Energy Balance: Egg Production and Spawning

Crab mating generally occurs from May through October (van Engle 1958). When a female is approaching sexual maturity, a male crab will carry the female beneath him until she molts and will not cannibalize her when she molts. Following shedding, mating lasts from 5 to 12 hours. Females mate once and store sperm to fertilize all subsequent batches of eggs. Two to nine months may elapse between mating and spawning (van Engle 1958). If mating occurs in May, the first egg mass may be laid in August. Females that mate in August and September are unlikely to spawn until the following May or June. Females can spawn throughout the entire summer and may spawn more than once. Spawning is rapid and is completed in $\approx 2$ hours (van Engle 1958). The number of eggs produced per female ranges from 500,000 to 8,000,000 with bigger females producing more eggs (Prager et al. 1990). It is not known whether bigger females produce higher quality eggs. Spawned eggs are carried on the abdomen of the female for $\approx 2$ weeks until the larvae emerge. Larval release occurs at least two months after mating, during early May through September (van Engle 1958). Newly hatched larva are carried out into nearshore ocean waters where they progress through seven or eight zoea stages and are recruited back into an estuary upon reaching the megalops stage (Epifanio 1995).

In the model, after a female mates, it has the capacity to start producing eggs. The mating status for the crab is set to accumulating eggs and the number of eggs which the female must produce before it spawns is generated (Prager et al. 1990):

$$10^6 = -2.248 + 0.377 *CW + e$$ (A.53)

where $e$ is distributed as a normal RV with mean 0 and SD = 1.39 and CW is in cm. The number of eggs to be generated is updated each time the crab spawns.

It is assumed that females only generate eggs if their energy balance is positive ( $\delta G /\delta t > 0$ in Eqn A.30) and if the crab's mass is greater than 75% of its maximum mass, $G_$max (g), the crab ever attained. If the crab's mass is below this threshold, all excess energy is put into regaining this lost mass until the crab reaches 75% of $G_{\text{max}}$ at which point the proportion of excess energy put into eggs increases linearly from 0 at 75% to 1 at the $G_$max. This condition ensures that starved reproductive crabs will first regain lost mass before putting energy into reproduction. If a crab's ovaries are full, the crab is unable to spawn and the rate of food ingestion is greater than the crab's energy costs, then the crab's rate of egestion is increased so that $\delta G/\delta t =0$.

It is assumed that each egg involves a fixed investment of energy. The precise energy content of blue crab eggs is not known. For the crab Thalamita crenata (Latreille), the energy content of its eggs are $\approx$ 0.0454 cal/egg (or 0.19 J/egg) (Kannupandi et al. 1999) with a wet weight of $\approx$20.47 $\mu$g per egg. Blue crab eggs are $\approx$0.25 mm in diameter (Churchill 1917-1918). We assume that if a mature female blue crab releases $\approx 2.6\times 10^6$ eggs (Prager et al. 1990), these eggs would have a wet weight of $\approx$ 53 g and have a total energy content of $\approx$ 118,000 cal (494,000 J). Thus, the number of eggs produced per gram of excess energy is $\approx 22,000$ eggs.

In the model, crabs may produce eggs during the winter and summer. Once the number of eggs produced by the crab reaches the number needed in Eqn (A.50), its mating status is changed from accumulating eggs to preparing to spawn and it no longer accumulates eggs. The crab spawns if the temperature (Eqn A.3) is above $T_$min spawn$= 19\ensuremath{^\circ\text{C }}$. If the temperature is above $T_$max spawn the crab spawns, but all its eggs will suffer mortality in the maturation pot (Appendix A.5.13). Once a crab spawns, its eggs are added to the maturation pot (Appendix A.5.13), the number of eggs that the crab must generate before it can spawn again is generated according to Eqn (A.50) and the mating status of the crab is set back to accumulating eggs.