# Reflection on Biomathematic Lizard Research Essay

## What the Paper Found

The title of the scientific paper analyzed in this report is “The rock-paper-scissors game and the evolution of alternative male strategies” by Sinervo and Lively. Sinervo and Lively studied side-blotched lizards and looked at their throat-color polymorphism.

The polymorphism is visible when the males mature and can be used for territory defense. They described the different colors of the males and how aggressive they are. “Males with orange throats are very aggressive and defend large territories. Males with dark blue throats are less aggressive and defend smaller territories. Males with prominent yellow stripes on their throats are ‘sneakers’ and do not defend territories” (Sinervo 240). Higher levels of aggression are linked to higher levels of testosterone.

Sinervo and Lively estimated male fitness by the number of females that a male monopolizes added to the number of females that he shares with other males. Looking at previously measured data each year from 1991 to 1995, there were significant changes in morph frequency where the population cycled the different colors. In 1991 there was a high frequency of blue, then in 1992 high frequency of orange to high frequency of yellow in 1993 to1994, and back to blue in 1995.

Blue females were lost to the aggressive orange males and it can be seen that the decline of blue from 1991 to 1992 was because the orange males had a higher monopoly of females and were taking the blue males’ females. In 1992 or 1993 no morph had a clear fitness advantage. The decrease in orange males was due to the yellow males because for each orange neighbor a yellow males’ monopoly was increased by 0.23 females and shared females was increased by 0.54 females.

In 1995 orange males lost 0.55 shared females to yellow males. From 1993 to 1995 yellow males decreased in frequency partially due to “lower monopolization of female home ranges by yellow males, compared to blue or orange males” (Sinervo 240). Each blue male during this time period gathered “0.25 shared females for each yellow neighbor” (Sinervo 240). The pattern observed in 1991 returned in 1995.

## About the Biomath

This article is remarkable because many biomathematic papers do not test their theories and equations with actual data. Instead, this paper initially gathered the data about the side-blotched lizards and then developed the model and parameters for this stable lizard three morph system. The mathematics of this paper begins by creating a parameter for morph fitness which is defined as fitness from monopolizing female territories and shared access to females. The fitness is written in a compact matrix form to generate a pay-off matrix describing “the relative fitness of each rare morph in competition with a common morph” (Sinervo 242).

From the data, the authors gathered it is visible that none of the morphs are evolutionary stable strategies, because the morph does not have “higher fitness than the other morphs when it is both rare and common” (Sinervo 242). This characteristic of the morphs was included in the model, creating dynamic oscillations in frequency, which is seen in the data. One last parameter created is “the frequency of the *i ^{th}*morph in the next generation” is determined by “the probability of adult morph survival to the next year and relative fitness of each morph is adjusted by the proportion of new recruits in the next year.

The math visible in the paper is not entirely complicated as it is mostly composed of basic algebra to create the parameters from the data. Many matrices were used to create the model and some of them were left off of the paper, possibly because they could be placed in supplementary material and save space in the article. Matrices are important to modeling populations and the manipulation of the matrices to generate a working model is important. For people very familiar with population modeling some of the math can be left out, but for people with a background up to Calculus II will need to see the manipulations to fully understand how the authors get from the parameters to the model.

Articles found in Nature seem to condense the methodology of the mathematics in biomathematics articles. As seen in class attempting to go through the math step by step with small bits of information from the was used to generate the model makes it slightly difficult to thoroughly understand the mathematics and methodology behind developing the model. For this particular paper, it was extremely helpful having the data in front of us to use to go through the mathematics and theory to verify whether the mathematics was applicable to the known biological data and whether the model applied to the data found between the years 1991 and 1995.

## Conclusion

It is simply amazing how something seen in life can be modeled and better understood as to why it exists. In the abstract, the paper says that multiple morphs challenge evolutionary theory and the yellow, blue, orange side-stripped lizards exist in a stable three morph system when it should be that a single strategy would prevail in the population. Modeling the population and noticing that the yellow, blue, orange morph colors cycle in a specific way due to their specific ways of accessing females is a really solid way to support what happens in nature although it is uncommon and may seem unlikely.