# Variation of Traits in a Population Stereolithography (.STL) Model Files and Lesson Plan

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Variation of Traits in a Population

Hits the standard:
Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.

Lesson Brief:
Traits within a population vary around the average value. Probability can be used to understand this variation. Variation within a population is necessary for natural selection to occur as it allows for different reproductive success, or genetic fitness, based upon the traits. In this activity we will examine how variability occurs and how this variation in the value of a trait takes on a predictable statistical distribution.

Background:
The value of traits within a population of a species are not fixed but show some variation around an average value. The distribution of values can change over time. For example, the students in the school have various heights, but the average height will be predictable within an age group. If trait values are influenced by several random and independent factors, they will often form a bell-shaped curve with the average value most likely and values that are greater or lesser than the average being less common the further they are from the average.
Within species, some traits will partly determine the reproductive success of individuals. Different traits therefore allow for different reproductive success, one key criteria for natural selection to occur. The length of the beak within a bird species shows some small variation around the mean for the species. Changes in the lengths of beaks of finches has been studied on islands. In years when seeds are sparse and finches must access very tough seeds to gain enough protein to survive and reproduce. In these years, finches with shorter, stronger beaks may be at an advantage. However, in years with abundant and diverse seeds available, longer beaks that can pull seeds from cracks and holes may be advantageous and outweigh the advantage of cracking open one type of seed that is a lower proportion of what is available.
We will assume that beak length within a population of these island birds determines the strength versus collecting trade-off. We will use the Variation model to simulate the distribution of beak lengths after predicting what the distribution should look like.
Each penny with hit one peg in each row on the way down. Each of these represents a binomial outcome—it can drop to the left or the right, with the probability of each direction equal. Pr(left) = Pr(right) = 0.5. There are 4 such occurrences for each penny, analogous to flipping a coin 4 times. There are thus 2^4=16 possible outcomes. However, there are many paths that lead to the middle bin, which is most likely to end up being the tallest stack of pennies. There is only one path to the right-most bin, 4 falls to the right. Each trial thus only has a probability of 1/16 of landing here.

Activity:
Assemble the Variation model onto two stands. Pennies will be dropped into the top middle slot and allowed to fall into the lower bins. Predict the shape of the distribution across bins. Why does this happen? The bin with the greatest number of pennies is the population mean, [0_1548033648199_SoS_Trait_Variation_HS-LS3-3.zip](Uploading 100%) assign an average beak length to this bin, for example, 10 mm. Bins to the left and right are lengths 0.5 mm less or greater.
Draw out all of the possible outcomes of the penny drops (ex., left, right, right, left) and calculate the probability of each penny landing in the different bins. Does this distribution of probabilities match with your outcome if you drop 40 pennies?
Under what conditions would longer or shorter beaks be more advantageous? For natural selection to occur there must be:

1. Variation in the trait within the population,
2. A genetic basis for the trait value so that it can be passed on to the next generation, and
3. An influence on the survival to reproductive age or probability of reproduction or number of offspring.
What would shift the distribution of beak lengths in the population?
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