Lesson objectives the different types of variation To include intraspecific and interspecific variation AND the differences between continuous and discontinuous variation, using examples of a range of characteristics found in plants, animals and microorganisms AND both genetic and environmental causes of variation. An opportunity to use standard deviation to measure the spread of a set of data and/or Student’s t-test to compare means of data values of two populations and/or Spearman’s rank correlation coefficient to consider the relationship of the data.

Variation The presence of variety (of differences between individuals)

Variation within species

Variation between species Usually obvious. Variation used to classify one species from another.

Continuous & Discontinuous Continuous variation: A full range of intermediate phenotypes between two extremes. Discontinuous variation: Discrete groups of phenotypes with no or very few individuals in between

What causes variation?

Inherited / genetic variation Genes (inherited from parents) Alleles (versions of these genes) Sexual reproduction – random shuffling of alleles – new combinations of parental alleles in offspring Mutations – “mistakes” in the DNA change base sequence and may bring about a new version of the gene (i.e. a new allele)

Mutations When cells divide they need new chromosomes to fill the nucleus. The chromosomes replicate and sometimes a mistake is made, causing a change in a gene on that chromosome. This is called a mutation. We all inherit some mutations but usually we aren’t aware of them as we have 2 copies of each gene.

Can mutations have other Causes? Radiation can increase the number of mutations. This includes any high energy rays such as ultra violet X rays Ionising radiation Some chemicals can also lead to mutations such as Mustard Gas which has been used in chemical warfare.

Are Mutations Always Bad? Mutations provide variation For the individual mutations can be bad, good or neutral. Without them there would be no differences between individuals, and this would mean everyone would be equally likely to survive or die. Mutations create variation which leads differences in success at surviving which leads to natural selection and therefore the possibility of evolution.

Attached earlobes (recessive Free earlobes (dominant)

Environmental causes of variation

A combination of both? Environmental and genetic variation are linked. E.g. Height Not all genes are active at any one time. Changes in the environment affect which genes are active.

Question to try: For each of these examples of variation between sunflower plants, suggest whether they are caused by genes alone, environment alone, or an interaction between both. The height of the plant The colour of the plant petals The diameter of the mature flower The percentage of seeds that develop after fertilisation

Look at the following data 50 petals for the flowers of a rush (Luzula sylvatica) 3.1 3.2 2.7 3.0 3.3 2.9 3.4 2.8 3.5 Calculate the mean petal length of this sample Count up the number of petals of each length. Draw a histogram to display these results. What is the mode for these results? What is the median petal length?

Standard Deviation This measures the spread of the data from the mean. There is more variation in leaf length so leaves in this group varies a lot from the mean. There will be a large standard deviation There is less variation in leaf length so overall each leaf is closer to the mean There will be a small standard deviation

Displaying the data These leaf lengths can be drawn as histograms and the spread of the data compared Number of leaves Number of leaves Leaf length (mm) Leaf length (mm)

Calculating the Standard deviation This means the sum of This the symbol for mean n is the number of values

Worked Example Tree Height (m) A 22 B 27 C 26 D 29   Tree Height (m) A 22 B 27 C 26 D 29 Adding and subtracting the standard deviation to the mean will include 68% of the data.

Error Bars These can be drawn onto a graph. They’re drawn by adding 1SD to the value and subtracting 1SD from the value. They can be added to line or bar graphs. From our example on tree height Mean = 26 SD = 2.9 26+ 2.9 = 28.9 26-2.9 = 23.1 30 28 26 24 22 20 18 Mean Height (m)

Produce a list of human characteristics to fill the following table Produce a list of human characteristics to fill the following table. For each state if it is environmental / inherited or both. State whether it is continuous or discontinuous. Inherited Environmental Both

Students T Test This is a statistical test to determine whether 2 sets of data are statistically different. A continuous characteristic such as length, height, width, mass can be measured and compared between 2 different groups eg males and females lower shore and upper shore sun and shade leaves

Null Hypothesis This is a negative statement. Usually it will state that there is no link between 2 factors. eg There is no similarity between 2 sets of data

To be able to use the T Test, the data must be normally distributed. The mean height is likely to be close to the peak of the curve frequency Height of men (cm)

When comparing the distributions for male and female height there is a difference in the position of the mean but there is also a lot of overlap. Are they statistically different?

Collate and display the data as histograms to determine whether each set is normally distributed Numbers We need to know whether the data is significantly different from each other by comparing the means and the spread of the data, so we will need to calculate: The means of each set The standard deviations of each set Length (mm) Numbers Length (mm)

The Student T Formula This compared the means This compares the standard deviations squared (known as the variances

Understanding What The value of t means The value of t which is calculated must be compared to the table of values. Work out the number of degrees of freedom (n1+ n2 )- 2 If the value of T is equal to or more than the critical value there is significant difference between the two sets of data Probability  0.05 0.025 0.01 Degrees of freedom   1 6.3138 12.7065 31.8193 2 2.9200 4.3026 6.9646 3 2.3534 3.1824 4.5407 4 2.1319 2.7764 3.7470 5 2.0150 2.5706 3.3650 6 1.9432 2.4469 3.1426 7 1.8946 2.3646 2.9980 8 1.8595 2.3060 2.8965 9 1.8331 2.2621 2.8214 10 1.8124 2.2282 2.7638 11 1.7959 2.2010 2.7181 12 1.7823 2.1788 2.6810 13 1.7709 2.1604 2.6503 14 1.7613 2.1448 2.6245 15 1.7530 2.1314 2.6025 16 1.7459 2.1199 2.5835 17 1.7396 2.1098 2.5669 18 1.7341 2.1009 2.5524 19 1.7291 2.0930 2.5395 20 1.7247 2.0860 2.5280 T table