Lecture 9: Logistic Growth & Life Tables Flashcards
Define carrying capacity. What variable is used for it?
the maximum number of individuals that can be supported by a particular environment
represented by K
How does carrying capacity vary? Why?
with the quality of the environment
K will be lower if the environment is of poor quality and vice versa
If there are less resources in an environment, less individuals will be able to survive there
Describe the logistic growth model?
A method of modelling population growth that factors in the limitations on growth that carrying capacity presents
what is the equation for logistic growth? List the variables
dN/dt = rN(1-N/K)
dN/dt = population growth r = per capita rate of increase N = number of individuals in the population K = carrying capacity
Which part of the logistic growth equation is responsible for constraining population growth as pop size increases?
(1-N/K) acts as a modifier of r
When (1-N/K) is a small number, how is r effected?
Negligibly
What happens when (1-N/K) is a # approaching K?
Fewer and fewer individuals are added per unit time until N = K
When N = K, what is the per capita rate of increase?
0
ie, no individuals are being added to the population per unit time
What kind of shape does the logistic growth curve have?
An S-shape curve
What does (1-N/K) tell us about the population?
How close the population is to carrying capacity
if it’s closer to 1 = further from K
if it’s closer to 0 = closer to K
What occurs as the population size (N) approaches K?
a) per capita birth rate DECREASES
and/or
b) per capita death rate INCREASES
Which results in the per capita rate of increase (r) DECREASING
(r = b-d) so
if b
T or F: population growth speeds up as the size approaches K
FALSE
because the death rate will increase and/or the birth rate will decrease
So less individuals are being added to the population per unit time
At what population size (N) is growth the fastest? Explain
At K/2
When N is small, the population is far from K, and r will be large because individuals are able to produce many offspring but the amount of individuals reproducing is small - slow growth
When N is approaching K, r is small because the number of deaths is increasing and number of births is decreasing = growth is slow
When N is halfway to K, N and r are intermediate values so growth is the fastest
What are the 3 phases of the logistic growth model?
- establishment phase
- boom phase
- stabilization phase
Describe the establishment phase of the logistic growth model
Population size (N) is small, so growth is slow because even if everyone who can produce is reproducing, there are still only a few individuals reproducing
bottom of the curve closest to axes (left)
Describe the boom phase of the logistic growth model
Growth is fastest because N is big, but not approaching K yet
Everyone is not producing at max rate because r is being modified
halfway up the curve (when K/2)
Describe the stabilization phase of the logistic growth model
Growth is slow because N is large and approaching K
Individuals are not reproducing at max rate and many individuals will be dying
the plateau at the top of the curve
if the environment has a carrying capacity, then the population growth is dependent on _____ ____
population density
What are birth and death rates dependent on?
population density
When does negative density dependence occur?
When the growth rate DECREASES as population size increases
most common
What two kinds of factors affect negative density dependence? Explain them
- intrinsic factors: physiological responses to high density (stress)
- extrinsic factors: environmental factors impacting birth/death rates as population density increases
Give an example of how intrinsic factors affect negative density dependence
High density of white-footed mice induces hormonal changes that:
- delay sexual maturity (reduce birth rate)
- depress immune system (increase death rate)
- r will decrease
Give some examples of extrinsic factors that affect negative density dependence
- resource availability (more individuals, less food/water/shelter/breeding territory = more death/less birth)
- patterns of predation can change when population is large (more vulnerable; more death)
- disease/parasite transmission is higher (more death)
What are the 3 ways density dependence can occur?
- Death rate increases as N approaches K (death rate is density dependent)
- Birth rate decreases as N approaches K (birth rate is density dependent)
- both death rate increases and birth rate decreases as N approaches K
Describe positive (inverse) density dependence. When is the usually seen?
Density dependence that occurs when the intrinsic growth rate (r) INCREASES as population size increases
Usually occurs in very small population sizes
What is the Allee effect?
A decline in reproduction or survival that occurs when the population size is SMALL
Give an example of the Allee effect?
The positive correlation between seed production and population size in cowslip plants
When the population size is large, the number of seeds produced per individual is also large.
When the pop size is small, the number of seeds produced per individual is also small
Describe density independent factors and give some examples
Factors that are unrelated to population size that influence the births and deaths of a population
- flood
- drought
- hurricane
- tornado
- heat wave
- fire
