Population Models

WFB 174

Principles of Wildlife Management

For your technical paper, you will construct several population models that will help you determine how your species’ population changes over time. These models will serve as the primary data input for you to discuss potential scenarios of population and habitat management. The population dynamics section will have 5 parts:

• A model of population growth with no mortality
• A graph of population growth over time
• A stable population model with “real” survival and birth data
• A sensitivity analysis
• A text section that discusses the results of the models and documents your demographic parameters

1. Model 1: Population model with no mortality (survival rate = 1)
1. In this model, you will construct a spreadsheet that models an initial population of 100 individuals (either pairs or females) for 10 years. The initial data that you will need will be:

i. Longevity of the species. This parameter will dictate the number of age classes in your model. For example, if your species lives to 5 years of age, you will have 5 age classes: 0-1 years, 1-2 years, 2-3 years, 3-4 years, and 4-5 years. (All individuals will die when they reach the maximum age class).

ii. Each age class will have its own birth rate based on information from the literature.

iii. Age structure of the population. This information will dictate the initial distribution of the 100 females (or pairs) in each age class at time = 0. These will likely be the most difficult data for you to find. Consider the birth rates as a clue to age structure.

2. Graph of geometric population growth. This assignment is simply a graph of the values you derived in your first population model.
3. Population model with “real” survival rates. For this model, you will now add age-specific survival rates (from the literature) to the model. Your population should remain stable at approximately 100 individuals (or pairs). All other parameters (age distribution, longevity, birth rates) should be the same as model 1.
4. Sensitivity analysis – A sensitivity analysis is used to develop a better understanding of which parameters have the most influence on a model. In this case, you will determine whether birth rates or survival rates have a greater effect on population growth rates.
1. Increase survival rate for all age classes by 10% (If s = 0.8, increase it to 0.88) and note the change in final population size. Return survival rate to its original value.
2. Increase reproductive rate for all age classes (that reproduce) by 10%. In this case, if reproductive rate = 2.0, increase it to 2.2. What is the change in final population size?
3. Which change had a greater effect on final population size? Return parameters to their original values.
4. Use the parameter that had the lower effect on final population size. What size increase in this parameter would be necessary to have the same effect as the parameter change that had the greater effect? For example, say a 10% increase in survival rate increased the final population to 350, whereas the 10% increase in birth rates only increased the final population size to 150. How much further would you need to increase birth rates to achieve a final population of 350?
5. Written Population Dynamics section
1. Justification for all parameters from the literature. If you can not find values in the literature, you must provide a logical explanation for use of those values.
2. Discussion of your population models. For example, if birth rates are typically 2.0 for all age classes, but you had to use 1.8 to stabilize your population, why are the values different?
3. Calculation of lambda and doubling time
4. Type of growth curve (see Fig. 5-5 and 5-6, page 60 in Population Dynamics chapter). Where does your species fall on the r-K continuum (and why)?
5. Discussion of your sensitivity analysis.

i. You might want to present this in a Table:

Parameter	% change	Final pop size
Stable model	NA	102
s	10	350
b	10	150
b	40	350

i. How will the results of the sensitivity analysis affect your future management recommendations? This can be brief, as you will discuss this further in the Population and Habitat Management section.