Recency has no bearing if the conditions were severe enough to wipe out, prior to reproduction primarily, of those unable to survive and reproduce on whatever foods were available. It could be done in one generation. If all the foods we had to live on were potatoes say, and everyone who could not survive and reproduce on this were to die of starvation or disease, then whoever did survive could theoretically (nature is never that theoretical)pass on their potatoe only survival genes to their offspring. mg