Population Viability Analyses PVAs are SIMULATION models of likely - - PowerPoint PPT Presentation

Population Viability Analyses

• PVA’s are SIMULATION models of likely

trajectory of population in question into the future, based on the BEST current ESTIMATES of demography & environmental impacts. Therefore, by definition, they are only best GUESSES

• BUT PVA’s can be VERY useful to

conservation biologists, especially if properly constructed AND interpreted.

Overview of Population Viability Analyses

Richard Pettifor & Marcus Rowcliffe Institute of Zoology, ZSL SACWG/Darwin Initiative Project Training

Example PVA Black box

• f breeders

• perating?

• f breeders and

Appendix 3. Flow chart describing the density dependent, stochastic population model for the Svalbard barnacle goose.

Population Viability Analyses

It should always be borne in mind that population viability analysis is essentially an exercise in probability. Figures produced by population viability analysis are the probabilities of given population trajectories over given time scales; the decision on how certain a population's persistence must be, and over what time scale, before it is classified as safe, remains largely subjective.

What PVA’s are NOT

• PVA’s do NOT give certainty to predictions

into the future

• PVA’s only give PROBABILISTIC

behaviour into the future: NOT absolute numbers

• ONLY as good as the data on which they

are based: GARBAGE IN; GARBAGE OUT

What PVA’s CANNOT DO

• They CANNOT tell you what N(t+100) will be

UNLESS ASSUMPTIONS (ie environment & demography) remain IDENTICAL to those assumed in model

• VERY unlikely they can tell one anything

about population behaviour too far into the future: THEREFORE PVA’s need frequent updating (5 yrs) using the LATEST information available

PINK-FOOTED & GREYLAGS

PINK-FOOTED & GREYLAG GEESE POPULATIONS TO 1984

50 60 70 80 YEAR 20000 40000 60000 80000 100000 POPULATION SIZE

Ln Population size with time ie r

9 10 11 12 50 60 70 80 Year Ln population size

PINK-FOOTED & GREYLAG GEESE POPULATIONS INTO LATE 1990s

50 60 70 80 90 100 YEAR 50000 100000 150000 200000 250000 POPULATION SIZE

How good are the data?

• REMEMBER: GARBAGE IN, GARBAGE OUT

BUT HERE WE HAD

• 30+ yrs of “good” population estimates
• Reasonable estimates of demography
• No evidence to suggest sudden change in

population behaviour

How good are the data?

• Many published PVA’s & PVA’s used for

“conservation” are based on:

• Short time series
• Poor population estimates (rare or cryptic
• r wide-ranging etc)
• Often poor demographic data with very

small sample sizes

• Survival estimates often non-existent

Why use PVA’s

• Population estimates into the future obtained

from PVA’s are MODELS, not GOSPEL TRUTH BUT

• PVA’s useful in exploring WHAT IF? scenarios,

either +’ve or –’ve

• Sensitivity analyses (elasticities) very informative
• Ultimately, should be used to inform WHAT

further data are needed, & WHERE conservation action should be targetted

Svalbard Barnacle Goose

Svalbard Barnacle Goose

Svalbard Barnacle Goose

• Demography:
• What we can measure:
• Total Population Size: (Nt)
• Brood size: (Bt)
• Proportion of young: (Pjt)

Svalbard Barnacle Goose

Demography: We know: (Nt), (Bt), (Pjt) We can infer:

• Number of Juveniles (Jt) = (Nt)*(Pjt)
• Successfully Breeding Adults (Abt) = 2*[(Jt)/(Bt)]
• Number of 2nd yr birds (It) = (Jt-1)*(St-1)
• Potential breeding adults (Apt) = (Nt) - (Jt) - (It)
• Breeding Ratio (Rt) = (Abt)/(Apt)
• Productivity (Ft) = (Jt)/(Apt)
• Survival Rates (St) = [(Nt+1) - (Jt+1)]/(Nt)

SvBG – Population Growth

55 60 65 70 75 80 85 90 95 Year 1000 10000 Population size (log scale)

SvBG – annual growth rate r

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 7 7.5 8 8.5 9 9.5 Ln lagged Population Annual Growth Rate ( r)

SvBG – density dependence?

