1. By Janet Nguyen Period 4- 2014
Population Ecology
By Janet Nguyen
Period

2. What is Population Ecology?
It is the study of how species interact in their habitat, effected both by space and time.
It deals with birth rates, death rates, total population, carry capacity, and the maximum growth rate of the population.

3. Exponential vs. Logistic Growths
Exponential Growth
Logistic growth
Means that there are no limiting factors to the population
Represented by a J-shaped curve
Mostly theoretical, except in the case of humans (we have removed most limiting factors from our environment)
The population is regulated by limiting factors, like predators, limited amounts of food and water, etc.
Represented by a S-shaped curve
Once the population hits the environment’s carry capacity, the population shrinks below K before it expands again

4. Variable and Equations
N = population size at the beginning of period
r(max) = maximum rate of growth of the population
* r = (# of births - # of deaths)/ N
t = time
K = Carry Capacity
dY = amount of change
dN/dt = change of population over time
Logistic Growth: dN/dt = r(max) x N
Exponential Growth: dN/dt = r(max) x N x (K-N)/K
Population Growth: dN/dt = Births - Deaths

5. Exponential Growth Example #1 dN/dt = r(max) x N Rate of change =
There are 190 rabbits in a field, which is under the carry capacity of the field. If the rate of growth is , then predict the population of rabbits next year.
Because it is UNDER carrying capacity, we know to use the equation for EXPONENTIAL growth.
dN/dt = r(max) x N
Rate of change =
-0.093(190) =
To predict the population, add the rate of change to the current population:
= 172 bunnies

6. Example #1 Explained
Because you are asked to predict the next year’s population, you have to do two things:
Find the rate of growth of the population { r(max) x N}.
Once you have found the rate of change, add your answer ( ) to the original population (190) to get 172 bunnies.
* Your rate of growth can be either negative or positive: if it is negative, that means there are more deaths than births, and if it is positive, then vice versa.

7. Logistic Growth Example #2 Rate of Change = = 0.2 x 40 x (70-40)/70
A population of lady bugs produces baby lady bugs, which leads to a high growth rate of the population. There are currently 40 lady bugs in the garden, and their r(max) = 0.2 lady bugs/month per capita. The carrying capacity of the garden is 70 lady bugs. What will their rate of change be in this logistic growth situation?
Because it says ‘logistic growth’ we know to use the equation for logistic growth
dN/dt = r(max) x N x (K-N)/K
Rate of Change =
= 0.2 x
40 x
(70-40)/70
= 3.42 lady bugs/ month

8. Example #2 Explained Plug the variables into the given equation
r(max) defined as 0.2
N (original population) defined as 40
K (carrying capacity) defined as 70
Calculate and your answer will be 3.42 lady bugs/month

9. More Population Ecology
Example #3
There are 265 turtles living in a lake. Their birth rate was found to be turtles/year per capita and their death rate was found to be turtles/year per capita. What is the rate of population growth per year and is it increasing or decreasing?
Rate of growth can be found by subtracting the death rate from the birth rate.
dN/dt = Birth rate – Death rate
Rate of Change =
0.045
0.296 =
Because the answer is positive (+) the rate of population growth is increasing.

10. Example #3 Explained
Always remember that the rate of growth of a population is just the death rate subtracted from its birth rate.
Plug in the birth rate and death rates as defined in the problem (3.41 and 2.96)
Calculate
When the rate of change is positive, the population is increasing.
When the rate of change is negative, the population is decreasing.

11. More Population Ecology
Example #4
A new group 1,492 birds is brought to Mt. Diablo. As scientists study them over the next year, they see that the death rate is 0.395, dropping the population to Over that same year, what was the birth rate for the group of birds?
dN/dt is the change in population; to find that, subtract the final population from the start population.
dN/dt = (B – D) x N
1134 -
1492 =
- 358 dN/dt
Set up an equation to find the birth rate:
- 358 = (B – 0.395) x 1492
1492
1492
B – 0.395 =
B = 0.155

12. Example #4 Explained
Two things need to be found: the change in population, then the birth rate. (You have to find the change in population before solving for B)
To find the change in population, subtract the original population from the final population.
Once you’ve done so, plug the respective variables into the equation (dN/dt = (B – D) x N) and solve for B like you would solve any other linear equation.

13. More Population Ecology
Example #5
Given the following information on Population A and Population B, fill in the tables below. The information was gathered over reproductive cycle, or one year.
Parameter
Population A
Population B
Initial #
500
300
# Established
100 30
# that Die 20
Fill in the tables on the next slide 

14. Example #5 Cont. Parameter Population A Population B B (births) 100 30
D (deaths) 20
b (birth rate per capita)
Births/total population = 100/500 = 0.2
Births/total population = 30/300 = 0.1
d (death rate per capita)
Deaths/total population =
20/500 = 0.4
100/300 = 0.33
r (per capita rate of increase)
Birth rate – death rate = 0.2 – 0.4 = 0.16
Birth rate – death rate
= 0.1 – 0.33 = 0.23

15. Example #5 Cont. Time (year) Population A Size 500 (500 x 0.16 = 80) 1
500
(500 x 0.16 = 80) 1
580
(580 x 0.16 = 93) 2
673
(673 x 0.16 = 108) 3
781
(781 x 0.16 = 125) 4
906
* To find the population size in the next generation, take the population and multiply by the rate per capita increase (0.16) and add the answer to the population- your final answer will be the size of the population the next year

16. Need more help? https://www.youtube.com/watch?v=c6pcRR5Uy6w