topic 4 - logistic Flashcards
(25 cards)
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
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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
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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
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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)
