Ecological Research

, Volume 23, Issue 2, pp 289–297 | Cite as

Describing size-related mortality and size distribution by nonparametric estimation and model selection using the Akaike Bayesian Information Criterion

  • Kenichiro Shimatani
  • Satoko Kawarasaki
  • Tohru Manabe
Original Article

Abstract

When we calculate mortality along a gradient such as size, dividing into size classes and calculating rates for every class often involves a trade-off: fine class intervals produce fluctuating rates along the gradient, whereas broad ones may miss some trends within an interval. The same trade-off occurs when we want to illustrate size distribution by a histogram. This paper introduces nonparametric methods, published in a statistical journal, into forest ecology, in which the fine-class strategy is used in an extreme way: (1) a smoothly changing pattern is approximated by a fine step function, (2) the goodness-of-fit to the data and the smoothness along the gradient are formulated as a weighting sum within a Bayesian framework, (3) the Akaike Bayesian Information Criterion (ABIC) selects the weighting system that most appropriately balances the two demands, and (4) the values of the step function are optimized by the maximum likelihood method. The nonparametric estimates enable us to represent various patterns visually and, unlike parametric modeling, calculations do not demand the determination of a functional form. Mortality and size distribution analyses were conducted on 12-year forest tree monitoring data from a 4 ha permanent plot in an old-growth warm–temperate evergreen broad-leaved forest in Japan. From trees of 11 evergreen species with a diameter at breast height (DBH) greater than 5 cm, we found three types of trend with increasing DBH: decreasing, ladle-shaped and constant mortality. These patterns reflect variations in life history particular to each species.

Keywords

Akaike Bayesian Information Criterion Akaike Information Criterion Diameter at breast height Evergreen forest Population dynamics 

