Biomass dynamics of higher-order tree branches: An analysis of the model

Galitskii, V. V.

doi:10.1134/s2079086413050034

Cited by 6 publications

(12 citation statements)

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“…The empty green and blue asterisks -µ#19 and µ#31 (see an asterisk in the inset in Fig. 3 for #19 as an example how to find these values μ) correspond to natural spruce data (Tsel'niker 1994) and their modeled interpretations (Galitskii 2013) (Tables 1 and 2). T2=log2(Np/2), Np=Ng*ng,fix or Ng,fix*ng (see text) is evolutionary "time" measured by the number of doublings of Np along a trajectory.…”

Section: On Properties Of Point Setsmentioning

confidence: 66%

“…It allowed propagating the model of the tree's branches system at all the real range of µ (0, 3). For modern spruce, parameter value obtained (Galitskii 2013) is μ≈1.8. It lies in the range [1, 2) that corresponds to a set of linear elements (conifer needles) according to notions of fractal geometry (Feder 1988).…”

Section: Introductionmentioning

confidence: 95%

“…Then we propagated the model to a system of regular branches of all orders that carry green biomass of respective sections of the tree (for example, spruce) in its ontogenesis (Galitskii 2013). The attempt of parameterization of this model of regular branches system of spruce using the data of lifespan (Tsel'niker 1994) of branches tD,j (j = 1, ..., 4) of all orders (Table 1) has shown inadequacy of this model since such a model tree could have only branches of the first order, whereas the real spruce in the Moscow region has branches of four orders.…”

Section: Introductionmentioning

confidence: 99%

“…In previous publications (Kazimirov 1971;Treskin 1973;Kramer and Kozlowski 1979), two features of spruce growth were described, and in article (Galitskii 2013) two corresponding sub-models were added to the sectional model of the spruce branch system.…”

Section: Introductionmentioning

confidence: 99%

“…Other parameters are same as for real spruce. The model of regular branches is supplemented only with the submodel of initial growth deceleration (Galitskii 2013). The inset shows a 1-branch on a larger scale, asteriskthe appearance of 1-branch at μ = 0.24966 for the spruce parameter set #19, (Tables 1 and 2); (after Galitskii 2017).…”

Section: Introductionmentioning

confidence: 99%

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Fractal Features of Proto-Plant’s Origin and their Possible Consequences

Galitskii

2016

Preprint

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The extension of the sectional model of the spruce crown's dynamics into diapason (0, 1) of the fractal parameter μ has demonstrated the existence of green biomass on branches of three orders in form of photosynthesizing (green) points. We investigated the growth of point sets on an interval as a model of the origin of proto-plants, which are formed due to endosymbiosis of cyanobacteria and protists. The fractal properties of the sets of evenly placed points and group sets were studied using the box-counting method. For the group sets, the character of dependence μ on the growing total number of points changes radically differently depending on whether the number of the points per group or the number of groups was fixed. As the host does not have the initial infrastructure needed for an increase in cyanobacteria per group, the first path is implemented and μ decreases from 1 to 0.25 when groups consist of two points per group. If and when the host develops necessary anatomical features (infrastructure), the second pathway is realized and μ grows to 1. The combined trajectory of μ initially demonstrates a slow growth of the size of the photosynthetic system and then an exponential growth after the development of the host's infrastructure. Similar fractal peculiarity also characterizes trees and is an innate property of plants. Assumptions on the morphological recapitulation of proto-plant in higher plants' ontogenesis (embryogenesis and seed germination) and also a possibility to fix the number of cyanobacteria per group are discussed.

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Section: On Properties Of Point Setsmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations