Distance sampling with animal movement August 30, 2018 Richard - PowerPoint PPT Presentation

Distance sampling with animal movement August 30, 2018 Richard Glennie University of St Andrews rg374@st-andrews.ac.uk

The Snapshot Assumption ◮ Each surveyed transect is a snapshot of the population.

The Snapshot Assumption ◮ Each surveyed transect is a snapshot of the population. ◮ The number of animals inside the transect is fixed. ◮ The distance of each animal is fixed.

The Snapshot Assumption ◮ Each surveyed transect is a snapshot of the population. ◮ The number of animals inside the transect is fixed. ◮ The distance of each animal is fixed. ◮ When animals move the snapshot assumption is violated.

The Snapshot Assumption ◮ Each surveyed transect is a snapshot of the population. ◮ The number of animals inside the transect is fixed. ◮ The distance of each animal is fixed. ◮ When animals move the snapshot assumption is violated. Violations 1. Responsive movement: survey protocol, left truncation, or double observer methods (Conn et al. 2018).

The Snapshot Assumption ◮ Each surveyed transect is a snapshot of the population. ◮ The number of animals inside the transect is fixed. ◮ The distance of each animal is fixed. ◮ When animals move the snapshot assumption is violated. Violations 1. Responsive movement: survey protocol, left truncation, or double observer methods (Conn et al. 2018). 2. What about movement independent of the observer?

N = n ˆ p ˆ

Bigger n p N = n ↑ ↑ ˆ ˆ

Bigger n p Smaller ˆ N = n ↑ ↑↑ ˆ ˆ p ↓

Simulation Study 100 100 ● 90 90 ● 80 ● 80 70 70 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS Relative Bias (%) Relative Bias (%) ● 60 60 ● 50 50 ● ● 40 40 30 30 ● ● 20 20 ● ● 10 10 ● ● ● ● ● 0 0 ● ● −10 −10 50 100 150 200 250 300 0.5 1 1.5 2 2.5 3 3.5 4 Animal Speed (as % of Observer Speed) Animal Speed (m/s) Estimated percentage bias in estimated abundance from a simulated line (left) and point (right) transect survey.

Survey protocol How to reduce bias?

Survey protocol How to reduce bias? ◮ Search further perpendicular to the line or further from the point.

Survey protocol How to reduce bias? ◮ Search further perpendicular to the line or further from the point. ◮ Use a snapshot method.

Survey protocol How to reduce bias? ◮ Search further perpendicular to the line or further from the point. ◮ Use a snapshot method. ◮ Avoid counting overtaking animals in line transects or newly arrived individuals in point transects.

travelled path x Average over all paths: Average over all locations: DS time, e.g,: g x p detected g x segment of path. to get probability of detection in a r 100 h r detected! Use hazard of detection in a very small observer animal’s path observer MDS x d x g x p located at x detected g x x animal x d x

travelled path x Average over all paths: Average over all locations: DS time, e.g,: g x p detected g x segment of path. to get probability of detection in a r 100 h r detected! Use hazard of detection in a very small observer animal’s path observer MDS x d x g x p located at x detected g x x animal x d x

travelled path x Average over all paths: Average over all locations: h r MDS observer animal’s path detected! Use hazard of detection in a very small time, e.g,: DS 100 x d x to get probability of detection in a segment of path. g x detected p g x r p g x observer animal x x d x 1.0 0.8 0.6 g(x) 0.4 0.2 0 5 10 15 20 25 30 x g ( x ) = P ( detected | located at x )

travelled path x Average over all paths: DS 100 observer animal’s path detected! Use hazard of detection in a very small time, e.g,: h r to get probability of detection in a r observer segment of path. g x detected p g x MDS x d x Average over all locations: animal x 1.0 0.8 0.6 g(x) 0.4 0.2 0 5 10 15 20 25 30 x g ( x ) = P ( detected | located at x ) ∫ ˆ p = ˆ g ( x ) π ( x ) d x

travelled path x Average over all paths: DS 100 observer animal’s path detected! Use hazard of detection in a very small time, e.g,: h r to get probability of detection in a r observer segment of path. g x detected p g x MDS x d x Average over all locations: animal x 1.0 0.8 0.6 g(x) 0.4 0.2 0 5 10 15 20 25 30 x g ( x ) = P ( detected | located at x ) ∫ ˆ p = ˆ g ( x ) π ( x ) d x

travelled path x Average over all paths: DS time, e.g,: MDS observer animal’s path detected! Use hazard of detection in a very small to get probability of detection in a r Average over all locations: segment of path. g x detected p g x observer x d x animal x 1.0 0.8 0.6 g(x) h ( r ) = 100 0.4 0.2 0 5 10 15 20 25 30 x g ( x ) = P ( detected | located at x ) ∫ ˆ p = ˆ g ( x ) π ( x ) d x

