Letter | Published:

Estimating the Malthusian Parameter from Census Data

Nature volume 204, page 810 (21 November 1964) | Download Citation



IN reporting1 the results of experiments designed to examine consequences of the theory surrounding the concept of the innate capacity for increase, or Malthusian parameter2,3, attention was directed to an unexplained discrepancy. From a linear regression of log total numbers on time, the experimental populations increased by an average of 6.082 times per three weeks, with 1 per cent confidence limits of 6.026 and 6.138, whereas age-specific life and fertility data independently obtained suggested that the value should have been 4.478. This discrepancy alone would have meant no more than that the experimental methods used in obtaining the life and fertility data depressed some or all of the rates of development, etc., but, by coincidence as it now seems, another method of evaluating the census observations suggested a value of 4.664, which is in accord with that calculated from the life and fertility table data. This value was obtained as follows: it was assumed that the population growth could be described as a first order process: where M is a matrix the elements of which are numerical values of the dependence of stage i at time t + 1 on stage j at time t (i, j = 1,2, …, s), where there are s morphologically distinguishable stages in the population, and nt and nt + 1 are column vectors specifying the number of individuals in each stage at times t and t + 1. From census observations made at intervals of 3 weeks, M was estimated for this period by: where V is the variance/covariance matrix between the numbers of individuals at time t and W is the covariance matrix between the numbers of individuals at times t and t + 1. The first estimate, that forming the basis of the earlier discussion1, will be referred to as M1 and was: which has a dominant latent root of 4.664 with an associated stable (column) vector of [0.455 0.875 0.055 0.152]′.

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  1. 1.

    , J. Anim. Ecol., 32, 221 (1963).

  2. 2.

    , and , The Distribution and Abundance of Animals (Chicago, 1954).

  3. 3.

    , The Genetical Theory of Natural Selection (New York, 1958).

  4. 4.

    , Verh. int. Kongr. Ent., Wien, 2, 309 (1962).

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  1. Pest Infestation Laboratory, Agricultural Research Council, Slough, Bucks.



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