TITLE: Email about estimating competition with basal area
DATE: 2020-08-14
AUTHOR: John L. Godlee
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I was thinking about how to estimate competition in a woodland 
plot, without using geo-referenced tree locations. This email goes 
through some thoughts I had on why plot-level basal area isn't a 
good way to estimate competition.

  Hi, I've been thinking more about this situation of estimating 
competition using plot-level basal area. It doesn't sit right with 
me. It appears to me that two plots could have identical basal 
areas but different levels of competition between individuals. 
Below are two examples which I'm tentatively putting forward to 
demonstrate my point. You might disagree with my reasoning, and I'm 
open to being corrected.

  Imagine two plots of identical area, and identical plot-level 
basal area, 5 m^2 ha^-1, for example. The number of trees varies 
between plots, however. In order to achieve identical plot-level 
basal areas the basal areas of individual trees must be different 
between plots. In plot A there are 50 trees, each with a basal area 
of 0.1 m^2. In plot B there are 100 trees with basal areas of 0.05 
m^2. Despite having identical plot-level basal areas, in plot A 
competition will be lower than plot B, because the trees are not as 
close together and therefore crown and root interaction will 
decrease. Previous work has shown that basal area doesn't have a 
linear relationship with crown area, it's more like a sigmoid curve 
or a saturating curve, the key takeaway being that in a small tree, 
unit increase in basal area will lead to a greater increase in 
crown area than a unit increase in a large tree. I think including 
stem density in the model could do a better job of estimating 
competition than plot-level basal area.

  Next, imagine two other plots, both of which have 100 trees, 
arranged in an evenly spaced grid pattern. In plot A, all trees 
have a basal area of 0.05 m^2, while in plot B half the trees have 
a basal area of 0.01 m^2 and half have a basal area of 0.09 m^2. 
Both plots have a basal area of 5 m^2, but plot B will have weaker 
crown competition interactions than plot A. The reason being that 
the large trees in plot B will not be negatively affected by the 
presence of the smaller trees. In this scenario, I think including 
information on the variance of basal area (or should it be area 
under the distribution of basal area?) within a plot might improve 
estimates of competition. I would expect a higher variance of basal 
area would cause lower overall competition, due to diminished 
plot-level competition interactions, but I'm less certain on this.

  Let me know what you think to the above points if you want to 
take the discussion further. It's a shame we don't have more plots 
with X-Y coordinates for individual trees. There's a tonne of very 
convincing research on methods to estimate neighbourhood 
competition in forestry.

Thinking about it more, it may be useful to weight the competition 
contribution of individuals based on their basal area. Weight the 
competitive contribution of large trees vs. small trees. I would 
expect large trees to exert a greater competitive effect than small 
trees. Maybe the weighting should be based on pairwise comparisons 
of basal area among all trees in the plot? A positive competition 
effect would result between a pair if individual A was larger than 
individual B, and increase positively the larger individual A was 
than individual B.