On 27 March 2015 an article appeared in Science Advances (SA) about the bright plumage of birds. A summary of the article is found in Science News (SN). I quote from both articles. This analysis is an example of a possible abduction outline from this article.

Initial Observation

Some birds have very colorful plumage.

Preliminary Conditions

There are two theories posed to explain how bright plumage came to be:

A₁: Natural Selection. "Bright colors stood out to predators as the birds protected their nests, so the birds that blended in to their surroundings survived." (SN)
A₂: Sexual Selection. "The bright colors of the male’s tail attracted females." (SN)

Each of the theories could explain the initial observation (as described above).

Both of these theories satisfy at least half of the criteria for a scientific theory and therefore have scientific merit as is shown by the following tables (the criteria, #1, #2, etc., is given in a previous section).

Criteria	Condition Met?	Rationale for the Natural Selectiion Theory
#1	yes	The theory is not complicated and has no inconsistencies
#2	yes	No fundamental principles are violated.
#3	yes	This theory explains the initial observation.
#4	yes	The theory applies to the area of investigation and does not go far beyond.
#5	yes	Competent, well-known researchers put forward the theory.
#6	no	No information about this.
#7	no	No math is mentioned.
#8	yes	No outside agenda is known.

Criteria	Condition Met?	Rationale for the Sexual Selection Theory
#1	yes	The theory is not complicated and has no inconsistencies
#2	yes	No fundamental principles are violated.
#3	yes	This theory explains the initial observation.
#4	yes	The theory applies to the area of investigation and does not go far beyond.
#5	yes	Competent, well-known researchers put forward the theory.
#6	no	Not known.
#7	no	Not known.
#8	yes	No outside agenda is known.

Data (All of the data is from the Science Advances article.)

D₁: Across species, males increased in brightness and hue at a greater rate than did females.
D₂: There was often more variation in plumage color within a sex than between them.
D₃: There was greater variation in male hue than in sexual dichromatism in hue and female hue was not more variable than sexual dichromatism in hue.
D₄: There were more evolutionary transitions in brightness to monochromatism (that is, both sexes were dull, medium, or bright) than to dichromatism.
D₅: Evolutionary transitions were equally likely to result in increases or decreases in brightness by one or both sexes.
D₆: Transitions to monochromatism were equally likely to come from changes in males or females.
D₇: Evolutionary changes in hue were also more frequent toward monochromatism than dichromatism, and again, transitions were equally likely to result in increases or decreases in hue by one or both sexes.
D₈: Transitions toward monochromatic hue were also equally likely to come from changes in males or females.
D₉: Similar changes in the color of both sexes (that is, toward both dull or both bright) were primarily related to indices of natural selection.
D₁₀: Changes in one sex (leading to sexual dichromatism) were related to indices of both sexual and natural selection.
D₁₁: In these 489 monochromatic species, brighter plumage was associated with migratory behavior, breeding in the subtropics, semiprecocial young, male parental care, and open (noncavity) nests (table S2).
D₁₂: Duller plumage in both sexes was associated with sedentary behavior, breeding in the tropics, altricial young, lack of male parental care, and cavity nesting.
D₁₃: Plumage with more UV/blue/green reflectance in both sexes was associated with larger body mass, sedentary behavior, semiprecocial young (that is, gulls with white UV-reflecting plumage), male parental care, and nesting in trees (table S2).
D₁₄: More red/orange reflectance (lower PC2) in the plumage was associated with smaller body mass, migratory behavior, altricial young, lack of male parental care, and nesting on the ground.
D₁₅: Sexual differences in brightness and hue were associated with changes in male plumage across mating systems, and not to changes in female plumage.
D₁₆: Dichromatism in hue was greater in species with relatively larger testes, a correlate of sperm competition.
D₁₇: Female plumage changed according to nest height to decrease predation when the male didn't provide "child care". The colors of those males did not vary in brightness or hue in relation to nest height.

Evaluation Chart

	Natural Selection	Sexual Selection
D1	no	yes
D2	yes	no
D3	no	yes
D4	yes	no
D5	yes	no
D6	yes	no
D7	yes	no
D8	yes	no
D9	yes	no
D10	no	yes
D11	no	yes
D12	yes	no
D13	yes	no
D14	no	yes
D15	no	yes
D16	no	yes
D17	yes	no

Result

From this data (Natural Selection - 10, Sexual Selection - 7), the Natural Selection theory would be the better theory between these two options according to this analysis. Here is what the authors of the study concluded:

"This suggests that natural selection has been the most important source of selection on plumage color in monochromatic species, and thus, bright colors in both sexes are unlikely to be due to a correlated response in females to sexual selection on male plumage. Overall, both natural and sexual selection have influenced the evolution of bird coloration, but in many respects, they have acted on two different axes: sexual selection on an axis of sexual differences and natural selection on an axis of color (for example, dull or bright) in both sexes. Thus, debate about the causes of variation in bird coloration may be resolved by recognizing that natural and sexual selection have generally acted on two different axes."