0.1 0.2 0.3 0.4 0.5 0.6 7 7.5 8 8.5 9 9.5 Ln lagged Population Proportion Juveniles

SvBG – density dependence?

1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 7 7.5 8 8.5 9 9.5 Ln lagged Population Annual Brood Size

SvBG – density dependence?

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 7 7.5 8 8.5 9 9.5 Ln lagged Population Crude Annual Survival

SvBG – density dependence?

• DD apparent in key demographic breeding

parameters

• Substantiated by analysing ringing data
• Also Pollard’s & other DD tests
• BUT no DD in crude annual survival

estimates

• Similarly, no evidence from MARK (CMR)

analyses of ringed birds

SVBG PVA from data 1952 - 1992

The BLACK BOX:

• Stochastic Leslie matrix model but

modified to account for seasonal variation in mortality (from ringing data)

• Stage-structured (from ringing data)
• Incorporates density dependence
• Incorporates effects of environmental

factors

SVBG PVA from data 1952 - 1992

70 75 80 85 90 95

Year

2,000 4,000 6,000 8,000 10,000 12,000 14,000

Population

Observed Predicted

SVBG PVA from data 1952 - 1992

20 40 60

Year

4,000 8,000 12,000

Population size

SVBG PVA from data 1952 - 1992

• Long-time series
• Good annual data on demographic

parameters

• Good knowledge of environmental factors
• All parameterisation supported by

intensive statistical analyses of over 3,000 birds ringed and 50,000 resightings

• Text book example of how to do a PVA

SVBG PVA from data 1952 - 1992

Wrong

WRONG

WRONG!!!!

Why did we get it so wrong?

• 1) Research on Svalbard difficult

logistically (& expensive): therefore established colonies with previous research history studied

• 2) These colonies are the oldest, & dd on

breeding most pronounced

• 3) New colonies being established, but

their contribution unknown

Why did we get it so wrong? (2)

• 4) Barnacle Goose Management Scheme

came into affect in 1994, just as our initial work finished (1992)

• 5) Currently much greater mobility of

winter flocks than previously established

• 6) Since mid-90’s, also changed spring &

autumn staging posts, increasing survival.

• i.e. SvBG behaviour changed in ways

UNPREDICTED from 30+ years previous intensive study!!

SVBG PVA from data 1952 - 1992

70 75 80 85 90 95

Year

2,000 4,000 6,000 8,000 10,000 12,000 14,000

Population

Observed Predicted

SvBG Population Growth 1958 - 2003

1960 1970 1980 1990 2000 5000 10000 15000 20000 25000 30000 Year Population size

However, all is not lost!!

• FIRST, we recently revisited our 5 goose PVA’s

done in mid-90’s against actual observed population growth: in 4/5 instances we had good agreement

• SECOND, we have rerun our models using

updated info (especially wrt dd), & good overall agreement

• THIRD, our sensitivity analyses remained sound
• FOURTH, our early PVA’s redirected our

research to specific Q’s & hypotheses.

Remember? Why use PVA’s

• 1) Population trajectories – hmmm…?
• 2) Elasticities – what demographic factors

are driving the popn dynamics?

• 3) What “offtake” are populations capable
• f withstanding (assuming NO CHANGE in

environment or demography)?

• 4) At what point should we be concerned

with catastrophic but rare events?

ELASTICITIES i.e. population sensitivity to parameter change

0.3 0.6 0.9 Productivity intercept 0.1 0.25 0.4 Productivity pair-duration slope 0.5 1 Probability of decline 0.04 0.09 0.14 Productivity temperature slope 1 2 3 4 Autumn survival intercept 0.5 1 1 2 3 4 Winter survival intercept 0.2 0.4 0.6 Winter survival intercept variance

• 0.13
• 0.09
• 0.05

Autumn survival age slope 0.03 0.06 0.09 Winter survival density variance

Example population trajectories

• ver 100 years

a) model parameters unchanged; b) no dd in productivity; c) dd in productivity x 5; d) autumn survival increased 2x; e) autumn survival decreased (40%).

