Korean journal of applied entomology (한국응용곤충학회지)

Korean Society of Applied Entomology (한국응용곤충학회)
권호 표지
DOI QR코드

DOI QR Code

A Short Review for the Estimation Method of Intrinsic Rate of Natural Increase According to the Setting of Initial Age for the Study Cohort in the Lotka Life Table

로트카 생명표에서 연구 집단의 초기연령 설정에 따른 내적자연증가율 추정방법에 대한 고찰

  • Dong-soon, Kim (Majors in Plant Resource Sciences & Environment, College of Applied Life Science, SARI, Jeju National University)
  • 김동순 (제주대학교 생명자원과학대학(SARI))
  • Received : 2022.08.15
  • Accepted : 2022.10.04
  • Published : 2022.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Life table-related studies in insect ecology have been an interesting topic for insect researchers. Two calculation methods are commonly applied to estimate the intrinsic rate of natural increase (rm) in the life table statistics. The first method is to estimate an approximate rm by dividing the natural logarithm of the net reproductive rate (R0) by mean generation time (T) (namely mean generation time-based method). Another approach is to apply the Lotka-Euler equation derived from the population growth equation of Lotka-Volterra to estimate accurate rm using the maximum likelihood method (Lotka-Euler equation-based method). In the latter case, there is a difference in the estimated rm value when the initial age class of the target cohort was set to "0" or "1", which confused the application. In this short review, a brief history of the calculation process of the life table was reviewed. It was again confirmed in the Lotka-Euler equation-based method that the form of $\sum\limits_{x=1}^{w}e^{-rx}l_xm_x=1$ should be applied to estimate rm when the first age class was set to zero, while the form of $\sum\limits_{x=0}^{w}e^{-r(x+1)}l_xm_x=1$ when set to one.

곤충생태 분야에서 생명표와 관련된 연구는 곤충연구자들에게 많은 관심을 받는 주제중 하나이다. 보통 두 가지 방법으로 생명표 통계량중 내적자연증가율을 추정하고 있는데, 첫 번째 하나는 순증가율(R0)에 자연로그를 취하고 평균세대기간(T)으로 나누어 근사치를 계산하는 방법이다(세대기간-기반 추정법). 다른 하나는 로트카-볼테라 개체군 생장 방정식에서 유도하여 최대우도법으로 정확한 내적자연증가율을 추정하는 방법이다(로트카-오일러식-기반 추정법). 후자의 경우 대상 집단의 초기 연령등급을 "0" 또는 "1"로 설정함에 따라 추정값에 차이가 발생하여 적용에 혼란이 제기되었다. 본 고찰에서는 생명표 통계량 계산과정의 역사를 간단히 정리하고, 로트카-오일러식-기반 추정법에서 최초 연령등급을 1로 설정한 경우 $\sum\limits_{x=1}^{w}e^{-rx}l_xm_x=1$의 형식, 반면 최초 연령등급을 0으로 설정한 경우 $\sum\limits_{x=0}^{w}e^{-r(x+1)}l_xm_x=1$의 형식을 적용해야 함을 재확인하였다.

Keywords

Acknowledgement

This work was supported by the 2022 education, research and student guidance grant funded by Jeju National University. We are grateful to Sustainable Agriculture Research Institute (SARI) in Jeju National University for providing the experimental facilities.

