arXiv subjects

Marc Mangel

Publications and source records attributed to Marc Mangel.

4 recordsLinked to original sources

arXiv2014

Avoiding tipping points in fisheries management through Gaussian Process Dynamic Programming

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

q-bio.QM↗

arXiv2013

Compensatory dynamics of fish recruitment illuminated by functional elasticities

Models of Stock Recruitment Relationships (SRRs) are often used to predict fish population dynamics. Commonly used SRRs include the Ricker, Beverton-Holt, and Cushing functional forms, which differ primarily by the degree of density dependent effects (compensation). The degree of compensation determines whether recruitment respectively decreases, saturates, or increases at high levels of spawning stock biomass. In 1982 J.G. Shepherd united these dynamics into a single model, where the degree of compensation is determined by a single parameter, however the difficulty in relating this parameter to biological data has limited its usefulness. Here we use a generalized modeling framework to show that the degree of compensation can be related directly to the functional elasticity of growth, which is a general quantity that measures the change in recruitment relative to a change in biomass, irrespective of the specific SRR. We show that the elasticity of growth can be calculated from short-term fluctuations in fish biomass, is robust to observation error, and can be used to determine general attributes of the SRR in both continuous time production models, as well as discrete time age-structured models. This framework may be particularly useful if fisheries time-series data are limited, and not conducive to determining functional relationships using traditional methods of statistical best-fit.

q-bio.PE↗

arXiv2013

Functional morphology, stable isotopes, and human evolution: a model of consilience

Foraging is constrained by the energy within resources and the mechanics of acquisition and assimilation. Thick molar enamel, a character trait differentiating hominins from African apes, is predicted to mitigate the mechanical costs of chewing obdurate foods. The classic expression of hyperthick enamel together with relatively massive molars, termed megadontia, is most evident in {\it Paranthropus}, a lineage of hominins that lived ca. 2.7 to 1.2 million years ago. Among contemporary primates, thicker molar enamel corresponds with the consumption of stiffer, deformation-resistant foods, possibly because thicker enamel can better resist cracking under high compressive loads. Accordingly, plant underground storage organs (USOs) are thought to be a central food resource for hominins such as {\it Paranthropus} due to their abundance, isotopic composition, and mechanical properties. Here, we present a process-based model to investigate foraging constraints as a function of energetic demands and enamel wear among human ancestors. Our framework allows us to determine the fitness benefits of megadontia, and to explore under what conditions stiff foods such as USOs are predicted to be chosen as fallback, rather than preferred, resources. Our model predictions bring consilience to the noted disparity between functional interpretations of megadontia and microwear evidence, particularly with respect to {\it Paranthropus boisei}.

q-bio.PE↗

arXiv2005

Implications of Aging in Bacteria

Motivated by recent research of aging in E. coli, we explore the effects of aging on bacterial fitness. The disposable soma theory of aging was developed to explain how differences in lifespans and aging rates could be linked to life history trade-offs. Although generally applied for multicellular organisms, it is also useful for exploring life history strategies of single celled organisms such as bacteria. Starting from the Euler-Lotka equation, we propose a mathematical model to explore how a finite lifespan effects fitness of bacteria. We find that that there is surprisingly little loss of fitness when the bacterium has limited opportunities to reproduce. Instead, the fitness gained each time the bacteria reproduces decreases rapidly, and investing resources to survive to reproduce the first few times is likely more advantageous than investing additional resources to try to maintain cell integrity longer.

q-bio.PE↗