Fisher’s measure of variability in repeated samples

Fisher (1943) claimed that the expected value of sample variance number species found in large samples, each n specimens taken from same population, is asymptotically ?log2. This at odds with ?logn obtained directly Ewens Sampling Formula (ESF), where ? specifies rate which new are found. To resolve this apparent contradiction, we assume frequency spectrum population determined by ESF and samples disjoint subsets drawn sequentially single population. We find an explicit formula for required p arbitrary size; limit equally-sized it indeed has obtain theorems size under various limiting regimes as p,n or both tend to ?. discuss further behavior present all revisit Fisher’s log-series distribution observed typical a future, sample.