Kazuo Hozumi

Ecological and mathematical considerations on self-thinning in even-aged pure stands

It is emphasized in growth analysis of self-thinning populations that relative mortality rate pertains to the difference between relative growth rates and net assimilation rates, each of which are definable on a mean plant size basis or on a biomass basis. The time trends of the ratio of relative mortality rate to relative growth rates to be expected according to Tadakis, Shinozakis and Hozumis models are compared with that of the eastern white pine population, and a good agreement is exhibited. As an alternative to Hozumis model, a new model is constructed to unite the logistic theory of plant growth and the 3/2 power law concerning self-thinning, which so far have usually been applied independently to growth analysis. To construct the model the following assumptions are made: the fundamental equation to relate mean plant weight with density in self-thinning population proposed by Shinozaki, and a special population with a specific initial density which follows thew-p trajectory of the 3/2 power law type and has an exponential decrease in its density with biological time. Properties of the model are examined from ecological and mathematical viewpoints.

Ecological and mathematical considerations on self-thinning in even-aged pure stands: I. Mean plant weight-density trajectory during the course of self-thinning

Ecological and mathematical considerations were made on Shinozakis, Tadakis and 3/2 power law models for the mean plant weight-density trajectory under self-thinning in even-aged pure stands, and interrelationships among these models were discussed. To overcome the discrepancy between the observed trajectory of the eastern white pine population and the one predicted from Tadakis model, a new model was proposed. To construct the model the assumptions were made so as to incorporate the good properties of Tadakis and Shinozakis models in early stages of growth into those of the 3/2 power law model observed in later stages. Applicability of the model was tested for the pine population, which showed a good fit to the data. The growth analysis on the basis of the model revealed the growth curve of the pine followed a λw-type logistic cruve and suggested the existence of a lag time, a hyperbolic relationship between biological and physical time and a clear dependence of survivorship curves on initial density.

Evaluation of the light interception by non-photosynthetic organs in aLarix leptolepis plantation

Vertical changes in relative light intensity within the canopy of a 19-year-old (as of 1982) plantation of Japanese larch were investigated before and after defoliation. The relative light intensity at 1.3m above the ground was 6% before defoliation, while it was about 20% after defoliation. The leaf area index and the total longitudinal section area of such non-photosynthetic organs as stems and branches were in the range 4.84 to 5.61 ha/ha and 0.788 to 0.798 ha/ha, respectively. An equation ofI′(z)/I0=exp[-(KFF(z)+KcC(z)], which gives a description of light attenuation within a canopy, was proposed on the assumption that the relative light intensityI′(z)/Io at a depthz from the canopy surface is affected by both the cumulative densities of leaf areaF(z) and the longitudinal section area of non-photosynthetic organsC(z) existing above that depth. The value of the extinction coefficient for the leavesKF was computed to be 0.31–0.36 ha/ha, while that for the non-photosynthetic organsKc was computed to be 1.4–1.7 ha/ha. The functionC(z) was proportional toF(z), orC(z)=aF(z) where the constanta was 0.11–0.13. The proposed equation led to the formula,I′(z)/I0=exp[-KF(z)]. The apparent extinction coefficientK was partitioned into two terms as follows,K=KF+aKc. The value ofK was estimated to be 0.46–0.59 ha/ha, and was about 1.5 times larger than ofKF.

Analysis of Growth Curve of Stem Volume in Some Woody Species Using the u-w Diagram

Growth curves of stem volume without bark were analyzed on the basis of theu-w diagram and the growth model equivalent to the Bertalanffy model. Some trees experienced several growth phases, in which characteristic values of growth changed. Presumable factors to cause the shifting of growth phase were discussed. In a 130-year-old sugi at Kaneyama in Yamagata Prefecture, estimated rates of anabolism and catabolism were related by a linear relationship with time delay of about 30 years.

Ecological and mathematical considerations on self-thinning in even-aged pure stands: III. Effect of the linear growth factor on self-thinning and its model

A new model is proposed to unite the logistic theory of plant growth and the 3/2 power law of self-thinning, which so far have been applied independently to growth analysis. To construct the model the following assumptions are made: a general logistic curve of mean plant weight, a modified form of the formula to show the rule of constancy of the final yield, which is generalized to cover the conditions of different combinantions of density and linear factor supply in a nonself-thinning population and a special population with a specific initial density which follows thew-ρ trajectory of the 3/2 power law type and has an exponential decrease in its density with biological time. Model calculations show that the Sukatschew effect is successfully formulated, that there should be a minimum factor supply below which self-thinning does not occur and that thew-ρ trajectory should be segregated acoording to the level of the linear factor supply.

