Spatial modelling of prawn (shrimp) abundance from large-scale marine surveys using penalised...

Spatial modelling of prawn (shrimp) abundance

from large-scale marine surveys using penalised regression

splines

Charis Burridge, Geoff Laslett (CMIS) & Rob Kenyon (CMAR)

30 November 2009

CSIRO Mathematical and Information Sciences

Location of the fishery being surveyed

Australia

Northern Prawn Fishery

Great B

arrier Reef

0 100 200 300 400

Kilometers


Introduction to the Northern Prawn Fishery (NPF)

• Typical annual earnings > $100 million• ~40 yrs fishing, most in Gulf of Carpentaria• Measures taken to conserve multi-species stocks:

(an input-controlled fishery up till now, i.e.control over number of vessels & gear type/size, also spatial and temporal closures)

-- fleet size ~100 vessels in 2001, now ~50; -- NPF closed to fishing 7 months; -- coastline nursery areas closed all year

• Apr-May mainly banana prawns (daytime allowed)• Sept-Nov mainly tiger & endeavour prawns (night only)


1970 1980 1990 2000 2010

0

100

200

300

400

500

Brown tiger prawn (Penaeus esculentus)

Management target

Sy/

Sm

sy (

%)

1970 1980 1990 2000 2010

StockProjected Stock at 2001 management level Projected Stock at 2005 (25% gear cut)

Projected Stock at 2005 (95% CI) Projected Stock at 2005 (5% CI)

Grooved tiger prawn(Penaeus semisulcatus)

Management target

Stock decline for tiger prawnsStock decline for tiger prawns


NPF integrated prawn monitoring project

• An international review by Rick Deriso in 2001 confirmed CSIRO advice that these species were over-exploited

• He strongly recommended introducing fishery-independent surveys to augment the stock assessment process with unbiased indices of prawn abundance

• The Northern Prawn Fishery Management Advisory Council funded a desktop study to scope up survey design options (Dichmont, Vance, Burridge et al; 2002)

• Two surveys a year have been funded since Aug 2002 (initial cost AUD 500K per year; increased fuel & charter costs in recent years have pushed this up towards AUD 1M)


Design considerations

• Cost-effective: NPF fishers pay ~ full cost (now > $5000 per at-sea day, ~1 FTE staff [big team])

• Include 7 commercial prawn species• Timing of survey (month, moon phase, charter)• Sampling frame for spawning index

-- based on spatial distribution of historical & current fishing effort Aug/Sep

• Sampling frame for recruitment index -- based on well-known or inferred coastal/inshore nursery habitat + allowance for migration offshore

• Hierarchical stratification – regional; sub-regional; depth; in order to-- improve precision by capturing large-scale spatial variation for 4 main commercial species; -- control spatial distribution of sampling effort over a very large area (300,000 sq.km. in Gulf of Carpentaria alone)


136°0'0"E

136°0'0"E

138°0'0"E

138°0'0"E

140°0'0"E

140°0'0"E

142°0'0"E

142°0'0"E

16°0'0"S 16°0'0"S

14°0'0"S 14°0'0"S

12°0'0"S 12°0'0"S

Gulf of Carpentaria

QLDNT

SH N.Gr

SH S.Gr

SH W.Van

SH E.Van

SH Tully

SH W.Morn

SH N.Morn

SH E.Morn

DE N.Gr

DE S.Gr

DE W.Van

DE E.Van

DE Tully

DE W.Morn

DE N.Morn

DE E.Morn

Sampling frame for spawning survey (3 regions Jun/Jul/Aug): Groote, Vanderlins and Mornington; based on spatial distribution of historical & current fishing effort Aug/Sep


Sampling frame for recruitment survey (5 regions Jan/Feb): (Groote, Vanderlins, Mornington, SEGulf & Weipa) based on known/inferred inshore nursery habitat + some offshore movement

