Math 124: Paper 1

This paper is based on an article by Patrick Krug.1. This article is meant for bioscientists; reading the whole report is surely useful in all sorts of ways, but it’s a bit technical and only the information I extract below matters for your paper.

Synopsis: Sea slugs, which live along the Southern California coast, produce thousands of microscopic larvae each year. These larvae locate and settle onto a patch of vaucherian seaweed, before developing into sea slugs. This study looked at the ability of sea slug larvae to detect this kind of seaweed at different tide heights. We think that instead of randomly swimming until they find this seaweed (as was previously believed), these larvae actually ”smell” the seaweed when they are passing over it in the water. They do this, it is believed, by detecting chemicals that slowly leach out of the seaweed. This study attempts to support this theory by analyzing the ability of larvae to distinguish the smell of this seaweed just as the tide is coming in – when the chemicals are most concentrated – and at high tide – when the chemicals are more dilute due to the rising tide.

Methods: Just before the tide came in, one water sample containing filtered sea water was collected away from the patch of seaweed. This sample is the control (it is coded 99). Once the tide washed in, water samples were collected above a patch of vaucherian seaweed every five minutes, for a total of thirty minutes. Each of these samples was then divided into six, so that there are six replicates for each time point. There are seven time points (0-30 minutes) so there are a total of 42 observations, excluding the control. The control was divided into five replicates.

Fifteen slug larvae were then injected into each of the replicates, and the proportion of larvae that metamorphosed was recorded. This proportion is a function of the ability of the larvae to detect the chemicals from the seaweed.

The data from this study have been sent to you in csv format and can be seen in plain text on the second page of this assignment. It should be easy to open it with any spreadsheet program if you want to use one. The data are small and simple, however, so hand calculation should not be an issue.

You need to address the questions below in your essay. The questions should NOT be answered separately; rather, your essay should answer all of these (and more) in a comprehensive analysis of the data. You should keep in mind that this is a study based on a selection of information; utilize the inferential techniques we have covered. Please make sure you work with others to read over your work so as to ensure clarity. I encourage you to work with other students in class and collectively come to understandings of the material. Do not consult anyone outside of our course and, of course, make all answers your own. Your answers should be printed rather than handwritten. If this presents a problem for you, please let me know. Also, please attach handwritten calculations and notes for each question if you think seeing your reasoning and work will help me interpret what you have done.

There are a number of different ways to approach the questions below reasonably. Different approaches have different strengths and weaknesses; you should grapple with this before setting about analyzing the data. Even though there are multiple reasonable ways to approach these questions, there are many more unreasonable ways to analyze the data. In other words, while there might be multiple correct “answers” the questions below, there are many more wrong answers.

Questions

The central question your paper needs to address is whether or not the evidence supports the idea that seaslugs “smell” vaucherian seaweed. In addressing this question, your paper should:

1. use univariate descriptive statistics to summarize data within the eight groups,
2. utilize appropriate inferential statistics to extend sample data to general claims, and 3. use graphics to illustrate the relationships you describe in numbers and text.

1Krug, P.J. and R.K. Zimmer. 2000b. “Larval settlement: chemical markers for tracing production, transport, and distribution of a waterborne cue.” Marine Ecology Progress Series, vol. 207: 283-296.

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