Mathematical Model and Dynamics Analysis of the Stingless Bee (Trigona sp.) in A Colony (original) (raw)

A Quantitative Model of Honey Bee Colony Population Dynamics

PLoS ONE, 2011

Since 2006 the rate of honey bee colony failure has increased significantly. As an aid to testing hypotheses for the causes of colony failure we have developed a compartment model of honey bee colony population dynamics to explore the impact of different death rates of forager bees on colony growth and development. The model predicts a critical threshold forager death rate beneath which colonies regulate a stable population size. If death rates are sustained higher than this threshold rapid population decline is predicted and colony failure is inevitable. The model also predicts that high forager death rates draw hive bees into the foraging population at much younger ages than normal, which acts to accelerate colony failure. The model suggests that colony failure can be understood in terms of observed principles of honey bee population dynamics, and provides a theoretical framework for experimental investigation of the problem.

Modeling Honey Bee Populations

PLOS ONE, 2015

Eusocial honey bee populations (Apis mellifera) employ an age stratification organization of egg, larvae, pupae, hive bees and foraging bees. Understanding the recent decline in honey bee colonies hinges on understanding the factors that impact each of these different age castes. We first perform an analysis of steady state bee populations given mortality rates within each bee caste and find that the honey bee colony is highly susceptible to hive and pupae mortality rates. Subsequently, we study transient bee population dynamics by building upon the modeling foundation established by Schmickl and Crailsheim and Khoury et al. Our transient model based on differential equations accounts for the effects of pheromones in slowing the maturation of hive bees to foraging bees, the increased mortality of larvae in the absence of sufficient hive bees, and the effects of food scarcity. We also conduct sensitivity studies and show the effects of parameter variations on the colony population.

Modelling Food and Population Dynamics in Honey Bee Colonies

PLoS ONE, 2013

Honey bees (Apis mellifera) are increasingly in demand as pollinators for various key agricultural food crops, but globally honey bee populations are in decline, and honey bee colony failure rates have increased. This scenario highlights a need to understand the conditions in which colonies flourish and in which colonies fail. To aid this investigation we present a compartment model of bee population dynamics to explore how food availability and bee death rates interact to determine colony growth and development. Our model uses simple differential equations to represent the transitions of eggs laid by the queen to brood, then hive bees and finally forager bees, and the process of social inhibition that regulates the rate at which hive bees begin to forage. We assume that food availability can influence both the number of brood successfully reared to adulthood and the rate at which bees transition from hive duties to foraging. The model predicts complex interactions between food availability and forager death rates in shaping colony fate. Low death rates and high food availability results in stable bee populations at equilibrium (with population size strongly determined by forager death rate) but consistently increasing food reserves. At higher death rates food stores in a colony settle at a finite equilibrium reflecting the balance of food collection and food use. When forager death rates exceed a critical threshold the colony fails but residual food remains. Our model presents a simple mathematical framework for exploring the interactions of food and forager mortality on colony fate, and provides the mathematical basis for more involved simulation models of hive performance.

Competition of the Bee Colonies - a Computer Model and its Applications

Biocybernetics and Biomedical Engineering, 1982

The development of a genus depends always on the environment in which it lives and all the conditions which exist in its domain of activity. Almost always in the nature there are some rival dependencies as the results of competition for food. The paper presents an attempt at modelling description of the passive competition phenomenon among the bee families concerning a common source of food. This phenomenon has been analyzed to show the rules of division of limited food reserve and the use of this reserve. The influences of following factors have been discussed: —strength of a bee family, efficiency, location and the "attraction" of a food source,— searching, transmission and the exchange of information, —influences of random factors, weather etc. A digital simulation model realized on the Odra 1300 and R-32 computers has been used.

