New Zealand sea lion pupping rate

New Zealand sea lion pupping rate Project: POP2006 Dave Gilbert Louise Chilvers Presentation 19 September 2008 1

Goal: to estimate proportion of cows that breed as a function of age Definition of breeder Cow that gives birth, including when the pup dies or is stillborn Identification of breeders Codify behaviour comment field and use a criterion or fit a mixture of breeder and nonbreeder distributions to frequencies 2

3 Main behaviour frequencies 2129 351 473-13 29 2007 1974 278 299-11 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 NOTHING WITH PUP NURSING DEAD CALLING BIRTH SEASON

Use of behaviour comment field Behaviour was codified into: Birth observations: BIRTH, STILLBIRTH, DEADPUP Breeder observations: NURSING, WITHPUP, CALLING Nothing: NURSINGYEARLING, SUCKLINGFROMCOW, DEAD, NOTHING, PREGNANT For each cow we know: Season it was tagged whether tagged or branded 4

How do we distinguish exactly which cows pupped and which were alive but didn t? There are a few definite breeders Most breeders could be identified if observed for long enough 1 3-year-olds are definite nonbreeders 37% of observations are breeder observations Occasionally non-breeders produce breeder observations 5

Probable breeder observations Number of breeder observations (excluding birth, stillbirth and dead pup) 0 5 10 15 20 25 30 Birth observed Stillbirth or dead pup observed 1- to 3-year-olds (offset) Other 0 5 10 15 20 25 30 35 40 45 50 55 Total number of observations in a season 6

Two methods to estimating pupping rate 1. Specify a criterion that categorises each cow each season as a breeder or nonbreeder (e.g. a birth observation or at least 2 breeder observations) 2. Estimate probability density functions to explain observation frequencies that depend on whether a cow breeds. Estimate the proportion of breeders and non-breeders in the mixture 7

Breeder observations proportions Observation frequencies (branded; age >= 4 years) Number of breeder observations (excluding birth, stillbirth and dead pup) 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Birth observed Stillbirth or dead pup observed Other Observation frequencies (tagged; age >= 4 years) 0 5 10 15 20 25 30 35 40 45 50 55 Total number of observations in a season 8

Error caused by criterion method Because the probability of getting a breeder observation each time a breeding cow is observed is only 0.37, some breeders will not be identified E.g. if a breeder is seen 4 times the probability of getting zero breeder observations is 0.63 4 =0.16 These observations will be indistinguishable from those of a non-breeder seen 4 times and the criterion method will wrongly identify it as a non-breeder 9

Method 2 Scenario mixtures Example scenario out of 256: 2000 breed 2001 breed 2002 breed 2003 non-breed 2004 non-breed 2005 non-breed 2006 breed 2007 non-breed Need to calculate the likelihood of the actual observations under each scenario, multiply it by the likelihood of that scenario and add them 10

Method 2 Another scenario Another scenario : 2000 breed 2001 non-breed 2002 breed 2003 non-breed 2004 breed 2005 non-breed 2006 breed 2007 non-breed The likelihood of a scenario depends on age, branded/tagged and the sequence, i.e. this one is less likely than the previous because of the serial correlation 11

Total observation frequencies Births incl dead (branded) Births & brandings (tagged) 0 5 10 15 N = 97 Mean = 25.82 CV = 0.32 0 5 10 15 N = 138 Mean = 13.13 CV = 0.56 Frequency of observations 0 5 10 15 20 25 30 Breeder obs >0 (branded) N = 216 Mean = 25.76 CV = 0.38 0 5 10 15 20 Breeder obs >0 N = 727 Mean = 11.7 CV = 0.65 3-year-old (branded) 3-year-old (tagged) 0 1 2 3 4 5 6 N = 13 Mean = 5.85 CV = 0.96 0 20 40 60 80 N = 213 Mean = 4.94 CV = 0.97 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Total number of observations in a season 12

Pupping rate conditional on last year Ratio breeders to total known alive (criterion-based) Proportion of observations that satisfy criterion 0.0 0.2 0.4 0.6 0.8 1.0 PREVIOUS SEASON All (N=2568) Pupped (N=703) Seen, no pup (N=789) Not seen (N=813) 5 10 15 20 Age 13

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 mortality parameters and treat the unseen cows as a mixture of dead, nonobserved non-breeders and a very few non-observed breeders 14

Mortality and nonobservability mixture Cow tagged year y t Observations year y-1 Observed Alive but not observed Dead Observations year y Observed Alive but not observed Dead 15

Pupping rate Estimated breeding probability Probability 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Population mean Pup previous year No pup previous year (31%) 0 2 4 6 8 10 12 14 16 18 20 Age 16

Survival and tag retention Probability of surviving following year Annual survival 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1992 1993 1991 1990 2003 1999 2001 2002 1998 2000 1987 Survival (including tag retention) First year cohort survival 0 2 4 6 8 10 12 14 16 18 20 Age 17

