R. H. M. Langer, S. M. Ryle, O. R. Jewiss, The Changing Plant and Tiller Populations of Timothy and Meadow Fescue Swards. I. Plant Survival and the Pattern of Tillering, Journal of Applied Ecology, Vol. 1, No. 1 (May, 1964), pp. 197-208
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Langer et al. (1964) studied this question.