Consideration of translocation into a growth model of a plant organ
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 during a given time interval Δt is expressed aswhere 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 () (Ogawa and Kira, 1977, Niklas, 1994):where 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:where , respectively.
Application to the diagrammatic analysis
Hozumi, 1985, Hozumi, 1987 proposed a 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).
References (16)
Problems of organic growth
Nature
(1949)- et al.
The ecology of leaf life spans
Ann. Rev. Ecol. Syst.
(1982) Phase diagrammatic approach to the analysis of growth curve using the diagram—Basic aspects
Bot. Mag. Tokyo
(1985)Analysis of growth curve of stem volume in some woody species using the diagram
Bot. Mag. Tokyo
(1987)- et al.
Estimation of seasonal changes in translocation rates in leaves of a Japanese larch stand
Bot. Mag. Tokyo
(1991) Plant Growth Curves
(1982)- et al.
Respiration and photosynthesis in cones of Norway spruce (Picea abies (L) Karst.)
Trees
(1987) - et al.
The seasonal course of respiration and photosynthesis in strobili of Scots pine
For. Sci.
(1981)
Cited by (1)
Scaling relations based on the geometric and metabolic theories in woody plant species: A review
2019, Perspectives in Plant Ecology, Evolution and SystematicsCitation Excerpt :In addition, we reevaluated the metabolic scaling of respiration and gross photosynthesis based on the observed results of forest trees where self-thinning does (Ninomiya and Hozumi, 1983a, 1983b; Hagihara and Hozumi, 1986; Yokota and Hagihara, 1998) or does not occur (Ninomiya and Hozumi, 1981; Yokota et al., 1994), as well as seedlings (Ogawa et al., 1985a, b; Ogawa, 1989). This metabolic scaling leads to a generalization of von Bertalanffy’s (1949) model from the viewpoint of not only plant growth (Hozumi, 1985), but also fruit growth (Ogawa, 2009a). This study introduces the published results on the scaling relations for five woody species of Pinus densi-thunbergii Uyeki, Chamaecyparis obtusa (Sieb.