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

1. 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

2. 0 100 200 300 400 Kilometers Location of the fishery being surveyed Northern Prawn Fishery Great Barrier Reef Australia CSIRO Mathematical and Information Sciences

3. 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) CSIRO Mathematical and Information Sciences

4. Stock decline for tiger prawns ProjectedStock at 2001 management level Projected Stock at 2005 (25% gear cut) Stock Projected Stock at 2005 (95% CI) Projected Stock at 2005 (5% CI) 500 Brown tiger prawn (Penaeus esculentus) Grooved tiger prawn(Penaeus semisulcatus) 400 300 Sy/Smsy (%) 200 100 Management target Management target 0 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 CSIRO Mathematical and Information Sciences

5. 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) CSIRO Mathematical and Information Sciences

6. 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) CSIRO Mathematical and Information Sciences

7. 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 CSIRO Mathematical and Information Sciences

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

9. 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    CSIRO Mathematical and Information Sciences

10. BayesX website – note the recent update CSIRO Mathematical and Information Sciences

11. 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) CSIRO Mathematical and Information Sciences

12. 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 CSIRO Mathematical and Information Sciences

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

14. 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 CSIRO Mathematical and Information Sciences

15. Stability/convergence of North Groote variance – achieved after 15000 iterations (or so!) CSIRO Mathematical and Information Sciences

16. Checking for autocorrelation in parameters – achieved when keep 1 record in 60 (~20 minutes to run on my laptop) CSIRO Mathematical and Information Sciences

17. Observed brown tiger (P. esculentus) density in Jan/Feb CSIRO Mathematical and Information Sciences

18. Spatially smoothed brown tiger density – rare in Weipa, abundant around Mornington & improving CSIRO Mathematical and Information Sciences

19. 95th %ile for smoothed brown tiger density CSIRO Mathematical and Information Sciences

20. Observed grooved tiger (P. semisulcatus) density in Jan/Feb CSIRO Mathematical and Information Sciences

21. Smoothed grooved tiger density – rare in SE Gulf and common in Weipa CSIRO Mathematical and Information Sciences

22. 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 CSIRO Mathematical and Information Sciences

23. 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 CSIRO Mathematical and Information Sciences

24. CMIS/EI Charis Burridge Research statistician Phone: +61 7 3826 7186 Email: charis.burridge@csiro.au Web: www.csiro.au/group Thank you Contact UsPhone: 1300 363 400 or +61 3 9545 2176Email: Enquiries@csiro.au Web: www.csiro.au