Multi-state open robust design models for dealing with incomplete sampling and imperfect detection: an example with sperm whales and opportunistic photo-ID data. Presented at the 32nd Annual European Cetcean Society Conference in La Spezia, Italy, 2018

Abstract

Information on abundance and demography is essential to assess the status of populations, inform conservation and management measures and evaluate effectiveness of those measures. Application of capture-mark-recapture (CMR) methods to photo-identification data has been extensively used to estimate abundance and life history parameters of cetacean populations. Yet, the challenges and costs of obtaining longitudinal observations of wide ranging marine animals frequently hampers CMR studies. Use of opportunistic photographic data may be an alternative, if modelling takes into account potential biases from imperfect detection and incomplete sampling. We applied covariate-based open models (POPAN) and multi-state open robust design (MSORD) to estimate demographic parameters of sperm whales summering in the Azores from data collected opportunistically by whale watching operators and researchers. Best fitting POPAN models accounting for heterogeneity in capture probabilities estimated annual abundances with a positive trend ranging from 351 (95%CI: 234-526) to 718 (95%CI: 477-1082). Best fitting MSORD models, which explicitly incorporated permanent and temporary emigration and uncertainty from imperfect detection, showed little interannual variation in abundances, ranging from 275 (95%CI: 174-436) to 367 (95%CI: 230-585). Both POPAN and MSORD models estimated constant and high survival of sperm whales 95% (CV=0.07) and 93% (CV=0.12), respectfully). MSORD models also indicated individual sperm whales had short residency times in the study area and there was an equal flow of animals in and out of the area between years. This study demonstrates the potential of MSORD models to overcome the many challenges associated with the analysis of opportunistic data from wide ranging species. By accounting for imperfect and variable detectability, this model can reduce bias and improve precision of abundance and demographic estimates.

Full text

Multi-state open robust design models for dealing
with incomplete sampling and imperfect detection:
an example with sperm whales and
opportunistic photo-ID data
Rebecca M Boys, Cláudia Oliveira, Sergi Pérez-Jorge,
Rui Prieto, Lisa Steiner, Mónica A. Silva
© KE Adventure

•Wide-ranging
Azores
Steiner et al., 2015
Estimating demographic parameters of highly-mobile species

•Dedicated sampling
•Wide-ranging
Azores
Steiner et al., 2015
Estimating demographic parameters of highly-mobile species

•Dedicated sampling
•Opportunistic sampling
Eco-tourism (whale watching)
Citizen Science
•Wide-ranging
Azores
Steiner et al., 2015
Estimating demographic parameters of highly-mobile species
R. Prieto@ImagDOP

Problem: Heterogeneity
Uneven sampling
Movements
Heterogeneity
in capture
probability
Biased estimates
Lower precision

Problem: Heterogeneity
Uneven sampling
Movements
Heterogeneity
in capture
probability
Biased estimates
Lower precision
Aim:
•Open covariate-based model
•Multi-state model

•Open POPAN model with covariate describing variation in capture
•PriorCapL function
–Was the animal seen in previous time periods?
Time 1
?
Time 2
?
Time 3
?
Solution: Open covariate-based POPAN model
Lisa Steiner

Outside
study area:
Unobservable
Solution: Multi-State Open Robust Design (MSORD)
(Pollock 1982; Kendall et al. 1997; Schwarz and Stobo 1997; Kendall and Bjorkland 2001)
Inside study area:
Observable
•Multi-state models with Pollock’s Robust Design
•Accounts for imperfect detection

POPAN: Demographic parameters
Inside study area
•Capture probability
•Survival
•Annual abundance
Super-population size
Entry probability
Outside study area

MSORD: Demographic parameters
Inside study area
•Capture probability
•Survival
•Annual abundance
•Remaining probability
•Residence time
Outside study area
Temporary emigration
Entry probability

Study site and dataset
R. Medeiros@ImagDOP
•July-start September
•POPAN:2009-15 (7 years)
•MSORD:2011-15 (5 years)
0
10
20
30
40
50
60
70
80
90
100
0
500
1000
1500
2000
2500
1987
1989
1991
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
Number survey days
Cumulative number individuals
Year
no. survey days cum no. ind

Study site and dataset
R. Medeiros@ImagDOP
•July-start September
•POPAN:2009-15 (7 years)
•MSORD:2011-15 (5 years)
0
10
20
30
40
50
60
70
80
90
100
0
500
1000
1500
2000
2500
1987
1989
1991
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
Number survey days
Cumulative number individuals
Year
no. survey days cum no. ind

=
Inside study area
Observable
Temporary emigration: Even-flow
MSORD: Estimates of inter-annual movement
Outside study area
Unobservable
Varied between years from 0.22-0.66

Probability of entry, remaining and average residence
Start summer
0.40 (SE=0.047)
End summer
0.33 (SE=0.041)
MSORD: Estimates of intra-annual movement
Study area
Residence: 3 weeks
Remaining: low 0.053 (SE=0.025)

POPAN MSORD
PriorCapL Time Since Marking
0.95 (95%CI=0.56-0.99) 0.93 (95%CI=0.73-1.00)
High and constant
Consistent with results from other studies
MSORD and POPAN: Survival

0
200
400
600
800
1000
1200
2009 2010 2011 2012 2013 2014 2015 2016
Total abundance estimate
Year
POPAN
POPAN: Abundance
Super-population estimate: 1468 (95%CI: 1202.8 – 1791.0)

0
200
400
600
800
1000
1200
2009 2010 2011 2012 2013 2014 2015 2016
Total abundance estimate
Year
MSORD
POPAN
MSORD: Abundance

0
200
400
600
800
1000
1200
2009 2010 2011 2012 2013 2014 2015 2016
Total abundance estimate
Year
MSORD
POPAN
MSORD: Abundance
More Precise Less Biased

Model comparison
MSORD
Imperfect detection
Transience (Time Since Marking)
Temporary emigration
 Intra-annual pooling of data
 Coarse estimates

POPAN
 Super-population
 Transience (PriorCapL)
 Temporary emigration
 Biased annual abundance
MSORD
Imperfect detection
Transience (Time Since Marking)
Temporary emigration
 Intra-annual pooling of data
 Coarse estimates
Model comparison

•Permitted us to derive key population
parameters
Importance and applicability
JorgeFontes@ImagDOP

•Permitted us to derive key population
parameters
•Importance of using appropriate CMR
methods for modelling:
–Opportunistic data
–Wide-ranging species
Importance and applicability
JorgeFontes@ImagDOP

•Permitted us to derive key population
parameters
•Importance of using appropriate CMR
methods for modelling:
–Opportunistic data
–Wide-ranging species
•MSORD reduces bias, improves
precision and reliability of estimated
parameters
Importance and applicability
JorgeFontes@ImagDOP

Thank you for your attention
rebeccaboys@hotmail.com
Azores Whale Lab
whales.scienceontheweb.net
We acknowledge IFAW for providing photo-identification data from 1987-1993
Biosphere Expeditions and clients of Whale Watch Azores for making data collection possible
Sara Magalhães, Tiago Sá, João Medeiros, Yves Cuenot, Pablo Chevallard Navarro, and numerous
volunteers that over the years helped with data collection and organization of the photo-identification
catalogue.
We are deeply grateful to Gary White, Bill Kendall, Jim Hines, James Nichols and Paul Conn for offering
guidance and advice on CMR modelling.
JorgeFontes@ImagDOP