Wednesday, January 7, 2015

Sara's Fast Plant Mini Lab Report

The Effects of Artificial Selection on Fast Plants

Calculations & Statistical Analysis:
Figure 1:
For this experiment we measured all of the individual leaf lengths for each plant and calculated the average leaf length for each plant. A histogram of the average leaf length of all the plants  was created with a sample size of 57(figure 1).  The graph is not a bell curve shape but, instead is skewed.  The histogram shows that most of the plants have an average leaf length from 4mm to 10mm. The histogram also shows that there were a few plants that had extremely high leaf lengths of 18mm and 20mm. With the average leave lengths mostly being below 10 mm caused for the skew shape of the graph (Figure 1).  The average  length of the parent population is 8.84 mm and the median is 8.5 mm. The SEM was about .45 and a standard deviation of about 3.39 which, would have caused the the histogram to appear skewed.   The 95% CI is 7.94 to 9.74 which, would have contributed to the histogram to be skewed due to the spread of the data(Figure 1). 



Figure 2: 
  As a class we decided to select for plants with an average leaf length of 12 mm or higher therefore, we cut the plants who did not fit that criteria. We ended up with 8 plants as survivors after the selection (shown in Figure 2). The graph is not a bell curve just like the graph of the population before the selection (Figure 1 and 2).  The shape changed due to the change in the data. The mean of the data is 13.88mm and the median is 13.75mm which, would have caused the graph to shift.  The standard deviation is 1.26 which, shows that there was not much of a fluctuation in the data in Figure 2. However, the P generation had a higher standard deviation which, shows that there was more spread of data (as shown in Figure 1). The SEM was 0.45 and there was a 95% CI of 12.98 to 14.78.  This 95% CI of the survivors was not significantly than the 95% CI of the P generation since the two do not overlap each other (Figures 1and 2).

Figure 3: 
The last set of data collected was the average leaf length for all of the plants in the next generation.  This data was collected on Day 9 after planting of the first generation of offspring of the survivors. We did the same thing we did the other two times we had collected data which, was measure all the leaves per plant and then average the length of those leaves.  Then those values were graphed in a histogram.   This histogram is more of a bell curve shape but, slightly more to the left side.That would be because there were more plants with average leaf lengths that were lower. The mean of the average leaf lengths is about 6.5mm and the median of the the data is 6.3mm (Figure 3).  The histogram shows that most of the plants had an average leaf length from 6 mm to 7.5 mm ( Figure 3). There were only few that had an average leaf length from 10.5 mm to 12mm.  There was a standard deviation of about 1.81 with a SEM of about 0.31.  Compared to the survivors (Figure 2) the standard deviation for the F1 generation is higher which shows that there was more of a spread of data because there are more plants that were planted.  The 95% CI is 5.83 to 7.09 and it doesn’t overlap the 95% CI of the survivors (Figure 2) which, means that they are not significantly close to each other.  The F1 95% CI does overlap the P generation (Figure 1) a little which, means that they are significantly close to each other.







   Discussion:
Conclusion:
The experiment conducted relates to the evolution domain in the course and specifically with artificial selection.  By doing this lab I was able to see that artificial selection sometimes doesn’t always mean that the trait selected for is not necessarily a gene that is passed down from generation to generation rather it is a random trait. That is based off the evidence shown in the F1 generation (figure 3) with the mean being lower than the survivors after the selection (figure 2).  Also with the 95% CI not overlapping it showed that they were not significantly close.  If the trait was able to be passed down the two 95% CI should overlap due to the fact that the points in the F1 generation would be higher since the average leaf length would be higher. Also that the lengths would be similar to those of their parents since that is where the trait came from.  As shown in Figure 3 the average leaf lengths of the plants are mainly low and few are 12mm or higher unlike the average leaf lengths in Figure 2.   Therefore, based on that data the results did not turn out the way I had hypothesized.   Some limitations in the experiment could have lead to the results to be different from expected.  One limitation would be keeping the plants 10 cm from the light that was provided.  We used textbooks to regulate the distance but, once the plants grew and one textbook was removed it was hard to keep the plants at the right distance.  Reason being that by removing the last textbook would make the plants too far away from the light and the textbook kept the plants a little too close as well.

