Workshop on "Age-structured models in population dynamics and economics at the Vienna Institute of Demography, October 27-28, 2003

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Asymptotic behaviour for a class of non-monotone delay differential systems with applications

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family covers a wide set of models used in structured population dynamics. By exploiting the stability and the monotone character of the linear ODE, we establish sufficient conditions for both the extinction of all the populations and the permanence of the system. In the case of DDEs with autonomous coefficients (but possible time-varying delays), sharp results are obtained, even in the case of a reducible community matrix. As a sub-product, our results improve some criteria for autonomous systems published in recent literature. As an important illustration, the extinction, persistence and permanence of a non-autonomous Nicholson system with patch structure and multiple time-dependent delays are analysed.Comment: 26 pages, J Dyn Diff Equat (2017

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

Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect

The East Atlantic Bluefin Tuna Fisheries: Stock Collapse or Recovery?

A discrete time, multi-gear, and age structured bio-economic model is developed for the East Atlantic bluefin tuna fisheries, a paradigmatic example of the difficulties faced in managing highly migratory fish stocks. The model is used to analyse alternative management strategies for the Regional Fisheries Management Organisation (RFMO) managing this fishery, and to investigate some of the policy implications. For the various scenarios, the optimal stock level varies between 500–800,000 tonnes, which compares with a stock level of 150,000 tonnes in 1995. In other words, there is a very strong case for rebuilding the stock. Moreover, the sustainability of the stock is threatened unless a recovery programme is implemented; indeed, the alternative may be stock collapse. Second, to rebuild the stock, Draconian measures are called for: either outright moratoria over fairly lengthy periods, or possibly a more gradual approach to steady state given by a Total Allowable Catch (TAC) at a low level for an extended period of time. Third, the cost of inefficient gear structure is very high indeed.Bioeconomic model, bluefin tuna, optimal management., Resource /Energy Economics and Policy, Q22,

Why Economists Reject Long-Term Fisheries Management Plans?

Most fisheries agencies conduct biological and economic assessments independently. This independent conduct may lead to situations in which economists reject management plans proposed by biologists. The objective of this study is to show how to find optimal strategies that may satisfy biologists and economists' conditions. In particular we characterize optimal fishing trajectories that maximize the present value of a discounted economic indicator taking into account the age-structure of the population as in stock assessment methodologies. This approach is applied to the Northern Stock of Hake. Our main empirical findings are: i) Optimal policy may be far away from any of the classical scenarios proposed by biologists, ii) The more the future is discounted, the higher the likelihood of finding contradictions among scenarios proposed by biologists and conclusions from economic analysis, iii) Optimal management reduces the risk of the stock falling under precautionary levels, especially if the future is not discounted to much, and iv) Optimal stationary fishing rate may be very different depending on the economic indicator used as reference.fisheries management, age-structured models, discounting, Fmsy, Fmax, northern stock of hake

The Dynamics of an Open-access Fishery: Baltic Sea Cod

This paper sets up a dynamic open-access model of a single industry exploiting a single resource stock. The model is applied empirically to describe the dynamics of the eastern Baltic Sea cod fishery. The theoretical model is based on the benchmark papers by Smith (1968, 1969). Types of steady state are discussed theoretically and the theory is applied to the eastern Baltic Sea cod fishery. The empirical path the fishery has been following since 1982 is determined and how it relates to the optimal path to steady state is discussed. Comparisons are made to other empirical studies, and the stability of the steady state is evaluated. The paper concludes that the Baltic Sea cod stock likely is on a path to a stable steady state, and it might not be a problem that the stock is below safe biological limits.Baltic sea cod, bio-economics, dynamic entry/exit, fisheries, open-access, stability of steady state, Resource /Energy Economics and Policy, Q21, Q22,