"Science is facts. Just as houses are made of stones, so is science made of facts. But a pile of stones is not a house and a collection of facts is not necessarily science." ~ Jules Henri Poincare, French scientist, author

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I got data! Hooray!!  Now what?

As exhilarating as actually collecting data in the field is, analyzing data in the lab can be just as frustrating.  A lot of the processes that go into analyzing data are rather tedious, and it's quite easy to see where the term "number crunching" came from.  Thankfully with the advent of computers, much of the work has been made easier.

After I had taken pictures of my quadrats in the field, I needed to actually sit down to count mussels and measure their size, which I did by width because no matter how a mussel is situated in a picture, you can always measure it's shell width.  This is what my original pictures of quadrat three looked like:

Left: picture of the whole quadrat

 

 

 

 

 

 

Right: close-up of the center of the quadrat.

 

Can you distinguish where individual mussels start and stop?  Neither could I.  So the first thing I did was to lighten the picture a little, and focus it more.  We ended up with this:

Much better.  Of course, I didn't count mussels using this small a picture.  Click here to view the picture in it's original size, and to read an explanation of how I counted and measured the mussels.

After I had recorded how many mussels were in each quadrat, and the widths of all the mussels, I was ready to start doing some calculations.  First I calculated the density of mussels per meter². Next I calculated the average mussel width for each quadrat.  Finally I put in the tidal height of the quadrats, and began to look for patterns.  A raw data set can look pretty messy with long lists of numbers, rough calculations, and graphs that don't mean anything.  When scientists go to publish their data, they only publish the really important parts, or the figures and tables that show their results most clearly.  I've included a summary of my data and a few important graphs.

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While a table is a nice, organized way to present data, people really have to read it over and think carefully in order to glean any meaningful information out of it.  Graphs are usually the preferred way to present numerical data because they make patterns easier to see.  However, it can be difficult to fit all of the information you want to present onto a graph, so tables are nice to have as references and for clarification.  One of the critical things to notice in this data table is that the tidal height for quadrat 1 is 3m while the tidal height of quadrat 2 is 3.5m.  When I was in the field I put down my first quadrat, and then decided that I wanted to take a sample above it.  So, quadrat 2 was actually higher than quadrat 1.  In the following graphs, I put the quadrats in order of tidal height, so while it may seem counter-intuitive that 2 comes before 1, in actuality it's a better illustration of how mussels are distributed along my transect.

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Figure 1: Graph showing mussel density for quadrats arranged in decreasing tidal height. 

Right away you can see how graphs make patterns easier to see.  In a results section, each graph presented should answer a question, preferably one of the major questions being investigated.  This graph answers the question, "where in the Nahant rocky-intertidal community are mussels most dense?"  There is clearly a peak in mussel density in quadrats one, three, and four, between 2.5 and 3m above the low water line.  In the field I observed that the ascophyllum canopy is also most dense in this area, which provides a lot of protection for mussels.  Between quadrats seven and eight, 1 and 0.5m above the low water line, Chondrus crispus, a shorter, more leafy red algae, becomes the dominant seaweed and no longer provides protection from desiccation, thermal stress, or predators (Bertness, 1999), which is probably why we don't see any mussels present in quadrats 8 and 9.

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Figure 2: Graph showing average mussel shell width of quadrats arranged in decreasing tidal height.  Quadrats 8 and 9 have been removed from analysis since they did not have any mussels present.  Results from Tukey-Kramer ANOVA are also displayed, denoted by letters.  Levels not connected by the same letter are significantly different.

The question this graph answers is, "Where in the Nahant rocky-intertidal community do mussels have the widest (largest) shells?"  Mussels seem to have the largest shells in quadrats three, four, five, and six, between 2.5 and 1.5m above the low water line.  By comparing this graph to the one in Figure 1, we can ask the question, "Do mussels have larger shells when there is a higher or lower density of them?" Looking at quadrats 3 and 4, it appears that mussels have larger shells in conjunction with higher densities.  We call this a positive correlation between density and shell size.  Looking at every other quadrat, however, it appears that there is a negative correlation between density and shell size, or that mussels have larger shells in conjunction with lower densities.  Which is it?  Does density have an effect on mussel size?  To answer that question we need to run a regression analysis (Figure 3).

The other information displayed in Figure 2 are the results of a one-way ANOVA test.  ANOVA stands for analysis of variance and it is a statistical test that can answer the question, "Are there significant differences in this group of data."  In this case, we want to know if there are significant differences in mussel size between quadrats.  If there are significant differences, it would be interesting to find out why, or what factor (or set of factors) is influencing mussel size.  Quadrats with different letters from one another are statistically significant in their differences.  This means that quadrat 3 has significantly larger mussels than quadrats 1,2,4,6, and 7, and quadrats 1 and 4 are significantly different from one another.  This is rather interesting since quadrats 1, 3, and 4 have the highest densities of mussels (Figure 1).  Could density be having an effect on the shell sizes of mussels?  Again, to answer this question we need to look at a regression plot (Figure 3).

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Figure 3: Regression plot showing the relationship between size and density. R²=0.403 and p<0.0001

A regression plot answers the question, "Is there a relationship between these two variables?"  In this case we want to know if there is a significant relationship between mussel density and size.  Surprisingly, this graph shows a positive relationship, indicated by the slope of the red line.  Regression plots are always reported with the R² value and p-value.  The R² value tells us how strong the relationship we see is.  An R² value of 1 would mean a very strong relationship, or that mussel size is entirely dependant on mussel density.  For this regression, R²=0.403, which means that about 40% of the variance (difference) in shell size can be accounted for by density. The p-value tells us how significant the relationship is.  When we perform a regression analysis, what we are actually doing is testing a null hypothesis.  In this case, our null hypothesis is that mussel density has no effect on mussel shell size.  Our p-value tells us whether we can accept or reject this hypothesis.  Generally, p-values less than 0.05 are accepted as statistically significant and indicate a rejection of our null hypothesis.  In this case the p-value is less than 0.0001.  This is a very significant result and allows us to reject the hypothesis that mussel density has no effect on mussel shell size, and accept our alternative hypothesis (which is simply the converse of our null hypothesis) that mussel density is having some effect on mussel shell size.  Based on all of the data gleaned from this regression plot, we would expect that the more dense a mussel bed is, the larger the mussels in that bed will be.  This result is in opposition to previous data.  According to Petraitis (1995) there is a strong negative correlation between body size and density for mussels.  However, my results can only account for 40% of the variation seen.  That means that something else, or a combination of other factors, is influencing the difference we see in shell size by 60%.  Probable factors are things we already know affect the life of mussels in the rocky intertidal; predation, competition for resources, desiccation, wave, and thermal stress.  We would have to design further experiments to investigate these other factors in order to get a look at the big picture and find out exactly what is effecting mussel size at Nahant.

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Doing Work In the Lab

 

 

Ecology of Disease Vector class working with mosquito larvae in Bermuda

 

 

 

 

Analyzing pictures and putting together web pages in the computer lab.

 

 

 

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The Cycle of Science

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