Question

The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To study how the tree adapts to its varying habitats, researchers collected twigs with $$ \begin{array}{|ccc|} \hline & \text { Altitude of origin } & \text { Respiration rate } \\ \text { Tree } & X(\mathrm{~m}) & Y(\mu \mathrm{l} / \mathrm{hr} \cdot \mathrm{mg}) \\ \hline 1 & 90 & 0.11 \\ 2 & 230 & 0.20 \\ 3 & 240 & 0.13 \\ 4 & 260 & 0.15 \\ 5 & 330 & 0.18 \\ 6 & 400 & 0.16 \\ 7 & 410 & 0.23 \\ 8 & 550 & 0.18 \\ 9 & 590 & 0.23 \\ 10 & 610 & 0.26 \\ 11 & 700 & 0.32 \\ 12 & 790 & 0.37 \\ \hline \end{array} $$ attached buds from 12 trees growing at various altitudes in North Angus, Scotland. The buds were brought back to the laboratory and measurements were made of the dark respiration rate. The accompanying table shows the altitude of origin (in meters) of each batch of buds and the dark respiration rate (expressed as \(\mu\) l of oxygen per hour per mg dry weight of tissue). \(^{33}\) (a) Create a scatterplot of the data. (b) If your software allows, add a regression line to summarize the trend. (c) If your software allows, create a scatterplot with a lowess smooth to summarize the trend.

Short answer

The scatterplot should show each tree's altitude and respiration rate as points. A regression line summarizes the trend by showing the expected increase or decrease in respiration rate with altitude if a linear pattern existed. A lowess smooth offers a non-linear perspective of the data trend.

Step-by-step solution

Plot the Scatterplot

Firstly, gather all the given pairs of altitude (X) and respiration rate (Y) from the table. Use a graphing tool or software capable of creating scatterplots. Plot each pair as a point where the x-coordinate corresponds to the altitude of origin and the y-coordinate corresponds to the respiration rate. Label your axes appropriately.

Add a Regression Line

If the software permits, use the built-in functionality to fit a linear regression line through the points. This line will minimize the sum of the squared differences between the observed values and the values predicted by the line (least squares method). This line can help visualize the overall trend in the data.

Create a Lowess Smooth Scatterplot

A Lowess (Locally Weighted Scatterplot Smoothing) is a non-parametric regression method that combines multiple regression models in a k-nearest-neighbor-based meta-model. If your software allows, add a lowess smooth to the scatterplot to see the trend in the data across different values of altitude.

Key concepts

Regression Line

When studying the relationship between two variables, such as altitude and dark respiration rate in rowan trees, a regression line is a powerful tool. This line, often calculated using the method of least squares, represents the best fit for the observed data, providing a way to succinctly describe the main trend.

By plotting the regression line on a scatterplot that showcases original altitudes (X) and respiration rates (Y) of the rowan tree buds, researchers can determine if there is a general increase or decrease in respiration rate with altitude. The slope of the line indicates the direction and strength of the relationship; a positive slope means that as one variable increases, the other tends to increase as well, which could suggest altitude influences dark respiration rate. Interpreting this line can thus give insights into potential physiological adaptations the plants might have developed to cope with varying altitudes.

Lowess Smooth

A scatterplot with a Lowess smooth, short for Locally Weighted Scatterplot Smoothing, shows the trend in the observed data more flexibly than a strict linear regression line. Unlike a regression line, which assumes a single straight-line relationship between variables across the entire data set, a Lowess smooth creates a smoothed curve that can reveal nuanced patterns within subsets of the data.

This non-parametric technique gives weight to nearby points, fitting multiple smaller models to subsets of the data based on proximity, which are then combined to produce a smooth curve. Such a plot can be especially helpful in complex ecological studies like altitude adaptation, where the relationship between altitude and respiration rate might not be purely linear but could vary at different altitudes or within specific altitude ranges.

Dark Respiration Rate

The dark respiration rate is a measure of the metabolic rate of plants when not photosynthesizing, i.e., in the dark. It represents the amount of oxygen consumed by plant tissues, here specifically buds of the rowan tree, which signifies the energy required to maintain basic cell functions.

Understanding dark respiration rates is key to studying plant physiology and ecology, as it affects plant growth and could be an indicator of how a plant is responding to its environment. In altitude adaptation studies, variations in the dark respiration rate at different altitudes could provide clues on how trees acclimatize to lower oxygen levels or to temperature changes that are common with changes in elevation.

Altitude Adaptation Studies

Research into how living organisms adapt to high altitudes, such as in the case of rowan trees, is comprehensive under the umbrella of altitude adaptation studies. These studies are crucial for understanding the biological and ecological strategies organisms employ to survive and thrive under the low oxygen and temperature conditions that characterize high-altitude environments.

Patterns of physiological traits like the dark respiration rate can shed light on evolutionary processes and contribute to our understanding of environmental influence on species distribution. By examining these patterns across different altitudes, scientists can glean insights into the underlying genetic and physiological mechanisms that support altitude adaptation, information that is becoming ever more critical in the face of global climatic changes.