Raleigh plot
Raleigh or Rayleigh plots are closely related to the Rayleigh test, a directional statistical test. A Raleigh plot can serve as a graphical representation for a Raleigh test that maps a mean vector to a circular plot. Raleigh plots have many applications in the field of chronobiology.
General interpretation
A Raleigh plot is statistical graphic, usually in the shape of a circle. Dashes along the circumference of the circle denote values such as directions, time of day, or phase. Dots on the circumference of the circle represent values for individuals in the tested population. An arrow rooted in the center of the circle, known as the mean vector, shows the average measurement of the tested population.[1][2] The length of the mean vector is denoted as r and measures statistical dispersion. The more concentrated the dots on the circumference are in a particular region, the longer the arrow on the plot will appear, and the higher the r value will be. Raleigh plots are also capable of showing more than one mean vector, particularly in instances when the mean vector for each specific group in the study wants to be displayed or when mean vectors between groups are seek to be compared.
Examples
The following example to the left is a Raleigh plot with a high r value and low statistical dispersion. The dashes on the circumference of the circle denote the cardinal directions: North, East, South, and West. Blue and yellow dots indicate individuals from different groups being tested, and the position of the dots indicate in which direction each tested individual is traveling. Due to the high overall concentration of individuals going in the northeast direction, the mean vector is much longer. Compare this figure with the following figure on the below:
In this example, the Raleigh plot has a low r value and high statistical dispersion. Both yellow and blue dots are spread along the circumference of the circle, indicating many individuals are traveling in different directions. The largest cluster of individuals, a group traveling southwest causes the mean vector to be pointed in the southwest direction. Due to the high amount of other tested individuals traveling in directions different from this group, however, the mean vector becomes much smaller in this figure.
Uses in chronobiology studies
Butterfly migration studies
Raleigh plots have been used in chronobiology studies on the biological clocks behind monarch butterfly migration patterns. They are particularly relevant for studying sun compass orientation in migrating butterflies.
In butterfly migration studies, the Raleigh plot maps the orientation of the butterfly when allowed to fly, where the circumference is marked as a compass, with N at the top position. Given the plotted data points, a mean r vector is drawn to indicate the mean orientation of the butterflies in a particular condition.[3][4]
In his studies on the neurobiology of butterfly migration, Steven M. Reppert observes the oriented flight behavior of monarch butterflies. Reppert explains how Raleigh plots are used to handle butterfly orientation data and as tools for the data analysis.[5]
In a 2012 study by Reppert and colleages on the sufficiency of an antenna for proper time compensation and sun compass orientation in the monarch butterfly, Raleigh plots were used to present the mean flight orientation of butterflies subjected to different study conditions. Along the edge of the circle, degrees 0º (north) through 360º are shown, the orientation of each butterfly is marked with a dot, and a mean vector is drawn to represent the mean flight orientation recorded.[1]
A 2018 review was conducted by Reppert and de Roode on the mechanisms of monarch butterfly migration. The researchers use Raleigh plots, also referred to as circlegrams, to represent butterfly orientation data. Each dot indicates the orientation in which a butterfly individual flew continuously for 5 minutes or longer, and the vector points in the mean direction (some degrees from north) with a magnitude proportional to the mean orientation.[6]
Protein and gene expression studies
Raleigh plots can be used to help visualize circadian rhythms of protein or gene expression, and how their phases are affected by other variables or induced-conditions.
