Background State-space model Simulation study Future work

Analysis and interpretation of acoustic array data:estimating horizontal movement

Martin W. Pedersen, Kevin Weng26 November 2012PFRP PI meeting

University of Hawaii at Manoa

Background State-space model Simulation study Future work

Equipment for acoustic data collection

Photo credit: Vemco.

Background State-space model Simulation study Future work

Example: Palmyra rubble pile array

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−162.126 −162.124 −162.122 −162.120 −162.118

5.87

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Palmyra rubble pile array

Longitude

Latit

ude

A

AA B

BB

C

CC

D

DD

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JJ

S1

S2 S3

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S8S9S10

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● Receivers100 m radiusRef tags

Background State-space model Simulation study Future work

Acoustic array data

Mar Apr May Jun Jul

Tag ID: 46894, # data: 32173

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IIJJ

Background State-space model Simulation study Future work

Sources of transmission error

I Time of day.

I Water movement (swells,currents).

I Water column stratification(thermocline etc.).

I Time since deployment(biofouling).

I Bottom topography (signalblocking).

Background State-space model Simulation study Future work

Horizontal movements

Current approaches

I Kernel estimation.

I Local polynomial regression.

Advantages: Quick way to get an overview of data.

Drawbacks: No biological interpretation, no account for errors oruncertainties in data.

Background State-space model Simulation study Future work

State-space model (SSM)

A model with two components:

I Process model (describing movement).

I Observation model (describing data collection).

Appealing model because it describes the mechanisms underlyingthe data.

Patterson et al. 2008 TREE, Schick et al. 2008 Ecol. Lett.

Background State-space model Simulation study Future work

Movement model

Simple random walk

xt = xt−1 + et , et ∼ N(0, 2Dt).

The parameter D is related to the movement rate of the fish.

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Simulated RW Espinoza et al. 2011

Background State-space model Simulation study Future work

Observation model

What do we observe and how does it relate to location?

P = f (d)

0 100 200 300 400 500

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Distance from receiver, meters

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ectio

n pr

obab

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Detection probability

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y

Background State-space model Simulation study Future work

Observation model

What do we observe and how does it relate to location?

P = f (d)

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0

Distance from receiver, meters

Det

ectio

n pr

obab

ility

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−400 −200 0 200 400

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Detection probability

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Background State-space model Simulation study Future work

Observation model - presence information

Likelihood of location given detection.

L ∝ f (d)

0 100 200 300 400 500

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Distance from receiver, meters

Like

lihoo

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loca

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Likelihood of location (detection)

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Background State-space model Simulation study Future work

Observation model - absence information

Ping rate is known from manufacturer.

L ∝ 1− f (d)

0 100 200 300 400 500

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Distance from receiver, meters

Like

lihoo

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DetectionNo detection

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Likelihood of location (no detection)

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Background State-space model Simulation study Future work

Noise conditions

Use reference tag detection efficiency, zt , as a proxy for noiseconditions.

Lt ∝ f (d , zt)

Background State-space model Simulation study Future work

Simulation study

Scenario 1 - constant noise conditions

I Check consistency of parameter estimates.

I Compare state-space model performance with otherapproaches.

Scenario 2 - varying noise conditions

I Compare results with and without using reference taginformation.

Background State-space model Simulation study Future work

Comparing SSM with other approachces

600 800 1000 1200 1400

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Distance between receivers (m)

Mea

n di

stan

ce e

rror

(m

)SSMLocal polyKernel

Background State-space model Simulation study Future work

Covariate information from reference tag

0 20 40 60 80 100 120 140

0.0

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time (hours)

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ectio

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ficie

ncy

Background State-space model Simulation study Future work

Movement estimation (500 m btw receivers)

True SSM no cov. SSM w cov. (dashed is 95% CI)

0 20 40 60 80 100 120 140

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time, hours

x, m

eter

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time, hours

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time, hours

x, m

eter

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time, hours

y, m

eter

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Background State-space model Simulation study Future work

Movement estimation (500 m btw receivers)

True SSM no cov. SSM w cov. (dashed is 95% CI)

0 20 40 60 80 100 120 140

1000

3000

5000

time, hours

y, m

eter

s

90 95 100 105

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3400

time, hours

y, m

eter

s

0 20 40 60 80 100 120 140

1000

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time, hours

y, m

eter

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90 95 100 105

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time, hours

y, m

eter

s

Background State-space model Simulation study Future work

Future work

I Apply to real data.I Develop guidelines for acoustic array design.I Applications to other types of presence/absence data.

Background State-space model Simulation study Future work

Future work

I Apply to real data.I Develop guidelines for acoustic array design.I Applications to other types of presence/absence data.

Thank you for listening!