Single-Species Populations III: Simple Models in Discrete Time

Question 1

Describe a problem with the discrete logistic

Answer 1

• fractional individuals can be outputted because r is a real number
• fractional individuals do not exist

Question 2

How are fractional individuals removed from the discrete logistic?

Answer 2

• truncating in R
• introduce randomisation into the number of new individuals using the Poisson distribution

Question 3

What is the Poisson distribution?

Answer 3

• a discrete distribution that is specified by the mean (becomes more symmetrical as the mean increases)
• there is only one parameter

Question 4

What does the Poisson distribution introduce?

Answer 4

• demographic stochasticity

Question 5

What is demographic stochasticity?

Answer 5

fluctuations driven by natality and morbidity stochasticity

Question 6

As average population size decreases…

Answer 6

• percentage fluctuation increases
• sometimes resulting in chance extinction when K < 50

Question 7

Chance extinction is more likely in

Answer 7

K-selected species

Question 8

What is the consequence of demographic stochasticty for r-selected species?

Answer 8

must survive in large groups to prevent the combined population destruction of both environmental and demographic stochasticity.

Question 9

List some risks of small populations

Answer 9

• demographic stochasticity
• Allee effect
• genetic drift

Question 10

Describe genetic drift

Answer 10

decreases genetic diversity within populations when operating on a constrained gene pool

Question 11

Give an example of genetic rescue

Answer 11

Florida panther (Puma concolor cougar), which did not naturally recover from the effects of drift on its small population
- human intervention in the form of panther translocation from Texas in 1995 facilitated recovery

Question 12

Describe the Allee effect

Answer 12

weak or strong

Question 13

Describe the weak Allee effect

Answer 13

per capita population growth rate remaining low (there is no boom phase) when population sizes are small.

Question 14

Describe the strong Allee effect

Answer 14

negative population growth below some critical threshold.

Question 15

List three examples of the Allee effect in wild populations

Answer 15

• musk ox
• African wild dogs
• kakapo

Question 16

Describe the Allee effect in musk ox

Answer 16

• relies upon group defence as an anti-predator strategy
• disintegrates on group size reduction

Question 17

Describe the Allee effect in African wild dogs

Answer 17

rely upon large group sizes for their pack hunting behaviours

Question 18

Describe the kakapo

Answer 18

• heaviest parrot species
• flightless
• ground-nesting
• nocturnal
• low basal metabolic rate that allows it to subsist on low-quality food

Question 19

Describe K selection in the kakapo

Answer 19

• decades-long lifespan
• small clutch size
• clutch frequency of 2-7 years, depending on the abundance of high-quality food for offspring rearing

Question 20

Describe kakapo restoration

Answer 20

• Stewart Island, onto which no mustelids were introduced
• 1977 there were 100-200 birds discovered, however these were being predated upon by cats
• lowest population size reached by the Kakapo was 51 birds, with an asymmetric weighting towards males
• 1980-1997, birds were translocated to Whenua Hou, Te Kakahu, Anchor and Maud islands, and an intensive and costly recovery programme introduced

Question 21

Describe the kakapo recovery programme

Answer 21

• fitting every bird with a smart transmitter for tracking
• annual catching and health inspection
• refilling island feeding stations to supplement nutrient acquisition
• remote monitoring
• 69 cases of chick removal (on failure of food supply) for artificial incubation and hand rearing to eliminate demographic stochasticity
• stringent biosecurity protocols
• traps for predator deterrence
• helicoptering 21 kakapo affected with kakapo aspergillosis

Question 22

Describe kakapo aspergillosis

Answer 22

• 2019 outbreak on Codfish island for intensive treatment
• 12 to recover and 9 deaths, 2 of which were adult females named Hoki and Huhana, and 7 chicks and juveniles from the 2019 cohort

Question 23

Describe kakapo immunity

Answer 23

• low immunity
• hypothesized to be linked to the genetic erosion arising from their small population

Question 24

Describe the general decline of British birds

Answer 24

From a 1975 index of 100, 130 species have all declined to roughly 90.

Question 25

Describe the specific decline of British birds

Answer 25

• wetland and water birds have decreased to roughly 86
• woodland birds to approximately 71
• farmland birds to approximately 44

Question 26

Describe discrete time population dynamics in closed systems with high r

Answer 26

• r values between 1 and 2 are associated with dampened oscillations (decreased randomness) followed by 2 point limit cycles
• r>3, deterministic yet unpredictable chaos is outputted, relative to the starting population size

Question 27

Describe deterministic chaos generally

Answer 27

• large recruitment in a single generation allows the population to exceed K
• coupled to overcompensating density-dependence
• for high Nt, Nt+1 will decrease
• ‘boom-bust’ cycling

Question 28

Describe deterministic chaos specifically

Answer 28

• plotting Nt against Nt+1 shows an equilibrium, but it is not stable
• the only point of stability is when Nt = K
• equilibrium is never reached
• Nt ≠ Nt+1