On the Effects of Artificial Feeding on Bee Colony Dynamics: A Mathematical Model

PLOS ONE, 2016

This paper proposes a new mathematical model to evaluate the effects of artificial feeding on bee colony population dynamics. The proposed model is based on a classical framework and contains differential equations that describe the changes in the number of hive bees, forager bees, and brood cells, as a function of amounts of natural and artificial food. The model includes the following elements to characterize the artificial feeding scenario: a function to model the preference of the bees for natural food over artificial food; parameters to quantify the quality and palatability of artificial diets; a function to account for the efficiency of the foragers in gathering food under different environmental conditions; and a function to represent different approaches used by the beekeeper to feed the hive with artificial food. Simulated results are presented to illustrate the main characteristics of the model and its behavior under different scenarios. The model results are validated with experimental data from the literature involving four different artificial diets. A good match between simulated and experimental results was achieved.

The computer model of the bee colony

System Science, vol. 9, No. 3 1983, pp. 83 - 95, 1983

The paper presents a model of a bee colony. The model consists of 10 basic modules: reproduction, collection of food, environment, atmospheric conditions, food economy, potential demand, control and meeting the demand, honey capping and uncapping, and building of honeycombs. A program simulating the behavior of the model has been written in FORTRAN. The values of the model parameters based on the estimation and on the separate identificational experiments are given in the Appendix. The model can be considered successful since the results of the simulation correspond fairly well with the values of the real system.

The Formal Model for the solitary bee Osmia bicornis L. agent‑based model

2023

Solitary bees provide an important ecological and agricultural service by pollinating both wild plants and crops, often more effectively than honey bees. In the context of worldwide pollinators' declines, it is important to better understand the functioning of populations under multiple stressors at larger spatial and temporal scales. Here we propose building a detailed, spatially-explicit agent-based model of one of the best-studied species of solitary bees, Osmia bicornis L. In this Formal Model, we review various aspects of O. bicornis biology and ecology in detail and provide descriptions of their planned implementations in the model. We also discuss the model gaps and limitations, as well as inclusions and exclusions, allowing a dialogue with the reviewers about the model's design. The ALMaSS model of O. bicornis aims to provide a realistic and detailed representation of O. bicornis populations in space and time in European agricultural landscapes. The model will be a part of the Animal, Landscape and Man Simulation System (ALMaSS); thus will be able to utilise a highly detailed, dynamic ALMaSS landscape model. It will consider the behaviour of all bee life stages daily and use state transitions to allow each individual to decide their behaviour. The development of egg-to-pupa stages in the nest will be temperature-driven. Adult bees, after they emerge from the nest in spring, will interact with the environment. They will be able to search for suitable nesting locations, provision their brood cells with pollen and reproduce. Modelled females will balance offspring size and ‡ ‡ ‡ § © Ziółkowska E et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. number following the optimal allocation theory, but local environmental factors will modify their actual parental investment decisions. The model will include the daily mortality rate for the egg-to-pupa stages, overwintering mortality, and background mortality outside the nest. We will also consider the risk of open-cell parasitism as increasing with the time the brood cell is open. With the level of detail suggested, the model will be able to simulate population-level dynamics in response to multiple factors at the landscape scale over long periods. The European Food Safety Authority (EFSA) has suggested O. bicornis as a model organism for non-Apis solitary bees in the pesticide risk assessment scheme. Therefore, we hope our model will be a first step in building future landscape risk assessments for solitary bees.

How to model honeybee population dynamics: stage structure and seasonality

Mathematics in Applied Sciences and Engineering, 2020

Western honeybees (Apis Mellifera) serve extremely important roles in our ecosystem and economics as they are responsible for pollinating $ 215 billion dollars annually over the world. Unfortunately, honeybee population and their colonies have been declined dramatically. The purpose of this article is to explore how we should model honeybee population with age structure and validate the model using empirical data so that we can identify different factors that lead to the survival and healthy of the honeybee colony. Our theoretical study combined with simulations and data validation suggests that the proper age structure incorporated in the model and seasonality are important for modeling honeybee population. Specifically, our work implies that the model assuming that (1) the adult bees are survived from the egg population rather than the brood population; and (2) seasonality in the queen egg laying rate, give the better fit than other honeybee models. The related theoretical a...