Canadian Journal of Fisheries and Aquatic Sciences

Figure S3

Fig. S3: Relationship between tuna age and length (left) and weight (right), as modelled by the Dynamic Energy Budget model for Atlantic bluefin tuna (Thunnus thynnus). For comparison, the growth curve used by ICCAT (International Commission for the Conservation of Atlantic Tunas) is also plotted (red line).

Figure S4

Fig. S4 Age-length keys of anchovy (Engraulis encrasicolus), sardine (Sardina pilchardus) and sprat (Sprattus sprattus) calculated from the small pelagic survey data over the period 2008 to 2013. For sprat (n=100, years = 2013) a linear model was used, where L(t) is the expected length at age t. For sardine (n=4744, years = 2009-2014) and anchovy (n=4412, years = 2009-2014) seasonal variability was accounted for using Somers’ model (Somers 1988), with , where L_∞ is the model asymptote for average length, K is as measure of the exponential rate of approach to asymptotic length, t₀ is the theoretical age at which the average length would be zero, C is the amplitude of the growth oscillation and t_s is the inflexion point.

Table S1

Table S1. Biological parameter values of major prey species found in the stomach contents of juvenile Atlantic bluefin tuna (Thunnus thynnus). The ranges of energetic densities were taken from literature (see Appendix 1: Energetic density). Lengths of sardine, anchovy and sprat were calculated using the linear relationship between otolith (oto) length and individual (ind) fish length (), and their body mass was obtained by converting these lengths using an annual length weight key (). Direct length measurements were not needed for mackerel and squid, and otolith lengths or beak lower rostral lengths (LRL) were directly converted to weight (). All relationships were calculated from the small pelagic survey biological data. Parameter estimates and relationships were always significant. We specified the number of data points (N) on which the relationships were based and the range of values for which it was specified.

Energetic density (kJ/g wet weight)
Sardine		Anchovy		Sprat							Mackerel				Squid
4.00-14.40		2.67-12.81		3.7-12.40							6.00-10.30				5.01-6.46
	R2		a		b			N				range				range
Sardine	0.86		0.46		0.14			50				1.6 - 2.9				9.3 - 17.5
Anchovy	0.78		0.62		0.18			53				1.9 - 3.8				8.6 - 3.8
Sprat	0.24		0.98		0.06			47				1.2 - 1.8				0.9 - 11.1
			c			d			N				range				range
Mackerel			0.88			3.09			36				7.2 - 36.2				2.0 - 3.1
Squid			7.07			2.24			61				3.0 - 215.2				0.9 - 4.2
	year		e				f			N				range				range
Sardine	2011		4.40*10-3				3.2			229				1.7 - 45.0				6.5 - 18.0
	2012		2.29*10-3				3.47			220				2.0 - 46.0				6.5 - 17.0
	2013		4.09*10-3				3.24			216				2.5 - 27.0				7.5 - 15.0
Anchovy	2011		2.97*10-3				3.29			195				3.0 - 22.5				8.5 - 15.0
	2012		4.76*10-3				2.1			168				4.0 - 22.0				8.5 - 15.0
	2013		4.10*10-3				3.18			126				2.0 - 22.0				8.0 - 15.0
Sprat	2011		6.50*10-3				3.03			139				1.7 - 13.0				6.5 - 18.0
	2012		5.19*10-3				3.15			171				2.0 - 15.0				7.0 - 11.5
	2013		6.61*10-3				3.03			153				1.0 - 10.8				6.0 - 11.5

Table S2

Table S2 Dynamic equations of the non-standard Dynamic Energy Budget model developed and validated for Pacific bluefin tuna (Thunnes orientalis, Jusup et al. 2011) and reparameterised for Atlantic bluefin tuna (T. thynnus) for use in this study. t denotes time and T temperature. Processes are usually defined in terms of energy and are thus measured in J.

State and auxiliary variables
Symbol	Definition			unit
E(t)	Amount of energy in reserve tissue			J
V(t)	Volume of structural tissue			cm3
L(t)	Structural volumetric length			cm
EH(t)	Level of maturity			J
ER(t)	Status of the reproductive buffer			J
E0	Initial energy reserve of an egg			J
Energy fluxes
Metabolic process	Energy flux
Assimilation (A)
Utilization (C)
Somatic maintenance (S)
Growth (G)
Dynamics of state variables, reproduction state
State variable	Dynamic equation
Energy in reserve
Structural length
Maturity (H) level
Auxiliary functions
Auxiliary functions	Functional form
Shape correction function
Efficiency of internal heat production
Arrhenius equation
Shape factor

Table S3

Table S3 Dynamic Energy Budget parameters for Atlantic bluefin tuna (Thunnus thynnus) and their values.

Symbol	Definition	Value	Unit
Basic DEB parameters
{ṗAm}	Maximum surface-area-specific assimilation rate	124.8	J cm-2 d-1
[EG]	Volume-specific cost of structure	7163	J cm-3
v̇	Energy conductance	0.09542	cm d-1
[ṗM]	Volume-specific somatic maintenance rate	5.149	J cm-3 d-1
{ṗT}	Surface-area-specific somatic maintenance rate	1877	J cm-2 d-1
k̇J	Maturity maintenance rate coefficient	1.362	10-2 d-1
κ	Fraction of mobilized reserve allocated to soma	0.8222
EbH	Maturity at birth (b)	0.2253	J
EpH	Maturity at puberty (P)	2.937	107J
Other DEB parameters
EjH	Maturity at the end of the larval stage	2566	J
E2H	Half-saturation maturity	7050	J
EyH	Maturity at the end of the early juvenile phase	1.629	106 J
TA	Arrhenius temperature	6398	K
δ1M	Shape factor in the larval stage	0.1475
δ2M	Shape factor in the adult stage	0.2531

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