Matching Items (36)

Mathematical Modeling of Honeybee Population Dynamics

Description

Honeybees are important pollinators worldwide and pollinate about one-third of the food we consume. Recently though, honeybee colonies have been under increasing stress due to changing environments, pesticides, mites, and viruses, which has increased the incidence of
colony collapse.

Honeybees are important pollinators worldwide and pollinate about one-third of the food we consume. Recently though, honeybee colonies have been under increasing stress due to changing environments, pesticides, mites, and viruses, which has increased the incidence of
colony collapse. This paper aims to understand how these different factors contribute to the decline of honeybee populations by using two separate approaches: data analysis and mathematical modeling. The data analysis examines the relative impacts of mites, pollen, mites, and viruses on honeybee populations and colony collapse. From the data, low initial bee populations lead to collapse in September while mites and viruses can lead to collapse in December. Feeding bee colonies also has a mixed effect, where it increases both bee and mite populations. For the model, we focus on the population dynamics of the honeybee-mite interaction. Using a system of delay differential equations with five population components, we find that bee colonies can collapse from mites, coexist with mites, and survive without them. As long as bees produce more pupa than the death rate of pupa and mites produce enough phoretic mites compared to their death rates, bees and mites can coexist. Thus, it is possible for honeybee colonies to withstand mites, but if the parasitism is too large, the colony will collapse. Provided
this equilibrium exists, the addition of mites leads to the colony moving to the interior equilibrium. Additionally, population oscillations are persistent if they occur and are connected to the interior equilibrium. Certain parameter values destabilize bee populations, leading to large
oscillations and even collapse. From these parameters, we can develop approaches that can help us prevent honeybee colony collapse before it occurs.

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Date Created
2019-05

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Worker Policing Mechanisms in Ponerine Ant Species

Description

For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on

For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds the mechanisms detailing the selection of new reproductives and the suppression of ovarian development in rejected reproductives. We investigated the mechanisms of worker policing, one of the primary methods of ovarian suppression, through continuous video observation for a period of five days at the start of colony instability. Observations suggest policing in H. saltator is performed by a majority of a colony, including potential reproductives, and requires multiple events to fully discourage ovarian growth.

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Date Created
2018-12

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Analysis of Egg-Laying Rates of Harpegnathos Saltator Through Different Methods of Observation

Description

Insects have intricate systems they depend on for survival. They live in societies where every individual plays an important role. Ants are a great example of this observation. They are known for having structurally sound societies that ensure the livelihood

Insects have intricate systems they depend on for survival. They live in societies where every individual plays an important role. Ants are a great example of this observation. They are known for having structurally sound societies that ensure the livelihood of the colony. The ant species analyzed for this research, Harpegnathos saltator, portrays a structured colony and serves as a useful example of levels of hierarchy. In the colony of H. saltator, one can find a queen, gamergates, workers, and male ants living underground in Southern India. Recording and analyzing egg-laying rates are important in this study because of the amount of information it provides. It is used especially when observing the relationship among the gamergates in colonies with varying colony sizes. Three different methods were used to record the egg-laying rates, each providing insight into valuable information. Results show that the smaller colonies with fewer identified gamergates do share an equal amount of egg-laying. In larger colonies, it appears that there are more active identified gamergates than others. Egg-laying duration times are smaller in colonies with fewer gamergates. It is also found that the presence of brood does not affect egg-laying rates and reproductive inhibition could be a possibility based on two of the colonies observed F65 and F21. Based on the data found, a more active colony that attempts to maintain stability by demonstrating aggression may be affecting the reproduction of gamergates. Future work that would further strengthen the research and conclusions made would involve further observation of colonies, both large and small, with varying numbers of gamergates. More observation involving behavior among gamergates and workers would also be beneficial. Mathematical modeling could also be incorporated to create equations that could determine information about colonies based on size, number of gamergates, and egg-laying rates.

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Created

Date Created
2017-12

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Identifying Robustness in the Regulation of Collective Foraging of Ant Colonies Using an Interaction-Based Model With Backward Bifurcation

Description

Collective behaviors in social insect societies often emerge from simple local rules. However, little is known about how these behaviors are dynamically regulated in response to environmental changes. Here, we use a compartmental modeling approach to identify factors that allow

Collective behaviors in social insect societies often emerge from simple local rules. However, little is known about how these behaviors are dynamically regulated in response to environmental changes. Here, we use a compartmental modeling approach to identify factors that allow harvester ant colonies to regulate collective foraging activity in response to their environment. We propose a set of differential equations describing the dynamics of: (1) available foragers inside the nest, (2) active foragers outside the nest, and (3) successful returning foragers, to understand how colony-specific parameters, such as baseline number of foragers, interactions among foragers, food discovery rates, successful forager return rates, and foraging duration might influence collective foraging dynamics, while maintaining functional robustness to perturbations. Our analysis indicates that the model can undergo a forward (transcritical) bifurcation or a backward bifurcation depending on colony-specific parameters. In the former case, foraging activity persists when the average number of recruits per successful returning forager is larger than one. In the latter case, the backward bifurcation creates a region of bistability in which the size and fate of foraging activity depends on the distribution of the foraging workforce among the model׳s compartments. We validate the model with experimental data from harvester ants (Pogonomyrmex barbatus) and perform sensitivity analysis. Our model provides insights on how simple, local interactions can achieve an emergent and robust regulatory system of collective foraging activity in ant colonies.