References

  1. Akaike H (1980a) On the use of predictive likelihood of a Gaussian model. Ann Inst Stat Math 32:311–324CrossRefGoogle Scholar
  2. Akaike H (1980b) Likelihood and the Bayes procedure. In: Bernardo NJ, DeGroot MH, Lindley DV, Smith AFM (eds) Bayesian statistics. University Press, Valencia pp 141–166Google Scholar
  3. Ayer M, Brunk HD, Ewing GM, Reid WT, Silverman E (1995) An empirical distribution function for sampling with incomplete information. Ann Math Stat 26:641–617CrossRefGoogle Scholar
  4. Barndorff-Nielsen OE, Cox DR (1989) Asymptotic techniques for use in statistics. Chapman and Hall, LondonGoogle Scholar
  5. Beckage B, Clark JS (2003) Seedling survival and growth of three forest tree species: the role of spatial heterogeneity. Ecology 84:1849–1861CrossRefGoogle Scholar
  6. Bigler C, Bugmann H (2003) Growth-dependent tree mortality models based on tree rings. Can J For Res 33:210–221CrossRefGoogle Scholar
  7. Carey EV, Brown S, Gillespie AJR, Lugo AE (1994) Tree mortality in mature lowland tropical moist and tropical lower montane moist forests of Venezuela. Biotropica 26:255–265CrossRefGoogle Scholar
  8. Caspersen JP, Kobe RK (2001) Interspecific variation in sapling mortality in relation to growth and soil moisture. Oikos 92:160–168CrossRefGoogle Scholar
  9. Condit R, Hubbell SP, Foster RB (1995) Mortality rates of 205 neotropical tree and shrub species and the impact of a severe drought. Ecol Monogr 65:419–439CrossRefGoogle Scholar
  10. Davies SJ (2001) Tree mortality and growth in 11 sympatric Macaranga species in Borneo. Ecology 82:920–932Google Scholar
  11. Duchesne L, Ouimet R, Moore J-D, Paquin R (2005) Changes in structure and composition of maple-beech stands following sugar maple decline in Québec, Canada. For Ecol Manage 208:223–236CrossRefGoogle Scholar
  12. Eggermont PPB, LaRiccia VN (2001) Maximum penalized likelihood estimation, vol I. Density estimation. Springer, HeidelbergGoogle Scholar
  13. Franklin JF, Shugart HH, Harmon ME (1987) Tree death as an ecological process. Bioscience 37:550–556CrossRefGoogle Scholar
  14. Fujita T, Itaya A, Miura M, Manabe T, Yamamoto S (2003) Long-term canopy dynamics analyzed by aerial photographs in a temperate old-growth evergreen broad-leaved forest. J Ecol 91:686–693CrossRefGoogle Scholar
  15. Gratzer G, Canham C, Dieckmann U, Fischer A, Iwasa Y, Law R, Lexer MJ, Sandmann H, Spies TA, Splechtna BE, Szwagrzyk J (2004) Spatio-temporal development of forests—current trends in field methods and models. Oikos 107:3–15CrossRefGoogle Scholar
  16. Harcombe PA (1987) Tree life tables. BioScience 37:557–568CrossRefGoogle Scholar
  17. Hély C, Flannigan M, Bergeron Y (2003) Modeling tree mortality following wildfire in the southeastern Canadian mixed-wood boreal forest. For Sci 49:566–575Google Scholar
  18. Ishiguro M, Sakamoto Y (1983) A Bayesian approach to binary response curve estimation. Ann Inst Stat Math B 35:115–137CrossRefGoogle Scholar
  19. Ishiguro M, Sakamoto Y (1984) A Bayesian approach to the probability density estimation. Ann Inst Stat Math B 36:523–538CrossRefGoogle Scholar
  20. Ishiguro M, Sakamoto Y, Kitagawa G (1997) Bootstrapping log likelihood and EIC, an extension of AIC. Ann Inst Stat Math 49:411–434CrossRefGoogle Scholar
  21. Kohyama T (1993) Size-structured tree population in gap-dynamic forest—the forest architecture hypothesis for the stable coexistence of species. J Ecol 81:131–143CrossRefGoogle Scholar
  22. Kubota Y, Hara T (1995) Tree competition and species coexistence in a sub-boreal forest, northern Japan. Ann Bot 76:503–512CrossRefGoogle Scholar
  23. Lorimer CG, Dahir SE, Nordheim EV (2001) Tree mortality rates and longevity in mature and old-growth hemlock-hardwood forests. J Ecol 89:960–971CrossRefGoogle Scholar
  24. Manabe T, Nishimura N, Miura M, Yamamoto S (2000) Population structure and spatial patterns for trees in a temperate old-growth evergreen broad-leaved forest in Japan. Plant Ecol 151:181–197CrossRefGoogle Scholar
  25. Miura M, Manabe T, Nishimura N, Yamamoto S (2001) Forest canopy and community dynamics in a temperate old-growth evergreen broad-leaved forest, south-western Japan: a 7-year study of a 4-ha plot. J Ecol 89:841–849CrossRefGoogle Scholar
  26. Moloney KA (1986) A generalized algorithm for determining category size. Oecologia 69:176–180CrossRefGoogle Scholar
  27. Monserud RA (1976) Simulation of forest tree mortality. For Sci 22:438–444Google Scholar
  28. Monserud RA, Sterba H (1999) Modeling individual tree mortality for Austrian forest species. For Ecol Manage 113:109–123CrossRefGoogle Scholar
  29. Nishimura N, Hara T, Miura M, Manabe T, Yamamoto S (2002) Tree competition and species coexistence in a warm-temperate old-growth evergreen broad-leaved forest in Japan. Plant Ecol 164:235–248CrossRefGoogle Scholar
  30. Parker GR, Jeopold DJ, Eichenberger JK (1985) Tree dynamics in an old-growth, deciduous forest. For Ecol Manage 11:31–57CrossRefGoogle Scholar
  31. Picard N, Bar-Hen A, Guédon Y (2003) Modelling diameter class distribution with a second-order matrix model. For Ecol Manage 180:389–400CrossRefGoogle Scholar
  32. Platt WJ, Evans GW, Rathbun SL (1988) The population dynamics of a long-lived conifer (Pinus palustris). Am Nat 131:491–525CrossRefGoogle Scholar
  33. Sakamoto Y (1991) Categorical data analysis by AIC. Kluwer, DordrechtGoogle Scholar
  34. Sheil D, May RM (1996) Mortality and recruitment rate evaluations in heterogeneous tropical forests. J Ecol 84:91–100CrossRefGoogle Scholar
  35. Ueno S, Tomaru N, Yoshimaru H, Manabe T, Yamamoto S (2002) Size-class differences in genetic structure and individual distribution of Camellia japonica L. in a Japanese old-growth evergreen forest. Heredity 89:120–126PubMedCrossRefGoogle Scholar
  36. Vandermeer J (1978) Choosing category size in a stage projection matrix. Oecologia 32:79–84CrossRefGoogle Scholar
  37. Woodall CW, Grambsch PL, Thomas W, Moser WK (2005) Survival analysis for a large-scale forest health issue: Missouri oak decline. Environ Monit Assess 108:295–307PubMedCrossRefGoogle Scholar
  38. Woods KD (2000) Dynamics in late-successional hemlock-hardwood forests over three decades. Ecology 81:110–126Google Scholar
  39. Woods KD (2004) Intermediate disturbance in a late-successional hemlock-northern Hardwood forest. J Ecol 92:464–476CrossRefGoogle Scholar
  40. Wyckoff PH, Clark JS (2000) Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches. Can J For Res 30:156–167CrossRefGoogle Scholar
  41. Yang Y, Stephen JT, Huang S (2003) Modeling individual tree mortality for white spruce in Alberta. Ecol Model 163:209–222CrossRefGoogle Scholar
  42. Zhao D, Borders B, Wilson M (2004) Individual-tree diameter growth and mortality models for bottomland mixed-species hardwood stands in the lower Mississippi alluvial valley. For Ecol Manage 199:307–322Google Scholar

Copyright information

© The Ecological Society of Japan 2007

Authors and Affiliations

  • Kenichiro Shimatani
    • 1
  • Satoko Kawarasaki
    • 2
  • Tohru Manabe
    • 3
  1. 1.The Institute of Statistical MathematicsTokyoJapan
  2. 2.Transdisciplinary Research Integration CenterResearch Organization of Information and SystemsTokyoJapan
  3. 3.Kitakyushu Museum and Institute of Natural HistoryKitakyushuJapan

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