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

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.

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

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

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 -0.093, 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) = -17.76 To predict the population, add the rate of change to the current population: 190+ -17.67 = 172 bunnies

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 ( -17.76) 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.

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

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

More Population Ecology Example #3 There are 265 turtles living in a lake. Their birth rate was found to be 0.341 turtles/year per capita and their death rate was found to be 0.296 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 = 0.341 - 0.045 0.296 = Because the answer is positive (+) the rate of population growth is increasing.

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.

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 1134. 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 - 0. 24 = + 0.395 + 0.395 B = 0.155

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.

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 

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

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

Need more help? https://www.youtube.com/watch?v=c6pcRR5Uy6w https://www.youtube.com/watch?v=rXlyYFXyfIM http://www.khanacademy.org/science/biology/crash-course-ecology-2/v/crash-course-ecology-02 http://www.brightstorm.com/science/biology/ecology/population-growth/