Jennifer Mohawk, a researcher at the University of Texas Southwestern Medical Center, used multiple Raleigh plots to illustrate PER2::LUC expression in her publication, “Methamphetamine and Dopamine Receptor D1 Regulate Entrainment of Murine Circadian Oscillators.”[2] Specifically, Mohawk investigated how injections of methamphetamine and D1 antagonist SCH-23390 would shift the peak time of PER2 expression in the liver, lung, pituitary gland, and salivary gland. In these plots, the Raleigh plot can be interpreted as a 24 hour clock with CT 0 at the top of the circle and CT 12 at the bottom of the circle. Each arrow represents the average peak phase of PER2::LUC expression of each group. The strength of the phase clustering is symbolized by the length of the arrow, meaning stronger clustering or closer data points resulting in longer arrows. The individual data points are plotted on the outside of the circle and their unique color and shape resemble the different groups of conditions. At ZT 7 is a pink box that shows the timing of the methamphetamine injection. Mohawk and the other collaborators on this article compare the angle of the vector, or the mean phase, between the different groups in order to determine if methamphetamine injections induced statistically significant phase changes of PER2::LUC expression within the different glands and organs.[2]
Similarly, Tsedey Mekbib, who at the time was a PhD candidate in Biological and Biomedical Sciences at the Morehouse School of Medicine, utilized Raleigh plots to depict how the knockdown of SIAH2 impacted the rhythmic expression of all other genes in both males and females. After profiling the entire transcriptome via RNA sequence on the liver at frequent time intervals, the expression of peak timing for all rhythmically expressed genes was plotted on Raleigh plots for each group. These Raleigh plots contain vectors that represent the average peak phase. However, instead of differing the length of the vectors to illustrate the variability in the data points, Mekbib and the other collaborators added a +/- 95% confidence interval that is represented by red range along the circle. In addition to the typical Raleigh plot, the left half of the circle is shaded darker to better visualize the night phase occurring between CT 12 and CT 24.[7]
Additionally, Raleigh plots were utilized by Elizabeth Maywood, an English researcher at the MRC Laboratory of Molecular Biology in Cambridge, to visualize how pacemaking activity and synchrony between host SCN cells lacking VIP can be restored with a wild-type SCN graft. These plots show vectors that represent the phase of the host SCN cells, measured by PER2::LUC expression. Each plot has a value representing the mean vector length with time points where the cell phases are closer in sync having a value closer to 1. Maywood and other collaborators showed that VIP-null host SCN cells synchrony deteriorated over time based on the mean vector length of the Raleigh plots decreasing, and concluded that paracrine signaling from an introduced wild-type SCN graft is sufficient to restore the synchrony between SCN cell pacemakers based on the mean vector length increasing after the graft was introduced.[8]
See also
- Rayleigh test
- Circular distribution
- Sun compass in animals
- Butterfly
- Monarch butterfly migration
- Suprachiasmatic nucleus
References
- ^ a b Guerra, Patrick A.; Merlin, Christine; Gegear, Robert J.; Reppert, Steven M. (2012-07-17). "Discordant timing between antennae disrupts sun compass orientation in migratory monarch butterflies". Nature Communications. 3 (1): 958. doi:10.1038/ncomms1965. ISSN 2041-1723. PMC 3962218. PMID 22805565.
- ^ a b c "Methamphetamine and Dopamine Receptor D1 Regulate Entrainment of Murine Circadian Oscillators". PLOS ONE. 8 (4): e62463. 2013-04-23. doi:10.1371/journal.pone.0062463. ISSN 1932-6203.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ Mouritsen, Henrik; Derbyshire, Rachael; Stalleicken, Julia; Mouritsen, Ole Ø.; Frost, Barrie J.; Norris, D. Ryan (2013-04-30). "An experimental displacement and over 50 years of tag-recoveries show that monarch butterflies are not true navigators". Proceedings of the National Academy of Sciences. 110 (18): 7348–7353. doi:10.1073/pnas.1221701110. ISSN 0027-8424. PMC 3645515. PMID 23569228.
- ^ Franzke, Myriam; Kraus, Christian; Gayler, Maria; Dreyer, David; Pfeiffer, Keram; el Jundi, Basil (2022-02-01). "Stimulus-dependent orientation strategies in monarch butterflies". Journal of Experimental Biology. 225 (3): jeb243687. doi:10.1242/jeb.243687. ISSN 0022-0949. PMC 8918799. PMID 35048981.
- ^ Steven Reppert (UMass) Part 2: Monarch Butterfly Migration: A Time-Compensated Sun Compass, retrieved 2023-04-11
- ^ Reppert, Steven M.; de Roode, Jacobus C. (2018-09). "Demystifying Monarch Butterfly Migration". Current Biology. 28 (17): R1009 – R1022. doi:10.1016/j.cub.2018.02.067.
{{cite journal}}: Check date values in:|date=(help) - ^ Mekbib, Tsedey; Suen, Ting-Chung; Rollins-Hairston, Aisha; Smith, Kiandra; Armstrong, Ariel; Gray, Cloe; Owino, Sharon; Baba, Kenkichi; Baggs, Julie E.; Ehlen, J. Christopher; Tosini, Gianluca; DeBruyne, Jason P. (2022-07-05). Liu, Andrew C. (ed.). ""The ubiquitin ligase SIAH2 is a female-specific regulator of circadian rhythms and metabolism"". PLOS Genetics. 18 (7): e1010305. doi:10.1371/journal.pgen.1010305. ISSN 1553-7404. PMC 9286287. PMID 35789210.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ Maywood, Elizabeth S.; Chesham, Johanna E.; O'Brien, John A.; Hastings, Michael H. (2011-08-23). "A diversity of paracrine signals sustains molecular circadian cycling in suprachiasmatic nucleus circuits". Proceedings of the National Academy of Sciences. 108 (34): 14306–14311. doi:10.1073/pnas.1101767108. ISSN 0027-8424. PMC 3161534. PMID 21788520.