Estimated observation proportions Group Total obs = 0 Percent Breeder obs = 0 Breeder obs = 1 Breeder obs 2 Percent of observed cows Branded breeders 0 2.3 4.9 92.8 Tagged breeders 1.8 10.3 15.1 74.6 Branded nonbreeders 50.4 99.2 0.5 0.3 Tagged nonbreeders 70.1 99.3 0.4 0.3 18

Total observation distributions Estimated total observation density Probability 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Tagged breeders, zeros 1.8% Branded breeders, zeros 0% Tagged non-breeders (3 y), zeros 64.8% Tagged non-breeders (20 y), zeros 78.3% Branded non-breeders (3 y), zeros 43.4% Branded non-breeders (20 y), zeros 62.4% 0 10 20 30 40 50 60 Total observed 19

Total observations Total observations Negative binomial model (zeroes censored) Branded 'breeders' Tagged 'breeders' Frequency of total observations 0 5 10 15 0 50 100 150 200 250 300 350 N = 216 Ov er-dispersion 6.4 Fitted zeros 0% Negative binomial Poisson 'Non-breeders' branded + tagged N = 100 Ov er-dispersion 13.7 Fitted zeros 69.5% Negative binomial Poisson 0 10 20 30 40 50 0 10 20 30 40 50 60 N = 727 Ov er-dispersion 6.4 Fitted zeros 1.8% 3-year-olds Negative binomial Poisson N = 213 Ov er-dispersion 13.7 Fitted zeros 64.8% Negative binomial Poisson 0 10 20 30 40 50 60 Count 0 10 20 30 40 50 60 20

Breeder observation frequencies Breeder observation frequencies (>3 years) Beta-binomial model Total obs 25 to 55 Total obs 20 to 24 Frequency of breeder observations 0 5 10 15 0 10 20 30 40 N =163 Est % non-breeders with 25-55 total obs 2 % branded 0.9 % tagged Beta-binomial Ov er-disp=2.8 Binomial Ov er-disp=0.6 Total obs 15 to 19 N =212 Est % non-breeders with 15-19 total obs 2.5 % branded 1.2 % tagged Beta-binomial Ov er-disp=1.5 Binomial Ov er-disp=0.6 0 5 10 15 20 0 20 40 60 80 100 120 N =148 Est % non-breeders with 20-24 total obs 1.4 % branded 0.7 % tagged Beta-binomial Ov er-disp=1.8 Binomial Ov er-disp=0.6 Total obs 10 to 14 N =313 Est % non-breeders with 10-14 total obs 4.8 % branded 2.4 % tagged Beta-binomial Ov er-disp=1.2 Binomial Ov er-disp=0.6 0 10 20 30 40 50 Count 0 10 20 30 40 50 21

Total observations as mixtures Observation frequencies Tagged 3-year-olds Tagged 4-5-year-olds 0 10 20 30 40 50 60 N = 213 Observ ed mean = 4.9 Fitted mean = 6 Breeders Non-breeders Total 0 20 60 100 N = 484 Observ ed mean = 7.8 Fitted mean = 8.2 Frequency of total observations 0 20 40 60 80 Tagged 6-7-year-olds N = 313 Observ ed mean = 7.7 Fitted mean = 8.8 0 20 40 60 80 Tagged 8-10-year-olds N = 476 Observ ed mean = 7.7 Fitted mean = 9.4 Tagged 11-14-year-olds Tagged 15-20-year-olds 0 20 40 60 80 N = 352 Observ ed mean = 8.8 Fitted mean = 11.7 0 2 4 6 8 N = 46 Observ ed mean = 5.7 Fitted mean = 11.3 0 10 30 50 Count 0 10 30 50 22

Some parameter values Parameter Max pupping rate (average) Max pupping rate (prev breeder) Max pupping rate (prev non-breeder) Age max pupping (y) Prob of a breeder obs (breeder) Prob of a breeder obs (non-breeder) Mean total obs/season (breeder) Mean total obs (branded breeder) Mean total obs (3 y, non-breeder) Mean total obs (20 y, non-breeder) Est 0.61 0.85 0.26 13 0.37 0.001 11.7 22.6 2.1 1.2 23

More parameter values Parameter Pupping rate reaches half max (y) Pupping rate falls to half max (y) Max survival & tag retention Age at max survival (y) Mean 1 st year survival (excl 1987) Survival at age 20 y Max observability (2003) Min observability (2000) Neg-binom overdispersion (breeders) Neg-binom overdispersion (nonbreeders) Est 7 17 0.99 2 0.54 0.55 1.20 0.49 6.4 13.7 24

Conclusions Necessary to estimate breeders with no breeder observations by using a mixture model (12% tagged breeders not identified) High breeding serial correlation (breeders 3 times as likely to breed following year) Maximum population pupping rate is 61% at age 13 y Possibly 20% of cows do not return to rookery each year (not modelled) First year survival varies a lot (37-73%) Observations over-dispersed (excessive zeros and ones) 25

Conclusions Estimated breeding probability Probability 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Population mean Pup previous year No pup previous year (31%) 0 2 4 6 8 10 12 14 16 18 20 Age 26