Estimation of the intrinsic rate of natural increase and its error by both algebraic and resampling approaches

The intrinsic rate of natural increase or Malthusian parameter plays a key role fields as diverse as ecology, genetics, demography and evolution. It characterizes the growth of a population in a determinate environment. Since its rigorous statistical estimation requires of intensive calculation, the use of a computer becomes essential. The two main approaches to the calculation of the Malthusian parameter, its error and confidence intervals have been implemented in a program and have been compared by means of an example.

[1]  R. Lenski,et al.  APHID GENOTYPES, PLANT PHENOTYPES, AND GENETIC DIVERSITY: A DEMOGRAPHIC ANALYSIS OF EXPERIMENTAL DATA , 1982, Evolution; international journal of organic evolution.

[2]  R. Lenski The Statistical Analysis of Population Growth Rates Calculated from Schedules of Survivorship and Fecunidity , 1982 .

[3]  B. Efron,et al.  A Leisurely Look at the Bootstrap, the Jackknife, and , 1983 .

[4]  P. H. Leslie On the use of matrices in certain population mathematics. , 1945, Biometrika.

[5]  Joseph S. Meyer,et al.  Estimating Uncertainty in Population Growth Rates: Jackknife vs. Bootstrap Techniques , 1986 .

[6]  L. Birch,et al.  The intrinsic rate of natural increase of an insect population , 1948 .

[7]  M. Slatkin,et al.  Finding confidence limits on population growth rates. , 1991, Trends in ecology & evolution.

[8]  W. Schaffer Optimal Reproductive Effort in Fluctuating Environments , 1974, The American Naturalist.

[9]  P. H. Leslie SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS , 1948 .

[10]  R. Dorazio,et al.  Statistical Inference in Life-Table Experiments: The Finite Rate of Increase , 1984 .

[11]  S. Wratten,et al.  Patterns of aphid resistance in the genus Vicia , 1984 .

[12]  D.SC. PH.D. F.R.S. T. R. E. Southwood Kt Ecological Methods , 1978, Springer Netherlands.

[13]  B. Efron The jackknife, the bootstrap, and other resampling plans , 1987 .

[14]  M. Boyce Population growth with stochastic fluctuations in the life table. , 1977, Theoretical population biology.

[15]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[16]  D. Daley Bias in estimating the Malthusian parameter for Leslie matrices , 1979 .

[17]  P. Holgate,et al.  Matrix Population Models. , 1990 .

[18]  B. Charlesworth Selection in Populations with Overlapping Generations. V. Natural Selection and Life Histories , 1973, The American Naturalist.