Problem Set 1 Population Size and Growth

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Michigan State University *

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355

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Biology

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Feb 20, 2024

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Problem Set 1: Population Size and Growth IBIO 355: Ecology Name____________________________ ID______________ Problem sets must be turned in by the beginning of class on February 15 (you must turn it in using the D2L Dropbox). Late problem sets will not be accepted. You must complete the problem set individually. The problem set is worth a total of 25 pts, and will consist of 2% of your final class grade. 1. After taking Ecology, you become interested in birds and decide to conduct a six year study of Cardinals at Picnic Point. During the first year, you estimate the Cardinal population size via a mark-recapture study. You sample Cardinals for two days by catching them with nets and then placing unique color bands around their legs. On the first day, you catch and mark 75 Cardinals. On the second day, you catch 80 Cardinals, of which 40 are marked. Estimate the size of this Cardinal population. (3 pts) 2. In the next 5 years, you estimate Cardinal population sizes in the same way, and find that their size in the 2 nd year is 162, in the 3 rd year is 175, in the 4 th year 189, in the 5 th year 204, and in the 6 th year is 220. What is the geometric rate of increase for this population assuming resources have been unlimited? (3 pts) 3. During 2015, you estimated the population size of Cardinals at Picnic Point. You find that there were 58 individuals. In examining historical data from Picnic Point, you find that 162 Cardinals were at Picnic Point in 1960. What has been the geometric rate of increase of Cardinals at Picnic Point since 1960 (assuming it has been constant over that time period and that resources have been unlimited)? (3 pts)

4. You go to Hawaii for spring break where, because of the good climate, Cardinals (which were introduced there) breed continuously throughout the year. In addition, these Cardinals exhibit density-dependent growth (their population grows according to the logistic equation), with their carrying capacity of 350 individuals on the Big Island determined by the size of the island. If r 0 = 0.1 individuals / (individual*year), by how many individuals would the population change in the first year after introduction if the original population size was 480 Cardinals? (4 pts) 5. Using the information in problem 4, what is the maximum positive change in the number of individuals per year (that is, the maximum value of dN/dt)? (3 pts) 6. Again using problem 4, at what population size would per capita growth rate be the highest? (3 pts)

7. Each row of graphs describes either a density-independent or density-dependent population. Please complete the two empty graphs using the information of the provided line. Label which row demonstrates density-independent or density-dependent population growth. For the one row of graphs where it should be included, circle where K is on each of the three graphs. (6 pts) A. Density-_____________ population growth B. Density-_____________ population growth dN Ndt Population Size (N) N Time dN dt Population Size (N) dN Ndt Population Size (N) N Time dN dt Population Size (N)

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