How long would it take to become a giant squid?

Abstract

Laboratory and field studies suggest that cephalopod growth occurs rapidly and is linked to temperature throughout a short life span. For giant squid such as Architeuthis, a paucity of size-at-age data means that growth is only inferred from isolated field specimens, based on either statoliths or isotopic analyses of tissue. In this study we apply simple growth models to obtain projections of the life span required to achieve the Architeuthis average body mass in scenarios which include an energy balance between rates of food intake and expenditure on growth and metabolism. Although the analysis shows that a wide range for the estimated life span is possible, energy conservation suggests that achievement of a larger size would be assisted by slower exponential growth early on. The results are compared with a sparse set of size-at-age data obtained from male and female Architeuthis wild specimens and possibly hint at some behavioural differences between males and females.

Appendices

Appendix 1

Life span t _max as a function of transition age t*

The simple two-phase model of Eq. 2 implies a dependence between the final body mass B _max and the critical transition age t* and hence that for any specified hatchling size A _B , B _max is a function of transition age t*, exponential body mass growth rate coefficient m _B and life span t _max . Equivalently, for a specified hatchling size A _B , final body mass B _max and exponential body mass growth rate coefficient m _B , the relationship between life span t _max and the transition age t*, by basic geometry is t _max = t* + (B _max  − B*)/m _B B* which on substituting for ${B^{\ast}=A_{B} e^{m_{B}t^{\ast}}}$implies that t _max is a function of the transition age t* given by

$$ t_{max} \,(t^{\ast} )=t^{\ast} +\left( {\frac{1}{m_B }} \right)\left[ {\left( {\frac{B_{max}}{A_B }} \right)e^{-m_B t^{\ast} }-1} \right] $$

(A1)

Appendix 2

Estimates for parameters q ₁ and q ₂

A. Parameter q ₁

An estimate for the parameter q ₁ can be obtained from observed food-intake-rate of captive individuals of the Australian Giant Cuttlefish Sepia apama (Grist and Jackson 2004). It was noted by O’Dor et al. (2005) that at a body mass of 229 g, the feeding rate F _r was 36 g per day (hence 36/229 = 16% body mass per day), so with the energy equivalent in food (animal tissue) of 4.1868 kJ g ⁻¹ and typical cephalopod efficiencies of 50% wastage and 90% assimilation through digestion,

$$ q_{1}=F_{r}/ B^{0.75} = (0.5 \times 0.9) \times (36 \times 4.1868)/(229^{0.75}) = 1.15 \quad [\hbox{kJ/day/g}^{0.75}] $$

(A2)

B. Parameter q ₂

Metabolic rate M _r scales with B ^0.75 where B is body mass and is proportional to oxygen consumption rate O _c . Hence O _c = k ₁ B ^0.75 where k ₁ is in practice also a temperature-dependent constant. Seibel et al. (2000) found that citrate synthase activity y _cs is given by y _cs  = aB ^b (where a and b are constants) and in squid mantle muscle is highly correlated with the whole animal oxygen consumption rate.

For a tentacle obtained from an Architeuthis estimated to have had a body mass B = 20,000g, they obtained at 20°C that y _cs  = 0.76 and b = −0.25 and hence it follows that a = 0.76/(20000)^−0.25 = 9.0380 so that

$$ y_{cs} = 9.038 B^{-0.25}\quad [\hbox{unspecified units/g}] $$

(A3)

For pelagic cephalopods in general, Seibel et al. (2000) found also that oxygen consumption rate O _c [μ mol/g/h] can be expressed in terms of citrate synthase activity by the linear relationship

$$ O_{c}=0.72 y_{cs}-0.043\quad [\mu \hbox{mol/g/h}] $$

(A4)

Combining Eq. A3 and A4 together, an estimate for the oxygen consumption rate of Architeuthis at 20°C is given by O _c = 0.72(9.0380 B ^−0.25) − 0.043 or

$$ O_{c}=6.5074 B^{-0.25}-0.043\quad [\mu \hbox{mol/g/h}] $$

(A5)

which, when expressed equivalently in ml/g/day (using a conversion factor of 0.5348) and evaluated over the whole animal body mass approximates to

$$ O_{c }=3.4802 B^{0.75}\quad [\hbox{ml/day}] $$

(A6)

The factor by which oxygen consumption rate (and hence k ₁) would reduce when temperature is reduced from 20°C to 5°C was obtained as 0.7 from comparison of the metabolic rates determined for the deep sea squid Vampyroteuthis infernalis and Histeoteuthis heteropsis by Seibel et al. (1997, 2000).

At an ambient temperature of 5°C in the deep sea, an estimate for Architeuthis oxygen consumption rate is hence

$$ O_{c }=0.7 \times (3.4802 B^{0.75}) $$

(A7)

$$ =2.4361 B^{0.75}\quad [\hbox{ml/day}] $$

(A8)

Using the value of 0.01926 kJ/mL metabolic energy released per mL of oxygen expended, the metabolic rate at 5°C would then be M _r = 0.01926 × (2.4361 B ^0.75) or

$$ M_{r }=0.0469 B^{0.75}\quad[\hbox{kJ/day}] $$

(A9)

so that q ₂ = 0.0469 day/kJ/g ^0.75.