Midterm formulas

Question 1

Discrete Growth Formula

Answer 1

N(T) = λ^T * N(0)

Question 2

Continuous Growth Formula

Answer 2

N(t) = e^(rt) * N(0)

Question 3

Relationship between λ and r

Answer 3

λ = e^r

Question 4

Discrete time leads to what kind of growth?

Answer 4

Geometric Growth

Question 5

Continuous time leads to what kind of growth?

Answer 5

Exponential Growth

Question 6

How do you find r?

Answer 6

r = (lnN2 - lnN1)/(t2-t1)

Question 7

Assumptions of exponential growth model?

Answer 7

1. No immigration, no emigration
2. No change in environmental factors
3. No genetic structure
4. Constant birth and death
5. Continuous growth with no time lags
6. No age or size structure

Question 8

What is a generation?

Answer 8

All individuals produced within a single life cycle

Question 9

What is generation time?

Answer 9

The average duration of a life cycle between birth and reproduction

Question 10

Net reproductive rate

Answer 10

∑bxlx = R(0)

Question 11

Generation time formula

Answer 11

G = ∑xbxlx/∑bxlx

Question 12

Intrinsic rate of increase per year for age structured population (Per capita rate of increase)

Answer 12

r = lnR(0)/G

Question 13

Direct factors of density dependent regulation

Answer 13

1. Aggression
2. Cannibalism
3. Territoriality
4. etc

Question 14

Most important indirect factor of density dependent regulation

Answer 14

Resource exploitation

Question 15

Example of indirect regulation of population through density dependence

Answer 15

Overpopulation leads to fewer resources, leading to decreased fecundity

Question 16

The logistic equation for density dependent population growth

Answer 16

r = -[r(0)/K]*N + r(0)

Question 17

What is K?

Answer 17

Carrying capacity

Question 18

Properties of the logistic equation

Answer 18

1. Has a solution
2. Describes a sigmoid curve
3. For N(0)>K, regulates down to carrying capacity
4. Rate of change of population size is zero for N=0 and N=K
5. Rate of change of population size is an inverted parabola as a fcn of N
6. The per capita rate of change of population size is a linearly decreasing fcn of N

Question 19

What is the Ricker Model used for?

Answer 19

Density dependent growth in discrete time

Question 20

Ricker Model formula

Answer 20

N(t+1) = N(t)e^[r(0)(1-{N(t)/K)]

Question 21

What is a closed population?

Answer 21

No emigration or immigration

Question 22

What characterizes an open population?

Answer 22

There is emigration and immigration

Question 23

What is a metapopulation?

Answer 23

A population within a group of populations between which members of the different populations migrate.