Example research essay topic: Population Growth Population Increases - 1,455 words

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Modeling Population Growth First of all, lets give definition to population growth. The term basically explains how the population changes with time (decreases or increases). It is controlled by the death and birth rates. According to the main ideas of modeling population growth, the rate at which a population changes depends on at least three factors (Modeling Population Growth: Main Ideas, n. p. ). Lets examine the models of animal population growth and the three factors depending on which the population rate changes.

They are as follows: Net Birth Rate for the Population Lets assume that population increases or decreases linearly in proportion to its current value. According to Modeling Population Growth: Main Ideas, a net birth rate is the constant of proportionality and depends on several factors: The proportion of animal population that will mate The number of offspring for each mating pair The proportion of population that will die during the next Period of time (n. p. ). The second factor is overcrowding and scarcity of resources Quantity of animals (the size of population) depends on natural resources such as land and / or food availability. Sometimes animal population is too large to be supported by the available resources (n. p. ) Harvesting Harvesting of fishing is the term describing the removal of a constant number of individuals from a population during each time period (n.

p. ). This factor, evidently, cannot be applied to the models demographers use for human population growth. Harvesting or fishing is usually made by people. Besides, sometimes the harvesting is accomplished to artificially reduce quantity of animal population to reduce the number of animals who needlessly die from starvation or other natural causes (n. p. ).

Yet, unregulated harvesting can result in extinction. The duration of time when population increases or decreases depends on whether the population has a mating season (for example, the mammals) or whether the population reproduces continuously (like bacteria, some insects, and domesticated rabbits) (n. p. ). How can we include harvesting or fishing into our mathematical model? Lets assume that the constant number of individuals (h) is removed from the population during the certain period of time. In such a way, the differential equation can be as follows: dP/d The Natural (Exponential) Growth Model.

One of the very famous population models is the mathematical model of population growth, proposed by Thomas R. Malthus. Actually, this is the earliest model of population growth, which is a basis for most future modeling of biological populations (Malthusian Growth Model n. p. ). According to Malthus, A thousand millions are just as easily doubled every 25 years by the power of population as a thousand. But the food to support the increase from the greater number will by no means be obtained with the same facility (Growth Models, Part 2 n.

p. ). The biologists use the following equation that models the change of a population as being proportional to the number of individuals in the population (Unbounded Populations n. p. ). If P (t) is the number f individuals in population as time t, and k is a positive constant, the equation is as follows: d P/d t = k P According to it, general solution of d P/d t = k P is C exp (kt). C represents population at the time we first consider it, where exp is just another way to write ee-to-the (n.

p. ). Besides, to get a certain solution, we need to have experimental observations that are able to explain the following: The initial population; The net birth rate. k is the coefficient that determines whether the population will grow without limit, or whether it will become extinct (n. p. ). Lets illustrate the model of exponential growth with the following example. According to Malthus model, if the population consisting of 1. 000 individuals increases to 1. 500 individuals over the course of ten years, the population consisting of 10. 000 individuals will increase to 15. 000 individuals over the same period of time.

The mathematical model used by Malthus is the model, which has only one parameter and one variable. The parameter is known to researcher, whereas the variable is the figure that changes over the course of time and represents the figure we are interested in observing. Population is the variable and the population growth rate is the parameter. The Malthus model has many applications except of population growth. For example, the large populations of animals are not limited by the environmental factors are grow in accordance with the exponential model. Limits of Growth We also need to note that population grows within a certain limits.

In such a way we need to modify our population model to predict the fact that many populations have a so-called limiting population that is determined by the carrying capacity of their environment The term overcrowding as well as coefficient of overcrowding are the easiest ways to model a limiting population. The equation is as follows: dP/dt = k P - A P 2 In other words, the overcrowding term is proportional to the square of the current population. If we assume that A > 0, the negative sign in the second term indicates that this term decreases the population (n. p. ). This is the logistic model of growth. In the model using exponential growth (the logistic growth) the individuals are not limited by land, food, disease or other factors.

Yet, these factors are important and there is an upper limit to the number of individuals the environment can support. Ecologists refer to this as the carrying capacity of the environment (Logistic Growth, n. p. ) If the solution of this differential equation is a constant (it doesnt change over the certain period of time) we consider that differential equation has an equilibrium solution: P (t) = C (constant). In this model the individuals are not limited by food or disease factors and have constant birth rate. In this model the birth rate is mostly the only factor that controls the speed of population growth.

If the birth rate is high, the population can quickly become overcrowded. In this situation the ecologists often apply harvesting or fishing to regulate quantity of individuals in population. Natural and Coalition Models of Growth The following table represents data, proving that population grows exponentially. Year (CE) Population (millions) Year (CE) Population (millions) 1000 200 1940 2295 1650 545 1950 2517 1750 728 1955 2780 1800 906 1960 3005 1850 1171 1965 3345 1900 1608 1970 3707 1910 1750 1975 4086 1920 1834 1980 4454 1930 2070 1985 4850 Sources: (1) A.

L. Austin and J. W. Brewer, "World Population Growth and Related Technical Problems", IEEE Spectrum 7 (Dec. 1970), pp. 43 - 54. (2) U. S. Census Bureau.

The Natural model of growth used for biological populations considers that dP/dt = kP and proposes that the rate of growth is proportional to population. k represents the productivity rate. Lets emphasize the productivity rate and rewrite the equation as follows: 1 /P dP/dt = k Now lets revert to the model proposed by Heinz von Foerster, Patricia Mora, and Larry Admit. Their model is called a Coalition Growth Model, where the productivity rate is not a constant. The scientists propose to interpret the productivity rate as |an increasing function of P, or a function of the form kPh where the power h is positive and presumably small (if h were 0, this would reduce to the natural model) (Growth Model, Part 3. 1 n. p. ) ) Comparing the animal model of population growth with that of humans, we need to underline that people live within the worlds ecosystems. (Teaching Evolution, Activity 8 n.

p. ). There is an interrelation between biological evolution in populations and the model of human population growth. The human population increases in geometrical progress. Yet, they also can reach limits to growth.

It can stop growing because of increase or death rate or decrease of birth rate as well as certain biological / economic /geographical factors. Bibliography: Growth Models, Part 2. Retrieved December 9, 2005. web Growth Model, Part 3. 1. Retrieved December 9, 2005. web Logistic Growth.

Retrieved December 9, 2005. web Malthusian Growth Model. Retrieved December 9, 2005. web Teaching Evolution, Activity 8. Retrieved December 9, 2005. web The Geometry Center.

Limits of Growth... Retrieved December 9, 2005. web The Geometry Center. Modeling Population Growth: Main ideas. Retrieved December 9, 2005. web The Geometry Center.

Unbounded Populations... Retrieved December 9, 2005. web

Research essay sample on Population Growth Population Increases