Should We Care If Models Are Phenomenological or Mechanistic?

Identifying patterning behavior in a plant infestation of insect pests

In this study, we developed a mechanistic model formulated as a system of reaction-diffusion equations (RDE) to explore the spatiotemporal dynamics of a theoretical pest with a tillering host plant in a controlled rectangular plant field. Local perturbation analysis, a recently developed method of analysis for wave propagation, was utilized to determine patterning regimes resulting from the local and global behaviors of the slow and fast diffusing components of the RDE system, respectively. Turing analysis was done to show that the RDE system does not exhibit Turing patterns. With bug mortality as the bifurcation parameter, regions with oscillations and stable coexistence of the pest and tillers were identified. Numerical simulations illustrate the patterning regimes in 1D and 2D settings. The oscillations suggest that recurrences in pest infestation is possible. Moreover, simulations showed that patterns produced in the model are strongly influenced by the pests' homogeneous dynamics inside the controlled environment.

Controversial Roles of Oxygen in Organismal Responses to Climate Warming

AbstractDespite the global ecological importance of climate change, controversy surrounds how oxygen affects the fate of aquatic ectotherms under warming. Disagreements extend to the nature of oxygen bioavailability and whether oxygen usually limits growth under warming, explaining smaller adult size. These controversies affect two influential hypotheses: gill oxygen limitation and oxygen- and capacity-limited thermal tolerance. Here, we promote deeper integration of physiological and evolutionary mechanisms. We first clarify the nature of oxygen bioavailability in water, developing a new mass-transfer model that can be adapted to compare warming impacts on organisms with different respiratory systems and flow regimes. By distinguishing aerobic energy costs of moving oxygen from environment to tissues from costs of all other functions, we predict a decline in energy-dependent fitness during hypoxia despite approximately constant total metabolic rate before reaching critically low environmental oxygen. A new measure of oxygen bioavailability that keeps costs of generating water convection constant predicts a higher thermal sensitivity of oxygen uptake in an amphipod model than do previous oxygen supply indices. More importantly, by incorporating size- and temperature-dependent costs of generating water flow, we propose that oxygen limitation at different body sizes and temperatures can be modeled mechanistically. We then report little evidence for oxygen limitation of growth and adult size under benign warming. Yet occasional oxygen limitation, we argue, may, along with other selective pressures, help maintain adaptive plastic responses to warming. Finally, we discuss how to overcome flaws in a commonly used growth model that undermine predictions of warming impacts.

Understanding the combined effects of multiple stressors: A new perspective on a longstanding challenge

Wildlife populations and their habitats are exposed to an expanding diversity and intensity of stressors caused by human activities, within the broader context of natural processes and increasing pressure from climate change. Estimating how these multiple stressors affect individuals, populations, and ecosystems is thus of growing importance. However, their combined effects often cannot be predicted reliably from the individual effects of each stressor, and we lack the mechanistic understanding and analytical tools to predict their joint outcomes. We review the science of multiple stressors and present a conceptual framework that captures and reconciles the variety of existing approaches for assessing combined effects. Specifically, we show that all approaches lie along a spectrum, reflecting increasing assumptions about the mechanisms that regulate the action of single stressors and their combined effects. An emphasis on mechanisms improves analytical precision and predictive power but could introduce bias if the underlying assumptions are incorrect. A purely empirical approach has less risk of bias but requires adequate data on the effects of the full range of anticipated combinations of stressor types and magnitudes. We illustrate how this spectrum can be formalised into specific analytical methods, using an example of North Atlantic right whales feeding on limited prey resources while simultaneously being affected by entanglement in fishing gear. In practice, case-specific management needs and data availability will guide the exploration of the stressor combinations of interest and the selection of a suitable trade-off between precision and bias. We argue that the primary goal for adaptive management should be to identify the most practical and effective ways to remove or reduce specific combinations of stressors, bringing the risk of adverse impacts on populations and ecosystems below acceptable thresholds.

What is the status of metabolic theory one century after Pütter invented the von Bertalanffy growth curve?

Metabolic theory aims to tackle ecological and evolutionary problems by explicitly including physical principles of energy and mass exchange, thereby increasing generality and deductive power. Individual growth models (IGMs) are the fundamental basis of metabolic theory because they represent the organisational level at which energy and mass exchange processes are most tightly integrated and from which scaling patterns emerge. Unfortunately, IGMs remain a topic of great confusion and controversy about the origins of the ideas, their domain and breadth of application, their logical consistency and whether they can sufficiently capture reality. It is now 100 years since the first theoretical model of individual growth was put forward by Pütter. His insights were deep, but his model ended up being attributed to von Bertalanffy and his ideas largely forgotten. Here I review Pütter's ideas and trace their influence on existing theoretical models for growth and other aspects of metabolism, including those of von Bertalanffy, the Dynamic Energy Budget (DEB) theory, the Gill-Oxygen Limitation Theory (GOLT) and the Ontogenetic Growth Model (OGM). I show that the von Bertalanffy and GOLT models are minor modifications of Pütter's original model. I then synthesise, compare and critique the ideas of the two most-developed theories, DEB theory and the OGM, in relation to Pütter's original ideas. I formulate the Pütter, DEB and OGM models in the same structure and with the same notation to illustrate the major similarities and differences among them. I trace the confusion and controversy regarding these theories to the notions of anabolism, catabolism, assimilation and maintenance, the connections to respiration rate, and the number of parameters and state variables their models require. The OGM model has significant inconsistencies that stem from the interpretation of growth as the difference between anabolism and maintenance, and these issues seriously challenge its ability to incorporate development, reproduction and assimilation. The DEB theory is a direct extension of Pütter's ideas but with growth being the difference between assimilation and maintenance rather than anabolism and catabolism. The DEB theory makes the dynamics of Pütter's 'nutritive material' explicit as well as extending the scheme to include reproduction and development. I discuss how these three major theories for individual growth have been used to explain 'macrometabolic' patterns including the scaling of respiration, the temperature-size rule (first modelled by Pütter), and the connection to life history. Future research on the connections between theory and data in these macrometabolic topics have the greatest potential to advance the status of metabolic theory and its value for pure and applied problems in ecology and evolution.