136°0'0"E

136°0'0"E

138°0'0"E

138°0'0"E

140°0'0"E

140°0'0"E

142°0'0"E

142°0'0"E

16°0'0"S 16°0'0"S

14°0'0"S 14°0'0"S

12°0'0"S 12°0'0"S

Gulf of Carpentaria

QLDNT

SH N.Gr

SH S.Gr

SH W.Van

SH E.Van

SH W.Morn

SH N.Morn

SH E.Morn

SH W.Kar

SH E.Kar

SH S.We

SH N.We

DE N.Gr

DE S.Gr

MI W.Van

MI E.Van

DE W.Morn

DE N.Morn

DE E.Morn

DE W.Kar

DE E.Kar

DE S.We

DE N.We

DE W.Van

DE E.Van


Aims of spatial smoothing of prawn density

• Hitherto, we have reported a design-based relative abundance index for the whole survey area – essentially a weighted sum of the mean in each stratum

• Now we want to capture more information about the spatial distribution of prawns in each survey

• And prepare an index from this model-based approach• A Bayesian approach to the spatial modelling makes it

easy to construct a credible (or “confidence”) interval for the index

• The software called BayesX offers a useful suite of smoothing models implemented via a Markov Chain Monte Carlo approach

• It’s also free


BayesX website – note the recent update


Spatial models for prawn abundance/density

• 2-D penalised regression splines with 1st order random walk penalty

• Basic concepts:• MCMC iterative approach aims to produce a large sample from

the posterior distribution of the model coefficients (here with a diffuse Inverse Gamma prior on the variance); it is usual to discard the results of early iterations, so that start-up bias in the process is mimimised

• Spatial domain is gridded and a set of 2-D spline ‘kernels’ set up so that the centre-point of each kernel sits on a grid intersection: these are the prediction variables in the model; log(prawn density) is the response variable

• (Kernel) regression coefficients for a given iteration follow a 2-D 1st order random walk: coefficients of neighbouring kernels differ less than those of distant kernels (the smaller the variance of this random walk, the smoother the surface – prior can be a diffuse inverse Gamma)


Publications on P-splines by BayesX team

• Fahrmeir, L., Lang, S., 2001. Bayesian inference for generalized additive mixed models based on Markov random field priors. J. Roy. Statist. Soc. C 50, 201–220.

• Lang, S., Brezger, A., 2004. Bayesian P-splines. J. Comput. Graphical Statist. 13, 183–212.

• Brezger, A. & Lang, S., 2006. Generalized structured additive regression based on Bayesian P-splines.Computational Statistics & Data Analysis, 50, 967 – 991


Problem: lots of empty space & vast no. of parameters if want to capture fine-scale detail in regions where we do have data

135 136 137 138 139 140 141 142

-18

-17

-16

-15

-14

-13

-12

Longitude

Latit

ude

Recruitment Survey


Solution: local coordinates for each region (PC scores from lat/lon of sites + frame); map all other regions to (0,0);

simultaneously fit 6 sub-models => fewer knots, higher density

135 136 137 138 139 140 141 142

-18

-17

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-15

-14

-13

-12

Longitude

Latit

ude

Recruitment Survey

Model sectors

N GrooteN&W MorningtonS GrooteSE GulfVanderlinsWeipa


Stability/convergence of North Groote variance – achieved after 15000 iterations (or so!)

0 200 400 600 800 1000

0.0

0.5

1.0

2003

0 200 400 600 800 1000

0.0

0.5

1.0

1.5

2004

0 200 400 600 800 1000

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

2005

0 200 400 600 800 1000

0.0

0.5

1.0

1.5

2006

0 200 400 600 800 1000

-0.5

0.0

0.5

1.0

2007

0 200 400 600 800 1000

0.0

0.5

1.0

2008


Checking for autocorrelation in parameters – achieved when keep 1 record in 60 (~20 minutes to run on my laptop)

