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

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

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.