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# BCOR 102 Study Material for Final Exam BCOR 102 - A

UVM

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##### BCOR 012 (Biology- Alison Brody and Melissa Pespeni)

###### Brooke Pietrafesa

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This 3 page Study Guide was uploaded by Hannah Taylor on Wednesday May 4, 2016. The Study Guide belongs to BCOR 102 - A at University of Vermont taught by Donald Stratton, Jane Molofsky in Spring 2016. Since its upload, it has received 14 views. For similar materials see Evolution and Ecology in Biology at University of Vermont.

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Date Created: 05/04/16

Study focus questions Stratton Chapters 1-7, 10 This is not a guarantee of what will or won’t be on the exams, but it covers most of the highlights and should provide a good basis for studyin g. Chapter 1, Exponential Population growth: Equations: (know these equations but, more importantly, what they mean and how and when they are used) • dN/dt = rN rt • N=tN e0 • λ = N t+1/ Nt • N= N λ t t 0 Concepts: • What assumptions are in those simple models? • You should be able to graph N vs time for a population growing exponentially with various values of r • You should know when to use discrete vs continuous formulations of the model • How can you predict future population size? What is the doubling time for populations with various values of r and lambda? • You should understand the concepts of environmental and demographic stochasticity and why they matter. Chapter 2, Logistic Population Growth Equations: • dN/dt = rN(1-N/K) Concepts: • You should be able to graph the relationship between the various variables (r, N, dN/dt and time as in figs 2.3 and 2.4) for various values of r and K • What happens when N>K? when N<K? • What are the assumptions of the logistic model? • Show graphically where the equilibrium population sizes are. Are they stable? • Time lags can cause the population to oscillate above and below K. Oscillations are bigger at larger values of r. The discrete model has a built-in time lag of one year. How do the population dynamics (N vs time) change as r chandes? Chapter 3. Applied population dynamics Equations: M 1 m 2 • N = n (this simple form of the equation is good enough) 2 Concepts: • What are the assumptions of the mark-recapture technique for estimating € population size? • Be able to interpret a stock-recruit graph [ N(t+1) vs N(t) ] to identify the equilibrium population size, and how the shape will change as r increases. Be able to determine the stability of the equilibrium. • What do fisheries and wildlife biologists mean by “harvestable excess”? How can you determine that value from the stock-recruit graph? • Understand the logic behind the constant harvest and constant effort fishing rules, and why rule 2 is usually preferred. Chapter 4, Life tables Equations: • R 0 Σ l x x • G = (Σ x lxb x / R 0 • r = ln(R0)/G (approx) Concepts: • Be able to set up a life table, fill in missing values, and calculate0R • How do people gather the data for a life table? • What do l xnd b mxan? • What is the relationship between R a0d λ? • Understand the general concepts of the stable age distribution, reproductive value and life expectancy. Chapter 5, Stage structured population growth Equations: • N t+1 A N t Concepts: • Be able to draw a life-cycle graph. • Be able to translate that life-cycle graph to matrix notation. • What is the difference between age- and stage- (or size)- based life cycle graphs? • Be able to multiply the transition matrix with the pop size vector to calculate the population distribution next generation. • What is the stable age (or stage) distribution? Chapter 6: Metapopulations Equations: • Start with the simple Levins model (islands only): dP =cP(1−P)−eP dt • how would you change that equation for the mainland-island model? Concepts: € • How can colonization and extinction allow persistence of species on a regional scale, even when individual populations are almost certain to eventually go extinct? • What is the equilibrium occupancy fraction, given colonization and extinction rates? How can you tell if that equilibrium is stable? • You should be familiar with one or two of the examples that we talked about. • You should understand the conceptual difference between the pure island model and the island-mainland model and how that difference affects the metapopulation dynamics. Chapter 7 Competition Equations: dN ⎛K −N −αN ⎞ dN ⎛K −N −βN ⎞ • 1 = 1N1⎜ 1 1 2⎟ 2 =r2N 2⎜ 2 2 1⎟ dt ⎝ K1 ⎠ dt ⎝ K2 ⎠ Concepts: • You should be able to draw the zero growth isoclines in state space, draw the € population trajectories for various starting positions, and determine whether the two species will coexist or not. • What is the meaning (in words) of α and β? • You should understand how relaxing some of the assumptions of the model (e.g. adding disturbance, competition/colonization tradeoffs, recruitment limitation) can expand the conditions for coexistence of competitors. • What is R* is and why it is useful? Chapter 10: Disease Equations: dS dI dR dt =−βIS , dt=βIS−kI , dt = kI Concepts • Rather than memorize the equations, understand the basic model (S,I,R) € • Know the meaning of the terms in the model (β, k) and why the model is set up the way it is. • Be able to identify the conditions where dI/dt=0. Why is that important? • What is the meaning of R and how do epidemiologists use that to understand the 0 spread of infectious diseases? • What is herd immunity? What is the minimum fraction of the population that must be vaccinated to prevent the spread of the disease?

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