https://doi.org/10.5061/dryad.g79cnp5xc

The accompanying data and associated R code can be used to fit models and perform calculations to estimate ages for Northern Resident killer whales that were first observed by scientists years after birth, so that their ages could not be directly estimated with confidence.

"ID_long_anon.csv" provides anonymised "long format" demographic data for the population of known-age NRKWs. Individual identifiers (IDs) are ananymised, except for individuals for which revised year-of-birth estimates are to be calculated. "ID_wide_anon.csv" provides "wide format" demographic data for the same individuals. These two data files are needed to parameterise the mathematical functions used to estimate ages. The "individual age estimate inputs.csv" file contains the data required to estimate ages for the (identified) individuals of unknown age, using the techniques described in this paper and implemented in the .R scripts mentioned below.

Description of the data and file structure

ID_long_anon.csv

ID: identifier for individual (anonymised except for individuals for which year-of-birth estimates are to be provided)
year: census year
status:
B - Indicates birth of a viable calf. Defined as any animal born during or after the preceding July-August field season that survived to the next July-August field season. Every B should be associated with a mother having a corresponding FC or C. See the animal’s “AGE_CONF” for certainty of the status’ year.
j - Denotes a juvenile animal that was alive during the current July-August field season. Defined as any male prior to sprouting, any female younger than 10 years of age who hasn’t yet become fecund, and any animal of unknown sex prior to 15 years of age (at which point the animal is presumed to be female).
fs - Denotes a male that was alive during the current field season, and attained sexual maturity (HWR > 1.4) prior to or during the current July-August field season.
s - Denotes a male that was alive during the current field season, and was sexually but not physically mature; HWR > 1.4 but fin growth still apparent.
M - Denotes a male that was alive during the current field season, and was physically mature (i.e. dorsal fin fully developed, asymptotic growth).
x - Denotes a female that was alive during the current field season, but whose reproductive status is not known. This status begins at 10 yrs of age, until the animal is certainly fecund (i.e. 2 yrs before her first calf). This status ends when an animal is certainly reproductively senescent, at age 50. As mentioned in the “r” status description, towards the end of the study it is not known whether a female will give birth again and so “x” status must be given until she does so.
r - Denotes a fecund female that was alive during the current field season and had not given birth between the preceding July-August field season and the present July-August field season. This status is evoked retroactively when an animal is observed with her first calf – “r” status should begin two years before the animal’s first calf (viable or not!) and continues until her last known calf (viable or not). This status must be bookended by calves (with the exception of the two years before an animal’s first calf). i.e. any female younger than 50 who has calved must be given “x” status until her next calf (at which point the statuses between “C”s change from “x”s to “r”s).
C - Indicates that a female gave birth to a viable calf between the preceding July-August field season and the current July-August field season. This indicates the continuity of a female’s fertility. Use C where it is not known whether the calf was her first or not, such as adult-sized animals near the beginning of the study that may have given birth but lost their first calves prior to start of study. Look to the “AGE_CONF” of the calf for the certainty of the status’ year. Do not use this variable to calculate births, use “BD” & “B” statuses.
FC - Indicates that a female gave birth to her first viable calf between the preceding July-August and the current July-August field seasons. This indicates the onset of a female’s fertility. Look to the “AGE_CONF” of the calf for the certainty of the status’ year. Do not use this variable to calculate births, use “BD” & “B” statuses.
p - Denotes a post-reproductive female that was alive during the current field season. Defined as any female of or over 48 yrs old.
md - Indicates the animal may be dead (i.e. the animal was not seen in the current year, but its group was not confidently censused that year either). When the animal's group was next seen in a complete encounter and the animal was still missing, it was declared dead. This status overrides all reproductive statuses. For males and animals of unknown sex, an animal’s reproductive status in the “md” year will be assumed to be the same as in the last year the animal was seen. For missing females, she is assumed the same status as the last year she was seen except if she turned 10 or 50 while missing, in which case her status changes from “j” to “x” and “x” to “p”, respectively.
D - Indicates animal is pronounced dead. Defined as an animal that was present or “md” during the preceding July-August field season but had disappeared by the current July-August field season.

exact: was this ID's status known exactly for this census year?
status.next: ID's status in the next census year
exact.next: will this ID's status be known exactly in the next census year?
mother.alive: is the ID's mother alive in this census year
oldest.ancestor: oldest known ancestor for this ID within the population
assumed.age: approximate age for this ID
newborn: was this ID a newborn in this census year?
FSEEN: is this census year the first year of observation for this ID?
juvenile: was this ID a juvenile in this census year?
gave.birth: did this individual (mother) give birth between the last census year and this one?
parity: how many known offspring has this individual (mother) birthed to date?
gives.birth: does this ID give birth between this census year and the next?
LSEEN: Is this the last census year in which this ID was observed?
missing: is this ID missing (mortality status uncertain) in this census year?
dies: does this ID die between this census year and the next?

