Danielle Clements- Ecological Modeling

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Dec 6, 2023

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Name:_____________________ Ecological interactions and evolution: Frequency dependent selection Turn in BOTH the completed excel sheet and this document on Blackboard! You should have the table filled out and one graph for each data sheet with the appropriate labeling. Ecological interactions among individuals (territorial defense, predator-prey relationships) strongly influence fitness, and so the traits that influence the outcome of these interactions are important targets of selection. Mate choice by females is an important interaction that is usually influenced by behavioral and morphological characteristics of males. How do we determine which traits of organisms are most important for fitness? One useful approach is to first obtain information on the relationship between variation in traits and variation in fitness. First, we graph the data before using mathematical models to establish relationships between variables. Good models allow scientists to see if the predictions of a model can be applied to different populations or to different environments. If they do not apply in other systems, this can tell us that we need to know more about how the system works and so inspires additional research. This module introduces the use of simple mathematical models in biology. The context of the model is to understand the role of negative frequency dependent mate selection in maintaining phenotypic variation in populations. In this, certain alleles might be favored when rare, but not favored when common! As you have learned, if this phenotypic variation has a genetic basis, then this variation provides the raw material for adaptive evolution. Lab Exercises – Part I In a species of cichlid fish, males can have either yellow or red fins that they use in displays to attract mates or defend their territories. The frequency of each color varies by population, but both fin colors are present in each population and individual fish cannot change their fin color. In the following activities you will test the hypothesis that the maintenance of both fin colors in populations is due to a type of balancing selection known as negative frequency dependent selection. According to this hypothesis, the fitness of fish with red fins is greater when fewer males have this trait (when more males have yellow fins). Similarly, the fitness of yellow fins is greater when fewer males have this trait (when more males have red fins). To test this hypothesis, the biologist set up several experimental pools with cichlids in which the frequency of males with red fins was controlled and recorded the offspring data. Please remember that we arbitrarily chose to track red fins - there is no inherent difference between the two colors, it’s only about how common each is. Observation (i) Number of Red Males per 100 Individual Fish (x) Average Number of Offspring per Red Male (y) 1 8 325 2 11 380 3 13 337 1

4 15 248 5 19 147 6 23 103 7 27 152 8 33 175 9 35 153 10 44 79 Instructions: Activity 1: Work Individually! Graph a SCATTER PLOT of the data in the table above on a sheet of paper. You can either PRINT THIS PAGE OUT AND DRAW IT BY HAND, then ATTACH A PICTURE OR you can USE THE DRAW FUNCTION TO DRAW ON TOP OF THIS GRAPH . We want to know how the relative frequency of red-finned males in the population affects fitness (the number of offspring per red-finned male). Please be sure to include axes labels and units, a title, and a trendline. X = Number of red males per 100 fish Y = Average number of offspring per red male 1. Draw a straight line through the data that you think best fits the data points (is as close to as many of the data points as possible. This is a linear model of your data. 2

2. Using the formula for a line (y = mx + b) determine the equation for your model by hand by choosing two points on your line and write it below (it’s obvious when students don’t do it by hand!) ___________________________________________________ 3. Using the equation you came up with, describe in words below how the frequency of male red finned fish in the population influences the fitness of red finned males in that population. Use the exact value of the slope from your model when describing this relationship (ex: For every red male added to the population, fitness….) Now that you have your model, it can be used to predict the number of offspring per red male (Ŷ) when the number of red males per 100 individuals varies (see instructions below) Looking at your graph, notice that the data points do not all fall on the line you drew. The distance that an observation at each value falls from the line you drew on the paper is what we term "error" (Figure 1). In a linear model, the line through the data that best explains, or fits, the data is the one that the observed data points are closest to and so has the lowest values of error across the range of data. We can evaluate how well a line fits the data by adding up (summing) the errors for all the data points. However, some errors may be negative (i.e. data points that fall below the line) while others are positive (some points will be above the line). So to evaluate how well a line (or linear model in this case) fits the data we first square the value of each error to get rid of the negative values and then sum these values for all data points. This procedure is formally described by the following where the "error sum of squares" is the summation of all of the (Y i – Ŷ i ) 2 values for every observation. N is the total number of observations. So now we can say the model that best explains the data is the one with the least sum of squares error. 3 ErrorSumOfSquares = ∑ i = 1 n ( Y i − ^ Y i ) 2

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Activity 2: Please remember we’re simply using red at random. The yellow morph experiences the same fitness changes as the red, just at the opposite times. For either morph, when they’re rare, the fitness is higher. There are only two morphs, so when red is rare, yellow must be common, and vice versa. 4. Open the Excel file entitled "Frequency dependent data", click on the "reproductive success" worksheet and edit the formula in cell C5 to reflect your equation (replace the m and b variables in that formula with the numbers you got for m and b from your equation). Copy cell C5 into the remaining cells in column C by dragging the square in the lower right corner to the rest of the cells. Then copy the formula in D5 (have a look at this formula and make sure you know what it is doing) into the remaining cells in column D. Next copy the cell E5 into the remaining cells in column E. 5. As a group: Compare the sum of squared error terms that each of you got for your line. Which member of your group had the "best fit line" and what was the equation and sum of squares? Student name ____________________________________________ Model equation __________________________________________________ Sum of Squares ___________________________________________________ 6. We can use Excel to calculate the best fit line for us, but now you know how it's done by hand! To do this, select the data (from A:5 and B:5 to A:14 and B:14). Now go to Chart (or insert Chart, depending on what version of excel you are using) and use the scatter plot option for your graph. Click on the actual data points in your chart and go to the drop down box under chart and "Add trend line" using the "linear" option and also use the option to "display equation on chart". (You may have to google how to do this for your version of excel, this is how it works on the one I'm using). What is the equation for the line that excel found? Save this graph to be turned in. It should include axes labels and units, a title, and a trendline with an equation. _____________________________________________________ 7. Explain the results of the model in the context of the original hypothesis. Does the data support the idea that the fitness of red (or yellow) finned males depends on how common red (or yellow) finned males are in the population? 4

8. What is the relationship between the frequency of red (or yellow) finned males and the fitness of red (or yellow) finned males? 9. How would you expect the frequency of red and yellow color morphs to change across generations if these colors were genetically determined? That is, an inheritable gene controls color rather than it being related to food, habitat, environment, randomness, etc. 10. Would you expect red or yellow alleles to ever become fixed or lost in the population? Explain. Activity 3 11. Click on the spreadsheet entitled frequency of red-finned morph. The data shown are the frequency of red finned males through time. Plot the data as you did earlier using the scatter plot graphing option and fit a line to the data. Save this graph to be turned in and, as always, include labels, units, and a descriptive title. 12. Explain in words exactly what is happening in this graph (using the terms "change in allele frequency", "time", "frequency dependent selection" and "fitness"). 5

13. Thinking about what might be happening in nature, why do you think the frequency of red finned males is changing over time in the way that it is - Do you think it's all due to mate choice? Assuming it is, why do you think female preference shifts between yellow and red? Do not anthropomorphize the fish (if your explanation sounds like it could be about humans, you’re probably doing this). 14. What would be a non-mate choice explanation? Turn in the completed excel sheet and this document to Blackboard by the end of your section! You should have the table filled out and one graph for each data sheet with the 6

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appropriate labeling. 7

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