This document summarizes a presentation about modeling animal movement data. It discusses using hidden Markov models to analyze GPS tracking data from Florida panthers. The initial analysis found 3 movement states but estimates of model complexity were too high due to not accounting for diurnal variation. Incorporating temporal patterns like diurnal variation into the transition probabilities greatly improved model fit. Overall, the presentation discussed challenges in animal movement modeling like overfitting due to model misspecification and how accounting for sources of variation can help address these issues.

1. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Model complexity and model choice for animal
movement models
Ben Bolker, McMaster University
Departments of Mathematics & Statistics and Biology
Guelph Biomathematics & Biostatistics Symposium
9 June 2016

2. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

3. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Acknowledgements
People Michael Li, Madelon van de Kerk,
Dave Onorato, Madan Oli; many unnamed field
biologists
Agencies US Fish and Wildlife Service, US Geological Survey,
US National Park Service
Funding NSERC Discovery grant, NSF IGERT program

4. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

5. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Animal movement: data
observations:
e.g. mass mark-recapture,
longitudinal density, direct
observation, telemetry
(VHF, GPS)
most methods provide a
sequence of times and
locations for each individual
q
q
q
q
θ1
θ2s1
s2
t1
t2
t3
t4

6. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
summaries:
home range
(convex hull, kernel
density estimate, etc.)
root-mean-squared
displacement
step length and turning
angle
covariates:
e.g. habitat map,
individual characteristics
(sex, age, weight . . . )
0
100
200
300
0 1 2 3
step length (log10m)
count
180
270
0
90
0
50
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250

7. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Animal movement: questions
simple description
how do animals’ movements change as a function of their
(internal or external) environment?
what does that tell us about their biology?
how might animals’ distributions, etc. change when conditions
(density, habitat, ...) change?

8. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

9. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Biological/conservation issues
Florida panther: Puma
concolor coryi
endangered subspecies
severely reduced habitat
small, isolated population
currently recovering
www.peer.org

10. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Panther movement questions
movement variation by sex
and life history stage
(juvenile, adult, mom with
kittens . . . )
effects of movement on
threats
(intraspecific aggression,
roadkill) ?
predicting the effects of
future changes in population
density / population
structure / habitat

11. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Panther movement data
panthers tracked, captured
GPS collars
18 males (13 male, 5 female,
1-15 years old)
3200 panther days,
hourly/bihourly; 49000
locations
?? per panther

12. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
example movement tracks
CatID: 48 CatID: 131 CatID: 189
0
10
20
30
0 5 10 15 20 0 5 10 15 20 0 5 10 15 20
x (km)
y(km)

13. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

14. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Hidden Markov models
finite mixture model with temporal dependence
discrete time steps
discrete latent state; transition matrix
observations from emission distributions
(continuous or discrete, univariate or multivariate)
multiphasic movement (Fryxell et al., 2008; Langrock et al.,
2012)

15. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Hidden Markov models (cont.)
state:
St ∼ Multinomial(St−1, µS,t)
µS,t = multi-logistic(XS,tβS )
emission:
Zt ∼ {Dist1(µZ1,St ), . . . , Distn(µZn,St )}
µZi ,St = g−1
(XZi ,tβZi ,St )

16. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Hidden Markov models (part 3)
forward-backward algorithm for estimating parameters
Viterbi algorithm for estimating most probable state sequences
depmixS4 package (Visser and Speekenbrink, 2010) (also
moveHMM (Michelot et al., 2016))
hidden semi-Markov models: allow for non-geometric dwell
distributions (Langrock, 2011; Augustine, 2016): move.HMM

17. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

18. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
State distributions
0.00
0.25
0.50
0.75
0.01 0.10 1.00 10.00
Step length (km)
0.2
0.4
0.6
−2 0 2
Turning angle (radians)
0.0
0.2
0.4
0.6
4 8 12
Dwell time (hrs)
State 1 2 3

19. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Parameter estimates
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dwell time
(scale)
dwell time
(shape)
step length
(scale)
step length
(shape)
turn angle
(direction)
turn angle
(dispersion)
0.25
0.50
0.75
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0
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1 2 3 1 2 3 1 2 3
State
Value
Sex
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F
M

20. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Tracks with Viterbi estimates
CatID: 48 CatID: 131 CatID: 189
0
10
20
30
0 5 10 15 20 0 5 10 15 20 0 5 10 15 20
x (km)
y(km)
factor(vitstates)
1
2
3

21. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Diurnal variation

22. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
what can we conclude so far?
good news
basic biology: males move faster, farther
three states are identifiable, sensible
dwell distributions approximately geometric
(HSMM → HMM)
bad news
diurnal variation in Viterbi results - but it’s not in the model!
estimates of model complexity are too high

23. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
what can we conclude so far?
good news
basic biology: males move faster, farther
three states are identifiable, sensible
dwell distributions approximately geometric
(HSMM → HMM)
bad news
diurnal variation in Viterbi results - but it’s not in the model!
estimates of model complexity are too high

24. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Model complexity (bad news)
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CatID: 139 CatID: 157 CatID: 185 CatID: 165
CatID: 137 CatID: 167 CatID: 155 CatID: 189
CatID: 48 CatID: 131 CatID: 94 CatID: 130
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Number of latent states
∆BIC
Sex
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M

25. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Model complexity (Manx shearwaters, Dean et al. (2013))
q
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q q q q q
0
1000
2000
3000
2 4 6 8 10
number of latent states
∆negativelog−likelihood
q
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min AIC
min BIC

26. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

27. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Expanding the model
Attempting to fix these problems:
extend the model to allow covariates
specifically, allow for diurnal variation
simplify model (log-Normal step length only)
fixed state-specific emissions parameters
(step length mean and std dev)
time-varying transition parameters
also try finite mixture models
(independent occupancy)
how much does this help?

28. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Expanding the model
Attempting to fix these problems:
extend the model to allow covariates
specifically, allow for diurnal variation
simplify model (log-Normal step length only)
fixed state-specific emissions parameters
(step length mean and std dev)
time-varying transition parameters
also try finite mixture models
(independent occupancy)
how much does this help?

29. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Temporal models
0 6 12 18 24
time
model
block
hourly
quad
sin

30. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Temporal patterns (step length)
1.6
2.0
2.4
0 5 10 15 20
Time of day
Meansteplength(log10m)
model
homogeneous (n=6)
block (n=4)
quadratic (n=5)
sin (n=5)
hourly (n=3)
observed

31. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Temporal patterns (autocorrelation)
0.00
0.25
0.50
0.75
1.00
0 10 20 30 40
Time of day
Autocorrelation
model
homogeneous (n=6)
block (n=4)
quadratic (n=5)
sin (n=5)
hourly (n=3)
observed

32. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Goodness of fit/model complexity
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0
500
1000
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3 4 5 6 7
number of latent states
∆BIC
model
q
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q
homogeneous
quadratic
sinusoid
block
hourly
# of parameters
q
q
100
200

33. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Model complexity: simulation
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number of latent states
∆BIC
type
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homogeneous
quadratic
sin
hourly

34. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Diurnal model: conclusions
diurnal structure greatly improves fit (∆BIC ≈ 500)
slightly improves latent-state issue (n = 6 → 5)
lots left to do!
seasonal variation
incorporate habitat, home range behaviour
etc. etc. etc.

35. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Outline
1 Animal movement
2 Florida panthers
3 Hidden Markov models
4 Basic analysis (van de Kerk et al., 2015)
5 Incorporating diurnal variation (Li, 2015)
6 Broader issues/outlook

36. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Big data and small models
simple model families +
model misspecification →
overparameterization
Gelman: “Sample sizes are never large”: (blog post)
N is never enough because if it were “enough” you’d
already be on to the next problem for which you
need more data.

37. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
An aside on AIC vs BIC
“should I use AIC or BIC? I
heard that AIC is
inconsistent ...”
complexity penalty = 2
(AIC) vs log(n) (BIC)
best prediction vs. model
identification (Yang, 2005)
effect size spectrum:
tapering or discrete?
effect
effectsize
type
discrete
tapering

38. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Animal movement: open challenges
Cognition/memory (Bracis
et al., 2015)
Intraspecific
interaction/collective
movement (Delgado et al.,
2014)
Continuous-time movement
models (Calabrese et al., 2016)
Edges, barriers, and corridors
(Beyer et al., 2016)
Efficient (big-data)
approaches (Brillinger et al.,
2008)
Putting it all together ...

39. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
Tools needed
cross-validation (Wenger and Olden, 2012)
protocols and tools for model checking (Potts et al., 2014);
score tests?
flexible computational frameworks
(ecologists can’t afford consultants/
there are too many species out there)

40. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
http://tinyurl.com/panthermoves;
http://www.slideshare.net/bbolker

41. Animal movement Panthers HMM Basic analysis Diurnal model Broader issues/outlook References
References
Augustine, B., 2016. Flexible, user-friendly hidden
(semi) Markov models for animal movement data.
Beyer, H.L., Gurarie, E., et al., 2016. Journal of
Animal Ecology, 85(1):43–53. ISSN 00218790.
doi:10.1111/1365-2656.12275.
Bracis, C., Gurarie, E., et al., 2015. PLOS ONE,
10(8):e0136057. ISSN 1932-6203.
doi:10.1371/journal.pone.0136057.
Brillinger, D.R., Stewart, B.S., et al., 2008. In
Probability and statistics: Essays in honor of David
A. Freedman, pages 246–264. Institute of
Mathematical Statistics.
Calabrese, J.M., Fleming, C.H., and Gurarie, E., 2016.
Methods in Ecology and Evolution, pages n/a–n/a.
ISSN 2041-210X. doi:10.1111/2041-210X.12559.
Dean, B., Freeman, R., et al., 2013. Journal of The
Royal Society Interface, 10(78):20120570. ISSN
1742-5689, 1742-5662.
doi:10.1098/rsif.2012.0570.
Delgado, M.d.M., Penteriani, V., et al., 2014. Methods
in Ecology and Evolution, 5(2):183–189.
Fryxell, J.M., Hazell, M., et al., 2008. Proceedings of
the National Academy of Sciences,
105(49):19114–19119. ISSN 0027-8424,
1091-6490. doi:10.1073/pnas.0801737105.
Langrock, R., 2011. Computational Statistics and Data
Analysis, 55(1):715–724. ISSN 01679473.
Langrock, R., King, R., et al., 2012. Ecology,
93(11):2336–2342. ISSN 0012-9658.
doi:10.1890/11-2241.1.
Li, M., 2015. Incorporating Temporal Heterogeneity in
Hidden Markov Models For Animal Movement.
Master’s thesis.
Michelot, T., Langrock, R., and Patterson, T.A., 2016.
Methods in Ecology and Evolution, in press.
doi:10.1111/2041-210X.12578.
Potts, J.R., Auger-Méthé, M., et al., 2014. Methods in
Ecology and Evolution, 5(10):1012–1022.
van de Kerk, M., Onorato, D.P., et al., 2015. Journal
of Animal Ecology, 84(2):576–585.
Visser, I. and Speekenbrink, M., 2010. Journal of
Statistical Software, 36(7):1–21.
Wenger, S.J. and Olden, J.D., 2012. Methods in
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2041210X.
doi:10.1111/j.2041-210X.2011.00170.x.
Yang, Y., 2005. Biometrika, 92(4):937–950.
doi:10.1093/biomet/92.4.937.