# Finding for evolution, comparing past flower numbers with present

In a hypothetical species of butterfly, wing spots are controlled by a single locus where BB individuals have blue spots, YY individuals have yellow spots, and BY individuals have green spots. Ten years ago, a previous collector randomly collected 1000 butterflies and reported finding 90 blues, 420 greens, and 490 yellows. You collect 40 blues, 320 greens, and 640 yellows. Has there been evolution in this population? If yes, is natural selection involved?

I have had many attempts at this question I calculated the p and q frequency for each using HW model.

For 10 years ago: 90+90+420/2000=0.3 BB 490+490+420/2000=0.7 YY

For now : 40+40+320/2000=0.2 BB 640+640+320/2000= 0.8YY

But I dont think I can know if evolution happened and natural selection from this (because Y allele in yellow for instance includes heterozygotes as well).

What do I do? Do I calculate the expected number of each and put it in Chi square test but how would I get natural selection from that? Please help

Has there been evolution in this population?

If $p$ differs in the population, then yes. If you $p_1$ and $p_{10}$ (the two different estimates at generation 1 and generation 10) are equal, then any deviation is caused by sampling error. Hence set $P_1 = P_{10}$ as the null hypothesis and performs a chi-square test.

Is natural selection involved?

For this we have to know the generation time and the population size. We can assume the generation to be of one year (10 generations). The population size $N$ could be estimated from genetic data of the sampled butterflies. The expected loss of genetic diversity per generation is $\frac{1}{2N}$ but you will need to consider any possible path by which one can go from $p_1$ to $P_{10}$ using a series of binomial distribution and sum up their probabilities. That being said, it is a little bit computationally expensive if $N$ is large but some Markov Model theory might give you some simplifications.

You see a question like this, you should just go ahead and calculate if the population is in Hardy-Weinberg Equilibrium, because that's almost certainly what's going to be asked.

For 10 years ago: 90+90+420/2000=0.3 BB 490+490+420/2000=0.7 YY

That notation is not helping. B = 0.3, Y = 0.7

BB = 90/1000 = 0.09 BY = 420/1000 = 0.42 YY = 490/1000 = 0.49

For now : 40+40+320/2000=0.2 B 640+640+320/2000= 0.8 Y

BB=0.04 BY=0.32 YY=0.64

The allele frequencies are changed, which by definition is evolution. But the populations were and remain in HWE, which suggests that all the requirements for that condition, which include there being no selection at present, are occurring.