Worksheet 2 Instructions: You will need to enter data and upload Worksheet #2 exercises excel file to your student file for full credit. In providing numerical answers, please round up to the nearest whole number. Q1: Rabbit Numbers Over Time a. The graph shows a sigmoid shaped curve. What is the name of this type of curve? b. The carrying capacity for rabbits is? c. During which month were the rabbits in exponential growth? Number of rabbits 60 40 20 Au gu st 1s t 1s t Ju ly Ju ne M ay 1s t 1s t 0 Q2: Logistic vs Exponential Growth Models a. Why are the two curves nearly identical at low population sizes? b. In terms of r, why does the logistic growth curve deviate from the exponential growth curve? c. What happens to r when N exceeds K? 50000 N exponential N logistic 45000 40000 35000 N 30000 25000 20000 15000 10000 5000 0 0 4 8 12 16 20 24 28 32 Time 36 40 44 48 52 56 60 Q3: Linear response of birth and death rates to population density under the Logistic Growth Model The logistic growth model assumes that b and d change linearly with N. Given this, 1) At what population size is K? 2) What is the value of r at K? 2 1.8 death rate 1.6 1.4 birth rate 1.2 1 0.8 0.6 0.4 0.2 0 1 25 50 75 100 P o p u la tio n S iz e Q4. Using the logistic growth equation and the excel spreadsheet \"Worksheet #2 Exercises,\" input the applicable data and answer the following questions. Given that the population demographics are as follows: dN/dt = rN(K-N/K) No = 25 r = 0.28 K = 125 1) What will the population size be after 15 years? 2) At what year will the population hit K? Q5: Birth and Death Rates versus population density, showing the Allee Effect (MVP). In reality birth and death rates do not necessarily change linearly with N. A documented phenomenon called Allee Effects is one example of violation of this assumption. Refer to Graph below to answer the following questions: a) Label line A (i.e., is it b or d rate)? b) Label line B (i.e., is it b or d rate)? c) What is point C? d) What is point D? e) Is r positive or negative between points C and D? 1 Line A Line B C 0.75 D 0.5 0.25 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 1 0 Population Size Q6: Lag-time effects Lag-time effects are another example of why the basic logistic growth model may not fit most populations well. According to the text, when are populations most susceptible to lag-time effects (answer relative to r)? What are the consequences of lag-time effects? Q7: Logistic growth model with variance Refer to the graph below to answer the following questions: a) What is the phenomenon that causes trajectories like projection A? b) What are the long-term consequences, in terms of b and d, of this phenomenon? 1200 1000 N 800 600 400 Projection A 200 0 0 20 40 60 Time 80 100