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            status	 for	 all	 stocks,	 we	 combined	 the	  data-limited	 models	 (Table	 1,	 Figure	 1).	  Bmsy	(Table	1,	Figure	2).	This	is	particularly
            estimates	 from	 the	 four	 models	 using	  Of	these,	265	(64%	of	those	below	Bmsy)	  striking	 in	 the	 northern	 hemisphere
            a	 super	 ensemble.	 The	 super	 ensemble	  are	 estimated	 to	 be	 below	 80%	 of	 the	  regions,	where	most	stocks	are	estimated
            method	goes	well	beyond	simply	averaging	  Bmsy	 level,	 which	 is	 the	 FAO	 (State	 of	  to	 be	 below	 the	 biomass	 that	 would
            across	individual	method	estimates.	Our	  World	Fisheries	and	Aquaculture)	SOFIA	  support	 MSY	 (Figure	 2).	 The	 exception
            super	ensemble	calibrated	a	combination	  definition  of  “overexploited.”  Therefore,   to	 this	 pattern	 was	 the	 Mediterranean
            of	the	four	individual	model	estimates	of	  for	the	149	stocks	between	Bmsy	and	80%	  and	 the	 Black	 Sea,	 where	 more	 stocks
            B/Bmsy via a random forest method fitted   of	Bmsy, significant yield may be foregone,   were	above	Bmsy.	Similarly,	the	majority
            to	 a	 dataset	 of	 nearly	 6,000	 simulated	  but	the	current	advice	under	FAO	is	that	  of	stocks	in	the	South	Atlantic	and	South
            fish stocks with known B/Bmsy.	Random	  they	are	fully	exploited	and	unfortunately,	  Pacific regions were below Bmsy.
            forests	 are	 a	 machine	 learning	 approach	  no	real	policy	change	would	be	called	for.  In	 the	 Atlantic,	 all	 of	 the	 FAO	 areas
            that	 allow	 for	 nonlinear	 relationships	  The	super	ensemble	was	employed	to	  have	a	median	value	for	estimated	stock
            between	 the	 predictors	 (the	 individual
            model	 estimates)	 and	 the	 response	 (the	  deal	with	individual	biases	in	each	of	the	  status	below	Bmsy,	except	eastern-central
            super	ensemble	estimate)	and	interactive	  models,	 but	 underlying	 patterns	 could	  Atlantic	 and	 southwest	 Atlantic	 (Table
            effects	 between	 the	 individual	 model	  still	be	detected.	For	example,	in	addition	  1)	 but	 with	 substantial	 variation	 in
            estimates	 while	 being	 relatively	 robust	                               status	 among	 stocks	 within	 each	 region.
            to over fitting. Previous analyses showed                                  Similarly, the northeast Pacific, northwest
            that	 a	 random	 forest	 super	 ensemble	                                  Pacific and southeast Pacific regions have
            consistently	 had	 the	 best	 or	 among
            the	 best	 performance	 characteristics
            when	 compared	 to	 other	 possible	 super
            ensemble	 regression	 models.	 The	 super
            ensemble	 outperformed	 the	 individual
            models	 in	 cross-validation	 on	 simulated
            data	with,	for	example,	a	median	absolute
            proportional	 error	 in	 B/Bmsy	 of	 0.32
            compared	to	0.42–0.56	for	the	individual	  Figure	 1)	 Global	 distribution	 of	 B/Bmsy	 status	 for
                                                 785	 analyzed	 stocks	 estimated	 by	 each	 data-limited
            models.                              method	and	the	super	ensemble	approach.
