Reverse Causality in Size-Dependent Growth

Oscar Garcia

Abstract


Size-dependent growth is likely to be growth-dependent size instead. Larger organisms do not necessarily grow faster, but faster-growing ones always tend to be larger. This fact has been generally ignored. Correct causality structures are essential for plausible predictions outside the range of the data. Some techniques potentially useful for studying these issues are brie y described. In forestry, the relevance of multiple size measures like volume, height, diameter and basal area greatly complicates the picture. Additionally, purely mathematical sources of growth-size correlations arise. Physiological considerations suggest avoiding stem thickness measures as explanatory variables in growth equations.

Keywords


Confounding, bias, consistency, path analysis, structural equation modelling, mixed eects, endogenous variables, instrumental variables, allometry.

Full Text:

PDF

References


Assmann, E., 1970. The Principles of Forest Yield Study. Pergamon Press, Oxford, England. 506 p.

Bollen, K. A., 2005a. Path analysis. In Encyclopedia of Biostatistics, volume 6, Armitage, P., and T. Colton, eds., second edition, pp. 3973–3977. Wiley.

Bollen, K. A., 2005b. Structural equation models. In Encyclopedia of Biostatistics, volume 6, Armitage, P., and T. Colton, eds., second edition, pp. 5269–5278. Wiley.

Bun, M. J. G., and V. Sarafidis, 2015. Dynamic panel data models. In The Oxford Handbook of Panel Data, Baltagi, B. H., ed., chapter 3, pp. 76–110. Oxford Uni- versity Press.

Damuth, J., 2001. Scaling of growth: Plants and ani- mals are not so different. Proceedings of the National Academy of Sciences 98(5):2113–2114.

Fox, J., 2006. Teacher’s corner: structural equation modeling with the sem package in R. Structural Equa- tion Modeling 13(3):465–486.

Garcia, O., 2017a. Cohort aggregation modelling for complex forest stands: Spruce-aspen mixtures in British Columbia. Ecological Modelling 343:109–122.

Garcia, O., 2017b. Estimating reducible stochas- tic differential equations by conversion to a least- squares problem. ArXiv e-prints (arXiv:1710.06021 [stat.ME]). URL: https://arxiv.org/abs/1710.06021.

Goulding, C. J., 1994. Development of growth models for Pinus radiata in New zealand – experience with management and process models. Forest Ecology and Management 69(1–3):331–343.

Huxley, J. S., 1932. Problems of Relative Growth. Methuen & Co., London. (Second Edition, Dover 1972).

Iriondo, J. M., M. J. Albert, and A. Escudero, 2003. Structural equation modelling: an alternative for as- sessing causal relationships in threatened plant popu- lations. Biological Conservation 113(3):367–377.

Lamb, E., S. Shirtliffe, and W. May, 2011. Structural equation modeling in the plant sciences: An example using yield components in oat. Canadian Journal of Plant Science 91(4):603–619.

Lee, M. J., and O. Garc´ıa, 2016. Plasticity and extrap- olation in modeling mixed-species stands. Forest Sci- ence 62(1):1–8.

Northway, S. M., 1985. Notes: Fitting site index equa- tions and other self-referencing functions. Forest Sci- ence 31:233–235.

Perry, D. A., 1985. The competition process in forest stands. In Attributes of Trees as Crop Plants, Cannell,

M. G. R., and J. E. Jackson, eds., chapter 28, pp. 481–

Institute of Terrestrial Ecology, Abbots Ripton, Hunts, England.

Russell, M. B., A. W. D’Amato, M. A. Albers, C. W. Woodall, K. J. Puettmann, M. R. Saunders, and C. L. VanderSchaaf, 2015. Performance of the Forest Vege- tation Simulator in managed white spruce plantations influenced by Eastern spruce budworm in Northern Minnesota. Forest Science 61(4):723–730.

Sheil, D., C. S. Eastaugh, M. Vlam, P. A. Zuidema,

P. Groenendijk, P. van der Sleen, A. Jay, and J. Van- clay, 2017. Does biomass growth increase in the largest trees? Flaws, fallacies and alternative analyses. Func- tional Ecology 31(3):568–581.

Strigul, N., D. Pristinski, D. Purves, J. Dushoff, and

S. Pacala, 2008. Scaling from trees to forests: Tractable macroscopic equations for forest dynamics. Ecological Monographs 78(4):523–545.

Strub, M., and C. Cieszewski, 2012. The compara- tive R2 and its application to self-referencing mod- els. Mathematical and Computational Forestry & Natural-Resource Sciences (MCFNS) 4(2):73–76.

Umbach, N., K. Naumann, H. Brandt, and A. Kelava, 2017. Fitting nonlinear structural equation models in R with package nlsem. Journal of Statistical Software 77(7):1–20.

Weiskittel, A. R., D. W. Hann, J. John A. Kershaw, and J. K. Vanclay, 2011. Forest Growth and Yield Modeling. Wiley-Blackwell. 430 p.

Wright, S., 1921. Correlation and causation. Journal of Agricultural Research 20(7):557–585.


Refbacks

  • There are currently no refbacks.



© 2008 Mathematical and Computational Forestry & Natural-Resource Sciences