topic 4 - logistic

Question 1

what is density dependence?

Answer 1

When birth and death rates (and therefore population growth rates) are influenced by the density of the population

Question 2

assumption of unlimited growth models

Answer 2

• Death rates are constant - unlimited growth models

d does not vary with population size/density (density independent)

Question 3

if density dependent, how will D reacti

Answer 3

Total # of deaths (D or dN) will increase as a straight line with N
increases at a constant rate proportional to N

Question 4

deaths that are D-D vs D-I - look at graphs

Answer 4

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?

Question 5

birth rates - density independence w unlimted growth?

Answer 5

b is contant

when increading, Bor bN increases at a constant rate (linearly)

Question 6

what about with d-d (more like nature) - d-d birth rates w unlimited growth?

Answer 6

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)

Question 7

look at summary D-i vs D-D graphs

Answer 7

ok

Question 8

positive linear dependence

Answer 8

look at graphs
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When there is a linear D-D increase In death rates and a D-D linear decrease in birth rate

Question 9

what does logistic pop. growth models assume

Answer 9

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

Question 10

what is r? how to calculate?

Answer 10

r = intrinsic or instantaneous rate of increase
r=b-d
b>d = r>0
b

Question 11

look at example of D-D in a real pop

Answer 11

ok

Question 12

what is carrying capacity (short)

Answer 12

Populations are stable - carrying capacity = a stable equilibrium point
b=d, r=0

Question 13

define carrying capacity. what does it depend on? when is pop growth positive/negative

Answer 13

• 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)

Question 14

what is the inflection point

Answer 14

Inflection point = halfway up y axis between 0 and k , max sustainable yield

Question 15

discrete logistic model - provided

Answer 15

Nt+1 = RNt(1-Nt/K)

Question 16

continuous time logistic pop model

Answer 16

provided

Question 17

look at graphs of logistic cont vs discrete and where K is

Answer 17

ok

Question 18

what happens when N is small

Answer 18

• 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

Question 19

what happens as N approaches K

Answer 19

• 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

Question 20

what happens when N=K

Answer 20

• When N=K, (1-N/K) = 0
Population growth rate declines to zero
No further increases in population size

Question 21

for cont logistic growth - why is rate of pop growth limited at low and high densities

Answer 21

t • Too few individuals to contribute

At high its bc intraspecific competition is limiting growth

Question 22

for cont - at what pop size is fastest rate of pop growth

Answer 22

half carrying capacity

Question 23

describe max sustainable yield + its use

Answer 23

• 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

Question 24

limitations and assumptions of the logistic growth model

Answer 24

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)

Question 25

when is logistic model best used

Answer 25

• 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
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