Goal: Pupping rate estimates to estimate proportion of for New Zealand cows that breed as a sea lions function of age Definition of breeder Project: POP2006 Cow that gives birth, including when the Dave Gilbert pup dies or is a stillbirth Louise Chilvers Presentation 12 June 2008 1 2
Use of behaviour comment Enderby main behaviour field frequencies SEASON BIRTH CALL DEAD NURSE WITH X PUP 2000 15 12 4 250 264 1132 Behaviour was codified into: 2001 17 16 12 245 296 1276 BIRTH, STILLBIRTH, DEADPUP, 2002 22 10 28 237 344 2121 PREGNANT 2003 3 34 3 393 612 2186 NURSE, WITHPUP, CALL 2004 31 34 1 509 617 2510 X, YNURSE, XSUCKLING, DEAD 2005 35 1 2 127 191 2063 2006 22 11 - 299 278 1974 2007 29 13 - 473 351 2129 3 4
Probable breeder observations How do we distinguish exactly which cows bred and which did 30 Birth observed not? Stillbirth or dead pup observed 1- to 3-year-olds (offset) Other 25 (excluding birth, stillbirth and dead pup) Number of breeder observations 20 • Most breeders can be unambiguously identified 15 • Each season a few are ambiguous (e.g. seen WITHPUP 10 once) • We have a modest number of 5 definite breeders but very few definite non-breeders (YNURSE) 0 0 5 10 15 20 25 30 35 40 45 50 55 Total number of observations in a season 5 6
Criteria for identifying breeder Two approaches to estimating Base: (1) birth, stillbirth, dead pup OR pupping rate (2) ≥ 2 of nursing, with pup or calling pup Alt1 : (1) birth, stillbirth, dead pup OR • Estimate a mixture of breeder (2) ≥ 2 of nursing, with pup or calling and non-breeder statistical pup OR distributions of observations (3) ≥ 1 of nursing, with pup or calling (that overlap slightly) pup AND ≥ 5 total observations • Specify criteria that categorise Alt2 : (1) birth, stillbirth, dead pup OR all cows each season as (2) ≥ 2 of nursing OR breeders or non-breeders (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 7 8
Mortality and observability Died or not observed? parameters • Need to account for non-breeders that are alive but not sighted Cow tagged year y t • Can be done easily for individuals for the years before the last Observations year y -1 sighting Breeder Non-breeder Non-breeder Dead • If last sighting was before 2007 observed observed not observed the cow may be dead or alive but not sighted • We therefore estimate Observations year y parameters for: Breeder Non-breeder Non-breeder Dead (1) mortality observed observed not observed (2) observability and treat the unseen cows as a combination of dead and non- observed non-breeders 9 10
Pupping rate Other pupping rates Annual breeding probability for average cow Annual breeding probability for average cow 1.0 1.0 0.9 0.9 Model smooth curve Base case Model arbitrary curve Alternative 1 0.8 Direct (incomplete mortality) 0.8 Alternative 2 0.7 0.7 0.6 0.6 Probability Probability 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Age Age 11 12
Mortality+tag loss Predicted numbers observed and survival 100 Probability of surviving following year Cohort 1987 Cohort 1990 Cohort 1991 80 1.0 a 60 a a 40 0.9 a a a b a 20 a a a nb b nb b a a n nb b a n a nb n b n 1987 nb a b n n n b a nb 0.8 100 a a a a a nb nb b nb n b nb a nb n a nb 0 b nb nb a n Cohort 1992 Cohort 1993 Cohort 1998 a a 80 a a 0.7 a a a a a 60 a a a a Annual survival ~ mortality a a a 40 a a 2000 b b a b b 0.6 b nb b a n a b nb n a n nb a n 20 n n n 1990 n a n nb n n nb Number nb n n 1998 n n b n n b n b b 1999 100 2001 b b b a 2002 b b 0.5 0 b b a Cohort 1999 a Cohort 2000 Cohort 2001 2003 a a 80 a a a a a a a a Survival (incl tag loss) a 0.4 60 a 1991 n Mortality (incl tag loss) n 1993 a n a n 1992 40 a First year cohort mortality a n n n n n n n n n 0.3 Mortality (excl tag loss) b n n 20 n b n n b n b n b n b b b b b 100 b 0 b b b b bb b b bb b b a 0.2 Cohort 2002 Cohort 2003 a a 80 b Breeders a n Non-breeders n a a n Known alive 60 0.1 a Model breeders a a Model non-breeders 40 a Model total alive n n n 0.0 n 20 n n n b b 0 2 4 6 8 10 12 14 16 18 20 0 bb b b b bb b b 1990 1995 2000 2005 1990 1995 2000 2005 1990 1995 2000 2005 Season Age 13 14
Pupping rate conditional on Developments last year (direct estimate) Proportion of females that breed • Mixture model 1.0 All cows (2000-2007) • Credibility intervals Pup previous season (2001-2007) No pup previous season (2001-2007) • High and low fecundity cows Proportion of observations that imply pupping 0.8 0.6 0.4 0.2 0.0 5 10 15 20 Age 15 16
Pupping rates from Pupping rates from autocorrelated pupping model autocorrelated pupping model Breeding probability (autocorrelated pupping model) Breeding probability (autocorrelated pupping model) 1.0 1.0 Population mean Population mean 0.9 0.9 Pup previous year Pup previous year No pup previous year No pup previous year Base case 0.8 0.8 0.7 0.7 0.6 0.6 Probability Probability 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Age Age 17 18
Predicted numbers observed from Conclusions autocorrelated model Pupping rate 100 Cohort 1987 Cohort 1990 Cohort 1991 80 Annual breeding probability for average cow 60 a 1.0 a a 40 a 0.9 a a b a Base case a a 20 a nb b nb b Alternative 1 a a n 0.8 nb b a n a nb n Alternative 2 b n nb a b n n nb nb 100 a a a a a a nb nb b nb nb nb a nb n a nb 0 b nb nb n a Cohort 1992 Cohort 1993 Cohort 1998 0.7 a a 80 a a 0.6 a a a a Probability a 60 a a a a a 0.5 a a 40 a a b b a b b b nb b 0.4 a n a b nb n a n nb a n n n 20 n n a n n nb nb n Number nb n n n nb 0.3 n n b n b b 100 b b b a b b 0 b b a a Cohort 1999 Cohort 2000 Cohort 2001 0.2 a a 80 a a a a 0.1 a a a a a 60 a n 0.0 a n n a n 40 a a 0 2 4 6 8 10 12 14 16 18 20 n n n n n n n n n b Age n n 20 nb n n b n b n b n b b b b b 100 b 0 b b b b bb b b bb b b a Cohort 2002 Cohort 2003 a Developments a 80 b Breeders a n Non-breeders n a a n Known alive 60 • Autocorrelated model a Model breeders a a Mean model breeders 40 a n Model nonbreeders n n Mean model nonbrdrs • Credibility intervals n 20 n Model total alive n n b b 0 bb b b b bb b b • Mixture model 1990 2000 1990 2000 1990 2000 Season 19 20
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