| 1. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Increasing effciency in the EBT algorithm
- 2019
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Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 179-205
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Konferensbidrag (refereegranskat)abstract
- The Escalator Boxcar Train (EBT) is a commonly used method for solving physiologically structured population models. The main goal of this paper is to overcome computational disadvantages of the EBT method. We prove convergence, for a general class of EBT models in which we modify the original EBT formulation, allowing merging of cohorts. We show that this modified EBT method induces a bounded number of cohorts, independent of the number of time steps. This in turn, improve the numerical algorithm from polynomial to linear time. An EBT simulation of the Daphnia model is used as an illustration of these findings.
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| 2. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Method development for emergent properties in stage-structured population models with stochastic resource growth.
- 2022
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Ingår i: <em>Springer Proceedings in Mathematics and Statistics</em>. - Cham : Springer International Publishing. ; , s. 33-58
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Konferensbidrag (refereegranskat)abstract
- Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. In this article, we use an aquatic ecological system containing one fish species and an underlying resource as our model. In particular, we study a class of stage-structured population systems, in both the deterministic and the stochastic settings, including stochasticity in such a way such that we allow the underlying resource to have a random growth rate. In these models, we study how properties connected to the fish species depend on different harvesting rates. To investigate models in the stochastic setting, we use Monte Carlo simulations to capture several of the emergent properties of the population. These properties have previously been studied in the deterministic case. In the stochastic setting, we get estimates for the expected outcome of population properties in our model, but we also get measures of dispersion. There are properties that emerge when introducing randomness in the model that cannot be studied in the deterministic cases, such as the probability of extinction. In this paper, we develop a method to derive this property. We also construct a method to determine the recovery potential of a species by introducing it in a virgin environment.
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| 3. |
- Aye, Tin Nwe, 1989-, et al.
(författare)
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Numerical stability of the escalator boxcar train under reducing system of ordinary differential equations.
- 2017
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Konferensbidrag (refereegranskat)abstract
- The Escalator Boxcar Train (EBT) is one of the most popular numericalmethods used to study the dynamics of physiologically structured population models.The original EBT model accumulates an increasing system of ODEs to solve for eachtime step. In this project, we propose a merging procedure to overcome computationaldisadvantageous of the EBT method, the merging is done as an automatic feature.In particular we apply the model including merging to a colony of Daphnia Pulex.
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| 4. |
- Canpwonyi, S., et al.
(författare)
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On the Approximation of Physiologically Structured Population Model with a Three Stage-Structured Population Model in a Grazing System
- 2022
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Ingår i: Springer Proc. Math. Stat.. - Cham : Springer. - 9783031178207 ; , s. 753-771
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Konferensbidrag (refereegranskat)abstract
- A great deal of ecological theory is based on simple Lotka-Volterra-type of unstructured population models in the study of complex population dynamics and communities. The main reason is to obtain important information for predicting their future evolution. In these unstructured models, it is assumed that all individuals in the population are identical, with the same birth and death rates, and consume equally from shared resources in a homogeneous environment. In reality, these assumptions are not biologically true but still forms a basis for modeling population ecology. We apply this paradigm on the grazing system consisting of coupled ordinary differential equations describing the dynamics of forage resource and livestock population in a grassland ecosystem. We do this by investigating the dynamics of the individuals at different life-history stages of juvenile and adult livestock. The mathematical derivation of the model is carried out to show how the physiologically structured population model can be approximated using a three stage-structured population model. Thus the resulting system of ordinary differential equations can be solved to predict density-dependent properties of the population since it provides a somewhat close-to-reality description of the natural and traditional grazing system. This model therefore certainly contains the needed information in the modeling methodology and accommodates the necessary amount of biological details about the population.
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| 5. |
- Nankinga, L., et al.
(författare)
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A Mathematical Model for Harvesting in a Stage-Structured Cannibalistic System
- 2022
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Ingår i: Springer Proc. Math. Stat.. - Cham : Springer. - 9783031178207 ; , s. 735-751
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Konferensbidrag (refereegranskat)abstract
- To increase the production of proteins in East Africa, aquaculture gained increased attention recently. In this paper, we study the interactions of a consumer-resource system with harvesting, in which African Catfish (Gl ar i as gar i epi nus) consume a food resource. The cannibalistic behavior of African Catfish is captured by using a four stage-structured system. The dynamics of food resource and African Catfish result in a system of ordinary differential equations called a stage-structured fish population model. Existence and stability of steady states are analyzed quantitatively. We have investigated eight different harvesting scenarios which account for yield of the fish stock. Results from the simulations revealed that harvesting large juveniles and small adults under equal harvesting rates gives the highest maximum sustainable yield compared to other harvesting scenarios. In contrast to non-cannibalistic models, we find an increase of the proportion of the adult individuals under harvesting.
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