Lecture 5: Population modelling 1 Flashcards
Assuming species-level conservation is worthwhile, how do we go about it?
Caughley (1994) noted a lack of integration between 2 general approaches (“paradigms”)
*the small population paradigm –theoretical work dealing with the problems of small populations
*the declining population paradigm –largely empirical work identifying and attempting to prevent the processes actually causing the decline of populations
distinction remains to some extent – major challenge is to unite the paradigms
The small population paradigm
*Genetic concerns: heterozygosity, inbreeding, drift, effective population size
*Demographic stochasticity: births and deaths and sex ratio
*Environmental stochasticity
*Minimum Viable Populations (MVP) & Population Viability Analysis (PVA)
*Metapopulation management
*Captive breeding
*Protected area design
The declining population paradigm
Identify and treat the causes of decline.
Casual threats
Essential to determine causal threats:
*correlations between decline and putative causes are not evidence of causation
*management actions must be run as experiments or nothing is learned
*consequences of action must be evaluated according to the standard rules of experimentation
-Lord Howe woodhen – good example
-California condor – example of poor practice
The Lord Howe woodhen (good example)
Lord Howe island
*c. 600 miles from Eastern Australia
*apparently undiscovered by humans until end of C. 18th
Series of ecological disturbances:
*pigs introduced, c. 1800
*visiting ships collected food in early 1800s
*human settlement, 1834
*dogs and cats introduced, < 1845
*goats introduced, <1851
*black rats, 1918
LH woodhens (flightless) endemic to the island – were in steady decline (Miller & Mullette 1985):
*by 1853, restricted to mountainous regions of island
* by 1920, restricted to summits of two least accessible mountains
*1969, conservation plight noted, monitoring begun
*numbers stabilised at about 8-10 pairs (with low of 6 pairs)
*alpine habitat saturated
*population unlikely to have been > 60 – 120 birds for > 100 years
assessment of threats: –intensive fieldwork by Miller (from 1978 – 1980)
assessed diet & habitat to rule out food shortages and habitat loss
surveyed rat abundance (black rats had been implicated in declines of other island endemics)
–rats most abundant where woodhen were concentrated
mapped pig distribution –pig / woodhen distributions – close in 2D but not in 3D
–i.e. pigs couldn’t access remote mountain peaks
conservation actions
*pigs eradicated –1979-81
*captive breeding programme –1980-83
*population stable at c. 180 birds (50-60 breeding pairs) –by 1987
*Thought to have carrying capacity of 220 (Brook et al. 1997)
*Around 250 in 2018 (Major et al. 2021)
*1147 in 2022 – following rodent eradication
–no sign of inbreeding depression
*despite prolonged small population size and small numbers of founders for breeding programme
–cost: c. US$ 200,000
The Californian Condor – example of poor practice
*New world vulture
*N America’s largest land bird
Rapid decline:
*C 19th, ranged from BC, Canada, to Arizona & New Mexico
*by 1940, range contraction to small area north of LA
*c. 60 individuals in 1950s?
*c. 20 birds in 1983
*1987, last 8 wild birds taken into captivity
assessment of threats:
*initial decline – habitat loss, shootings? –evidence poor
*1960s, food shortage? –provisioning at feeding stations from 1971-73
*1960s, link made between organochlorides (OCs) and egg-shell thinning
–potential application to condor recognised in 1970s but link was not investigated
*monitoring postulated as cause of breeding failure
*late-1980s, circumstantial link to OCs accepted as likely cause of decline –but DDT banned in US 1972
–1980’s lead poisoning identified (by retrospective analyses) as cause of death for 3 of 5 dead birds found in 1980s. Lead likely to come from deer carcasses, a significant problem for condors, owing to very strong digestion
conservation actions:
*1965, annual surveys begun - ceased in *1981, owing to unacceptable error
*1971, provisioning at feeding stations commenced - abandoned in 1973
*by 1987, all remaining 27 condors in captivity
*1991, reintroduction commenced
*2006, 44 wild individuals ≥ 6 years (201 in 2023)
cost: > US$ 35,000,000
Condor & woodhen: 2 very different scenarios
woodhen – single major threat, carefully identified and easily treated
condor – multiple interacting threats
–low birth rate and late sexual maturity → vulnerability
–poaching
–lead and DDT poisoning
–mortality from electric power lines
–egg collecting
–habitat destruction
–nevertheless, importance of identifying causal threats is clear
Key point is that the two stories are not directly comparable:
One a very defined population in a small area, the other an enormously wide ranging species in a complex urban/suburban/wild matrix. Nonetheless, they do serve to illustrate how things can be done methodically and well … or not.
Rhys Green provided follow-up info on the condor story. Now well acknowledged that lead poisoning was a major issue. Sadly, Americans sure ain’t gonna let no goddamn scientists tell them what kinda bullets they can use (even if they are being offered copper ammo for free!).
Distinction drawn between 2 paradigms in conservation
–most academic conservation aimed at a range of issues … but how much do they matter in practice?
–identifying causal threats is always the priority … but is characterised by an inability to generalise
Simple population models
Simple population models, model populations as a single entity (Nt)
2 standard approaches:
- Nt+1 = lambda Nt
· lambda is the growth parameter
. models “discrete time” population growth
&
- Nt = No e^rt
. r is the growth parameter
. models “continuous time” population growth
. No is the initial population size
Simple population models:
Discrete time (geometric) population growth
Nt+1 = lambda Nt
^ Can only say what population will be at next time horizon, not what it will be
at e.g.t + 0.7
It is useful for populations with clearly defined breeding season
lambda >1 = population growth
lambda <1 population decline
lambda = 1population stability
Simple population models:
Discrete time (geometric) population growth cont.
rearrange Nt+1 = lambda Nt
to lambda = Nt+1 / Nt
This gives the growth rate for one time-step
Can also be written as Nt= No lambda t
(where No is initial population size)
Thus, lambda = t =
square root of Nt/No
or (Nt/No)^1/t
