Pupping rate estimates to estimate proportion of for New Zealand - - PowerPoint PPT Presentation

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Pupping rate estimates for New Zealand sea lions

Project: POP2006

Dave Gilbert Louise Chilvers

Presentation 12 June 2008

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Definition of breeder

Cow that gives birth, including when the pup dies or is a stillbirth

Goal: to estimate proportion of cows that breed as a function of age

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Behaviour was codified into: BIRTH, STILLBIRTH, DEADPUP, PREGNANT NURSE, WITHPUP, CALL X, YNURSE, XSUCKLING, DEAD

Use of behaviour comment field

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Enderby main behaviour frequencies

2129 351 473

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29 2007 1974 278 299

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22 2006 2063 191 127 2 1 35 2005 2510 617 509 1 34 31 2004 2186 612 393 3 34 3 2003 2121 344 237 28 10 22 2002 1276 296 245 12 16 17 2001 1132 264 250 4 12 15 2000

X WITH PUP NURSE DEAD CALL BIRTH SEASON

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How do we distinguish exactly which cows bred and which did not?

• Most breeders can be

unambiguously identified

• Each season a few are

ambiguous (e.g. seen WITHPUP

• nce)
• We have a modest number of

definite breeders but very few definite non-breeders (YNURSE)

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Probable breeder observations

5 10 15 20 25 30 35 40 45 50 55 5 10 15 20 25 30 Total number of observations in a season Number of breeder observations (excluding birth, stillbirth and dead pup) Birth observed Stillbirth or dead pup observed 1- to 3-year-olds (offset) Other

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Two approaches to estimating pupping rate

• Estimate a mixture of breeder

and non-breeder statistical distributions of observations (that overlap slightly)

• Specify criteria that categorise

all cows each season as breeders or non-breeders

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Criteria for identifying breeder

Base: (1) birth, stillbirth, dead pup OR (2) ≥2 of nursing, with pup or calling pup Alt1 : (1) birth, stillbirth, dead pup OR (2) ≥2 of nursing, with pup or calling pup OR (3) ≥1 of nursing, with pup or calling pup AND ≥5 total observations Alt2 : (1) birth, stillbirth, dead pup OR (2) ≥2 of nursing OR (3)≥3 of nursing, with pup or calling pup

In all cases all breeders are assumed to be seen All others are non-breeders but not all non-breeders are seen

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Died or not observed?

• Need to account for non-breeders

that are alive but not sighted

• Can be done easily for individuals

for the years before the last sighting

• If last sighting was before 2007

the cow may be dead or alive but not sighted

• We therefore estimate

parameters for: (1) mortality (2) observability and treat the unseen cows as a combination of dead and non-

• bserved non-breeders

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Mortality and observability parameters

Breeder

• bserved

Non-breeder

• bserved

Non-breeder not observed Dead Cow tagged year yt Observations year y-1 Observations year y Breeder

• bserved

Non-breeder

• bserved

Non-breeder not observed Dead

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Pupping rate

2 4 6 8 10 12 14 16 18 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Annual breeding probability for average cow

Age Probability Base case Alternative 1 Alternative 2

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Other pupping rates

2 4 6 8 10 12 14 16 18 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Annual breeding probability for average cow

Age Probability Model smooth curve Model arbitrary curve Direct (incomplete mortality)

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Mortality+tag loss and survival

2 4 6 8 10 12 14 16 18 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Probability of surviving following year

Age Annual survival ~ mortality

1987 1990 1991 1992 1993 1998 1999 2000 2001 2002 2003

Survival (incl tag loss) Mortality (incl tag loss) First year cohort mortality Mortality (excl tag loss)

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Predicted numbers observed

20 40 60 80 100 Cohort 1987 b a nb a n b a nb a nb a nb a nb a nb a n Cohort 1990 b a nb a nb a n b a nb a nb a nb a n b a n Cohort 1991 b a nb a nb a n b a n b a n b a n b a nb a n 20 40 60 80 100 Cohort 1992 b a n b a n b a nb a nb a nb a n b a n b a n Cohort 1993 b a nb a n b a n b a n b a nb a nb a n b a n Cohort 1998 b a n b a n b a n b a n b a n b a n b a n b a n 20 40 60 80 100 Cohort 1999 b a n b a n b a n b a n b a n b a n b a n b a n Cohort 2000 bb a n b a n b a n b a n b a n b a n b a n Cohort 2001 bb n b n b a n b a n b a n b a n 20 40 60 80 100 1990 1995 2000 2005 Cohort 2002 bb a n b a n b a n b a n b a n 1990 1995 2000 2005 Cohort 2003 bb a n b a n b a n b a n 1990 1995 2000 2005 b n a Breeders Non-breeders Known alive Model breeders Model non-breeders Model total alive

Season Number

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Developments

• Mixture model
• Credibility intervals
• High and low fecundity cows

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Pupping rate conditional on last year (direct estimate)

5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0

Proportion of females that breed

Age Proportion of observations that imply pupping All cows (2000-2007) Pup previous season (2001-2007) No pup previous season (2001-2007)

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Pupping rates from autocorrelated pupping model

2 4 6 8 10 12 14 16 18 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Breeding probability (autocorrelated pupping model)

Age Probability Population mean Pup previous year No pup previous year

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Pupping rates from autocorrelated pupping model

2 4 6 8 10 12 14 16 18 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Breeding probability (autocorrelated pupping model)

Age Probability Population mean Pup previous year No pup previous year Base case

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Predicted numbers observed from autocorrelated model

20 40 60 80 100 Cohort 1987 b a nb a nb a nb a nb a nb a nb a nb a n Cohort 1990 b a nb a nb a n b a nb a nb a nb a nb a n Cohort 1991 b a nb a nb a n b a n b a n b a n b a nb a n 20 40 60 80 100 Cohort 1992 b a n b a n b a nb a nb a nb a n b a n b a n Cohort 1993 b a nb a n b a n b a n b a nb a nb a nb a n Cohort 1998 b a n b a n b a n b a n b a n b a n b a n b a n 20 40 60 80 100 Cohort 1999 b a n b a n b a n b a n b a n b a n b a n b a n Cohort 2000 bb a n b a n b a n b a n b a n b a nb a n Cohort 2001 bb n b n b a n b a n b a n b a n 20 40 60 80 100 1990 2000 Cohort 2002 bb a n b a n b a n b a n b a n 1990 2000 Cohort 2003 bb a n b a n b a n b a n 1990 2000 b n a Breeders Non-breeders Known alive Model breeders Mean model breeders Model nonbreeders Mean model nonbrdrs Model total alive

Season Number

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2 4 6 8 10 12 14 16 18 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Annual breeding probability for average cow

Age Probability Base case Alternative 1 Alternative 2

Developments

• Autocorrelated model
• Credibility intervals
• Mixture model

Conclusions

Pupping rate