Average over all paths: DS Average over all locations: g x p segment of path. to get probability of detection in a r time, e.g,: Use hazard of detection in a very small detected! animal’s path observer MDS observer x d x animal x 1.0 0.8 0.6 g(x) h ( r ) = 100 0.4 0.2 0 5 10 15 20 25 30 x g ( x ) = P ( detected | travelled path x ) g ( x ) = P ( detected | located at x ) ∫ ˆ p = ˆ g ( x ) π ( x ) d x

DS observer segment of path. to get probability of detection in a r time, e.g,: Use hazard of detection in a very small detected! animal’s path observer MDS Average over all locations: x animal 1.0 0.8 0.6 g(x) h ( r ) = 100 0.4 0.2 0 5 10 15 20 25 30 x g ( x ) = P ( detected | travelled path x ) g ( x ) = P ( detected | located at x ) Average over all paths: ∫ ∫ ˆ p = ˆ g ( x )ˆ π ( x ) d x ˆ p = ˆ g ( x ) π ( x ) d x

Simulation Study 100 100 ● 90 90 ● 80 ● 80 70 70 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS Relative Bias (%) Relative Bias (%) ● 60 60 ● 50 50 ● ● 40 40 30 30 ● ● 20 20 ● ● MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS 10 10 ● ● ● ● ● ● ● ● 0 ● ● 0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● −10 −10 50 100 150 200 250 300 50 100 150 200 250 300 350 400 Animal Speed (as % of Observer Speed) Animal Speed (as % of Observer Speed) Estimated percentage bias in estimated abundance from a simulated line (left) and point (right) transect survey for conventional distance sampling (DS) and with movement model included (MDS)

Overview ◮ Animal movement independent of the observer can have a substantial effect on estimates of abundance.

Overview ◮ Animal movement independent of the observer can have a substantial effect on estimates of abundance. ◮ The bias depends on the detection process and the relative movement of animals with respect to the observer.

Overview ◮ Animal movement independent of the observer can have a substantial effect on estimates of abundance. ◮ The bias depends on the detection process and the relative movement of animals with respect to the observer. ◮ MDS models can be used for line or point transects to incorporate knowledge of how animals move.

Overview ◮ Animal movement independent of the observer can have a substantial effect on estimates of abundance. ◮ The bias depends on the detection process and the relative movement of animals with respect to the observer. ◮ MDS models can be used for line or point transects to incorporate knowledge of how animals move. ◮ The paper on the MDS models is under revision. Paper will be available soon with an accompanying R package, moveds on GitHub r-glennie.

Overview ◮ Animal movement independent of the observer can have a substantial effect on estimates of abundance. ◮ The bias depends on the detection process and the relative movement of animals with respect to the observer. ◮ MDS models can be used for line or point transects to incorporate knowledge of how animals move. ◮ The paper on the MDS models is under revision. Paper will be available soon with an accompanying R package, moveds on GitHub r-glennie. ◮ Any questions or discussion welcome!

Key References ◮ Conn, P. B., & Alisauskas, R. T. (2018). Simultaneous modelling of movement, measurement error, and observer dependence in mark-recapture distance sampling: An application to Arctic bird surveys. The Annals of Applied Statistics, 12(1), 96-122. ◮ Glennie, R., Buckland, S. T., & Thomas, L. (2015). The effect of animal movement on line transect estimates of abundance. PloS one, 10(3), e0121333. ◮ Glennie, R., Buckland, S. T., Langrock, R., Gerrodette, T., Ballance, L., Shivers, S., Scott, M. and Perrin, W. F. (in prep). Incorporating animal movement into distance sampling.