Since the birth of social networks, a photograph often goes viral in which it is seen how, from the ground and looking up, the treetops are perfectly defined and separated from each other, as if they did not want to touch each other . It is a phenomenon that occurs in some species of trees, and that is best observed when they are species with tall trunks whose crowns are restricted to the upper stratum. With the proper perspective, this feature generates a very distinctive visual effect by forming irregular and uneven tile patterns.
In botany, this phenomenon is called crown shyness , and hypotheses about how it occurs and what type of adaptation it responds to have been under discussion for a hundred years.
How does the shyness of trees occur?
Despite the attractiveness of the phenomenon of shyness, it is little studied, for more than a century various hypotheses have been considered that try to explain it, some without much success.
One of the hypotheses is that it is an effect caused by the wind . The branches of the trees in movement would collide with each other, causing the breakage of those that grow more than they should. According to this hypothesis, the process would be produced by mere abrasion against neighboring branches, which would prevent the growth of new shoots where there is no room to grow. A higher wind force would leave the crowns further apart, with wider spaces between them, while calmer winds would result in denser tesserae with narrower rims.
However, these predictions do not correspond to reality . When shyness phenomena are observed, no correlation is found between the size of the hole and the average wind speed. In addition, in some cases, shyness is observed between trees of the same species, but it disappears when trees of different species interact with each other —even if both show shyness. It seems that it is not an effect caused by external factors, but by something intrinsic to the biology of trees .
Shyness as an evolutionary adaptation
In living things there are rarely structures or behaviors without an underlying evolutionary cause. And probably, the case of the shyness of trees is not an exception. The most accepted hypotheses currently to explain the shyness of trees have to do with competition.
Some tree species can detect subtle changes in light , including scattering that occurs in the far red part of the spectrum due to the presence of incipient shoots. These changes tell the plant where there will be leaves that will cast shade in the near future. Remember that sunlight is the main resource, along with water, to carry out photosynthesis. In this way, the trees anticipate the presence of that shade and inhibit the growth of leaves that are not going to be productive.
This phenomenon may be behind the shyness of the trees; they avoid growing where there are already branches, so as not to invest resources in producing organs that will be useless. The main engine would therefore be the competition for light.
In addition, it has recently been found that this ability to recognize neighboring branches can allow the plant to differentiate its relatives from other conspecific specimens with which they are not related, or from plants of other species. If this is the mechanism underlying tree shyness, it would explain why it occurs more frequently in forests where most individuals are related, and less frequently when trees are unrelated or do not belong to the same species. .
a mathematical pattern
The shape that the crowns of the trees acquire when shyness occurs responds to a pattern that can be modeled mathematically . Actually, it is the same mathematical principle that is hidden in the distribution of skin cells, in the ocelli of the compound eye of an insect, in the spots of a giraffe or in the seeds of a pomegranate. This type of pattern, in mathematics, is called a Voronoi diagram .
A Voronoi diagram is a division of space into regions defined by points . Each point has associated, around it, a portion of that space, which is called a cell . But not randomly or approximately, but following a very firm principle: an area of space always belongs to the region of the closest point. In this way, around the trunks, which would be the points of the Voronoi diagram, the tops of the trees, which would be the cells, are distributed. And the edges, which remain untouched, keep them defined.
However, unlike most observable patterns in nature, the tessellation caused by the shyness of trees does not always follow this principle; we find areas of the crowns that belong to trees whose trunk is not always the closest to that specific cell of space. In this case, the pattern is best defined by a weighted Voronoi diagram .
Competition-weighted Voronoi diagram
In a simple Voronoi diagram, all points have the same ‘weight’, that is, the same importance when drawing the cells to which they belong. The boundary of each cell is exactly halfway between their respective points. But in a weighted Voronoi diagram each point has its ‘weight’ , different from the rest. So a point that has more weight than another will have more influence over space, and its area will be much larger.
In trees, the main factor that has been observed to influence the ‘weight’ of the point they represent in the Voronoi diagram is the ability to compete. The most successful trees in competition have a higher ‘weight’ in the weighted Voronoi diagram, and therefore occupy a larger area.
This fact can provide researchers with tools to quantitatively approximate the competitive capacity of trees in a forest. From photographs a mathematical model can be established, following a weighted Voronoi diagram, with which to obtain the ‘weight’ of each tree in the model.
This article is dedicated to the mathematician Clara Grima.
References:
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Crepy, M. A. et al. 2015. Photoreceptor-mediated kin recognition in plants. New Phytologist, 205(1), 329-338. DOI: 10.1111/nph.13040
Goudie, J. W. et al. 2009. An empirical model of crown shyness for lodgepole pine (Pinus contorta var. latifolia [Engl.] Critch.) in British Columbia. Forest Ecology and Management, 257(1), 321-331. DOI: 10.1016/j.foreco.2008.09.005
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