Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research

Selectivity, pulse fishing and endogenous lifespan in Beverton-Holt models

Optimal management in a multi-cohort Beverton-Holt model with any number of age classes and imperfect selectivity is equivalent to finding the optimal fish lifespan by chosen fallow cycles. Optimal policy differs in two main ways from the optimal lifespan rule with perfect selectivity. First, weight gain is valued in terms of the whole population structure. Second, the cost of waiting is the interest rate adjusted for the increase in the pulse length. This point is especially relevant for assessing the role of selectivity. Imperfect selectivity reduces the optimal lifespan and the optimal pulse length. We illustrate our theoretical findings with a numerical example. Results obtained using global numerical methods select the optimal pulse length predicted by the optimal lifespan rule

Reconciling yield stability with international fisheries agencies precautionary preferences : The role of non constant discount factors in age structured models

International fisheries agencies recommend exploitation paths that satisfy two features. First, for precautionary reasons exploitation paths should avoid high fishing mortality in those fisheries where the biomass is depleted to a degree that jeopardise the stock's capacity to produce the Maximum Sustainable Yield (MSY). Second, for economic and social reasons, captures should be as stable (smooth) as possible over time. In this article we show that a conflict between these two interests may occur when seeking for optimal exploitation paths using age structured bioeconomic approach. Our results show that this conflict be overtaken by using non constant discount factors that value future stocks considering their relative intertemporal scarcity

Reconciling yield stability with international fisheries agencies precautionary preferences: the role of non constant discount factors in age structured models

International fisheries agencies recommend exploitation paths that satisfy two features. First, for precautionary reasons exploitation paths should avoid high fishing mortality in those fisheries where the biomass is depleted to a degree that jeopardise the stock's capacity to produce the Maximum Sustainable Yield (MSY). Second, for economic and social reasons, captures should be as stable (smooth) as possible over time. In this article we show that a conflict between these two interests may occur when seeking for optimal exploitation paths using age structured bioeconomic approach. Our results show that this conflict be overtaken by using non constant discount factors that value future stocks considering their relative intertemporal scarcity.European Commission (MINOW H2020-SFS-2014-2, number 634495, MYFISH, FP7-KBBE-2011-5, number 289257) and the Spanish Ministry of Economy Competitiveness (ECO2012-39098-C06-01, ECO2012-39098-C06-05 and ECO2012-35820

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Optimal periodic control for scalar dynamics under integral constraint on the input

International audienceThis paper studies a periodic optimal control problem governed by a one-dimensional system, linear with respect to the control u, under an integral constraint on u. We give conditions for which the value of the cost function at steady state with a constant control \bar u can be improved by considering periodic control u with average value equal to \bar u. This leads to the so-called "over-yielding" met in several applications. With the use of the Pontryagin Maximum Principle, we provide the optimal synthesis of periodic strategies under the integral constraint. The results are illustrated on a single population model in order to study the effect of periodic inputs on the utility of the stock of resource