topic 5

Question 1

assumptions of logistic growth - from topic 4

Answer 1

1. Simple density-dependence (linear & positive)
   Relaxed in more complex models; e.g. Allee effect (Topic 5)
   
   2. Responses to crowding are instantaneous (no time lags)
      Relaxed in time-lagged models (Topic 5)
   3. No age or genetic structure
      Can produce age-structured models (next topic)
   4. No impact of other species on population growth
      Can be included (next few weeks)
   5. Closed population & constant K
      Relaxed in more complex models

Question 2

non - linear density dependence- why?

Answer 2

D-D more complex than simple linear in nature
○ At intermediate pop. Levels - might be intraspecific competition
○ At higher densities - might be interactions w other species ie. Predators compounding death rate = exponential death rate
ex. 2 Although death rate may increase due to interspecific competition, maybe cooperation helps offset it
graphs

Question 3

inverse D-D?

Answer 3

not realistic for full range of densities
○ Opposite of interspecific competition
○ Not realistic for all densities but does come into play for certain situations, especially at low pop. Numbers - called the allee effect
•
b goes up and d goes down

Question 4

what is the allee effect? look at graphs

Answer 4

inverse D-D at low N

Question 5

why might you see allee effects - higher death rates

Answer 5

• Higher death rates in small pops. Because
• Lack of group cooperation
○ Increase predation risk
○ Reduced foraging efficiency
○ Unable to thermoregulate
• Small populations at risk of stochastic extinction &
negative genetic effects (e.g., inbreeding
depression)

Question 6

why might you see allee effects - lower b rates

Answer 6

• Mating failures
○ Pollination or fertilization failures ex some fish or corals that use passive reproduction
○ Males and females unable to locate one another
Stochastic variation in sex ratio

Question 7

consequences of allee effect - what is mvp, is it stable

Answer 7

○ At low pop their ability to cooperate declines
○ If density continued to increase the inverse density dependence would disappear
○ Mvp - unstable equilibrium, under this size pop. Is unlikely to continue to be viable
Death rate is density independent in the consequences graph, but still have mvp and carrying capacity

Question 8

look at graphs of allee. define MVP

Answer 8

• Either way you will see mvp and k exhibiting allee effects
Minimum viable population size (MVP): Min. # individuals required for a high probability of population survival over a given period of time

Question 9

why is mvp unstable

Answer 9

• Mvp unstable bc pops below this number will exceed to extinction
If they exceed k they will still decline, but will decline towards carrying capacity NOT to extinction
d=b at mvp, d=b at k, look at graph

Question 10

pop below mvp?

Answer 10

d>b, r<0

death rate > birth rate

Question 11

pop above K

Answer 11

d>b, r>0

large pop, death exceeds birth, pop decline towards k

Question 12

pop allee effects at intermediate N?

Answer 12

pop increase towards k

d<b>0 </b>

Question 13

what are time lags

Answer 13

• Amount of time it takes for a population to respond to change in environment (ie. Density)
Causes delayed density dependence
Population vital rates do not respond immediately to changes in N, i.e., they
experience time lags

Question 14

time lag examples

Answer 14

• GESTATION TIME: # born at a given time may be influenced by
densities present several time periods ago
○ # births depends on conditions when individuals became pregnant, after which there is a gestation period.
○ Lag time = gestation period
• DEATH IS NOT IMMEDIATE:
• Lag time = time between change in conditions (density) & when an individual actually dies
Ie. Starvation

Question 15

ex of more complex time lag interaction

Answer 15

interspecific can also cause time lags
Relating to more complex interactions:
Induced plant defenses may take time (after initial
herbivory) to accumulate
Delayed numerical responses of predators
— Gestation time Of predators

Question 16

what does timelag do to pop growth

Answer 16

Time lags result in population fluctuations (ossilations) • Pop. Might grow above carrying capacity - hasn’t responded immediately
• Then they will drop below carrying capacity - will begin to respond, also not immediate

Question 17

oscillations in discrete time logistic

Answer 17

Discrete model coarse density-dependent feedback (built in time lags)
Population growth rate adjusted once per discrete time interval
Without additional time lags, extent of oscillations depend on R (see simulation)
with added time lags - extent of oscillations depend on R and length of time lag

Question 18

look at graph of pop growth with and without time lag

Answer 18

ok

Question 19

time lags for cont. logistic?

Answer 19

no time lags - instantaneous feedback, no oscillations
can add a time lag to the model: dN/dt=rNt[1-N(t-tau)/k)
pop growth rate responds to pop size w time lag
n(t-tau) = pop size at time t-tau in the past

Question 20

what do time lags depend on

Answer 20

Extent of oscillations depend on:
Reproductive potential (R or r)
Higher R or r = greater “overshoot” or “undershoot” Of K
Length of time lag (tau)
Longer time lag = greater potential “overshoot” or
“undershoot” Of K
Longer tau = responding to population densities further in
the past

Question 21

forms of the model with conditions - look at graphs

Answer 21

when r or R and tau is small w no fluctuation - monotonic approach to equilibrium
aat intermediate values - damped oscillations
at greater values - stable limit cycles
chaos (high R,r, tau)
unstable cycles (VERY high R,r, tau)