Question

Using your knowledge of population ecology, discuss how various models of population growth (exponential, logistic, life tables, and age/stage structured models) can be used in community ecology, and discuss the cost/reward of the various models. In other words, how much ‘cost’ is assumed for each model type (inaccuracy, collection effort, complexity), and how does that relate to the ‘reward’ for each model type (accuracy, predictive power,

Answer 1

There are several methods to calculate population growth.

EXPONENTIAL METHOD

Populations with unlimited natural resources grow very rapidly, after which population growth decreases as resources become depleted. This accelerating pattern of increasing population size is called exponential growth. Exponential growth is calculated by the equation,

ΔN/ΔT=B−DΔN/ΔT=B−D

where ΔNΔN = change in number, ΔTΔT = change in time, BB = birth rate, and DD = death rate. The birth rate is usually expressed on a per capita (for each individual) basis. Thus, B (birth rate) = bN (the per capita birth rate “b” multiplied by the number of individuals “N”) and D (death rate) = dN (the per capita death rate “d” multiplied by the number of individuals “N”)

Exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. Bacteria is an example for exponential growth curve. This method can be used to identify the population growth of micro organisms in a laboratory conditon. This method is not possible to apply to calculate the population of organisms living in natural condition. In the real world, with its limited resources, exponential growth cannot continue indefinitely. Exponential growth may occur in environments where there are few individuals and plentiful resources. Exponential growth produces J-shaped curve'

LOGISTIC METHOD

In logistic growth, a population's per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity (K). Logistic growth produces S-shaped curve. This method is used when the growth rate of population due to births,deaths, and migrations takes place under normal situations and it is not subjected to any extra ordinary changes likes epidemic war,earth quake or any natural disaster etc. and the population follows the growth curve charecteristics of living things within limited space and economic opportunity

In age/stage structural model a population is usually represented by a vector, whose entries represent a specific population count: the number of individuals of a given species, of individuals of a given age or residual lifetime,... In this case, the dynamics is determined by a matrix, whose multiplication by a population vector is related to the next generation population vector. One of the main advantages of this kind of models is that, because of matrix transformations such as diagonalization, triangularization or Jordan decomposition, the problem can usually be put in a much simpler form, for analysis or solving.

life table is a a table which shows, for each age, what the probability is that a person of that age will die before his or her next birthday ("probability of death"). In other words, it represents the survivorship of people from a certain population.Life table examines the mortality rates of all the people who have Social Security to decide which actions to take.The concept is also of importance in product life cycle management. This method is widely used in epidemiology and public health.Life tables that relate to maternal deaths and infant moralities are important, as they help form family planning programs that work with particular populations. They also help compare a country's average life expectancy with other countries. Comparing life expectancy globally helps countries understand why one country's life expectancy is rising substantially by looking at each other's healthcare, and adopting ideas to their own systems. However, there are also weaknesses of the information displayed on life tables. One being that they do not state the overall health of the population. There is more than one disease present in the world, and a person can have more than one disease at different stages simultaneously.  Therefore, life tables also do not show the direct correlation of mortality and morbidity.