EVSP 342_Worksheet1_10Dec2023

Worksheet 1 Instructions: Calculate the answers for the following questions and answer them below. Be sure to show your math. If you’d like to do this Worksheet in Excel rather than in Word, you are welcome to do that and attach it instead. Each question is worth 10 points, 5 for the answer itself and 5 for showing/explaining your work. Partial credit will be given where appropriate. 1. Given that a deer population of 50 animals is increasing at a rate r of 0.4, how many deer will be added to the population in the first year (at the end of N 0 )? Hint: The Malthusian exponential growth model is N t = N 0 + r N 0 , where r represents the rate of change in population size. N t = N 0 + r N 0 N 0 = 50 r = 0.4 N t = 50 + (0.4*50) N t = 50 + 20 N t = 70 Answer: 20 deer will be added to the population in the first year. 2. Using the Malthusian exponential growth model from question 1, what will the same deer population size be in another year, at the end of N 1 . Hint: N 0 is no longer 50. You will need to calculate the new N 0 accounting for the number of individuals added last year. N t = N 0 + r N 0 N 0 = 70 r = 0.4 N t = 70 + (0.4*70) N t = 70 + 28 N t = 98 Answer: 98 will be the deer population size in another year, at the end of N 1 . 3. What will the population be in 2 years, at the end of N 2 ? N 0 = 98 r = 0.4 t = 2 0.4*98=39.2 39+98=137

Answer: 137 will be the deer population size in 2 years, at the end of N 2 . 4. If N 0 =50 and r =0.2, what will the population size be after 5 time periods? N1=50+(0.2*50) 50+10=60 N2=60+(0.2*60) 60+12=72 N3=72+(0.2*72) 72+14.4=86.4=86 N4=86+(0.2*86) 86+17.2=103.2=103 N5=103+(0.2*103) 103+20.6=123.6=124 Answer: 124 will be the deer population size in 5 years. 5. You can see if you want to predict N into the far future, using the Malthusian exponential equation will be time consuming. For predicting N into the future, we tend to prefer the continuous growth model where N t =N 0 *e rt . Using this equation, calculate the predicted population size after 5 time periods given that N0=50 and r=-0.2. Hint: e is a mathematical constant. N t = N 0 * e rt N 0 = 50 e = 2.71828183 r = -0.2 t = 5 N t = 50 * 2.71828183 (-0.2*5) N t = 50 * 2.71828183 (-1) N t = 50 * 0.367879 N t = 18.39395 Answer: 18 will be the deer population size in 5 years. 6. Given that r=0.023 per year, what will the population size be in 2010 if N0=1370 in 2000? N t = N 0 * e rt N 0 = 1370 e = 2.71828183 r = 0.023 t = 10 N t = 1370 * 2.71828183 (0.023*10) N t = 1370 * 2.71828183 (0.23)

As a land or wildlife manager, I would think that these types of population change predictions would be useful in understanding, evaluating, and helping with making informed decisions about the possible size of future populations and the likelihood of different outcomes would help develop more adaptive and realistic conservation strategies. They can assist with the knowledge of the possibility of a sudden increase or for populations that are at higher risk of decline from a predictable change and prioritize these interventions (i.e., preventing extinction, promoting population growth, anticipating how restored habitats may influence population dynamics, the impact of climate change, predicting the potential impact of hunting quotas, helping to set sustainable harvest levels, an invasive species threatening native wildlife, etc.). Overall, population change predictions can inform the development of policies related to hunting, habitat protection, and other human activities that impact wildlife. 10. What was the most interesting thing you have learned so far? Why is the most interesting to you? What I have found most interesting is that according to the mathematical models a population will tend to self-correct if not influenced by an outside source (i.e., disease, fire, flood, food shortage, etc.). Meaning that it will not exceed its carrying capacity or reach a population of zero. To me, this is interesting as it shows how nature has its way of self-leveling if left untouched.