                                                 to	a	primary	mode	slightly	above	B/Bmsy
            Estimating stock status
               We	computed	density	plots	to	explore	  (Figure	1),	the	super	ensemble	estimated
            the	 distribution	 of	 stock	 status	 globally	  many	 stocks	 to	 have	 a	 B/Bmsy	 below	 1,
            and	 within	 each	 FAO	 statistical	 region	  producing	 a	 second	 mode	 at	 B/Bmsy	 =
            through	 2013.	 We	 also	 compared	 our	  0.65.	 We	 investigated	 the	 distributions	  Figure	 2)	 Regional	 distribution	 of	 B/Bmsy	 status
            global	estimates	of	status	to	other	global	  of	the	underlying	data-limited	models	to	  analyzed	 stocks	 estimated	 by	 the	 super	 ensemble
                                                                                       approach.	Black	vertical	lines	indicate	B/Bmsy	=	1	with
            estimates	 of	 status.	 Additionally,	 we	  understand	the	cause	of	this	bimodality	and	  dark	gray	bars	indicating	±	20%	around	this	point.
            compared	 our	 approach	 to	 traditional	  found	that	the	Cmsy	and	COMSIR	models	  a	 median	 estimated	 status	 below	 Bmsy
            stock	 assessment	 estimates	 by	 matching	  were	mainly	responsible	for	this	pattern	in	  while  the  southwest  Pacific,  eastern-
            stocks	in	the	RAM	Legacy	database	with	  the	estimates.	In	a	sensitivity	analysis	for	  central Pacific and western-central Pacific
            those	 in	 the	 FAO	 catch	 database	 where	  Cmsy,	we	found	that	the	bimodality	was
            possible.	In	some	cases,	there	are	multiple	  due	to	the	prior	distributions	assigned	to	  have	 a	 median	 status	 at	 or	 above	 Bmsy
            RAM	 stocks	 that	 match	 a	 single	 “stock”	  the final year depletion, which are based   (Table	1).	The	eastern	and	western	Indian
            from	the	FAO	database	(e.g.,	tuna	stocks	or	  on	the	catch	trajectories.	This	bimodality	  Ocean	regions	are	in	better	condition	with
            Atlantic	cod).	In	these	cases,	we	matched	  carries	 forward	 into	 the	 super	 ensemble	  only	around	one-third	of	the	stocks	below
            the	 RAM	 stock	 status	 estimate	 to	 each	  estimates.	 However,	 the	 overall	 results	  Bmsy.	The	super	ensemble	estimated	that
            FAO	 region	 to	 which	 it	 could	 logically	  do	not	change	if	each	model	is	removed	  stocks	in	the	western	Indian	Ocean	have
            correspond.	We	also	compared	the	status	  individually	 from	 the	 super	 ensemble.	  the	highest	median	status	of	all	FAO	areas
            estimates	for	RAM	Legacy	assessed	stocks	  The	SSCOM	method	frequently	estimated	  (median	 =	 1.14).	 The	 long	 tails	 on	 the
            with	the	status	of	previously	unassessed	  stocks	 to	 be	 underexploited	 relative	 to	  distribution	of	stock	status	for	all	regions
            stocks	from	the	FAO	catch	database.  Bmsy	 (Figure	 1).	 The	 ensemble	 partly	  indicates	that	there	are	some	stocks	that
                                                 accounts	 for	 potential	 systematic	 bias	  are	 only	 lightly	 exploited	 and	 others
            Patterns                             through	the	relative	weightings,	but	these	  heavily	 exploited,	 with	 regard	 to	 recent
            Global patterns                      estimates	of	higher	biomass	still	affect	the	  catch	trends.
               At	 the	 aggregate	 global	 level,	 the	  overall	pattern.                Within	all	of	the	regions	a	substantial
            median	B/Bmsy	status	of	exploited	stocks	                                  number	 of	 stocks	 are	 estimated	 to	 be
                                                                                       within	 20%	 below	 Bmsy	 such	 that	 they
            is	 0.97,	 such	 that	 414	 stocks	 (52.7%)	 are	  Regional patterns       would	be	classed	as	“fully	exploited”	in
            estimated	to	be	below	the	Bmsy	reference	  For	8	of	the	15	FAO	regions,	over	50%	  previous	studies	(Figure	2).
            point	 based	 on	 a	 super	 ensemble	 of	  of	the	stocks	were	estimated	to	be	below

            10                                                 SAARC                                            JUNE 2018
                                                          OILS & FATS TOdAy
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