An algorithm for the simulation of the growth of root systems on deformable domains

Modeling root system growth around obstacles

State-of-the-Art models of Root System Architecture (RSA) do not allow simulating root growth around rigid obstacles. Yet, the presence of obstacles can be highly disruptive to the root system. We grew wheat seedlings in sealed petri dishes without obstacle and in custom 3D-printed rhizoboxes containing obstacles. Time-lapse photography was used to reconstruct the wheat root morphology network. We used the reconstructed wheat root network without obstacle to calibrate an RSA model implemented in the R-SWMS software. The root network with obstacles allowed calibrating the parameters of a new function that models the influence of rigid obstacles on wheat root growth. Experimental results show that the presence of a rigid obstacle does not affect the growth rate of the wheat root axes, but that it does influence the root trajectory after the main axis has passed the obstacle. The growth recovery time, i.e. the time for the main root axis to recover its geotropism-driven growth, is proportional to the time during which the main axis grows along the obstacle. Qualitative and quantitative comparisons between experimental and numerical results show that the proposed model successfully simulates wheat RSA growth around obstacles. Our results suggest that wheat roots follow patterns that could inspire the design of adaptive engineering flow networks.

Tree Physiology Optimization in Benchmark Function and Traveling Salesman Problem

Nature has the ability of sustainability and improvisation for better survival. This unique characteristic reflects a pattern of optimization that inspires the computational intelligence toward different scopes of optimization: a nondeterministic optimization approach or a nature-inspired metaheuristic algorithm. To date, there are many metaheuristic algorithms introduced with good promising results and also becoming a powerful method for solving numerous optimization problems. In this paper, a new metaheuristic algorithm inspired from a plant growth system is proposed, which is defined as tree physiology optimization (TPO). A plant growth consists of two main counterparts: plant shoots and roots. Shoots extend to find better sunlight for the photosynthesis process that converts light and water supplied from the roots into energy for plant growth; at the same time, roots elongate in the opposite way in search for water and nutrients for shoot survival. The collaboration from both systems ensures plant sustainability. This idea is transformed into an optimization algorithm: shoots with defined branches find the potential solution with the help of roots variable. The shoots-branches extension enhances the search diversity and the root system amplifying the search via evaluated fitness. To demonstrate its effectiveness, two different classes of problem are evaluated: (1) a continuous benchmark test function compared to particle swarm optimization (PSO) and genetic algorithm (GA) and (2) an NP-hard problem with the traveling salesman problem (TSP) compared to GA and nearest-neighbor (NN) algorithm. The simulation results show that TPO outperforms PSO and GA in all problem characteristics (flat surface and steep-drop with a combination of many local minima and plateau). In the TSP, TPO has a comparable result to GA.

A conceptual model of root hair ideotypes for future agricultural environments: what combination of traits should be targeted to cope with limited P availability?

BACKGROUND

Phosphorus (P) often limits crop production and is frequently applied as fertilizer; however, supplies of quality rock phosphate for fertilizer production are diminishing. Plants have evolved many mechanisms to increase their P acquisition, and an understanding of these traits could result in improved long-term sustainability of agriculture. This Viewpoint focuses on the potential benefits of root hairs to sustainable production.

SCOPE

First the various root-related traits that could be deployed to improve agricultural sustainability are catalogued, and their potential costs and benefits to the plant are discussed. A novel mathematical model describing the effects of length, density and longevity of root hairs on P acquisition is developed, and the relative benefits of these three root-hair traits to plant P nutrition are calculated. Insights from this model are combined with experimental data to assess the relative benefits of a range of root hair ideotypes for sustainability of agriculture.

CONCLUSIONS

A cost-benefit analysis of root traits suggests that root hairs have the greatest potential for P acquisition relative to their cost of production. The novel modelling of root hair development indicates that the greatest gains in P-uptake efficiency are likely to be made through increased length and longevity of root hairs rather than by increasing their density. Synthesizing this information with that from published experiments we formulate six potential ideotypes to improve crop P acquisition. These combine appropriate root hair phenotypes with architectural, anatomical and biochemical traits, such that more root-hair zones are produced in surface soils, where P resources are found, on roots which are metabolically cheap to construct and maintain, and that release more P-mobilizing exudates. These ideotypes could be used to inform breeding programmes to enhance agricultural sustainability.