References

  1. Andrewartha, H.G., Birch, L.C., 1954. The distribution and abundance of animals. Univ. Chicago Press, Chicago, IL. 
  2. Birch, LC., 1948. The intrinsic rate of natural increase of an insect population. J. Anim. Ecol. 17, 15-26. https://doi.org/10.2307/1605
  3. Carey, J.R., 1993. Applied demography for biologists with special emphasis on insects. Oxford University Press, New York.
  4. Carey, J.R., 2001. Insect biodemography. Annu. Rev. Entomol. 46, 79-110. https://doi.org/10.1146/annurev.ento.46.1.79
  5. Chi, H., 1988. Life-table analysis incorporating both sexes and variable development rate among individuals. Environ. Entomol. 17, 26-34. https://doi.org/10.1093/ee/17.1.26
  6. Chi, H., Liu, H., 1985. Two new methods for the study of insect population ecology. Bull. Inst. Zool. Acad. Sin. 24, 225-240.
  7. David, J.-F., Celerier, M.-L., Henry, C., 1995. Note on the use of the basic equation of demography. Oikos. Jun. 73, 285-288. https://doi.org/10.2307/3545922
  8. Deevey, E.S.J., 1947. Life tables for natural populations of animals. Q. Rev. Biol. 22, 283-314. https://doi.org/10.1086/395888
  9. Dublin, L.I., Lotka, A.J., 1925. On the true rate of natural increase as exemplified by the population of the United States. J. Amer. Statist. Ass. 20, 305-339.
  10. Goodman, D., 1982. Optimal life histories, optimal notation, and the value of reproductive value. Am. Nat. 119, 803-823. https://doi.org/10.1086/283956
  11. Google LLC, 2022. Google search. https://www.google.co.kr/ and https://scholar.google.co.kr (accessed on 3 August, 2022).
  12. Hawkins, B.A., Cornell, H.V., Hochberg, M.E., 1997. Predators, parasitoids, and pathogens as mortality agents in phytophagous insect populations. Ecol. 78, 2145-2152. https://doi.org/10.1890/0012-9658(1997)078[2145:PPAPAM]2.0.CO;2
  13. Heo, J.W., Kim, S.B., Kim, D.-S., 2022. Effects of intergenerational host plant alterations on developmental parameters of Spodoptera frugiperda (Lepidoptera: Noctuidae). J. Asia-Pac. Entomol. 25, 101945. doi:10.1016/j.aspen.2022.101945.
  14. Jha, R.K., Chi, H., Tang, L.-C., 2012. Life Table of Helicoverpa armigera (Hubner) (Lepidoptera: Noctuidae) with a Discussion on Jackknife vs. Bootstrap Techniques and Variations on the Euler-Lotka Equation. Formosan Entomol. 32, 355-375.
  15. Kim, D.-S., Lee, J.-H., 2002. Egg and larval survivorship of Carposina sasakii (Lepidoptera: Carposinidae) in apple and peach and their effects on adult population dynamics in orchards. Environ. Entomol. 31, 686-692. https://doi.org/10.1603/0046-225X-31.4.686
  16. Krebs, C.J., 1972. Ecology: the experimental analysis of distribution and abundance, 2nd ed. Harper and Row, New York.
  17. Lefkovitch, L.P., 1965. The study of population growth in organisms grouped by stages. Biometrics 21, 1-18. https://doi.org/10.2307/2528348
  18. Leslie, P.H., 1945. On the use of matrices in certain population mathematics. Biometrika 33, 183-212. doi:10.1093/biomet/33.3.183.
  19. Lotka, A.J., 1925. Elements of physical biology. Nature 116, 461. doi:10.1038/116461b0.
  20. Lotka, A.J., 1928. The progeny of a population element. Am. J. Hyg. 8, 875-901.
  21. Lotka, A.J., 1939. Theorie analytique des associations biologiques. Deuxieme Partie. Analyse demographique avec application particuliere a l'espece humaine. Actualites Sci. Industr. 780, 1-149.
  22. Maia, A, de H.N., Luiz, A.J.B., Campanhola, C., 2000. Statistical inference on associated fertility life table parameters using Jackknife technique: computational aspects J. Econ. Entomol. 93, 511-518. https://doi.org/10.1603/0022-0493-93.2.511
  23. Maia, A.H.N., Pazianotto, R.A.A., Luiz, A.J.B., Marinho-Prado, J.S.M., Pervez, A., 2014. Inference on arthropod demographic parameters: computational advance using R. J. Econ. Entomol. 107, 432-439. https://doi.org/10.1603/EC13222
  24. Morris, R.F., 1965. Contemporaneous mortality factors in population dynamics. Can. Entomol. 97, 1173-1184. https://doi.org/10.4039/Ent971173-11
  25. Morris, R.F., Miller, C.A., 1954. The development of life tables for the spruce budworm. Can. J. Zool. 32, 283-301. https://doi.org/10.1139/z54-027
  26. Murray, B.G., 1991. Comments on the use of Lotka's discrete equations. Oikos 62, 118-122. https://doi.org/10.2307/3545459
  27. Park, Y., Kim, K.H., Lee, J.-H., Kim, D.-S., 2022. Estimation of insect life table statistic. in: Lee, J.-H., Kim., D.-S., Jung, C., Park, Y.-L. (eds.), Research methodology in insect ecology. Seoul National University Press, Seoul, pp. 465-488.
  28. Pearl, R., Parker, S.L., 1924. Experimental studies on the duration of life. IX. New life tables for Drosophila. Am. Nat. 58, 71-82. https://doi.org/10.1086/279956
  29. Ricklefs, R.E., 1979. Ecology. Chiron Press, New York.
  30. Smith, D., Keyfitz, N., 1977. Mathematical demography: selected Papers. Springer-Verlag, Berlin.
  31. Southwood, T.R.E., 1978. Ecological methods with particular reference to the study of insect populations, 2nd ed. Chapman & Hall, London.
  32. Stearns, S.C., 1992. The evolution of life histories. Oxford Univ. Press, Oxford.
  33. Varley, G.C., 1947. The natural control of population balance in the knapweed gallfly (Urophora jaceana). J. Anim. Ecol. 16, 139-187. https://doi.org/10.2307/1493
  34. Varley, G.C., Gradwell, G.R., 1960. Key factors in population studies. J. Anim. Ecol. 29, 399-401. https://doi.org/10.2307/2213