Please solve for question 1.1 to 1.4. Thank you
Department. You have been tasked with deciding which of two biological reserve designs should be implemented in Southeastern Arizona, and the objective of your reserve is twofold: 1) maintain a healthy metapopulation of the federally threatened Sonoran Desert Tortoise, and 2) maximize the total species richness housed within your reserve. You will use the models from the lecture on metapopulation dynamics to tackle the first objective, and you will use the models from the lecture for the equilibrium theory of island biogeography to tackle the second objective. The two potential reserve designs are as follows: The Arizona Game and Fish Department has funds to buy 8,000 acres of land to establish their new reserve. Given the land that is available for purchase, they can either buy two 4,000- acre plots of land or eight 1,000-acre plots of land. Part I: Metapopulation Dynamics of the Sonoran Desert Tortoise Due to the size difference between the plots in the two reserve designs, you predict that extinction probability will differ between populations within those plots. To test this prediction, your research team from the Arizona Game and Fish Department carries out population viability analysis using stochastic models for Sonoran Desert Tortoise populations in one plot for each of the two reserve designs. Consistent with your prediction, you find that the extinction probability for the population in the 1,000-acre plot is estimated to be considerably higher (Pe=0.1 per year) when compared with the population in the 4,000-acre plot (Pe=0.02 per year). Use these data and the metapopulation dynamics equations from the lecture to answer the following two questions: 1.1. What is the probability that each of these populations (within a 100-acre plot and 4,000-acre plot) will go extinct over the course of the next 50 years? Show your work. 4,000-acre plot: . 1,000-acre plot: 1.2. What is the probability that the whole metapopulation will go extinct each year for the two reserves? Show your work. . Reserve A (two 4,000-acre plots): . Reserve B (eight 1,000-acre plots): As you might imagine, the Sonoran Desert Tortoise has limited dispersal capacity - it doesn't travel very far each day. For this reason, you predict that the distance between plots in the reserves will have a large impact on the colonization rate between those plots. To test this prediction, your research team from the Arizona Game and Fish Department tracks the movement of Sonoran Desert Tortoises for a year and finds that for the 8-plot reserve where plots are separated by only 3 miles, the colonization rate is much higher (Pc=0.04) when compared with the 2-plot reserve where the two plots are separated by 10 miles (Pc=0.005). Use these data. the data from the first section. and the metapopulation dynamics equations from the lecture to answer the following two questions: 1.3. How many plots are predicted to be occupied at equilibrium for each of the two reserve designs? Round to the nearest whole number and show your work. . Reserve A (two 4,000-acre plots): Reserve B (eight 1,000-acre plots): 1.4. In a paragraph, summarize your findings and explain which reserve design you recommend to the Arizona Game and Fish Department in order to maintain a healthy metapopulation of the federally threatened Sonoran Desert Tortoise. Make sure to use your results to support your decision
