SCN3230-ABED_1: Module 8 Lesson 4 - 2

Lesson 4 — Measuring Population Growth

Determining the Rates of Population Growth

Read pages 704 - 709

One of the biggest problems that field biologists face is how to get accurate population counts. Organisms that swim, run, hide, burrow, or fly and those that are dangerous or are very small are difficult to count. Estimation methods must be used. In this lesson, you will learn some of the sampling methods used and how to do some of the calculations that give the population numbers meaning to those who analyze the data (such as wildlife managers).

Density

Density is the number of individuals in a given unit of area (land) or volume (air or water).

Population density is calculated using the following formula

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»D«/mi»«mi»p«/mi»«/msub»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»N«/mi»«mi»A«/mi»«/mfrac»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»o«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»D«/mi»«mi»p«/mi»«/msub»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»N«/mi»«mi»V«/mi»«/mfrac»«/math»

For example, the population density of 75 dandelions in an area of 25m² is expressed as

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»D«/mi»«mi»p«/mi»«/msub»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»N«/mi»«mi»A«/mi»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»75«/mn»«mrow»«mn»25«/mn»«mo»§#160;«/mo»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»d«/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mi»e«/mi»«mi»l«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mo»/«/mo»«mo»§#160;«/mo»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/math»

Population density is a simple method to estimate the population size. However, the estimation cannot take into account unused spaces and is unaffected by population distribution patterns.

Population Growth

The size of a population is the result of four population determining factors at work. These factors can increase, decrease, or work together to maintain population size. They are natality, mortality, immigration, and emigration.

Natality: number of births
Mortality: number of deaths
Immigration: movement of individuals into a population
Emigration: movement of individuals out of a population

Population growth (ΔN) can be calculate using the following formula:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«mi»N«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mi»N«/mi»«mi»a«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mi»i«/mi»«mi»t«/mi»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»I«/mi»«mi»m«/mi»«mi»m«/mi»«mi»i«/mi»«mi»g«/mi»«mi»r«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mi»M«/mi»«mi»o«/mi»«mi»r«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mi»i«/mi»«mi»t«/mi»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»E«/mi»«mi»m«/mi»«mi»i«/mi»«mi»g«/mi»«mi»r«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«/mrow»«/mfenced»«/math»

Natality and immigration increase a population size. Mortality and emigration decrease a population size. The number of individuals in a population is expressed as N. The change in the number of individuals in a population is ΔN (delta N).

Growth Rate

The growth rate (gr) is the change in the number of individuals in a unit of time. Growth rate (gr) is positive if the population size is increasing and negative if it is decreasing.

Population growth rate (gr) can be calculated using the following formula:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»§#916;«/mi»«mi»N«/mi»«/mrow»«mrow»«mi»§#916;«/mi»«mi»t«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»p«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»p«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«/mrow»«mrow»«mi»c«/mi»«mi»h«/mi»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»i«/mi»«mi»m«/mi»«mi»e«/mi»«/mrow»«/mfrac»«/math»

Per Capita Growth Rate

The per capita growth rate (cgr) is the rate of change per individual. This represents the change in population size in relation to the initial population. The per capita growth rate (cgr) can be calculated using the following formula:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mi»g«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»§#916;«/mi»«mi»N«/mi»«/mrow»«mi»N«/mi»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«msub»«mi»N«/mi»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«msub»«mi»N«/mi»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«/mrow»«msub»«mi»N«/mi»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«/mfrac»«/math»

The per capita growth rate (cgr) is useful when comparing the population growth rates of two population with different sizes. For example, an increase of 20 individuals in a year for a population of 200 has a growth rate of 0.10. For a population of 2000, an increase of 20 individuals yields a much smaller per capita growth rate of 0.01.

Growth rate expresses how fast the population is increasing or decreasing. Per capita growth rate indicates the proportion of the change for which each individual in the initial population is responsible.

Example

During 18 months, the population of 300 field mice experienced 900 births and 400 deaths. 25 mice left the population and 75 mice joined the population.

Calculate the the population change (ΔN) of field mice.

http://www.w3.org/1998/Math/MathML

Calculate the growth rate (gr) of field mice population.

http://www.w3.org/1998/Math/MathML

Calculate the per capita growth rate (cgr) of field mice population.

http://www.w3.org/1998/Math/MathML

Calculate the per capita growth rate per year of field mice population.