Development of a Mathematical Method for Classifying and Comparing Tree Architecture Using Parameters from a Topological Model of a Trifurcating Botanical Tree

Sismilich, M.; Menzies, M. I.; Gandar, P.W.; Jameson, Paula E.; Clemens, John D.

doi:10.1006/jtbi.2003.3177

Cited by 7 publications

(4 citation statements)

References 45 publications

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“…The RTS model was developed on the premise that the architecture or branching of fine root systems may be represented as self‐similar fractals of root orders (Fig. 1; West et al ., 1999; Sismilich et al ., 2003). Branching pattern was chosen as the core of RTS because order can effectively categorize the heterogeneous fine root pool into more homogeneous subpopulations in a systematic manner, thereby facilitating comparisons across species of different root architectures (Pregitzer et al ., 2002; Withington et al ., 2006).…”

Section: Methodsmentioning

confidence: 99%

Fine root heterogeneity by branch order: exploring the discrepancy in root turnover estimates between minirhizotron and carbon isotopic methods

et al. 2007

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Summary• Fine roots constitute a large and dynamic component of the carbon cycles of terrestrial ecosystems. The reported fivefold discrepancy in turnover estimates between median longevity (ML) from minirhizotrons and mean residence time (MRT) using carbon isotopes may have global consequences.• Here, a root branch order-based model and a simulated factorial experiment were used to examine four sources of error.• Inherent differences between ML, a number-based measure, and MRT, a massbased measure, and the inability of the MRT method to account for multiple replacements of rapidly cycling roots were the two sources of error that contributed more to the disparity than did the improper choice of root age distribution models and sampling bias. Sensitivity analysis showed that the rate at which root longevity increases as order increases was the most important factor influencing the disparity between ML and MRT.• Assessing root populations for each branch order may substantially reduce the errors in longevity estimates of the fine root guild. Our results point to the need to acquire longevity estimates of different orders, particularly those of higher orders.

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Section: Methodsmentioning

confidence: 99%

Fine root heterogeneity by branch order: exploring the discrepancy in root turnover estimates between minirhizotron and carbon isotopic methods

et al. 2007

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“…c See Berntson (1997). d See Withney (1972), Berntson (1997) and Sismilich et al (2003). component is made up of one branch (entire since the path begins at the apex in this particular case), the second-order component is made up of one branch, and the third-order component is made up of four branches.…”

Section: Article In Pressmentioning

confidence: 99%

“…The tree-morphometric equivalent is called the 'branch'; and could be called in a clearer way 'internode' (see e.g. Sismilich et al, 2003).…”

Section: Analogous Objects and Variables Within Treesmentioning

confidence: 99%

On the transposition and the improvement of an allometric model from river networks to trees: identification of analogous objects, variables and modellings

Cudennec¹

2005

Journal of Theoretical Biology

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“…Horton [21], Shreve [30]), actual trees and shrubs in botany (e.g. Bell et al [5], de Reffye and Houllier [9], Godin et al [14], Sismilich et al [31]) and axon and dendrites in neuroanatomy (e.g. Ascoli [1], Devaud et al [11], Dityatev et al [12], van Pelt and Schierwagen [35], Verwer and van Pelt [45]).…”

mentioning

confidence: 99%

Stochastic continuous time neurite branching models with tree and segment dependent rates

Elburg

2011

Journal of Theoretical Biology

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In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. We derive explicit expressions for the time dependent probabilities p(γ,t) for finding a tree γ at time t, valid for arbitrary continuous time branching models with tree and segment dependent branching rates. We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number μ(f(n),t) do not depend on the distribution of the total branching probability over the terminal segments. In addition, we derive a system of differential equations for the probabilities p(n,t) of finding n terminal segments at time t. For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t. For comparison we discuss two cases where mean and variance of the number of terminal segments are exactly solvable. Then we discuss the numerical evaluation of the S-dependence of the solutions for the continuous time BES-model. The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees as measured by three tree symmetry indicators.

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Development of a Mathematical Method for Classifying and Comparing Tree Architecture Using Parameters from a Topological Model of a Trifurcating Botanical Tree

Cited by 7 publications

References 45 publications

Fine root heterogeneity by branch order: exploring the discrepancy in root turnover estimates between minirhizotron and carbon isotopic methods

Fine root heterogeneity by branch order: exploring the discrepancy in root turnover estimates between minirhizotron and carbon isotopic methods

On the transposition and the improvement of an allometric model from river networks to trees: identification of analogous objects, variables and modellings

Stochastic continuous time neurite branching models with tree and segment dependent rates

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