# CURM page of Katie Jones

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## Progress

Final Models for Paper

Figure 3

The prey loads varied greatly between the two locations ranging from 0.25 to 2.5 times the weight of the wasp (Fig #). The wasps in Newberry are small and therefore constrained from provisioning with large cicadas. They almost exclusively carry prey loads that are below their own weight. This is illustrated by the data points below the line of slope = 1. The wasps in St. Johns are larger as well as the cicadas they provision with. The majority of their prey loads are between 1.5 and 2.5 times their own weight. Of the wasps that provisioned with medium cicadas, the smaller wasps had higher prey loads. This suggests that if they were slightly smaller the prey load for carrying a medium sized cicada may exceed their limitations and they would then be constrained to carrying small cicadas such as the situation in Newberry. In fact, the smallest wasps in St. Johns provisioned with small cicadas. This is in support of our hypothesis that the wasps are selective based on size.

Wasp RWL vs Mass

This is a a scatterplot of wasp wet mass in relation to the wasp right wing length. The fitted model was obtained by taking the log of the dependent and independent variables and then performing linear regression on the tranformed data. The following is the results of the linear regression:

```Residuals:
Min        1Q    Median        3Q       Max
-0.271383 -0.082922 -0.001699  0.076912  0.345395

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.18820    0.13692  -30.59   <2e-16 ***
lnWaspRWL    3.27061    0.04234   77.25   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1173 on 403 degrees of freedom
(30 observations deleted due to missingness)
Multiple R-squared: 0.9367,     Adjusted R-squared: 0.9366
F-statistic:  5968 on 1 and 403 DF,  p-value: < 2.2e-16
```
Cicada RWL vs Mass
Stair-step Model

Thirtieth Meeting

 In Joseph Coelho's article called "Sexual size dimorphism and flight behavior in cicada killers, Sphecius speciosus", there is a dicusses on how once wasp size reaches a certain point, the wasp's wing growth starts to slow down. Therefore larger wasps have relatively short wings. We decided to examine this in our data. I ran a series of linear regressions on wasp mass vs. wasp RWL incrementing the number of data points I included. In looking at the coefficents of the power model (Power Model Coefficents), we see opposite of what we expected. Instead of the coefficent getting larger, it seems to be getting closer to 3.

Week 13

### Allometric Relations Between RWL and Mass

 Cicada species RWL-to-Mass equation conversion, x = RWL(mm), y = mass(mg) Ne.h. ${\displaystyle y=0.186096x^{2.288178}}$ D.o. ${\displaystyle y=0.030435x^{2.860248}}$ T.g. ${\displaystyle y=0.000362x^{4.104761}}$ T.b. ${\displaystyle y=0.043232x^{2.785633}}$

Week 12

 I worked on the kernal smoothing of the wasp RWL vs. the cicada RWL plot using different bandwidths and the "normal" kernal. Here are my results using bandwidths 2.7, 2.9, 3.2, 3.4 respectively: I also tried the kernal smoothing using the "box" kernal, but my results were not as successful. The following was the best results with a bandwidth of 4.
 I recreated the scatter plot of the cicada RWL vs. cicada wet mass after deleteing one of the wet mass values that looked like an invalid data entry. (It was a cicada wet mass of 15.01 mg and a cooresponding RWL of 41.68.) The results from the regression fit done by log transformation does not look like a good fit.
 I looked at each cicada species separately and plotted their RWL vs. wet mass and did a regression fit for each using log transformations. Here are the results for the four different cicada species:

Week 11

 I created a scatter plot of the cicada RWL vs. cicada WetMass and fit a power model to the data using natural log transformations. The power function is: ${\displaystyle y=0.0149563757*x^{3.0596013}}$ (Data for cicada fit)
 I performed lowess smoothing on the wasp RWL vs. cicada RWL in minitab. In this graph I used a binwidth of .21. I successfully downloaded R and figured out how to load data sets into R. I figured out how to use the ksmooth option in R, but I do not have a finished graph.

Week 8

I created several different bar graphs for the grouped wasp RWL vs. the mean cicada RWL using different bin widths. The bar graph below in the center appears to be the smoothest graph which has a bin width of 1.5.

>

Week 6-7:

The histogram on the left represents the frequencies in groups of wasps grouped in 1 unit intervals. The bar graph on the right represents the mean cicada right wing length for each group of wasps.

The image above on the left comes from Dr. Hastings's powerpoint presentation. I was able to reproduce the graph and my goal is to fit a power function to the data.

I am using linear regression to find a non-linear fit to this data. I calcluated the natural log for both the RWL and WetMass data sets and found the best fitting line to be: ${\displaystyle ln(y)=-4.1881995+3.2706125*ln(x)}$. Converting this to a power function gives: ${\displaystyle y=0.01517358*x^{3.2706125}}$

Week 5:

The graph on the left is the right wing lengths of the wasps vs. the cacadas. (Data) I calcuated the mean cicada size for the wasps that brought back more than one cicada and thus had more than one data input in the excel file. This graph is on the right. (Data)

Week 1:

I downloaded Miktex and have been playing around with that. I used the following link as a reference: [1]

I read about Career Options in Mathematics [2]