LIFE HISTORY OF LAKE HERRING OF LAKE HURON 291 



great fluctuations in the annual birth I'ate; and this woukl not allow a smooth 

 curve, as Hjort obtains, when the specimens are arranged according to their year 

 class and the percentage of individuals in each. " * * * ^^ increase of birth 

 rate or a diminution of natural mortality such as would cause the race of 10-year- 

 old herring to outnumber all the rest put together from 4 years old to 15, is very hard, 

 indeed, to imagine [1914]." "That 4-year herring normally show four rings we all 

 believe, but if in a hundred herring, mostly four-ringed, I find a few with three and a 

 few with five rings, am I bound to believe that these are younger and older fish mixed 

 up with the 4-year-oids; or may they not be merely variants or abnormal members 

 of the stock?" There is room for doubt * * * [Sherriff, 1922]." Thompson 

 (1914) refers to Miss Massy's (1914) experiments, which showed that 3-year-old 

 oysters reared in an aquarium had formed from two to seven rings in their shells. 

 Experiments on the formation of rings in oyster shells showed that the variations 

 from the mean in the number of rings in an age group appear to follow the laws of 

 chance, the mathematical laws that govern the phenomena of variation. As (15) 

 the samples of herring showed a similar variation about a mode (unimodal) as the 

 oysters, the critic believed that each sample comprised not different age groups but 

 one homogeneous age group v.ith a variable number of rings. Thompson points out 

 that in the haddock, cod, and plaice the size groups fall into several groups; normally 

 the size-frequency curves of these species are multimodal, not unimodal. 



Under Thompson's direction. Miss Sherriff (1922), a mathematician, attempts to 

 ascertain by mathematical analysis whether a sample of herring of a single shoal is a 

 homogeneous age group and whether "ringiness" is or is not a measure of age. She 

 concludes that the analysis favors the hypothesis of a homogeneous age group, but 

 that further studies must be made to definitely solve the problem. 



Birtwistle and Lewis (1923) and Lea (1924) discuss Miss Sherriff's criticisms. 

 The former authors point out that both symmetrical and asymmetrical curves may 

 come from the "laws of chance;" that asymmetrical curves may go along with 

 homogeneity or with heterogeneity, and that asymmetrical curves may even be the 

 results of several symmetrical curves combined. They construct an age-length 

 frequency curve for 389 plaice and point out that it is difficult to deduce from the 

 resulting asj'rnmetrical curve that the plaice are heterogeneous with respect to age. 

 If the age were in doubt, we might argue that all the plaice were two years and that 

 the number of rings on their scales varied, as Sherriff does in the herring; but in plaice, 

 experiments have shown that age estimation is a fact. "How are we going to recon- 

 cile these two positions, namely, that we can construct a curve from a sample of 

 herrings, which suggests that variations in length and scale rings are due to chance 

 and do not indicate age, and at the same time we can construct a sunilar type of curve 

 from a sample of plaice in which we do definitely know that the variations in length 

 and otolith rings do indicate four different age groups [p. 791?" 



Lea's paper is a direct reply to Miss Sherriff's. Analyzing Sherriff's and Thomp- 

 son's statements. Lea writes: 



It would appear, therefore, that there can be no doubt that Prof. D'Arcy Tliompson considers 

 the conformity between the empirical curves of frequency and the theoretical curves of variation 

 to be a criterion in deciding whether a sample of herrings contains one single year group or several. 

 To my mind it appears somewhat singular that he has made no attempt to demonstrate the justi- 