Experimental Evaluation: 
However, errors could have altered the outcome of the experiment.  For instance, we might not have measured the plants on the wrong day from what the experiment called for.  This could be due to there not being enough time in class to do so or forgetting or the 9th day which the leaves were suppose to be measured fell on a weekend.  That would lead to the leaves being able to grow a little longer which, made the averages bigger.   Another error would be the measurements of the leaves could be off and the math done for the averages could have been wrong as well which, would have lead to altered data.  Therefore, leads to different results.  Lastly, when cutting the plants that didn’t have an average leaf length of 12mm or higher could have been a source of error because too many could have been cut which, leads to a different amount of survivors.  The fact that no one had recorded the number of survivors is an error because when doing final calculations knowing the exact number of survivors would have lead to more accurate results.  If this experiment was done over then the math would have been done twice to ensure accuracy and the measuring could be done by two people as well for the same reason.  The cutting of the plants would have also be done more carefully by making sure that the right ones are being cut by double checking the data collected. Then recording the number of the survivors in order to have the correct amount in order to have more accurate calculations in the end.  Lastly, in regards on keeping track on what day of the experiment we were on would be done better in order to make measurements and steps are done at the right time in order to make sure that more accurate data could be collected.
     

Monday, December 1, 2014

Chigozie's Cell Size and Diffusion Argumentation

Cell Size and Diffusion Argumentation
       Almost all living cells depend on the process of diffusion to obtain essential nutrients that are needed for survival. As these nutrients are taken in by the cells, they are broken down. The resulting energy and molecular building blocks from the nutrients are used to make more cellular components. Because of this, a cell would grow by increasing in size. However, cells never get too big; they are always small. So, why are cells so small? In this lab, my lab group and I worked towards answering this one question. We were given two potential answers to this question. Explanation 1 stated, “Cells that have a larger surface area to volume ratio are more efficient at diffusing essential nutrients”. Explanation 2 stated, “The rate of diffusion is related to cell size. Nutrients diffuse at a faster rate through small cells than they do through large cells. After collecting and analyzing data with my lab group, I concluded that although our data seemed to support both explanations, Explanation 2 was more valid.

My lab group and I tested the validity of these different explanations by constructing a model cell using agar. Agar is a gel-like substance that we could easily manipulate and cut into a variety of shapes. In this lab, phenolphthalein (a chemical indicator that changes color when it comes in contact with an acid) was added to agar so that we could see how far the acid (in this case, vinegar) diffused into the model cell. The agar was blue and would turn a yellowish-clear color when the phenolphthalein in it came in contact with the vinegar. My group cut four different rectangular prisms from the agar. Two were relatively small, and two were relatively big. We measured the dimensions of the cubes and then placed them in a plastic container filled with vinegar.

Rectangular Prism Dimensions Before Diffusion

Rectangular Prism
Length
Width
Height
1 (Small)
2 cm.
2 cm.
1.5 cm.
2 (Big)
3.5 cm.
3.5 cm.
1.7 cm.
3 (Big)
3.5 cm.
3.5 cm.
1.6 cm.
4 (Small)
1.9 cm.
1.9 cm.
1.5 cm.

Rectangular Prisms of Agar before diffusion
 

We started timing the diffusion process with a stopwatch as soon as the cubes were placed in the vinegar. The cells began to change color (from blue to yellowish-clear) at approximately 7.3 seconds. We left the rectangular prisms in the vinegar for as long as time permitted us, which was 32 minutes and 9 seconds. At this time, we pulled out the rectangular prisms. Because of this time restriction, the vinegar was not able to diffuse all the way through the rectangular prism and we had to measure the dimensions of the part of the rectangular prism that the vinegar had not touched.

Dimensions of the Rectangular Prism Not Touched by Vinegar

Rectangular Prism
Length
Width
Height
1 (Small)
1 cm.
0.8 cm.
0.7 cm.
2 (Big)
2.5 cm.
2.5 cm.
0.5 cm.
3 (Big)
2 cm.
2.5 cm.
0.9 cm.
4 (Small)
0.9 cm.
0.5 cm.
0.5 cm.

