Gould SJ. Exaptation: A crucial tool for an evolutionary psychology. Journal of Social Issues, —65, Exaptation - a missing term in science of form. Paleobiology, —15, Jakobi N. AAI Books. Kamimura, A. Kawai N and Hara F. Pfeifer, B.
Blumberg, J. Meyer, and S. Kessel M and Gruss P. Murine developmental control gene. Science, —, Komosinski M and Ulatowski S. Framsticks: towards a simulation of a nature-like world, creatures and evolution. Floreano, J. Nicoud, and F. Kortmann R and Hallam J. Koza JR. Birk and J. Springer Verlag. Lichtensteiger L and Eggenberger P. Evolving the Morphology of a Compound Eye on a Robot.
Lindenmayer A. Mathematical models for cellular interactions in development. Journal of Theoretical Biology, —, Lipson H and Pollack J. Automatic design and manufacture of artificial lifeforms. Nature, —, Lund HH and Hallam, J. Evolving Sufficient Robot Controllers. IEEE Press, Lund HH and Miglino O. A more recent study tested the generality of these findings for species that are confined to a shallow-soil habitat that is of much greater global significance: granite outcrops Poot et al.
These studies showed that the shallow-soil endemics mostly differed in a predictable way from their congeners from deeper soils; they generally invested a larger portion of their biomass in roots, and distributed their roots more rapidly and more evenly over the container.
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Interestingly, the shallow-soil specialists achieved their apparent advantage by a different combination of the aforementioned traits. These results provide a possible explanation for the narrow endemism of many shallow-soil endemics because their root system traits seem to be adaptive in their own shallow-soil habitat in terms of obtaining access to fissures and water in the underlying rock, but are likely to be maladaptive in deeper soils.
Our TARSIERS tool is based on a functional—structural computational simulation model that aims to capture the important processes involved in the growth and development of root structures in a range of situations where water is the key limiting resource. The model was motivated by the experimental studies described above, but was constructed with the intention that it would form the basis of a flexible tool that could address questions about optimal structural rooting strategies in other conditions and plant species as well.
An important requirement of the model was that it be flexible enough to allow a wide range of strategies to be represented and explored, but simple enough that the application of an evolutionary optimization algorithm would be computationally feasible. The model runs on a daily time step and simulates the growth of a single plant's root structure through the soil following germination at the start of a seasonal wet rainy period through to the start of a seasonal dry drought period.
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The model is implemented in the R programming language R Development Core Team, and is freely available on request to the authors. For simplicity, only the primary and secondary roots are represented, since we assume that these are the most important in defining the overall architecture of the root system and its access to water, during both the initial wet period and the subsequent drought period. Shoot and fine roots are represented non-geometrically. An earlier version of the model is described in Renton et al.
The overall dynamics of the model are summarized and different aspects of the model illustrated in Fig. Processes of water uptake and growth are simulated on a daily time step top leading to the dynamic emergence of a three-dimensional root structure that is usually represented in two dimensions for convenience bottom. Strategy parameters are fixed for the lifetime of an individual plant, but can evolve over multiple generations.
Fixed parameters: model parameters determining characteristics of soil, water uptake and biomass, with description, units where relevant and the value used in this study; these parameters are kept fixed during evolutionary simulations. The soil is represented as a three-dimensional grid of cubic voxels.
Each voxel is defined to be either soil with a fixed available water-holding capacity, or impermeable rock, into which roots and water cannot penetrate. In a typical simple case, we could define the soil to be of a fixed depth d soil , with all voxels less than this depth having an available fixed water-holding capacity c water , and all voxels greater than this depth being impermeable Fig. This corresponds to a situation where there are no cracks in the underlying rock layer. In case we wish to simulate cracks, as we do in this study, we define some of the voxels at the top of the impermeable layer to be the entrance to cracks.
These are treated differently in the simulation from other soil voxels, as explained later. For this study, we assumed a relatively simple rainfall pattern, where rainfall occurs once every 2 weeks during the simulated rainy period, starting on day 1, and that the amount of rainfall is sufficient to fill the shallow soil profile completely and replenish any cracks in the underlying rock. The assumption that finer root structures emerge uniformly along the major roots may be reasonable, given that we only simulate the first few months of the plant's growth, in a period where soil moisture is relatively high and consistent.
Roots are able to access the water within the voxel in which they are located, and no other voxel's water. Roots take up water at their maximum potential rate until the total water available in the voxel falls to zero.
