MIT Department of Biology 7.014 Introductory Biology, Spring 2004 7.014 Spring 2004 PS 8 1 of 6 7.014 Problem Set 8 Please print out this problem set and record your answers on the printed copy. Problem sets will not be accepted late. Question 1 You are studying how the growth of a population of your favorite species of frog, Xenopustropicalis. You construct a massive pond for the frogs and provide them with an unlimitedfood supply. a) You begin your experiment with 50 frogs and after 10 months you find 61 frogs in yourpond. Assume a continuous growth model for the population.i) What is the intrinsic rate of increase in units of months-1 for the frogs (to thenearest hundredth)? ii) How long will it take for your initial population of frogs to double (in months)? b) You allow the population of frogs to increase to double the initial population, but then yourealize that you don’t really have the space or resources to allow the population to continue togrow unchecked. You consider two possible ways to naturally cut the rate of growth of thepopulation. i) You decide to simply cut the supply of food to the frogs (harsh though thismay sound you reason that it will cause a decrease in new breeding andeventually you will reach a steady state population). After another 10 months you find that you have population of 106 frogs. Assuming the value for rmax is the same as it was in part a, and that population growth is following the logisticequation, estimate what the carrying capacity (in number of frogs) is for yourenvironment. 17.014 Spring 2004 PS 8 2 of 6 Question 1, continued b) ii) Your second option is to introduce frog-eating snakes into your pond environment.You introduce a small number of snakes into the pond. After a few months you returnto your pond and find that the snake population has increased dramatically and that thefrog population has decreased equally dramatically. In fact there are now more snakes than frogs present in the pond. Provide two different predictions about what willhappen to the populations of snakes and frogs in the long term in your pondenvironment. Question 2 Survivorship curves allow one to understand a great deal about the survival and reproductionof a species. a) Draw three types of survivorship curves (label the axes) and explain what each graphrepresents. 27.014 Spring 2004 PS 8 3 of 6 Question 2, continued b) For each of the following groups choose the survivorship curve that best fits with their lifecycle and briefly explain why.i) A group of frogs that reproduce using external fertilization of millions of eggs. ii) A group of prize rose plants (assuming that they have a finite life span). iii) A group of human beings born in England in 1200 A.D. iv) A group of human beings born in England today. c) Pearl and Reed developed the logistic equation while modeling human population growth.They introduced the concept of K = carrying capacity. For the United States, Pearl and Reedestimated a carrying capacity of 197 million would be reached in 2300. Today the populationof the United States is approaching 300 million. i) In words, describe what carrying capacity is. ii) It is possible that their model is correct, and that the discrepancy is due to anincreased carrying capacity. What are some reasons that the carrying capacity wouldhave increased? iii) It is also possible that their model is correct, but that the discrepancy is due to a timelag. Explain what this would mean for the population in the future. 37.014 Spring 2004 PS 8 4 of 6 Question 3 Early in the evolution of life on earth, three major branches emerged, the bacteria line, thearchaea line and the nuclear line. The endosymbiotic theory proposes that all eukaryotes arederived from the nuclear line. a) Plants are thought to have evolved from the nuclear line cells that had formed a symbioticrelationship with bacteria. i) What type of bacteria would have been part of the symbiotic relationship thatgenerated the plants lineage? ii) What part of the plant cells is the modern day relative of the ancient bacteria? iii) The cellular process of _____________________________occurs here.What are the end products of that process? b) Other eukaryotes are thought to have evolved from the nuclear line cells that had formed asymbiotic relationship with different bacteria. i) What type of bacteria would have been part of the symbiotic relationship thatgenerated the non-plant lineage? ii) What part of the non-plant cell is the modern day relative of the ancient bacteria? iii) The cellular process of _____________________________occurs here.What are the end products of that process? c) Molecular evolutionary biologists use DNA as molecular chronometers to determinerelatedness of different species. They have data that strongly supports the endosymbiotictheory. Briefly describe what that data is. 47.014 Spring 2004 PS 8 5 of 6 Question 3 d) You want to determine the relatedness of the many different bacterial and eukaryoticspecies of the deep sea vent communities. Which DNA would be the most appropriate foryour studies? DNA encoding an oxygen binding protein. DNA encoding an enzyme needed for chemosynthesis DNA encoding an enzyme required for splicing DNA encoding an enzyme used in glycolysis. Why? e) Explain why the DNA sequence encoding a protein and not the protein sequence itself isused for comparison. 57.014 Spring 2004 PS 8 6 of 6 Question 4 You are a budding ecologist ready to get your start studying an old growth forest located onthe West Coast of the U.S. Just as you are preparing to go out and begin your research, amassive wildfire comes roaring through and destroys the entire forest. a) You make a trip out to the site a few months later to see what the ecosystem looks like.Expecting to find only a barren charred wasteland, you are shocked to find lots of wildflowersand weeds, along with some insects and birds. What characteristics must these plants havethat allows them to grow here? b) Twenty years later as a faculty member at a prestigious institution, you return to the site tofollow up on your initial characterization of the ecosystem and to pick some of the nice prettywildflowers. Once again you are shocked to find that site looks nothing like it did when youfirst arrived. Now you find many young trees and some underbrush along with many smallmammals, insects and birds. What made it possible for these new plant species to colonize thislocation? c) Now ready to retire,
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