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Date Created
2015-02-21

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Advanced Nonlinear Dynamics of Population Biology and Epidemiology

Description

Modern biology and epidemiology have become more and more driven by the need of mathematical models and theory to elucidate general phenomena arising from the complexity of interactions on the numerous spatial, temporal, and hierarchical scales at which biological systems

Modern biology and epidemiology have become more and more driven by the need of mathematical models and theory to elucidate general phenomena arising from the complexity of interactions on the numerous spatial, temporal, and hierarchical scales at which biological systems operate and diseases spread. Epidemic modeling and study of disease spread such as gonorrhea, HIV/AIDS, BSE, foot and mouth disease, measles, and rubella have had an impact on public health policy around the world which includes the United Kingdom, The Netherlands, Canada, and the United States. A wide variety of modeling approaches are involved in building up suitable models. Ordinary differential equation models, partial differential equation models, delay differential equation models, stochastic differential equation models, difference equation models, and nonautonomous models are examples of modeling approaches that are useful and capable of providing applicable strategies for the coexistence and conservation of endangered species, to prevent the overexploitation of natural resources, to control disease’s outbreak, and to make optimal dosing polices for the drug administration, and so forth.

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Date Created
2014-12-22

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Permanence of a General Discrete-Time Two-Species-Interaction Model With Nonlinear Per-Capita Growth Rates

Description

The per-capita growth rate of a species is influenced by density-independent, positive and negative density-dependent factors. These factors can lead to nonlinearity with a consequence that species may process multiple nontrivial equilibria in its single state (e.g., Allee effects). This

The per-capita growth rate of a species is influenced by density-independent, positive and negative density-dependent factors. These factors can lead to nonlinearity with a consequence that species may process multiple nontrivial equilibria in its single state (e.g., Allee effects). This makes the study of permanence of discrete-time multi-species population models very challenging due to the complex boundary dynamics. In this paper, we explore the permanence of a general discrete-time two-species-interaction model with nonlinear per-capita growth rates for the first time. We find a simple sufficient condition for guaranteeing the permanence of the system by applying and extending the ecological concept of the relative nonlinearity to estimate systems' external Lyapunov exponents. Our method allows us to fully characterize the effects of nonlinearities in the per-capita growth functions and implies that the fluctuated populations may devastate the permanence of systems and lead to multiple attractors. These results are illustrated with specific two species competition and predator-prey models with generic nonlinear per-capita growth functions. Finally, we discuss the potential biological implications of our results.

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Created

Date Created
2013-10

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Global Dynamics of a Discrete Two-Species Lottery-Ricker Competition Model

Description

In this article, we study the global dynamics of a discrete two-dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show

In this article, we study the global dynamics of a discrete two-dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show that for a certain parameter range, there exists a compact interior attractor that attracts all interior points except Lebesgue measure zero set. This result gives a weaker form of coexistence which is referred to as relative permanence. This new concept of coexistence combined with numerical simulations strongly suggests that the basin of attraction of the locally asymptotically stable interior period-2 orbit is an infinite union of connected components. This idea may apply to many other ecological models. Finally, we discuss the generic dynamical structure that gives relative permanence.

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Date Created
2012-03

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A Model for the Division of Labor Through Network Interactions

Description

We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost

We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost ci > 0 to the individual performing task i. We examine this process on complete graphs, bipartite graphs, and the integers, answering questions about the relationship between communication, defection rates and the division of labor. Assuming the division of labor is ideal when exactly half of the colony is performing each task, we nd that on some bipartite graphs and the integers it can eventually be made arbitrarily close to optimal if defection rates are sufficiently small. On complete graphs the fraction of individuals performing each task is also closest to one half when there is no defection, but is bounded by a constant dependent on the relative costs of each task.

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Created

Date Created
2015-05

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Modeling the Task Performance Dynamics of Social Insects

Description

Division of Labor among social insects is frequently discussed in regards to the colony's worker population. However, before a colony achieves a worker population, a queen is required to perform all of the tasks necessary for her survival: foraging, building

Division of Labor among social insects is frequently discussed in regards to the colony's worker population. However, before a colony achieves a worker population, a queen is required to perform all of the tasks necessary for her survival: foraging, building the colony, and brood care. A simple ODE model was developed through the use of a framework of replicator equations in dynamical environments to investigate how queen ants perform and distribute all of the tasks necessary for her and her colony's survival by incorporating individual internal thresholds and environmental stimulus. Modi�cations to the internal threshold, risk of performing the task, and the rate of increase of the environmental stimulus were also explored. Because of the simplicity of the model, it could also be used to measure the task performance of larger populations of social insects. However, the model has only been applied to the data collected from Pogonomyrmex barbatus single queen ants.

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Created

Date Created
2016-12

Mathematically Modelling Population Dynamics of the Honeybee Infected with Varroa destructor and the Related Viruses

Description

The decline of honeybee colonies around the world has been linked to the presence of the Varroa destructor, a mite acting as a virus vector for the Acute Bee Paralysis Virus. We developed a model of the infestation of the

The decline of honeybee colonies around the world has been linked to the presence of the Varroa destructor, a mite acting as a virus vector for the Acute Bee Paralysis Virus. We developed a model of the infestation of the Apis melliifera honeybee colony by the Acute Bee Paralysis Virus, which is transmitted by the parasitic Varroa destructor. This is a four dimensional system of nonlinear ODE's for healthy and virus infected bees, total number of mites in the colony and number of mites that carry the virus. The Acute Bee Paralysis Virus can be transmitted between infected and uninfected bees, infected mite to adult bee, infected bee to phoretic mite, and reproductive mites to bee brood. This model is studied with analytical techniques deriving the conditions under which the bee colony can fight off an Acute Bee Paralysis Virus epidemic.

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Created

Date Created
2015-12