ID_wide_anon.csv

ID: as above
Birth.Mother.certainty: Confidence in "Birth Mother" assignment, originally assigned for age estimation purposes (2005) and also used in ES' social analyses (2013-2016).
Known - Relationship established from close association of calf and/or confirmed by genetics [used in age estimation & social analyses]
Highly probable [used in age estimation & social analyses]
Probable - [considered reliable enough to be used in age estimation & social analyses]
Possible - [considered too tenuous to be used in age estimation or social analyses]
Unknown - For animals whose mother is unknown.
POD: Indicates acoustical pod membership, according to Bigg et al. (1990). “XXX” = unknown.
CLAN: Indicates acoustic clan group membership (A, G, or R). “X” = unknown.
A = A01, A04, A05, B01, C01, D01, H01, I01, I02 and I18 pods
G = G01, G12, I11 and I31 pods
R = R01 and W01 pods
GEN: Notes an animal’s generation with respect to its matrilineal lineage (Generation 0 being the original known matriarch’s generation).
COHORT: Notes an animal’s age cohort. This simply bins animals into five-year bins according to their YOB. There are 21 cohorts: the first beginning in 1915-1919 to the most current, animals born from 2015-2019. Animals are assumed to mainly socialize with animals within their own and immediately adjacent cohorts (i.e. within roughly ± 5 years of their age).
YOB: [previous] Best estimated year of birth. If there is any uncertainty of the animal’s birth year (as noted by AGE_CONF), the YOB noted is the median.
AGE_CONF: [old measure of confidence in YOB]previous] Indicates the confidence in the ageing method used for the animal, according to the 80% precision estimates in Olesiuk et al. (2005) Table 4. E.g. an animal with AGE_CONF = 2 is aged to ± 2 years.
YOB_min = YOB - AGE_CONF & YOB_max = YOB + AGE_CONF
Age_method: Denotes the ageing method used to determine an animal's YOB. Adapted from Peter Olesiuk's "PO" field.
b, b0.5, b1, b1.5, b2… = Year of birth accurately estimated based on size when first seen. This designation is restricted to animals born within the study period. Number indicates age (or mean of range in age) when first seen (e.g. an animal first seen in 1983 and judged to have been born in 1981 or 1982 would be denoted as b1.5). Used only when year of birth is known within +/- 1 year of estimate.
e2, e3, e4,… = Year of birth crudely estimated based on size when first seen. This designation is restricted to animals born prior to the study period. Number indicates approximate age when first seen (e.g. and animal first seen in 1973 when judged to be about 6 years of age would be denoted e6). Used only when other more accurate ageing techniques such as age at first birth or sexual maturity are not applicable).
fc = Year of birth estimated in reference to year in which it had its first calf (based on mean age at first birth of known-aged females)
o = Year of birth estimated in reference to year in which it had its first known calf (based on mean age at first birth of known-aged females with a correction for calf loss prior to the start of the study)
fs = Year of birth estimated in reference to year in which its dorsal fin HWR=1.4 (based on mean age of onset of sexual maturity for known-aged males)
PM = Year of birth estimated in reference to year in which its dorsal fin was completely developed (based on mean age of onset of physical maturity for known-aged males)
M = The latest year of birth estimated in reference to year in which it was first seen with a completely developed dorsal fin (based on mean age of onset of physical maturity for known-aged males). This provides an estimate of minimum age only. Year first seen -19
YOD_max: Indicates the year an animal was pronounced dead – the first year that an animal is not seen despite at least one good encounter with its matriline.
“NA” is given for all live and currently missing animals.
For captured animals, the year of capture is considered the animal’s year of death (in these cases an asterisk * precedes the year).
SEX: Indicates the animal’s sex. F = female; M = male; U = unknown.
Sex_method: Indicates the method by which an animal was sexed.
Assumed = no evidence sprouting by age 15, therefore assumed female
Calf = presence of calf suggests animal is female
Carcass = animal sexed when found dead
DNA = animal sexed through workup of biopsy sample
Dorsal size = animal sexed by the size of dorsal fin when first seen (applies to males who were mature at the start of the study
Observation = animal sexed in the field by pigmentation (e.g. breach, rollover)
Offspring = presence of offspring suggests animal is female (applies to females who were mature at the start of the study)
Photo/video = animal sexed by pigmentation in photo or underwater video
Sprouting = animal sexed by evidence of sprouting
"NA" assigned to all animals of Unknown sex
mother: Indicates the unique ID of an animal’s birth mother. Relationship established from close association of calf, or from genetics. Hypothetical mother sometimes indicated if two animals are thought to be siblings (e.g. A0A).
“XXX” = unknown
assumed.mother: as for "mother" but with several additional assumptions
max.parity: number of offspring
FSEEN: was the individual first observed when birth year could no longer be accurately estimated directly (see Age_method column)
DEAD: Is the individual known to be dead (based on data at the time this dataset was created)