0 20 40 60

-0.2

0.0

0.2

ngr

2

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

v an

2

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

seg

2

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

2

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

all

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

ngr

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

sgr

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

v an

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

nwm

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

ngr,1

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

ngr,18

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

ngr,31

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

sgr,1

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

sgr,18

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

sgr,31

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

v an,1

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

v an,18

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

v an,31

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

nwm,1

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

nwm,18

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

nwm,31

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

seg,1

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

seg,18

lag

corr

elat

ion

0 20 40 60

-0.2

0.0

0.2

seg,31

lag

corr

elat

ion


Observed brown tiger (P. esculentus) density in Jan/Feb

135 136 137 138 139 140 141 142

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Longitude

2003

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

2004

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

2005

135 136 137 138 139 140 141 142

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-13

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Longitude

2006

135 136 137 138 139 140 141 142

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-12

Longitude

Latit

ude

2007

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

20081:nlev

1P. esculentus prawns per hectare(0,1] (1,2] (2,5] (5,10] (10,20] (20,30] (30,Inf]


Spatially smoothed brown tiger density – rare in Weipa, abundant around Mornington & improving

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2003

135 136 137 138 139 140 141 142

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LongitudeL

atit

ud

e

2004

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2005

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2006

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2007

135 136 137 138 139 140 141 142

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LongitudeL

atit

ud

e

20081:nlev

1P. esculentus Predicted density(0,1] (1,2] (2,5] (5,10] (10,20] (20,30] (30,Inf]


95th %ile for smoothed brown tiger density

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2003

135 136 137 138 139 140 141 142

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-14

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LongitudeL

atit

ud

e

2004

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2005

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2006

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2007

135 136 137 138 139 140 141 142

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LongitudeL

atit

ud

e

20081:nlev

1P. esculentus 95th %ile fitted density(0,1] (1,2] (2,5] (5,10] (10,20] (20,30] (30,Inf]


Observed grooved tiger (P. semisulcatus) density in Jan/Feb

135 136 137 138 139 140 141 142

-18

-17

-16

-15

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-13

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Longitude

2003

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

2004

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

2005

135 136 137 138 139 140 141 142

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Longitude

2006

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

2007

135 136 137 138 139 140 141 142

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Longitude

Latit

ude

20081:nlev

1P. semisulcatus prawns per hectare(0,1] (1,2] (2,5] (5,10] (10,20] (20,30] (30,Inf]


Smoothed grooved tiger density – rare in SE Gulf and common in Weipa

135 136 137 138 139 140 141 142

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-12

Longitude

La

titu

de

2003

135 136 137 138 139 140 141 142

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-14

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-12

LongitudeL

atit

ud

e

2004

135 136 137 138 139 140 141 142

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-14

-13

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Longitude

La

titu

de

2005

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2006

135 136 137 138 139 140 141 142

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Longitude

La

titu

de

2007

135 136 137 138 139 140 141 142

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LongitudeL

atit

ud

e

20081:nlev

1P. semisulcatus Predicted density(0,1] (1,2] (2,5] (5,10] (10,20] (20,30] (30,Inf]


MCMC-based index (solid red & 90% credible interval) compared with design-based index (black diamonds & 90% mirror-match bootstrap confidence interval) for three species over 7 recruitment surveys

Year of recruitment survey

Glo

ba

l de

nsi

ty in

de

x

2

4

6

8

10

12

2003 2004 2005 2006 2007 2008 2009

M. endeavouri

2003 2004 2005 2006 2007 2008 2009

P. esculentus

2003 2004 2005 2006 2007 2008 2009

P. semisulcatus


Conclusions

• A ‘toe in the water’ in terms of exploiting BayesX capabilities; BayesX authors have promptly responded to my requests and added extra functionality

• BayesX can be used as a stand-alone package; I find it easier to import all BayesX results into R for graphical presentation – there is now an R package for this

• Spatial smoothing has produced similar indices to the design-based approach, but appears less sensitive to occasional enormous catches (a benefit)

• The spatial models reveal spatial contraction/expansion of the resource more directly than design-based indices

• The design-based and model-based confidence/credible intervals differ substantially – to be investigated

Thank you

CMIS/EICharis BurridgeResearch statistician

Phone: +61 7 3826 7186Email: [email protected]: www.csiro.au/group

Contact UsPhone: 1300 363 400 or +61 3 9545 2176

Email: [email protected] Web: www.csiro.au

Spatial modelling of prawn (shrimp) abundance from large-scale marine surveys using penalised...

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