Roots within a wet crack always take up water at the maximum rate. This may be a reasonable assumption during the simulated period of the wet season where there is regular rain and replenishment of water stored in rock cracks. For details of the algorithm used to calculate water uptake, see Supplementary Data 1.
The shoot is simulated only as a single biomass pool with no structure. If a wet crack has not yet been encountered by the plant, then the proportion allocated to the shoot is p shbmb ; if it has, then the proportion is p shbma. The proportion allocated to a particular root is simply its own relative growth weighting divided by the sum of the relative growth weightings for all roots main root and all laterals.
This assumption correspond to da Vinci's rule and the pipe model commonly used in tree modelling Shinozaki, ; Mandelbrot, ; Zimmerman, ; Prusinkiewicz and Lindenmayer, and ensures that roots grow faster when the plant is taking up more water, and that longer roots cost proportionally more than shorter roots due to their need to transport greater volumes of water for details, see Supplementary Data 2. The direction of the new segment is calculated as follows. The direction of a new lateral root segment is based on the current heading direction, with some stochastic variability, plus some gravitropism.
When a new root segment is added to the end of the main or lateral root, as described in the previous section, a check is made of whether the segment has passed into an impermeable voxel. If it has, then an adjustment is made to the final position. The end of the new segment is set to be on the impermeable layer.
If a root segment is found to have passed into a voxel defined to be the entrance of a wet crack then it continues its growth but the direction and spatial position of this growth are no longer simulated, as it is now assumed to be following along the crack. Lateral branching may occur at two different times, when the main root is growing vertically down before it encounters an impermeable surface, and when the main root encounters an impermeable surface.
The probability of branching during initial growth follows a logistic function of the distance from the top of the main root, and there may be a delay before the lateral starts to grow. The probability of branching after the main root encounters an impermeable surface follows a logistic function of the distance from the point of contact with the impermeable surface, and growth of any laterals produced proceeds immediately.
The main root and each of the lateral roots are also assigned a relative growth weighting when they are created that does not change with time; this represents the sink strength of the root. The model produces both graphical and numerical outputs. Numerical outputs allow some measure of the success of the strategy of the plant. For example, if the plant has not accessed any wet crack entrances by the start of the drought season, then it is deemed to have failed to establish and reproduce.
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If the plant has accessed a crack, then its relative success could be defined to be the number of cracks accessed or the total shoot biomass achieved, since these are likely to be important determinants of future growth and reproductive output. Other numerical outputs summarize important characteristics of the root structure, including the total root length and maximum radial root distance in different soil layers Renton et al. Phenotypic root structure realizations of the single TARSIERS genotype that was used as the starting point to generate the initial population for each of the four evolutionary runs.
The bottom row shows different phenotypic root structure realizations generated from the same genotype, all at the end of the growing period only day Note that one single genotype can produce different phenotypes; in these examples, just one of the six illustrated phenotypic realizations of the one genotype has successfully found a wet crack the final one at bottom right.
Soil depth is 25 cm in all cases. A measure for relative reproductive potential or evolutionary fitness is defined. The growth of each individual over its first seasonal wet period is simulated as described, and the numerical outputs of the model are then used to calculate the relative reproductive potential of the individual, according to the defined measure. The reproductive potential of an individual is thus estimated based on its growth within its first wet season, which is reasonable for perennials in seasonal environments where initial establishment is key to ultimate success, particularly plants that must find a wet crack within that first season in order to survive.
Once the plant has accessed a permanent water supply, its ultimate success is almost guaranteed. The first population now becomes the parent population. A new population of plants is then generated, of the same size as the first generation.
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The parents of each individual in the new population are selected at random from the individuals in the parent population, from a multinomial distribution with weightings equal to the parents' relative reproductive potential. The new population now becomes the parent population and this process is continued for a set number of populations or until a stopping criterion indicating stabilization of the evolutionary process is achieved.
It is possible, of course, that in any given evolutionary simulation the population may become extinct reproductive potential of all individuals in any generation is equal to zero ; if this happens repeatedly over many evolutionary simulations, then it may indicate that there is no suitable ecological strategy that achieves a positive reproductive potential with the given model parameter values, or that all individuals in the starting population are too different from any individual with a suitable ecological strategy. The random perturbation to the strategy parameters applied after averaging the values for parents is an important part of the evolutionary algorithm.