25 50 75 100 Year 5 10 15 20 Population (thousands) 25 50 75 100 5 10 15 20 Population (thousands) 25 50 75 100 0 25 50 75 100 25 50 75 100 a c b d e

Sensitivity Rules of Thumb

• 1) In “K-selected” species, it is generally the annual

survival of adults that is critical.

• 2) In “r-selected” species, it is generally annual

recruitment that is critical.

• 3) Density Independent trajectories tend to reach higher

values, but generally more susceptible to random crashes

• 4) Density dependence regulates populations, offering

“buffering” to crises

• 5) BUT dd CAN BE very hard to detect
• 6) Remember, dd can occur even in SMALL popns.

Quasi-extinction

• Generally used when population size

exceeds some subjective value e.g. look at risk of Sv Barnacle geese declining to 5

• r 10,000 birds from 25,000, or Pink-feet

(250,000+) declining to 100,000 birds.

• In other words, use values that are

biologically meaningful, BOTH from a modelling perspective & in terms of conservation.

Example dd population trajectories over 100 years under a) 0.01 annual risk of 50% catastrophic mortality, and b) 0.01 annual risk of 80% mortality.

4,000 8,000 12,000 25 50 75 100 Year 4,000 8,000 12,000 Population b a

Quasi- extinction risk

0.3 0.6 0.9 0.001 0.01 0.1 0.5 1

C a t a s t r

• p

h i c m

• r

t a l i t y (a) Quasi-extinction threshold = 1,000 Annual probability

• f catastrophe

Quasi-extinction probability

0.3 0.6 0.9 0.001 0.01 0.1 0.5 1

C a t a s t r

• p

h i c m

• r

t a l i t y (b) Quasi-extinction threshold = 10,000 Quasi-extinction probability Annual probability

• f catastrophe

Hunting offtake

1000 2000 3000 0.2 0.4 0.6 0.8 1 Additional loss from the population Quasi-extinction probability Quasi-extinction thresholds 1000 5000 10000

Svalbard barnacle goose quasi-extinction probabilities within 25 years resulting from increasing levels of loss of individuals from the population in the presence of density dependent regulation.

The Previous Predictions - CAUTION

• 1) Assumes model assumptions persist

into the future – as we’ve seen, this can be VERY unreliable

• 2) Need to exercise “PRECAUTIONARY

PRINCIPLE”

• 3) The confidence intervals are wide, & get

wider as time into future increases (i.e. greater uncertainty in predictions)

SUMMARY

At the heart of population viability analysis lies the interaction between environmental stochasticity and population demography. In the words of Soulé (1987), conservationists must grapple with the question: "What are the minimum conditions for the long-term persistence and adaptation of a species

• r population in a given place?". He goes on to state

that "This is one of the most difficult and challenging intellectual problems in conservation biology. Arguably, it is the quintessential issue in population biology, because it requires a prediction based on a synthesis of all the biotic and abiotic factors in the spatial-temporal continuum."

TAKE HOME MESSAGES (1)

• 1) Population trajectories into the future

are filled with uncertainty: behaviour can change in unpredictable ways. Be VERY wary of categorical statements & assess QUALITY of data used

• 2) Density-dependence CAN be a fact of

life in populations (even small ones) – detecting dd VERY difficult, but crucial for model behaviour

TAKE HOME MESSAGES (2)

• 3) Sensitivity analyses most “useful”

aspect of PVA’s, but often neglected

• 4) Quasi-extinction risk gives insight into

population behaviour as formulated in model

• 5) Modelling “catastrophic” events useful
• 6) Can give insight into “sustainable
• fftake” – but always phrase with sufficient

cautions!!

TAKE HOME MESSAGES (3)

• 7) PVA’s can help understand population

dynamics & targetting of conservation / research action – above all, they are FUN!!

• 8) Finally, PVA’s are not be all & end all of

simulating population dynamics. Behavioural & evolutionary ecology can help a lot (IBM’s & game-theory). Above all, use your own common sense & ecological knowledge!!