Discussion

Limits of the experimental systems

The experience suffers from certain methodological flaws. Firstly, the lack of repetition of the experiment makes impossible to observe the variability of the root structures or to compare the reaction times of the plants in order to obtain information on the type of signal transmitted if it takes place. A repetition would also have made it possible to estimate if the rapid reaction observed in this experiment was systematic or if it was a particular phenomenon. The second lacunar aspect of the experiment lies in the assumptions of the communication device. In order for the signal to allow the plant to orient its growth, it is necessary for the emitting plant to have an evolutionary interest in emitting a signal and for this signal to contain information on the relative direction of the nutrient quality gradient and, finally, that signal can be interpreted by the receptor plant. It is possible that all plants continuously emit similar signals in amounts proportional to the quality of their environment and thus create a signal gradient characterizing the soil quality gradients but this is unlikely from an evolutionary point of view because it means that the plant spends energy to increase competition in his environment. Except if we hypothesized that the signal comes from the plant in a disadvantageous environment, then it might be an evolutive advantage for a population to avoid a hostile environment.  

Crosstalk between the model and the experiment

In the model, we considered that the plants were enough separated so that there is no direct contact between their roots in the period of time taken into account. Each contact is thus due to mycorrhizae. From the data we got, it seems that the growth rate of mycorrhizae in the media is so low that there may be no contact in this period of time. By reducing the distance between the two plants, it is possible that contacts happen between roots, without mycorrhizae. Therefore we must remain critical about the nature of the contact. On the one hand, we can check on the generated graph and wonder if the parameters chosen seem to allow a contact between real roots. On the other hand, we have to compare it with the experiment. Possible contacts between roots can easily be seen with the naked eye. See mycorrhizae requires a microscope.
On the isolated simulations we did, we obtained a surprising result. The contact appears quicker with a mycorrhizae growth rate of 0.2 cm/day than with 0.4 cm/day while the distance has not changed. This can be partly explained since the structure from CRootBox is made with a part of stochasticity. This highlights the importance of repeating simulations and experiments and using statistical tools to interpret the results.

Improvement of the diffusion model

The model designed seems to be robust on the scale of phenomena studied. Plausible results are observed for all scales of values analyzed. The most obvious improvement is the determination of the parameters. Indeed the diffusion coefficients, the rate of production of signal molecules and the concentration necessary for the detection have been chosen arbitrarily and must be adapted to the medium, the signal and the types of roots studied. Only one type of plant has been analyzed by modeling, even if the results are a priori similar to any type of plants, the model should be run with different root phenotype in order to validate this assumption. More differentiation in the model of the collecting roots could be used to characterize the signal transmission time for each type of root and thus improve the specificity of the results that remain very general in this model. 
We consider that the emitting plant exudes the signal directly after the germination of the seeds. This is a huge assumption and it is important to remind that an active communication process is composed, in addition, at least of an identification of the signal to transfer and the creation of the signal, or at least a reaction to the environment in the case of passive communication. To this are added the transfer of the signal and possibly a response. Those phenomena take time and extend the communication time. We did not need to work on those phenomena because we find that transfer time is long enough to exclude the communication hypothesis. 

Conclusions

We tried to develop models allowing to test different circumstances. We can use them by varying different parameters such as the growth rate of roots and mycorrhizae, the distance between both plants, the diffusion coefficient, etc. It is very important to be critical regarding the results obtained. The modeling process sometimes provides very different results from the experimentation ones.
In the experiment provided by the American team, the response seems to happen very quickly. None of the communication ways we tested can explain such a quick response.