Elsevier

Ecological Modelling

Volume 220, Issue 12, 24 June 2009, Pages 1492-1494
Ecological Modelling

Consideration of translocation into a growth model of a plant organ

https://doi.org/10.1016/j.ecolmodel.2009.03.019Get rights and content

Abstract

Taking account of the Bertalanffy's differential equation on animal growth, plant growth is also considered as the net result of anabolism and catabolism. When we, however, consider the growth of a plant organ, it is necessary to add a term of translocation because it plays an important role in the growth of plant organs, such as leaf and fruit. Considering translocation, therefore, a growth model of a plant organ was proposed on the basis of the compartment model for estimating the carbon balance in the organ by using the experimental data on translocation, photosynthesis and respiration of a tropical fruit of durian (Durio zibethinus Murray). The present growth model of a plant organ belongs to an extended Bertalanffy's growth equation, and was possible to be transformed into the simple Bertalanffy's growth equation on the basis of the proportionality between the growth and translocation rates. The Bertalanffy's growth equation of a plant organ was also possible to apply to that of the whole plant on the assumption of the allomeric relationship between a plant organ and the whole plant.

Introduction

Growth is one of the most important characteristics of organisms (Hozumi, 1985). Quantitative aspects of growth, both on individual and population levels, are well described by growth curves, such as the exponential, Gompertz, Mitscherlich, logistic and Richards (cf. Thornley, 1976, Hunt, 1982). Although various equations have been proposed to simulate whole-plant growth curves, they are still limited in their applicability and flexibility.

Taking account of the Bertalanffy's differential equation on animal growth (von Bertalanffy, 1949), plant growth is also considered as the net result of anabolism and catabolism. Miyaura and Hozumi (1993) first provided an experiment evidence that a single tree growth can be expressed by the Bertalanffy's equation by directly measuring the rates of net production (anabolism) and death (catabolism). When we, however, consider the growth of a plant organ, it is necessary to add a term of translocation from other organs because it plays an important role in the growth of leaf (Hozumi and Kurachi, 1991) and fruit (Ogawa et al., 1996, Ogawa and Takano, 1997, Ogawa, 2002, Ogawa, 2004).

Chabot and Hicks (1982) proposed a balance equation of carbon of a single leaf during its life span from the viewpoint of a cost-benefit approach to leaf carbon economy. However, they did not consider the concept of translocation into their balance equation for the total net carbon gain of a single leaf, and in practice their equation is not easy to be manipulated. On the contrary, Hozumi and Kurachi's compartment model (1991) is simple and practical for estimating carbon balance of leaves. Based on the Hozumi and Kurachi's model, it was possible to estimate quantitatively the contribution of translocation of carbon in woody parts for supporting rapid growth of leaves in the early spring in a deciduous tree, Japanese larch (Larix leptolepis Gordon).

By modifying the compartment model in leaves proposed by Hozumi and Kurachi (1991), Ogawa et al. (1996) and Ogawa and Takano (1997) estimated the translocation of carbon into fruits of durian (Durio zibethinus Murray) and camphor tree (Cinnamomum camphora Sieb.), respectively. According to these two studies, photosynthetic assimilates translocated to the fruits were equivalent to 125% fruit dry mass in durian and 171% in camphor until fruit maturation, respectively.

Therefore I propose a growth model of a plant organ considering translocation by using some experimental data on translocation, photosynthesis and respiration of a tropical fruit of durian (Durio zibethinus Murray) (Ogawa et al., 1996). I also examine the relationship between this growth model and the Bertalanffy's growth model.

Section snippets

Growth model considering translocation in a plant organ

Ogawa et al. (1996), Ogawa and Takano (1997) and Ogawa, 2002, Ogawa, 2004 developed a compartment model to estimate the translocation balance of fruits of woody species. Their model is generalized into the compartment model of the translocation balance in a plant organ (Fig. 1). On the basis of the present model, growth rate Δw during a given time interval Δt is expressed asΔwΔt=ΔTrΔt+ΔPΔtΔRΔtΔDΔtΔGΔtwhere ΔTr/Δt is net translocation rate (Hozumi and Kurachi, 1991), defined as the rate of

Bertalanffy's equation scaled up to the whole plant from its plant organ

The following allometric relationship is usually realized between the dry masses of the whole plant (y) and an organ (w) (Ogawa and Kira, 1977, Niklas, 1994):y=gwhor1ydydt=h1wdwdtwhere g and h are coefficients. Considering this allometric equation, the Bertalanffy's equation of the whole plant is derived from that of a plant organ (Eq. (8)) as follows:dydt=γy(h+n1)/hβy(h+m1)/hwhere β=Bhg(1m)/handγ=Chg(1n)/h, respectively.

Application to the uw diagrammatic analysis

Hozumi, 1985, Hozumi, 1987 proposed a uw diagrammatical

Acknowledgements

This paper was among those presented at Eco Summit 2007 in Beijing, China. This study was supported in part by a Grant-in-Aid for Scientific Research (No. 19580170) from the Ministry of Education, Science, Sport and Culture, Japan, and a grant from the Sumitomo Foundation (No. 073010).

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