To begin with, the noun rank has nothing to do with the adjective rank.
The noun is of French origin (possibly Frankish ultimately) and originally denoted a series or line of things (range has the same origin); then specifically a line of warriors or soldiers (whence our 'rank and file'); then the successive lines, the first, second, third ranks, and so forth, in which soldiers are deployed; and finally, by way of one's position in the front, middle or rear rank, one's grade or standing.
The adjective rank is of Germanic origin; the precise line of descent is obscure but it seems originally to have denoted various attributes of the noble warrior: proud, haughty, rebellious, strong, vigorous, full-grown. In ME the martial connection faded and the word became used particularly of undesired and excessive strength, vigor and abundance; it was extended to vegetation (we still speak of 'rank weeds') and to loathsome behavior and smells (O mine offense is rank says Claudius); eventually it acquired such a strong negative connotation that came to mean 'corrupt, foul, festering', and eventually simply 'extremely (offensive)'.
See the Oxford English Dictionary, 1st edition.
When your source writes of rank dishonesty it probably does not intend any one of these later senses but (at some level) all of them simultaneously: extremely gross, corrupt, loathsome dishonesty.
Best Answer
Welcome to Biology.SE!
from one generation to anotheris equivalent tofrom parents to their childrenfrom any parent generation to any offspring generationthrough timeIf the expression
from one generation to anotherreally bothers you, then you can just consider the shortened sentence which bear the same meaning.One reason why there is this reference to generations is because it is common in population genetics models to assume for simplicity that generations are not overlapping. That is all parents reproduce only once and all die at this exact same time. As such an offspring is never alive in the same time as the parent. It is an unrealistic model for most species but it is a very helpful one.