Rectangular Prism after diffusion
 

            Afterwards, my lab group and I calculated the diffusion rates. Instead of just averaging the dimensions (length, width, height) and putting that average distance over time to find the rate, we had to find the dimensions of the space that had been touched by vinegar since the vinegar did not diffuse all the way through the rectangular prism. Mr. Hammer helped us greatly with the visualization and explanation displayed below. In order to find the dimensions of this space, we had to take the dimensions of the rectangular prism not touched by the vinegar, subtract it from its respective dimension of the original rectangular prism, and divide by two. For example, if the original length was 14 and the length of the rectangular prism not touched by vinegar was 5, we would do 14-5, which is 9, and divide by 2 and get 4.5 as one of the new dimensions that we will use to find the rate of diffusion.

How to Calculate the Sides Needed for the Calculation of the Rates of Diffusion

Side one= (original length minus non-diffused cube length) ∕2

Side two= (original width minus non-diffused rectangular prism width) ∕2

Side three= (original height minus non-diffused rectangular prism height) ∕2

Mr. Hammer's very useful diagram
 

Results of Calculations of Sides Used for Rates of Diffusion Calculations

Rectangular Prism
Side One
Side Two
Side Three
1 (Small)
0.5 cm.
0.6 cm.
0.4 cm.
2 (Big)
0.5 cm.
0.5 cm.
0.6 cm.
3 (Big)
0.75 cm.
0.5 cm.
0.35 cm.
4 (Small)
0.5 cm.
0.7 cm.
0.5 cm.

           

To find the rate of diffusion, we had to divide total distance travelled by the vinegar into the rectangular prism by the total amount of time the rectangular prisms spent in the vinegar. First, we had to average out the dimensions of in the table above for each rectangular prism (sum of length, width, and height divided by three). We then converted the total time, 32 minutes and 9 seconds, into seconds and got 1929 seconds in total. We divided each average dimension by 1929 seconds, the total time, to get the rate of diffusion for each rectangular prism.

Rates of Diffusion for Each Rectangular Prism

Rectangular Prism
Average Dimension
Rate of Diffusion
1 (Small)
.5 cm.
.000259 cm/sec.
2 (Big)
.53 cm.
.000276 cm/sec.
3 (Big)
.53 cm.
.000276 cm/sec.
4 (Small)
.57 cm.
.000294 cm/sec.

           

My lab group and I also calculated the surface area, volume, and ratio of surface area to volume.

All Calculations

Rectangular Prism
Surface Area (SA)
Volume (V)
Ratio of SA to V
Decimal Representation of SA to V Ratio
Rate of Diffusion
1 (Small)
20 cm.2
6 cm.3
10 : 3
3.33
.000259cm/sec.
2 (Big)
48.3 cm.2
20.825 cm.3
48.3 : 20.825
2.32
.000276cm/sec.
3 (Big)
46.9 cm.2
19.6 cm.3
46.9 : 19.6
2.39
.000276cm/sec.
4 (Small)
18.6 cm.2
5.415 cm.3
18.6 : 5.415
3.43
.000294cm/sec.

 

After analyzing all of this data, I concluded that Explanation 2 was more valid. Again, Explanation 2 states, “The rate of diffusion is related to cell size. Nutrients diffuse at a faster rate through small cells than they do through large cells”. At first, it looked like the data that we collected supported both explanations. Explanation 1 states, “Cells that have a larger surface area to volume ratio are more efficient at diffusing essential nutrients”. For Explanation 1, the rectangular prism with the largest surface area to volume ratio also had the highest rate of diffusion. However, rectangular prism 1 refutes this statement because it has the second largest surface area to volume ratio but the lowest rate of diffusion. For Explanation 2, the smallest cell (rectangular prism 4) had the fastest rate of diffusion. However, the other small cell (rectangular prism 1) also had the slowest rate of diffusion, so that rectangular prism also disproved Explanation 2. Because of this, I decided that rectangular prism 1 should not be totally considered for this conclusion. It is the only rectangular prism that refutes both explanations. After taking all of this into consideration, I noticed that the surface area to volume ratios for rectangular prisms 2 and 3 are different, but their rates of diffusion are not. One would expect them to have different rates of diffusion since their surface area to volume ratio is different. However, they have the same rate of diffusion. Because of this key piece of evidence, Explanation 2 is more valid. Rectangular prism 2 and 3 are both the two pieces of agar that we made relatively big, so they support Explanation 2 in that the bigger cells have the same rate of diffusion and also a lower rate of diffusion than that of the smallest cell.