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fast inference of behaviour underlying animal
movement and habitat use
Ian Jonsen
Sophie Bestley, Marie Auger-Méthé, Rob Harcourt, Mark Hindell, Clive McMahon,
Joanna Mills Flemming, Simon Wotherspoon
Society for Marine Mammalogy, Halifax, Nova Scotia
23-27 October 2017
background
Bayesian state-space models excel at inferring animal movement behaviours hidden
within error-prone location data
SSM-estimated locations from Argos data
southern elephant seal
SSM-estimated behavioural states
transient
resident
problem
Bayesian SSMs fit using Markov chain Monte Carlo (MCMC) methods are
computationally sloooowww
inference of environmental influence on movement behaviour not practical if N > 5-10
individuals
4.3 hours to converge
transient
resident
Bestley et al. 2013 PRSB 280: 20122262
solution
fit models via maximum likelihood using Template Model Builder (TMB)* in R with C++
templates
auto-differentiation & Laplace approximation for random effects
similar flexibility to Bayesian SSMs fit via MCMC
much, much faster
* Kristensen et al (2016) J Stat Software 70: 1-21
model
𝛄t = 0 – slow, tortuous
𝛄t = 1 – fast, directeddt = 𝛄t dt-1 + 𝜮t
changes in location
time-varying
move persistence
randomness in
movements
𝛄t varies continuously between 0 and 1 through time
- no discrete switches between behavioural states
can be fit to location data with or without error
Auger-Méthé et al. 2017 MEPS 565: 237-249
state-switching on ‘average’ 𝛄 time-varying 𝛄
computation time: 4.3 h computation time: 18 s
transient
resident
pelagic foraging trips
model 𝛾t as a function of covariates & include random effect(s) to account for
individual differences (k):
logit(𝛾t,k) ~ (𝛽0 – b0,k) + (𝛽1 – b1,k) xt,1,k + … + (𝛽n – bn,k) xt,n,k
environmental correlates of behaviour
environmental correlates of behaviour
salinity difference 500 – 200 m
sea surface height anomaly variability
toy example with random intercept:
logit(𝛾t,k) ~ (𝛽0 – b0,k) + 𝛽1xt,1,k
environmental correlates of behaviour
salinity difference Var(sea level anomaly)
aic = -12379 aic = -12330
75 s ~ 1000 x FASTER than MCMC
salinity difference Var(sea level anomaly)
aic = -12379 aic = -12330
-0.2 0.0 0.2 0.4 0.6 0.8
-500-450-400
Use of Water Column
Salinity Difference(-600/-200)
Depth(m)
Poorer	foraging Better	foraging
lowerpreydensity
&
shorterdives
higherpreydensity
&
longerdives
night dives
day dives
the bigger picture…
McMahon et al. In prep
-0.2 0.0 0.2 0.4 0.6 0.8
-500-450-400
Use of Water Column
Salinity Difference(-600/-200)
Depth(m)
Poorer	foraging Better	foraging
lowerpreydensity
&
shorterdives
higherpreydensity
&
longerdives
night dives
day dives
positive SAM negative SAM
the bigger picture…
McMahon et al. In prep
why is this useful?
continuous behavioural index provides more detailed view of movement patterns
computation speed +
flexible random effects +
simple model
deeper understanding of how animals actually use habitat
facilitates syntheses
of massive data
what’s next
infer behaviour from locations + diving + accelerometry
penalised spline regression for complex environmental relationships
integrate with spatial habitat models - behaviourally explicit
R package

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Ian Jonsen

  • 1. fast inference of behaviour underlying animal movement and habitat use Ian Jonsen Sophie Bestley, Marie Auger-Méthé, Rob Harcourt, Mark Hindell, Clive McMahon, Joanna Mills Flemming, Simon Wotherspoon Society for Marine Mammalogy, Halifax, Nova Scotia 23-27 October 2017
  • 2. background Bayesian state-space models excel at inferring animal movement behaviours hidden within error-prone location data SSM-estimated locations from Argos data southern elephant seal SSM-estimated behavioural states transient resident
  • 3. problem Bayesian SSMs fit using Markov chain Monte Carlo (MCMC) methods are computationally sloooowww inference of environmental influence on movement behaviour not practical if N > 5-10 individuals 4.3 hours to converge transient resident Bestley et al. 2013 PRSB 280: 20122262
  • 4. solution fit models via maximum likelihood using Template Model Builder (TMB)* in R with C++ templates auto-differentiation & Laplace approximation for random effects similar flexibility to Bayesian SSMs fit via MCMC much, much faster * Kristensen et al (2016) J Stat Software 70: 1-21
  • 5. model 𝛄t = 0 – slow, tortuous 𝛄t = 1 – fast, directeddt = 𝛄t dt-1 + 𝜮t changes in location time-varying move persistence randomness in movements 𝛄t varies continuously between 0 and 1 through time - no discrete switches between behavioural states can be fit to location data with or without error Auger-Méthé et al. 2017 MEPS 565: 237-249
  • 6. state-switching on ‘average’ 𝛄 time-varying 𝛄 computation time: 4.3 h computation time: 18 s transient resident
  • 8. model 𝛾t as a function of covariates & include random effect(s) to account for individual differences (k): logit(𝛾t,k) ~ (𝛽0 – b0,k) + (𝛽1 – b1,k) xt,1,k + … + (𝛽n – bn,k) xt,n,k environmental correlates of behaviour
  • 9. environmental correlates of behaviour salinity difference 500 – 200 m sea surface height anomaly variability toy example with random intercept: logit(𝛾t,k) ~ (𝛽0 – b0,k) + 𝛽1xt,1,k
  • 10. environmental correlates of behaviour salinity difference Var(sea level anomaly) aic = -12379 aic = -12330
  • 11. 75 s ~ 1000 x FASTER than MCMC salinity difference Var(sea level anomaly) aic = -12379 aic = -12330
  • 12. -0.2 0.0 0.2 0.4 0.6 0.8 -500-450-400 Use of Water Column Salinity Difference(-600/-200) Depth(m) Poorer foraging Better foraging lowerpreydensity & shorterdives higherpreydensity & longerdives night dives day dives the bigger picture… McMahon et al. In prep
  • 13. -0.2 0.0 0.2 0.4 0.6 0.8 -500-450-400 Use of Water Column Salinity Difference(-600/-200) Depth(m) Poorer foraging Better foraging lowerpreydensity & shorterdives higherpreydensity & longerdives night dives day dives positive SAM negative SAM the bigger picture… McMahon et al. In prep
  • 14. why is this useful? continuous behavioural index provides more detailed view of movement patterns computation speed + flexible random effects + simple model deeper understanding of how animals actually use habitat facilitates syntheses of massive data
  • 15. what’s next infer behaviour from locations + diving + accelerometry penalised spline regression for complex environmental relationships integrate with spatial habitat models - behaviourally explicit R package