Here is a brief introduction to some of the important parameters that we will need to understand to be able to study population ecology. For each of the parameters it is important that you know (1) the name of the parameter, (2) the algebraic symbol used to represent the parameter, (3) the units of measurement for the parameter, (4) how to calculate the parameter, and (r) how to describe (in words) what a particular value of that parameter means.
It is probably easiest for me to introduce these concepts using an example.
Imagine that in a population of 100 elephants that in one year 10 elephants are born and 5 elephants die.
1) Population Size (N) units- individuals. Measures the number of individuals in a population.
N = 100 individuals
In this population, there are 100 elephants.
2) Population Birth Rate (B) units- number of births per time. Measures the number of births per time that occur in a population.
B = 10 births/year
In this population, each year there are 10 births.
3) Population Death Rate (D) units- number of deaths per time. Measures the number of deaths per time that occur in a population.
D = 5 deaths/year
In this population, each year there are 5 deaths.
4) Population Growth Rate (dN/dt) units- number of idividuals per time. Measures the rate of change of the population size.
dN/dt = B - D
dN/dt = 10 births/year - 5 deaths/year = 5 individuals/year
In this population, the population size increases by 5 individuals each year.
5) Per Capita Birth Rate (b) units- births per time per individual. Measures the number of births per time averaged across all members of the population.
b = B/N
b = (10 births/year)/100 individuals = 0.10 births/year/individual
In this population, each year 0.10 babies are born for each individual in the population.
6) Per Capita Death Rate (d) units - deaths per time per individual. Measures the number of deaths per time averaged across all members of the population.
d = D/N
d = (5 deaths/year)/100 individuals = 0.05 deaths/year/individual
In this population, each year 0.005 individuals die for each individual in the population.
7) Per Capita Growth Rate (r) units = individuals/time/individual. Measure the rate of change in population size averaged across all individuals. The per capita growth rate can be calcuated two ways.
a) r = b - d
r = 0.10 births/year/individual - 0.05 deaths/year/individual = 0.05 ind/year/ind
b) r = (dN/dt)/N
r = (5 individuals/year)/100 individuals = 0.05 individuals/year/individual
In this population, each year 0.05 individuals are added for each individual in the population.
Practice Problem
In a population of 50 tigers, in one year 10 tigers are born and 20 tigers die. What is B, D, dN/dt, b, d, r?
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B= 10/YEAR , D = 20/YEAR , dn/dt = -10/year , b = 0.2 births/year/individual , d = 0.4 deaths/year/individual , r = -0.2 individuals/year/individual
ReplyDeleteNatascha, Thanks for posting your answers.
ReplyDeleteFor the population birth rate the units are births/year and for population death rates the units are deaths/year. I am sure that you were thinking that in your head, but you need to explicity write down the units every time. this is a concept that we need to be pounding into our students' heads over and over until it becomes second nature. Otherwise, all of the answers are correct.
You probably notices that when population growth rates are negative that populations are decreasing in size. Can you describe in words what each of these values of each parameter tells us about population growth in the tiger population?
My results were the same as Natascha's...
ReplyDeleteN = 50 tigers
B = 10 births/year
D = 20 deaths/year
dN/dt = B-D = 10births/year - 20 deaths/year = -10 individuals a year or a decrease in 10 individuals a year
b = B/N = 10 births/year / 50 individuals = .2 births/year/individual
d = 20 deaths/year / 50 individuals = .4 deaths/year/individual
r = b-d = .2 - .4 = -.2 individual/year/individual
To attempt to answer your previous question...the growth rate of the population growth rates are negative and decreasing in size. There are more deaths per year per individual in the population than there are births. Don't know if that is worded correctly or not. Basically for an example...tiger could be hunted and killed faster than they are able to reproduce thus causing the decrease in population. Or their food source could be decreasing in population causing more deaths per year than births.
Brandy,
ReplyDeleteI intentionally chose this example to illustrate an example of a population that had negative population growth. I want you to be comfortable working with both positive and negative growth rates (because they can both exist in the real world). Hopefully, after you have read the information about why exponential growth is unrealistic and "Logistic Growth" you will start to be able to understand some of the factors that determine whether or not populations are increasing or decreasing in size.