Canopy photosynthetic production in a Japanese larch forest. II: Estimation of the canopy photosynthetic production

Seasonal changes and yearly gross canopy photosynthetic production were estimated for an 18 year old Japanese larch (Larix leptolepis) forest between 1982 and 1984. A canopy photosynthesis model was applied for the estimation, which took into account the effect of light interception by the non-photosynthetic organs. Seasonal changes in photosynthetic ability, amount of canopy leaf area and light environment within the canopy were also taken into account. Amount of leaf area was estimated by the leaf area growth of a single leaf. The change of light environment within the canopy during the growing season was estimated with a light penetration model and the leaf increment within the canopy. Canopy respiration and surplus production were calculated as seasonal and yearly values for the three years studied. Mean yearly estimates of canopy photosynthesis, canopy respiration and surplus production were 37, 13 and 23 tCO2 ha−1 year−1, respectively. Vertical trend, seasonal changes and yearly values of the estimates were analyzed in relation to environmental and stand factors.

Canopy photosynthetic production in a Japanese larch stand. I. Seasonal and vertical changes of leaf characteristics along the light gradient in a canopy

In an 18 year old Japanese larch stand, leaf characteristics such as area, weight, gross photosynthetic rate and respiration rate were studied in order to obtain basic information on estimating canopy photosynthesis and respiration. The leaf growth courses in area and weight from bud opening were approximated by simple logistic curves. The growth coefficient for the area growth curve was 0.155–0.175 day−1, while that for the weight growth was 0.112–0.117 day−1. The larger growth coefficient in area growth caused the seasonal change in specific leaf area (SLA) that increased after bud opening to its peak early in May at almost 300 cm2 g−1 and then decreased until it leveled off at about 140 cm2g−1. The change inSLA indicates the possibility that leaf area growth precedes leaf thickness growth. The relationship between the coefficientsa andb of the gross photosynthetic rate (p)-light flux density (1) curve (p=bI/(1+aI)) and the mean relative light flux density (I′/I0) at each canopy height were approximated by hyperbolic formulae:a=A/(I′/I0)+B andb=C/(I′/I0)+D. Leaf respiration rate was also increased with increasingI′/I0. Seasonal change of gross photosynthetic rate and leaf respiration rate were related to mean air temperature through linear regression on semilogarithmic co-ordinates.

Effect of light interception by non-photosynthetic organs on canopy photosynthetic production

A canopy photosynthesis model was derived on the assumption that the light diminution within a canopy is caused by both leaves and non-photosynthetic organs. The light diminution by leaves and that by non-photosynthetic organs were taken into account separately in the Lambert-Beer equation of light extinction. The light flux density on the leaf surface at each depth was evaluated from the leafs share of light. The light flux density on the leaf surface thus obtained was incorporated into the Monsi-Saeki model of canopy photosynthesis. The proposed model was applied for estimating gross canopy photosynthesis in a 19-year-oldLarix leptolepis plantation where 38% of the light diminution was due to non-photosynthetic organs. The daily canopy photosynthesis on one summer day calculated using the present model was about 22% less than that calculated by the conventional Monsi-Saeki model, in which light interception by non-photosynthetic organs is neglected. The degree of such reduction in canopy photosynthesis through shading by non-photosynthetic organs was assessed in relation to parameters affecting light extinction, leaf photosynthetic characteristics, and light regime above the canopy.

Phase diagrammatic approach to the analysis of growth curve using theu-w diagram —Basic aspects

To analyze growth curve quantitatively theu-w diagram is proposed. Herew is defined as any growth quantity at a given time of observation andu is defined as the ratio of relative growth rate ofw tow. Theu-w diagram can be obtained by plotting a series of observed values ofu andw on log-log coordinates.Theu-w relationship constructed to lead a generalized form of the logistic and Mitscherlich curve results in the growth curve almost equivalent to the curve expected from the Bertalanffy differential equation and thus includes the Richards growth function as a special case. These results show that the approach using theu-w diagram appears to give a useful tool for the growth analysis in general and to be flexible.

Estimation of seasonal changes in translocation rates in leaves of a Japanese larch stand

To estimate the net rate of translocation in leaves of a larch stand, a new approach based on the summation method was proposed and given by a compartment model. The difference between the rate of translocation into and out of leaf biomass, namely, the net translocation rate (ΔTr/Δt), was usually expressed by the difference between the growth rate of leaf biomass and the surplus production rate provided that the rate of leaf loss due to leaffall and grazing can be considered negligible. The rate, ΔTr/Δt in a 19-yr-old larch stand, showed characteristic changes; it was positive from early April to late May, but after that it was negative until leaffall in late October. Our results confirmed that for the growth phase of positive ΔTr/Δt translocation of assimilate stored in non-photosynthetic organs was indispensable for the growth. To quantify this, the ratio of ΔTr/Δt to growth rate of leaf biomass was proposed.