The effect of population density on shoot morphology of herbs in relation to light capture by leaves

Plants change their shapes, depending on their environment, for example, plant height increases with increasing population density. We examined the density-dependent plasticity in shoot morphology of herbs by analysing a mathematical model which identifies a number of key factors that influence shoot morphology, namely (i) solar radiation captured by leaves; (ii) shading from neighbouring plants; and (iii) utilisation efficiency of resource by leaves, stems and veins. An optimisation theory was used to obtain optimal shoot morphology in relation to maximal light capture by leaves, under trade-offs of resource partition among organs. We first evaluated the solar radiation flux per unit leaf area per day for different shoot forms. Our model predicts that the optimal internodal length of the stem that brings about the maximal light capture by leaves increases with plant population density, and this is consistent with experimental data. Moreover, our simple model can also be extended to explain the morphological plasticity in other herbs (i.e. stemless plants) that are different from our model plants with a stem. These findings illustrate how optimisation theory can be used for the analysis of plasticity in shoot morphology of plants in response to environmental changes, as well as the analysis of diversity in morphology

Pigmentation pattern formation in butterflies: experiments and models

Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus. To cite this article: H.F. Nijhout et al., C. R. Biologies 326 (2003)

A moving grid finite element method applied to a model biological pattern generator

Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis

Pigmentation pattern formation in butterfly wigns: Global patterns on fore- and hind-wing

Pigmentation patterns in butterfly wings are one of the most spectacular & vivid examples of pattern formation in biology. In this chapter, we devote our attention to the mechanisms for generating global patterns. We focus on the relationship between pattern forming mechanisms for the fore- and hindwing patterns. Through mathematical modeling and computational analysis of Papilio dardanus and polytes, our results indicate that the patterns formed on the forewing need not correlate to those of the hindwing in the sense that the formation mechanism is the same for both patterns. The independence of pattern formation mechanisms means that the coordination of unified patterns of fore- and hindwings is accidental. This is remarkable, because from Oudeman's principle [10], patterns appearing on the exposed surface of fore-and hindwing at the natural resting position are often integrated to form a composite and unified adaptive pattern with their surrounding environment

Pigmentation pattern formation in the buttery wing of Papilio dardanus

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Pattern formation of scale cells in Lepidoptera by differential origin-dependent cell adhesion

We present a model for the formation of parallel rows of scale cells in the developing adult wing of moths and butterflies. Precursors of scale cells differentiate throughout each epithelial monolayer and migrate into rows that are roughly parallel to the body axis. Grafting experiments have revealed what appears to be a gradient of adhesivity along the wing. What is more, cell adhesivity character is maintained after grafting. Thus we suggest that it is a cell’s location prior to migration that determines its interactions during migration. We use nonlinear bifurcation analysis to show that differential origin-dependent cell adhesion can result in the stabilization of rows over spots

A Model for Colour Pattern Formation in the Butterfly Wing of Papilio dardanus

The butterfly Papilio dardanus is well know for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a geometrically accurate wing domain produce spatial patterns that are consistent with many of those observed on the butterfly. Our results suggest that the wing coloration is due to a simple underlying stripe-like pattern of some pigment inducing morphogen. We focus on the effect of key factors such as parameter values for model selection, threshold values which determine colour, wing shape and boundary conditions. The generality of our approach should allow us to investigate other butterfly species