209 research outputs found
Constant proportion harvest policies: Dynamic implications in the Pacific halibut and Atlantic cod fisheries
a b s t r a c t Overfishing, pollution and other environmental factors have greatly reduced commercially valuable stocks of fish. In a 2006 Science article, a group of ecologists and economists warned that the world may run out of seafood from natural stocks if overfishing continues at current rates. In this paper, we explore the interaction between a constant proportion harvest policy and recruitment dynamics. We examine the discrete-time constant proportion harvest policy discussed in Ang et al. We focus on constant proportion policies (CPPs). CPPs have the potential to stabilize complex overcompensatory stock dynamics, with or without the Allee effect, provided the rates of harvest stay below a threshold. If that threshold is exceeded, CPPs are known to result in the sudden collapse of a fish stock when stock recruitment exhibits the Allee effect. In case studies, we analyze CPPs as they might be applied to Gulf of Alaska Pacific halibut fishery and the Georges Bank Atlantic cod fishery based on harvest rates from 1975 to 2007. The best fit models suggest that, under high fishing mortalities, the halibut fishery is vulnerable to sudden population collapse while the cod fishery is vulnerable to steady decline to zero. The models also suggest that CPP with mean harvesting levels from the last 30 years can be effective at preventing collapse in the halibut fishery, but these same policies would lead to steady decline to zero in the Atlantic cod fishery. We observe that the likelihood of collapse in both fisheries increases with increased stochasticity (for example, weather variability) as predicted by models of global climate change
An Interactive Tool for the Computational Exploration of Integrodifference Population Models
Mathematical modeling of population dynamics can provide novel insight to the growth and dispersal patterns for a variety of species populations, and has become vital to the preservation of biodiversity on a global-scale. These growth and dispersal stages can be modeled using integrodifference equations that are discrete in time and continuous in space. Previous studies have identified metrics that can determine whether a given species will persist or go extinct under certain model parameters. However, a need for computational tools to compute these metrics has limited the scope and analysis within many of these studies. We aim to create computational tools that facilitate numerical explorations for a number of associated integrodifference equations, allowing modelers to explore results using a selection of models under a robust parameter set
Existence of Bistable Waves in a Competitive Recursion System with Ricker Nonlinearity
Using an abstract scheme of monotone semiflows, the existence of bistable
traveling wave solutions of a competitive recursion system with Ricker
nonlinearity is established. The traveling wave solutions formulate the strong
inter-specific actions between two competitive species
Influence of technological progress and renewability on the sustainability of ecosystem engineers populations
Overpopulation and environmental degradation due to inadequate resource-use
are outcomes of human's ecosystem engineering that has profoundly modified the
world's landscape. Despite the age-old concern that unchecked population and
economic growth may be unsustainable, the prospect of societal collapse remains
contentious today. Contrasting with the usual approach to modeling human-nature
interactions, which are based on the Lotka-Volterra predator-prey model with
humans as the predators and nature as the prey, here we address this issue
using a discrete-time population dynamics model of ecosystem engineers. The
growth of the population of engineers is modeled by the Beverton-Holt equation
with a density-dependent carrying capacity that is proportional to the number
of usable habitats. These habitats (e.g., farms) are the products of the work
of the individuals on the virgin habitats (e.g., native forests), hence the
denomination engineers of ecosystems to those agents. The human-made habitats
decay into degraded habitats, which eventually regenerate into virgin habitats.
For slow regeneration resources, we find that the dynamics is dominated by
cycles of prosperity and collapse, in which the population reaches vanishing
small densities. However, increase of the efficiency of the engineers to
explore the resources eliminates the dangerous cyclical patterns of feast and
famine and leads to a stable equilibrium that balances population growth and
resource availability. This finding supports the viewpoint of growth optimists
that technological progress may avoid collapse
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