MIT Department of Biology 7.014 Introductory Biology, Spring 2004 7.014 Spring 2004 PS 8 answers 1 of 5 Solutions to 7.014 Problem Set 8 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)?rtNt = Noe 61 = 50(er(10)) r = 0.02 months-1 ii) How long will it take for your initial population of frogs to double (in months)?Td = ln2/r Td = 0.693/.02 Td = 34.65 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. Nt = K / (1 + [(K-No)/No]e-rt)106 = K / (1+[(K-100)/100]*0.8187)K = 145 17.014 Spring 2004 PS 8 answers 2 of 5 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. One prediction would be that the snakes would eat all of the remaining frogs and then lacking afood supply would starve to death. Another prediction would be that the snake population woulddecline because there is not enough food, and this decline would allow the frog population torebound. Once the frog population reached a high enough level the snakes would start toincrease their population size because of increased food supply. Thus the two populations wouldoscillate out of phase with each other. 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. Log (NumberType I Type II Type III High Probability of Survival Steady Survival High Probability of Survival Low Probability of Survival Low Probability of Survival Age 27.014 Spring 2004 PS 8 answers 3 of 5 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.Type III curve, many eggs are fertilized but very few make it to adulthood. ii) A group of prize rose plants (assuming that they have a finite life span).Type I curve, these plants are taken care of and so will mostly survive until they die of old age. iii) A group of human beings born in England in 1200 A.D.Type III, there was very high infant mortality throughout most of human history, despite theinvestment that parents put into their offspring. (Type I for parental investment would also beok) iv) A group of human beings born in England today.Type I, modern medicine has decreased infant mortality a great deal and parents put a hugeinvestment into their children. 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.The maximum population that the system can support. 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? Increased agriculture, Increased energy into system from mining of fossil fuel. 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.It may be that their estimated carrying capacity is real but the time that it is taking humans torespond to the changes in the bioshere is so long. In that case the population has increasedbeyond the real carrying capacity, and will need to decrease until at carrying capacity. 37.014 Spring 2004 PS 8 answers 4 of 5 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? cyanobacteria ii) What part of the plant cells is the modern day relative of the ancient bacteria?chloroplast iii) The cellular process of photosynthesis occurs here. What are the end products of that process?You get ATP and NADPH in the light reactions. These are used to make Glucose and O2 is produce as a waste product. 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? A heterotrophic bacteria. ii) What part of the non-plant cell is the modern day relative of the ancient bacteria?mitochondria iii) The cellular process of respiration occurs here. What are the end products of that process?Respiration burns glucose to generate
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