Some populations of monkeyflower (Mimulus guttatus) can survive in soils with high concentrations of copper due to a copper-tolerance allele. This phenotypic trait is genetically determined.
Scientists conducted a field-selection study over two successive generations in an area adjacent to a newly opened copper mine to investigate how the frequency of copper-tolerant plants changes. Their observed results for the initial colonising population (Generation 0) and the subsequent generation (Generation 1) are shown in the table below:
| Generation | Observed: Sensitive to copper | Observed: Tolerant to copper |
|---|---|---|
| 0 | 160 | 40 |
| 1 | 140 | 60 |
The scientists want to use a chi-squared (χ2\chi^2χ2) statistical test to evaluate their results. They set up the following null hypothesis:
'The proportion of plants that are tolerant to copper will not change from Generation 0 to Generation 1.'
Calculate the expected number of plants of each phenotype in Generation 1 under the null hypothesis.
Calculate the chi-squared (χ2\chi^2χ2) value for Generation 1.
The critical value of χ2\chi^2χ2 at P=0.05P = 0.05P=0.05 (with 1 degree of freedom) is 3.8413.8413.841. State whether the null hypothesis should be accepted or rejected, and explain what this indicates about the probability that the observed differences arose by chance.
