Lush was the major figure in adapting the quantitative genetics of Fisher and Wright to animal breeding; his Animal Breeding Plans, first published in 1937, was the bible of a generation of quantitative-genetics-oriented animal breeders. (Here it is in a free download of a scan of the 1943 edition). This is not that book, but a 1994 printing of Lush's unpublished mimeographed notes on theoretical quantitative genetics, which he wrote in 1948. They were used in his advanced courses and widely circulated among animal breeders. He never put them in book form before his death in 1982. In 1994 they were edited for publication by A. B. Chapman and Robert R. Shrode, with a postscript by James F. Crow. It is likely that Lush's failure to publish was because he was intimidated by the arrival in his university of the opinionated and outspoken Oscar Kempthorne, who insisted on a standard of mathematical rigor that Lush was unaccustomed to.
The first part of Section 25.6, on pages 633-634 of Lush's book says:
The distinctness of family differences appears to have been important in the evolution of those species which are so organized socially that members of the same family help each other in feeding, in defense, in rearing the young, and in competition with other families. Bees, ants, and termites are conspicuous examples, but some of this occurs in many other species. Parental care for the young, even to the point of some self-sacrifice, is almost universal among birds and mammals. Man often cooperates with his relatives and neighbors, as well as competing with them. He does this to a rather extreme degree in human societies organized in clans or small tribes which are based on a "blood tie".
25.6 Evolutionary Aspects of Family Structure
The competition and selection among families thus introduced could make selection favor any genes which tend to cause their possessor to sacrifice himself for his deme, provided the sacrifice promotes the biological welfare of his relatives (some of whom will have some of the gene he has) enough to more than compensate for the genes lost in his own sacrifice. This may have had much to do with making qualities of altruism, self-sacrifice, patriotism, tribal loyalty, cooperativeness, etc., as abundant as they generally are in human societies which have a strong tribal, clan, or blood-tie basis, or which have departed from that basis only in the last few centuries.
The balance here is intricate, depending on how extreme the self-sacrifice, at what stage of the life cycle it occurs, how much this increases the biological success of the benefactor's relatives, how closely these are related to the benefactor, etc. The balance depends primarily on whether the greater biological success of the relatives will multiply the genes for altruism more than enough to compensate for the loss of those genes in the individual which sacrificed itself to gain some good for its deme. Formulas for expressing this quantitatively have barely begun to be explored.
Notice that he gets close to Hamilton's result ... "close but no cigar". Instead of summarizing the benefit to the relatives by an inclusive fitness change, and calling that b he first wants to know all the biological details of how the benefit works. He does not realize the utility of summarizing this by a single quantity, and that the resulting formula would be illuminating.
It becomes less surprising that Lush had this insight so early, when one considers that he wrote the pioneering papers on family selection in quantitative genetics, and was quite concerned with the effectiveness of selection of individuals based on measurements of their relatives.
Here is a biographical memoir of Lush, published in the series of memoirs of members of the National Academy of Sciences.
Incidentally, Lush's book may be purchased for only $8.50 by writing to
Iowa State University
Department of Animal Science
Attn: Ann Shuey
2255 Kildee Hall
Ames, IA 50011-3150
and sending her a check made out to "Iowa State University".
Her email address is: ashuey (at) iastate.edu