topic 4 - logistic Flashcards
what is density dependence?
When birth and death rates (and therefore population growth rates) are influenced by the density of the population
assumption of unlimited growth models
• Death rates are constant - unlimited growth models
d does not vary with population size/density (density independent)
if density dependent, how will D reacti
Total # of deaths (D or dN) will increase as a straight line with N
increases at a constant rate proportional to N
deaths that are D-D vs D-I - look at graphs
D-D deaths increases linearly when D-I is constant straight line - unlimited growth mode
D-D death numbers increases at an accelerating rate for D-D - slope is increasing
D-D is irl?
birth rates - density independence w unlimted growth?
b is contant
when increading, Bor bN increases at a constant rate (linearly)
what about with d-d (more like nature) - d-d birth rates w unlimited growth?
birth rate is constantly declining
due to intraspecific competition, a declime in birth rate with increasing N will be seen
number of births still increases over lime, but at a decelerating rate (eventually stabilizes)
look at summary D-i vs D-D graphs
ok
positive linear dependence
look at graphs
•
When there is a linear D-D increase In death rates and a D-D linear decrease in birth rate
what does logistic pop. growth models assume
positive linear D-D
graph- X shape, decreasing birth rate (b), increasing death rate (d)
can have different slopes, but general pattern / somewhat x shape
what is r? how to calculate?
r = intrinsic or instantaneous rate of increase
r=b-d
b>d = r>0
b
look at example of D-D in a real pop
ok
what is carrying capacity (short)
Populations are stable - carrying capacity = a stable equilibrium point
b=d, r=0
define carrying capacity. what does it depend on? when is pop growth positive/negative
- Maximum sustainable population size for a given organism based on prevailing environmental conditions
- Depends on supply of limiting resources (can vary within a species)
- Point at which intraspecific competition prevents further pop. growth
- •Population growth positive below K; negative above K
- Population growth begins to slow at K/2 (inflection point)
what is the inflection point
Inflection point = halfway up y axis between 0 and k , max sustainable yield
discrete logistic model - provided
Nt+1 = RNt(1-Nt/K)
continuous time logistic pop model
provided
look at graphs of logistic cont vs discrete and where K is
ok
what happens when N is small
• When N is small, (1-N/K) is close to 1
• Near straight line increase in population growth rate (dN/dt)
Population size N increases similarily to in the exponential growth model
what happens as N approaches K
• As N approaches K, (1-N/K) declines and limits growth
dN/dt starts to decline (at K/2)
No. individuals being added to population (N) slows down
what happens when N=K
• When N=K, (1-N/K) = 0
Population growth rate declines to zero
No further increases in population size
for cont logistic growth - why is rate of pop growth limited at low and high densities
t • Too few individuals to contribute
At high its bc intraspecific competition is limiting growth
for cont - at what pop size is fastest rate of pop growth
half carrying capacity
describe max sustainable yield + its use
• Industries (e.g., fisheries, wildlife management, etc.)
• Want to know the max. # indiv. that can be harvested, while allowing the population to return to K as quickly as possible (for another productive harvest)
• When N = K/2, the population is growing at its fastest rate
— This is your MSY
• If you harvest at N = K/2, the population can quickly recover
Allow you to maximize your harvest (yield) over time
limitations and assumptions of the logistic growth model
Closed population — relaxed in more complex models
Constant K— relaxed in more complex models
Assumes the simplest possible density-dependence (linear with N)
• Relaxed in more complex models; e.g. Allee effect (coming up)
Assumes responses to crowding are instantaneous (no time lags)
• Relaxed in time-lagged models (coming up)
Assumes every individual contributes equally to population growth
(no age or genetic structure)
•Can produce age-structured models (coming up)
No impact of other species on population growth
•Can be included in model (coming up)
when is logistic model best used
• Best fit for organisms growing by themselves (does not consider intraspecific competition, predation, parasitiism)
• Also best for organsims with fast life cycles and simple behavior
•
