the modern-day utility of MacArthur's consumer-resource model, a model with surprising complexity and depth: (i) to describe the model in uniquely accessible language, deciphering the mathematics toward cultivating deeper biological intuition about competition's inner workings regardless of what empirical toolkit one uses; (ii) to provide translation between biological mechanisms from MacArthur's model and parameters used to predict coexistence in MCT; (iii) to make explicit important but understated assumptions of MacArthur's model in plain terms; (iv) to provide empirical recommendations; and (v) to examine how key ecological concepts (e.g., r/K-selection) can be understood with renewed clarity through MacArthur's lens. We end by highlighting opportunities to explore mechanisms in tandem with MCT and to compare and translate results across ecological currencies toward a more unified ecological science.

Demystifying Fundamental Theories in Ecology

AbstractAs scientists, our collective goal is to make scientific progress in the pursuit of an absolute truth about the nature of the universe, through a feedback loop of observation, theory, and experimentation. What if a major limit to progress is not the science itself but rather in how broadly scientific ideas can be understood? In this introduction to a special feature, we highlight four articles, each tasked with demystifying a key theory in ecology for a general audience, with a special focus on aspects of each theory that have been misunderstood, misapplied, or underappreciated in some important way. These four theories are metabolic theory, competition theory based on consumer-resource models, mechanisms of coexistence in fluctuating environments, and metapopulation dynamics. We point out key ways in which each article applied best practices of accessible communication as well as challenges that might arise (and potential solutions for journals and authors) when attempting to publish articles with a deeper emphasis on explanation of fundamentals than a traditional article might provide.

Integrating Network and Meta-Ecosystem Models for Developing a Zoogeochemical Theory

Human activities have caused significant changes in animal abundance, interactions, movement and diversity at multiple scales. Growing empirical evidence reveals the myriad ways that these changes can alter the control that animals exert over biogeochemical cycling. Yet a theoretical framework to coherently integrate animal abundance, interactions, movement and diversity to predict when and how animal controls over biogeochemical cycling (i.e., zoogeochemistry) change is currently lacking. We present such a general framework that provides guidance on linking mathematical models of species interaction and diversity (network theory) and movement of organisms and non-living materials (meta-ecosystem theory) to account for biotic and abiotic feedback by which animals control biogeochemical cycling. We illustrate how to apply the framework to develop predictive models for specific ecosystem contexts using a case study of a primary producer-herbivore bipartite trait network in a boreal forest ecosystem. We further discuss key priorities for enhancing model development, data-model integration and application. The framework offers an important step to enhance empirical research that can better inform and justify broader conservation efforts aimed at conserving and restoring animal populations, their movement and critical functional roles in support of ecosystem services and nature-based climate solutions.

When is lethal deceptive pollination maintained? A population dynamics approach

BACKGROUND AND AIMS

Not all plant-pollinator interactions are mutualistic, and in fact deceptive pollination systems are widespread in nature. The genus Arisaema has a pollination system known as lethal deceptive pollination, in which plants not only attract pollinating insects without providing any rewards, but also trap them until they die. Many Arisaema species are endangered from various disturbances, including reduction in forest habitat, modification of the forest understorey owing to increasing deer abundance, and plant theft for horticultural cultivation. We aimed to theoretically investigate how lethal deceptive pollination can be maintained from a demographic perspective and how plant and pollinator populations respond to different types of disturbance.

METHODS

We developed and analysed a mathematical model to describe the population dynamics of a deceptive plant species and its victim pollinator. Calibrating the model based on empirical data, we assessed the conditions under which plants and pollinators could coexist, while manipulating relevant key parameters.

KEY RESULTS

The model exhibited qualitatively distinct behaviours depending on certain parameters. The plant becomes extinct when it has a low capability for vegetative reproduction and slow transition from male to female, and plant-insect co-extinction occurs especially when the plant is highly attractive to male insects. Increasing deer abundance has both positive and negative effects because of removal of other competitive plants and diminishing pollinators, respectively. Theft for horticultural cultivation can readily threaten plants whether male or female plants are frequently collected. The impact of forest habitat reduction may be limited compared with that of other disturbance types.

CONCLUSIONS

Our results have emphasized that the demographic vulnerability of lethal deceptive pollination systems would differ qualitatively from that of general mutualistic pollination systems. It is therefore important to consider the demographics of both victim pollinators and deceptive plants to estimate how endangered Arisaema populations respond to various disturbances.

Six personas to adopt when framing theoretical research questions in biology

Theory is a critical component of the biological research process, and complements observational and experimental approaches. However, most 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 personas one might adopt as a theorist: 'Advocate', 'Explainer', 'Instigator', 'Mediator', 'Semantician' and 'Tinkerer'. These personas 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 maths knowledge. Finally, we provide a roadmap that researchers new to theoretical research can use to identify a framing to serve as a blueprint for their own theoretical research projects.

Writing Accessible Theory in Ecology and Evolution: Insights from Cognitive Load Theory

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.