Fish usually reproduce when they have reached about half of the maximum size they are likely to reach (*L*_{max}). The size at which maturity is first reached is called size at first maturity (*L*_{m}), and the fraction *L*_{m}/*L*_{max}, called *reproductive load*, tends to be higher in small than in large fish. Thus, a goby with *L*_{max}=10 cm will have a value of *L*_{m}=7 cm, while in a basking shark with *L*_{max} ≅ 10 m, *L*_{m} will be about 4 m. Given that fish of different sizes have different growth rates, their different *L*_{m} values imply very different ages at first maturity (*t*_{m}).

*L*_{m} is available for few species when compared to the total number of fish species. Froese and Binohlan (2000) developed the following empirical equation based on available data from 467 fish stocks **(r ^{2}=0.89, s.e.=0.127) **in FishBase:

**log _{10} (L_{m})=-0.0782+0.8979·(log_{10}L_{∞}) ... 4.1) **

For species with no available *L*_{m} information, equation 4.1 can be used for the estimation of *L*_{m} (and its standard error, s.e.) from the available *L*_{∞} values of the species and the s.e. of the slope of equation 4.1. Such 'quick' estimates are useful for fisheries management in data-sparse situations (see section 6.5 on Fisheries Management).

• Find from FishBase 20 species with maximum lengths *L*_{max}<50 cm, 50< *L*_{max}<100 and *L*_{max}>100 cm with at least one record of *L*_{m}. Estimate the L_{m}/L_{max} ratio. Estimate the mean ratio for the three size classes. Compare the means. [**Hint: ** In Excel use ANOVA from **Tools/Data analysis ** to compare the three means.]

• Find from FishBase 10 species with no record of *L*_{m} but with at least one available set of von Bertalanffy growth parameter. Estimate the species' *L*_{m} from their *L*_{∞} using equation 4.1.

Fish differ from most other vertebrates in that for most species, parental care is very limited or non-existent. The typical bony fish produces a large number of small eggs which hatch and become part of the zooplankton, and which must beware of their parents (or other members of their species) if these are zooplankton feeders.

The high fecundity of bony fish has led many to believe that they can be exploited very strongly, i.e., that there will always be some recruits even if the parental stock is much reduced. This is called the 'million egg fallacy' and it has caused untold damage to fisheries, especially cod fisheries. Still, it is useful to know the relationship between numbers of eggs spawned and the weight of the mothers.

• A given fish species capable of reaching 50 cm, has the following fecundity-length relationship: *f*=0.03·*L*^{3.5}, where *f* is the number of eggs in a ripe female and *L* its length in cm. The same species has the length-weight relationship *W*=0.01·*L*^{3.0} where *W* is in g and *L* in cm. Use these relationships to calculate the relative fecundity of the largest females, and compare this with the relative fecundity of a female near first maturity, near 60% of L max.

• Redo the above calculations, but with exponents of 2.5 and 4.5 for the fecundity-length relationships. What are the implications of the results for the usefulness of marine protected areas, where female fish can get old (and hence large)?

There are a number of fish which give birth to live young or which construct nests for their eggs, or which practice buccal incubation, e.g., in the Nile tilapia. Some other fish, notably the cartilaginous sharks and rays, give birth to fully-formed pups or produce very large eggs from which fully-formed young are hatched.

• Write a one-page essay on why most fish species broadcast their eggs and exert no parental care, given the fact that parental care reduces the mortality of the young and is practiced by several successful groups of fishes.

As noted by Darwin, fish are extremely labile in their sex determination, i.e., there are lots of fish which change sex (e.g., wrasses, parrot fishes, groupers), at least, far more than in other vertebrate classes. These are called hermaphrodites. In some fishes the different life (and sex) stages differ so much in color and/or form that they were originally described as different species. Fish also give us neat examples of parasitic males, and other strange behaviors.

• Give one example of a hermaphroditic species where subsequent development phases look very different.

• Write a one-page essay about the different forms of hermaphroditism that exist and their distribution among fish families, and latitudinally.

• Write a one-page essay on the group(s) in which parasitic males occur and give possible reasons for their preponderance among these groups.