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study guide exam 2 - Bio 373 Study guide exam 2 1 Important...

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Bio 373. Study guide exam 2 1. Important concepts/phenomena to understand (use your learning comprehension skills to master them): 1. Why are mathematical models important? Because they can make predictions with numbers, can easily change assumptions because the numbers allow one to do so, can be used to test hypothesis. 2. How are mathematical models used in science? They are use to make predictions, and then challenge these predictions in mathematical language (numerically and analytically). A mathematical model is a quantitative hypothesis based on an explanation or theory; is a set of assumptions about an ecological system expressed in mathematical language. 3. Differences between deterministic and stochastic models a. Deterministic model: make the assumption that if we know the present condition of the system, we can predict its future. b. Stochastic model: incorporation some representation of randomness. c. Deterministic models perform the same way for a given set of initial conditions. Conversely, in a stochastic model, randomness is present and variable states are not described by unique values, but rather by probability distributions. 4. Differences between state variables and parameters: state variables are quantities used to describe the current condition of the system. So state variables change as the system changes. Parameters are quantities whose values do not change over time. 5. The fundamental processes used to model temporal population dynamics (population growth) : the fundamental processes are BIDE (birth, immigration, death, and
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emigration). These are the input-output budget framework (balance equation) are the basis for our models of population growth. 6. When is it feasible to assume immigration and emigration are not important in modeling the growth of a population? Closed population. A population could be considered closed when there is a very slow rate of immigration or emigration compared to the birth and death rates. 7. Exponential growth* a. Pattern set to explain: continuous increase or decrease over time b. Exponential growth equation: N t = N 0 e rt c. Long term solution of exponential growth equation: N(t)=(initial population)*exp(r*t) d. What values of r lead to increase, decrease and steady state of population: increase: greater than zero; decrease: less than zero; steady state: 0 e. Assumptions of exponential growth model: i. Birth and death rates occur continuously ii. No variation in birth and death rates from year to year iii. Individuals are the same iv. No immigration or emigration v. Birth and death rates are independent of population size 7. Geometric growth* a. Pattern set to explain: increase or decrease over discrete time intervals b. Geometric growth equation (difference equation): N t+1 = N t λ c. Long term solution of geometric growth model: N t = N o λ t d.
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