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.
