Thesis Abstract

Abstract
Logistic growth is a fundamental concept in population biology that describes how populations increase in size when resources are abundant and decrease when resources are scarce. The logistic growth model incorporates both exponential growth, where populations increase rapidly, and a carrying capacity, which represents the maximum population size that the environment can support. This study aims to investigate the impact of the logistic growth rate on the population dynamics of biological species. By manipulating the growth rate parameter in the logistic growth model, we can explore how changes in this parameter influence population size, growth patterns, and stability over time. Through simulations and mathematical analyses, we will examine how different growth rates affect population trajectories and the ability of species to thrive in their environments. Specifically, we will explore scenarios where growth rates are below, at, and above the intrinsic growth rate, which is the maximum rate of population increase under ideal conditions. Furthermore, we will investigate the relationship between the growth rate and the carrying capacity of a population. By varying the growth rate while keeping the carrying capacity constant, we can observe how different growth rates impact the population's ability to reach equilibrium and avoid overshooting the carrying capacity. Understanding the impact of the growth rate on population dynamics is crucial for predicting how biological species may respond to environmental changes, such as habitat loss, climate change, or the introduction of invasive species. By quantifying the effects of different growth rates, we can gain insights into the resilience of populations and their ability to adapt to changing conditions. In conclusion, this research project will contribute to our understanding of how the logistic growth rate influences the population dynamics of biological species. By exploring the relationship between growth rates, carrying capacity, and population stability, we can enhance our ability to predict and manage populations in natural ecosystems. Ultimately, this knowledge can inform conservation strategies and help ensure the long-term viability of species in a rapidly changing world.

Thesis Overview

INTRODUCTION
1.1 Background to the Study

A community is a small or large social unit (group of people) having something in common, such as norms, religion, values or identity. Examples of a community include; a country, village, town or neighbourhood. A community can also be defined as a group of interdependent plants or animals growing or living together in a natural condition or occupying a specified habitat.

Ecological definition of a community or biocoenosis is an assemblage or association of two or more different species occupying the same geographical area and in a particular time. The term community has a variety of uses. In its simplest form, it refers to group of organisms in a specific place and time.

Community ecology or synecology is the study of the interactions between species in communities on many spatial and temporal scales, including the distribution, structure, abundance, demography and interactions between coexisting populations. The primary focus on community ecology is on the interactions between populations as determined by specific genotypic and phenotypic characteristics. Modern community ecology examines patterns such as variation in species richness, equitability, productivity and food web structure. It also examines processes such as predator – prey population dynamics, succession, and community assembly [(Ricklefs & Verhoef Herman (2008)].

Species interact in various ways: competition, predation, parasitism, mutualism, commensalisms, etc. Competition is an interaction between organisms or species in which organisms or species struggle for limited resources. Predation is a positive-negative interaction between a predator specie and a prey specie in which the predator specie benefits while the prey specie is harmed. Parasitism is a non-mutual relationship in which one specie, the parasite benefits at the expense of the other specie called the host. Mutualism is an interaction between two species in which both benefit. Commensalism is a relationship among organisms in which one organism benefits while the other organism is neither benefited nor harmed (Holt, 1977).

Populations of animals or species are controlled by many factors. Natural selection is a broad term that describes one effect of these controls on population. One form of population control that can result in natural selection is competition. It is considered to be an important limiting factor of population size, biomass and species richness. The competition between individuals, populations and species is an evidence that competition has been the driving force in the evolution of large groups [Raven & Johnson (1999)].

There are a number of essential resources upon which organisms lives depend. Whenever these resources are limited, organisms are forced to compete for survival. Three resources that organisms are likely to compete for are space, water and food.

The types of competition are interference competition, exploitative competition, and apparent competition. Interference competition occurs when an individual of one specie directly interferes with an individual of another specie. Exploitative competition occurs when an individual of one specie consumes a resource, and that resource is no longer available to be consumed by a member of another species. Apparent competition is when two species share a predator [Holt (1977)].

These competitions lead to logistic growth rate caused by insufficient space, water and food. Every community consists of its population size, the carrying capacity of the population, and the logistic growth rate. How the population size and the carrying capacity affect a population is known, but how the logistic growth rate affects the population is a problem troubling the minds of individuals. That is why the logistic growth rate is considered as the area of interest.

1.2 Research Justification

Logistic growth of a population size occurs when resources are limited, thereby setting a maximum number an environment can support. Therefore, investigating its rate is very necessary.

The topic “Investigating the impact of logistic growth rate on the population of biological species” is scientifically well-posed due to its hypothetical form. It leads to a research design and analysis with scientific credibility such as the logistic equation.

This research might offer some empirical messages for scientists especially mathematicians and biologists about how to identify the effect of the growth rate of a population in a particular period, and also the importance of the carrying capacity of a population. The proposed study will help scientists in their investigations and serve as a guide to future researchers.

1.3 Purpose of the Study

The purpose of this study is to numerically investigate the impact of logistic growth rate on the population of biological species.

1.4 Scope of the Study

This study focuses on the logistic growth rate of a population due to the competition among species. It will consist of investigating the relationship of the variables in the model. The research topic explains variables such as the population size N, the carrying capacity K, the logistic growth rate r and the competition coefficient ∝. It explains different outcomes under different conditions like the relationship between the population size and the carrying capacity. It extends the understanding of the phenomena being investigated.