individual age estimate inputs.csv

As for "ID_wide_anon.csv" with the addition of
Ymin: commencement year of study
FSEEN.OLO: a female's (inferred) oldest living offspring at time of first sighting
FSEEN.OLOage: the estimated age of that offspring (see paper for details of sequential estimated-age-dependent age estimates)
FIRST.CALF.YEAR: if she was first seen without apparent offspring, this is the year in which a female's first calf was born
FIRST.SPROUT.YEAR: if a male's onset of dorsal fin growth was observed, this is the eyar in which it occurred
FIRST.MATURE.YEAR: if a male had already started to sprout when first observed, this is the year at which he attained a full size dorsal fin
FSEEN.MATURE.YEAR: if a male was initially observed with a full sized fin, it was in this year
age.method: the method used to estimate age in this paper, using the methods in the code supplied. See text for details.
EST - year of birth estimated based on size when first seen
OLO - "oldest living offspring" method
FC - "first calf" method
FS - "first sprout" method
FM - "first mature" method
FSF - "full size fin" (first seen physically mature) method
age.ref.year: the reference year at which the relevant ageing method is applied. For example, age.ref.year would be the year at which a female was first seen, if she were aged via the "oldest living offspring" method, while age.ref.year would be the birth year of a female's first calf, if she were aged via the "first calf" method.

Code/Software

"NRKW age uncertainty - FSEEN age distributions.R" coordinates, reading in data and calling other .R filed to perform calculations for different classes of individuals to which different age estimation methods are applied. Running this file, and in the files it calls, will apply the age-estimation procedure. "NRKW age uncertainty - oldest living offspring.R" implements the focal analysis from the main text of the paper, using the age of a female's oldest apparent offspring to estimate her age. "NRKW age uncertainty - motherhood delay.R" implements the procedure to estimate an initially offspring-less female's age based on the timing of her first (apparent) offspring. "NRKW age uncertainty - male sprouting.R" implements the procdure to estimate a male's age based on the timing of onset of dorsal fin growth ("sprouting"). "NRKW age uncertainty - male maturation.R" implements the procedures to estimate a male's age based either on the timing of attainment of a full-sized dorsal fin or on the fact that a male was physically mature when first observed. Other .R files provide supporting code.

Outputs:

After "NRKW age uncertainty - FSEEN age distributions.R" has been run, running "NRKW age uncertainty plots.R" plots the figures for the paper.

The estimated empirical year of birth probability distributions are contained in "birth year distributions.csv".

"revised_ages.csv" provides previous (Bigg et al. 1990; Olesiuk et al. 1990, 2005) year-of-birth estimates and uncertainty ("YOB" & "AGE_CONF columns, resectively) as well as new (from this paper) age and year-of-birth summaries for the same individuals. "estimate_summary.csv" summarises the new (from this paper) year-of-birth estimates.

For use of the resulting age estimates in future modelling work, we provide log-normal approximations of the analytical age-estimate distributions. These approximating distributions will facilitate, for example, inclusion as priors in Bayesian model fitting. See "NRKW age uncertainty - lnorm params.R". Other approximating distributions (e.g. gamma) would be possible with minor adjustments to the code.