| 1. |
- Liao, Jinbao, et al.
(författare)
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The dynamical models of activated sludge system : stochastic cellular automaton and differential equations
- 2012
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Ingår i: International Journal of Biomathematics. - 1793-5245. ; 5:5, s. 1250048-
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Tidskriftsartikel (refereegranskat)abstract
- A stochastic cellular automaton (CA) model for activated sludge system (ASS) is formulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations (ODEs) of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, complexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.
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| 2. |
- Lundström, Niklas L. P., 1980-, et al.
(författare)
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Meeting yield and conservation objectives by harvesting both juveniles and adults
- 2019
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Ingår i: American Naturalist. - : University of Chicago Press. - 0003-0147 .- 1537-5323. ; 193:3, s. 373-390
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Tidskriftsartikel (refereegranskat)abstract
- Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.
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| 3. |
- Meng, Xinzhu, et al.
(författare)
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Dynamics and management of stage-structured fish stocks
- 2013
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Ingår i: Bulletin of Mathematical Biology. - : Springer. - 0092-8240 .- 1522-9602. ; 75:1, s. 1-23
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Tidskriftsartikel (refereegranskat)abstract
- With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (in Theor. Popul. Biol. 73, 47-62, 2008) have derived as an approximation of a physiologically-structured counterpart. First, we rigorously prove the existence of steady states in both models, that the models share the same steady states, and that there exists at most one positive steady state. Furthermore, we carry out numerical investigations which suggest that a steady state is globally stable if it is locally stable. Second, we consider multiobjective harvesting strategies which account for yield, profit, and the recovery potential of the fish stock. The recovery potential is a measure of how quickly a fish stock can recover from a major disturbance and serves as an indication of the extinction risk associated with a harvesting strategy. Our analysis reveals that a small reduction in yield or profit allows for a disproportional increase in recovery potential. We also show that there exists a harvesting strategy with yield close to the maximum sustainable yield (MSY) and profit close to that associated with the maximum economic yield (MEY). In offering a good compromise between MSY and MEY, we believe that this harvesting strategy is preferable in most instances. Third, we consider the impact of harvesting on population size structure and analytically determine the most and least harmful harvesting strategies. We conclude that the most harmful harvesting strategy consists of harvesting both adults and juveniles, while harvesting only adults is the least harmful strategy. Finally, we find that a high percentage of juvenile biomass indicates elevated extinction risk and might therefore serve as an early-warning signal of impending stock collapse.
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| 4. |
- Meng, Xinzhu, et al.
(författare)
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Evolutionary dynamics in a Lotka–Volterra competition model with impulsive periodic disturbance
- 2016
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 39:2, s. 177-188
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop a theoretical framework to investigate the influence of impulsive periodic disturbance on the evolutionary dynamics of a continuous trait, such as body size, in a general Lotka–Volterra-type competition model. The model is formulated as a system of impulsive differential equations. First, we derive analytically the fitness function of a mutant invading the resident populations when rare in both monomorphic and dimorphic populations. Second, we apply the fitness function to a specific system of asymmetric competition under size-selective harvesting and investigate the conditions for evolutionarily stable strategy and evolutionary branching by means of critical function analysis. Finally, we perform long-term simulation of evolutionary dynamics to demonstrate the emergence of high-level polymorphism. Our analytical results show that large harvesting effort or small impulsive harvesting period inhibits branching, while large impulsive harvesting period promotes branching.
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| 5. |
- Zhang, Tongqian, et al.
(författare)
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The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments
- 2011
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Ingår i: Nonlinear dynamics. - : Springer Science and Business Media LLC. - 0924-090X .- 1573-269X. ; 64:1-2, s. 1-12
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a delayed pest control model with stage-structure for pests by introducing a constant periodic pesticide input and harvesting prey (Crops) at two different fixed moments is proposed and analyzed. We assume only the pests are affected by pesticide. We prove that the conditions for global asymptotically attractive 'predator-extinction' periodic solution and permanence of the population of the model depend on time delay, pulse pesticide input, and pulse harvesting prey. By numerical analysis, we also show that constant maturation time delay, pulse pesticide input, and pulse harvesting prey can bring obvious effects on the dynamics of system, which also corroborates our theoretical results. We believe that the results will provide reliable tactic basis for the practical pest management. One of the features of present paper is to investigate the high-dimensional delayed system with impulsive effects at different fixed impulsive moments.
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