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Table 1 Estimated parameters from the HMM-SSF fitted to zebra telemetry data

From: Flexible hidden Markov models for behaviour-dependent habitat selection

 

State/transition

Covariate

 

Estimate (95% CI)

Movement (SSF)

Encamped

Step length L

\(\beta ^{(1)}_1\)

\(-13.6\ (-14.8,\ -12.3)\)

log(L)

\(\beta ^{(1)}_2\)

\(-1.18\ (-1.21,\ -1.15)\)

cos(\(\theta\))

\(\beta ^{(1)}_3\)

\(-0.01\ (-0.07,\ 0.04)\)

Exploratory

Step length L

\(\beta ^{(2)}_1\)

\(-3.11\ (-3.36,\ -2.86)\)

log(L)

\(\beta ^{(2)}_2\)

\(-0.65\ (-0.78,\ -0.53)\)

cos(\(\theta\))

\(\beta ^{(2)}_3\)

\(1.46\ (1.33,\ 1.59)\)

Habitat (SSF)

Encamped

Bushed grassland

\(\beta ^{(1)}_4\)

\(0.21\ (0.03,\ 0.39)\)

Bushland

\(\beta ^{(1)}_5\)

\(-0.19\ (-0.46,\ 0.08)\)

Woodland

\(\beta ^{(1)}_6\)

\(-0.56\ (-1.08,\ -0.05)\)

Exploratory

Bushed grassland

\(\beta ^{(2)}_4\)

\(-1.00\ (-1.16,\ -0.83)\)

Bushland

\(\beta ^{(2)}_5\)

\(-2.19\ (-2.42,\ -1.96)\)

Woodland

\(\beta ^{(2)}_6\)

\(-1.96\ (-2.26,\ -1.66)\)

Transition probabilities (HMM)

Encamped − exploratory

Intercept

\(\alpha _0^{(1,2)}\)

\(-1.83\ (-1.98,\ -1.69)\)

cos\(\left( \frac{2 \pi \tau }{24}\right)\)

\(\alpha _1^{(1,2)}\)

\(0.03\ (-0.14,\ 0.21)\)

sin\(\left( \frac{2 \pi \tau }{24}\right)\)

\(\alpha _2^{(1,2)}\)

\(0.81\ (0.63,\ 0.99)\)

Exploratory − encamped

Intercept

\(\alpha _0^{(2,1)}\)

\(-1.26\ (-1.40,\ -1.12)\)

cos\(\left( \frac{2 \pi \tau }{24}\right)\)

\(\alpha _1^{(2,1)}\)

\(0.15\ (-0.02,\ 0.33)\)

sin\(\left( \frac{2 \pi \tau }{24}\right)\)

\(\alpha _2^{(2,1)}\)

\(0.14\ (-0.04,\ 0.32)\)

  1. Note, these are the untransformed \(\beta\) estimates and do not directly represent the mean and variance of the assumed gamma distribution; the turning angle (given by \(\theta\)) parameter represents the angular concentration of the von Mises distribution. L is the step length (km) and \(\tau\) is the hour of the day.