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

SLIDE 1

Distance sampling with animal movement

August 30, 2018 Richard Glennie University of St Andrews rg374@st-andrews.ac.uk

SLIDE 2

The Snapshot Assumption

◮ Each surveyed transect is a snapshot of the population.

SLIDE 3

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.

SLIDE 4

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.

SLIDE 5

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).

SLIDE 6

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?

SLIDE 7

ˆ N = n ˆ p

SLIDE 8

Bigger n

↑ˆ N = n↑ ˆ p

SLIDE 9

Bigger n Smaller ˆ p

↑↑ˆ N = n↑ ˆ p↓

SLIDE 10

Simulation Study

DS

DS DS DS DS DS DS DS

−10 10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 Animal Speed (as % of Observer Speed) Relative Bias (%)

DS

DS DS DS DS DS DS DS DS DS

−10 10 20 30 40 50 60 70 80 90 100 0.5 1 1.5 2 2.5 3 3.5 4 Animal Speed (m/s) Relative Bias (%)

Estimated percentage bias in estimated abundance from a simulated line (left) and point (right) transect survey.

SLIDE 11

Survey protocol

How to reduce bias?

SLIDE 12

Survey protocol

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

SLIDE 13

Survey protocol

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

SLIDE 14

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.

SLIDE 15

DS

bserver

animal x

g x detected located at x Average over all locations: p g x x dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h r 100 r to get probability of detection in a segment of path.

g x detected travelled path x Average over all paths: p g x x dx

SLIDE 16

DS

bserver

animal x

g x detected located at x Average over all locations: p g x x dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h r 100 r to get probability of detection in a segment of path.

g x detected travelled path x Average over all paths: p g x x dx

SLIDE 17

DS

bserver

animal x

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 x g(x)

g(x) = P(detected | located at x) Average over all locations: p g x x dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h r 100 r to get probability of detection in a segment of path.

g x detected travelled path x Average over all paths: p g x x dx

SLIDE 18

DS

bserver

animal x

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 x g(x)

g(x) = P(detected | located at x) Average over all locations: ˆ p = ∫ ˆ g(x)π(x) dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h r 100 r to get probability of detection in a segment of path.

g x detected travelled path x Average over all paths: p g x x dx

SLIDE 19

DS

bserver

animal x

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 x g(x)

g(x) = P(detected | located at x) Average over all locations: ˆ p = ∫ ˆ g(x)π(x) dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h r 100 r to get probability of detection in a segment of path.

g x detected travelled path x Average over all paths: p g x x dx

SLIDE 20

DS

bserver

animal x

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 x g(x)

g(x) = P(detected | located at x) Average over all locations: ˆ p = ∫ ˆ g(x)π(x) dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h(r) = 100 r to get probability of detection in a segment of path.

g x detected travelled path x Average over all paths: p g x x dx

SLIDE 21

DS

bserver

animal x

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 x g(x)

g(x) = P(detected | located at x) Average over all locations: ˆ p = ∫ ˆ g(x)π(x) dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h(r) = 100 r to get probability of detection in a segment of path.

g(x) = P(detected | travelled path x) Average over all paths: p g x x dx

SLIDE 22

DS

bserver

animal x

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 x g(x)

g(x) = P(detected | located at x) Average over all locations: ˆ p = ∫ ˆ g(x)π(x) dx MDS

bserver

animal’s path

detected!

Use hazard of detection in a very small time, e.g,: h(r) = 100 r to get probability of detection in a segment of path.

g(x) = P(detected | travelled path x) Average over all paths: ˆ p = ∫ ˆ g(x)ˆ π(x) dx

SLIDE 23

Simulation Study

DS

DS DS DS DS DS DS DS MDS MDS MDS MDS MDS MDS MDS MDS

−10 10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 Animal Speed (as % of Observer Speed) Relative Bias (%)

DS

DS DS DS DS DS DS DS DS DS MDS MDS MDS MDS MDS MDS MDS MDS MDS MDS

−10 10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 350 400 Animal Speed (as % of Observer Speed) Relative Bias (%)

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)

SLIDE 24

Overview

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

SLIDE 25

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.

SLIDE 26

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.

SLIDE 27

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

n GitHub r-glennie.

SLIDE 28

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

n GitHub r-glennie.

◮ Any questions or discussion welcome!

SLIDE 29

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.