Project Abstract

Abstract
The logistic growth model is a fundamental tool in population ecology, used to study the dynamics of biological species in changing environments. This research project aims to investigate the impact of logistic growth rate on the population size of biological species. By applying mathematical modeling and simulations, we explore how different growth rates affect the population dynamics and sustainability of species over time. Through a series of simulations using various growth rates, we analyze the population trajectories of species under different scenarios. Our results indicate that the growth rate plays a crucial role in determining the population size and stability. Species with higher growth rates tend to exhibit rapid population growth initially, but may face challenges such as resource depletion and increased competition as the population approaches carrying capacity. Conversely, species with lower growth rates show slower but more sustainable population growth, maintaining a relatively stable population size over time. By comparing the population dynamics of species with varying growth rates, we identify trade-offs between growth rate, population size, and resilience to environmental changes. Furthermore, we investigate how external factors such as environmental disturbances and carrying capacity influence the relationship between growth rate and population size. Our findings suggest that species with moderate growth rates may have a better chance of adapting to changing environments and fluctuations in resource availability. In addition, we explore the implications of different growth rates on species interactions and community dynamics. Species with high growth rates may outcompete others for resources, leading to shifts in community composition and potential ecosystem disruptions. On the other hand, species with lower growth rates may have a more stable coexistence with other species, contributing to the overall biodiversity and ecosystem resilience. Overall, this research contributes to our understanding of the complex interactions between growth rate, population dynamics, and ecosystem stability. By examining the impact of logistic growth rate on biological species, we gain insights into the factors influencing population size, sustainability, and community structure. This knowledge has implications for conservation efforts, ecosystem management, and the long-term viability of species in a changing world.

Project 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.