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Published in:
2022 | OriginalPaper | Chapter
9. Environmental Projects
Author : Peter McCullagh
Published in: Ten Projects in Applied Statistics
Publisher: Springer International Publishing
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Abstract
This chapter discusses two environmental projects, one concerned with understanding the effects of atmospheric warming on plants, and one concerned with the effects of plant species on the rate of infection in bumblebees.
The first project is an experiment designed to study the effect of atmospheric warming on photosynthesis in broadleaf trees and in conifers. It is a classical field experiment conducted over three years at two geographic sites in Minnesota, each site consisting of several blocks, with several plots per block. Ten boreal species are grown in each plot. Treatment is assigned to certain plots selected at random. Treatment consists of underground electrical cables to warm the soil, plus heating lamps to warm the air locally. The response variables are of two types. First, there is a range of photosynthetic variables measured on one leaf from each of several trees per plot at several points throughout the growing season. Second, on the same occasions, soil moisture content is measured on each plot.
For photosynthetic measurements, each observational unit is a leaf or a tree on specific date. There are many observational units per plot-date and each sample includes up to ten units per plot. For soil moisture content, each observational unit is a plot at a specific date. Thus, a statistical analysis of soil moisture content has many fewer observational units than an analysis of photosynthetic measurements.
Soil moisture content is governed largely by recent rainfall, so strong correlations are to be expected for moisture values recorded on the same date, and weaker serial correlations are also expected up to about two weeks.
Treatment increases evaporation, and is expected to have an effect on soil moisture content. Air temperature may also affect photosynthesis, but the availability of water is expected to dominate. It is anticipated that any such effect should be constant over years and over sites.
The effect of treatment on photosynthesis is not expected to be the same for each species, so it is best initially to examine the data species by species. Also, photosynthesis and soil water content are not expected to be independent. To the extent that changes in one cause changes in the other, it is clear that soil water content is the driver, and that the current value is most relevant. This rationale suggests first looking at how soil water content is affected by treatment, and then examining the conditional distribution given soil water content.
The bumblebee project studies whether the rate of infection in bumblebees depends on the foraging plants available. The bees were organized in microcolonies, each colony being housed in one tent for the two-week period. The foraging plants in one tent It is a classical design with five replicates or rounds, each round lasting two weeks. Nine tents were available for each round; they are labelled in three blocks of three. Each observational unit is one bee, but each experimental unit is one microcolony, or one tent in one round.
The discussion centers on observational units versus experimental units, the use of generalized linear mixed models, and the possibility of using beta-binomial models, or even generalized linear models with allowance for over-dispersion.