Dynamics in a discrete two-species competition model: coexistence and over-compensation

DYNAMICAL STUDY OF DISCRETE-TIME PREY–PREDATOR MODEL WITH CONSTANT PREY REFUGE UNDER IMPRECISE BIOLOGICAL PARAMETERS

The objective of this paper is to study the dynamical properties of a discrete-time prey–predator model under imprecise biological parameters. We consider refuge for prey species as a constant number. The equilibria of the model are obtained, and the dynamic behaviors of the proposed system are examined for the interval biological parameters. Simulations of the model are performed for different parameters of the model. Numerical simulations demonstrate that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.

How much detail and accuracy is required in plant growth sub-models to address questions about optimal management strategies in agricultural systems?

BACKGROUND AND AIMS

Simulations that integrate sub-models of important biological processes can be used to ask questions about optimal management strategies in agricultural and ecological systems. Building sub-models with more detail and aiming for greater accuracy and realism may seem attractive, but is likely to be more expensive and time-consuming and result in more complicated models that lack transparency. This paper illustrates a general integrated approach for constructing models of agricultural and ecological systems that is based on the principle of starting simple and then directly testing for the need to add additional detail and complexity.

METHODOLOGY

The approach is demonstrated using LUSO (Land Use Sequence Optimizer), an agricultural system analysis framework based on simulation and optimization. A simple sensitivity analysis and functional perturbation analysis is used to test to what extent LUSO's crop-weed competition sub-model affects the answers to a number of questions at the scale of the whole farming system regarding optimal land-use sequencing strategies and resulting profitability.

PRINCIPAL RESULTS

The need for accuracy in the crop-weed competition sub-model within LUSO depended to a small extent on the parameter being varied, but more importantly and interestingly on the type of question being addressed with the model. Only a small part of the crop-weed competition model actually affects the answers to these questions.

CONCLUSIONS

This study illustrates an example application of the proposed integrated approach for constructing models of agricultural and ecological systems based on testing whether complexity needs to be added to address particular questions of interest. We conclude that this example clearly demonstrates the potential value of the general approach. Advantages of this approach include minimizing costs and resources required for model construction, keeping models transparent and easy to analyse, and ensuring the model is well suited to address the question of interest.

Complex dynamics in a three-level trophic system with intraspecies interaction

In this paper, we present a three-level trophic food chain, including intraspecies interaction. In contrast with other analyses, we consider the effect on the third trophic level by the first-level parameters. The model shows complex, as well as, chaotic oscillations. Bifurcation diagrams show period doubling route to chaos and crises. Also from the forward and backwards sections of the bifurcation diagrams, we find hysteresis. This result implies the coexistence of attractors for the same parameter values. In particular, we consider the coexistence of a chaotic and a P1 attractors. Our results show that the regulation in the food chain is not exclusive to either a food-prey or prey-predator interaction, but to a more subtle food-prey-predator interaction, where, for some parameter values, a food-prey or a prey-predator regulation may dominate the system's dynamics. Finally, we consider the impact of the intraspecies interaction in the overall dynamics of the food chain.

Competitive interactions among raptors in boreal forests

We examined inter-specific interactions among goshawks ( Accipiter gentilis), common buzzards (Buteo buteo) and honey buzzards (Pernis apivorus) in western Finland in 1983-1996. Because goshawks are among the largest birds of prey species in boreal forests they may take over the nest of smaller and less-competitive forest-dwelling raptors when searching for suitable places for breeding. Accordingly, more than half of newly established goshawk territories were found on the territories previously occupied by the common buzzard and the honey buzzard. Otherwise, territory sharing between these species was rare. Fledgling production of honey buzzards was not associated with the presence of goshawks, probably owing to the almost 2 months later onset of breeding. This probably decreases competitive interactions between these two species. An intensive interference competition, instead, seemed to be evident between common buzzards and goshawks, because the fledgling production of common buzzards was decreased by 20% as a result of failures during incubation and nestling period in the vicinity (<1 km) of occupied goshawk nests. Similarly, territory occupancy of common buzzards till the next breeding season was significantly reduced in the presence of goshawks. Relatively high proportions of occupied buzzard territories (17%) in the study area were shared by breeding goshawks on the same territory. This suggests that although their diets are dissimilar they inhabit similar habitats and might compete for the available prime nesting habitats within forest landscapes. In addition, goshawks benefit from taking over the complete nests of other raptors, imposing upon the original owners of the nest, because building a large stick nest is probably energetically costly. As a large raptor, the goshawk apparently has a competitive advantage over smaller ones, and may have an ever-increasing impact on smaller birds of prey, if there is a lack of sheltered forests inducing competition for the available nest sites.