Writing mathematical ecology: A guide for authors and readers

Abstract

Mathematical techniques have a long and rich history in ecology, often serving as a virtual laboratory to test hypotheses, generate novel predictions, and investigate underlying ecological mechanisms. Recently, novel simulation techniques, advances in computing power, and numerical methods for implementing statistical models have significantly advanced our ability to integrate empirical and theoretical ecology. However, a divide still remains between mathematical and empirical studies, their readership, and integration into the broader literature. Because insights from mathematical ecology are far more general than the techniques employed, limitations in communicating mathematical advances to a broad spectrum of ecologists have arguably hindered ecology's progress, particularly in confronting theoretical predictions with empirical experiments and data. Here, we present a guide for both authors and readers of mathematical ecology, with the aim of increasing the accessibility of mathematical ecology for a broad group of ecologists. We provide a list of best practices when both writing and reading mathematical ecology, incorporating examples from this Special Feature of Ecosphere. This guide complements current guides for writing science, focusing specifically on effective communication of mathematics.

Writing statistical methods for ecologists

“…If a novel statistical approach is being used, then equations are usually necessary to demonstrate the fundamentals of the approach. Similar to others (e.g., Cronin & Schoolmaster, 2018;Shoemaker et al, 2021), we encourage the use of diagrams or directed acyclic graphs (i.e., a visual representation of model specification and parameter relationship) to help convey novel mathematical/statistical approaches to general audiences. However, for established statistical approaches, references to those approaches or even equations in other publications are usually sufficient.…”

“…There are resources that focus on how to effectively communicate mathematical concepts to scientists in other fields (Table 1). Recently, Shoemaker et al (2021) provide general guidance for writers and readers on communicating mathematics. Other resources provide guidance on writing Methods sections in general or how to write and report specific statistical details (Table 1).…”

“…There are resources that focus on how to effectively communicate mathematical concepts to scientists in other fields (Table 1). Recently, Shoemaker et al (2021) provide general guidance for writers and readers on T A B L E 1 References of interest for deeper dives into related concepts to writing statistical methods (not an exhaustive list).…”

An Empiricist’s Guide to Using Ecological Theory

“…Detailed step-by-step instructions for building biological models and fitting them to data have been provided (Pielou 1969;Otto and Day 2007;Bolker 2008;Bodner et al 2020). Recent work has helped to demystify the process of theory creation (Otto and Rosales 2020), has advocated for the training of more theoretical ecologists (Rossberg et al 2019), and has provided an overview of some of the challenges associated with communicating theory to a broad audience (Shoemaker et al 2021). However, this still leaves many empiricists who are interested in motivating their research with theory but who have little prior experience with math and models struggling to take the first step.…”

Introducing Mouffet, a unified framework to make model creation easier and more reproducible

“…Biological models have become an essential tool to better understand our world (Jackson et al, 2000; Shoemaker et al, 2021). They are now becoming more and more numerous and sophisticated, even more so with the recent progress made in machine learning, and especially deep learning (Borowiec et al, 2022; Christin et al, 2019; Guo et al, 2020).…”