Linear Model Analysis of G.Fortis populations shows natural selection acting in response to drought.

Introduction

Natural selection acts upon different phenotypes within a population: preserving those with higher fitness. This causes shifts in the frequency of certain phenotypes in populations, in response to environmental change. This analysis will test whether natural selection acted upon a G. fortis population on the island Daphne Major, in response to a severe drought between the years of 1976 and 1978. Comprehensive data was collected by Rosemary and Peter Grant of beak depth of an isolated endemic island population in response to this drastic change1. This allows for natural selection to tested for within a short time period. The severe drought limited the island’s food supply to large tough seeds, which larger beaks may be more efficient at opening. It is therefore hypothesized that natural selection would act upon the G. fortis population and lead to an increased mean beak size after the drought. The linear model analysis performed meets these expectations.

Methods

Beak depth of G. fortis individuals was collected from two separate years before and after the drought: 1976 and 1978 on Daphne Major by Peter and Rosemary Grant and measured in millimeters. The data used here was extracted from the Sleuth3 2package. The raw data of beak depth by year is shown in Figure 1.

Figure 1: Beak Depth by Year Scatterplot.

A linear model was fitted to this data and a linear regression was plotted to show the relationship between the year and mean beak depth of the population (Fig2). The confidence intervals of the slope were used to determine if there had been a significant change in mean beak depth between the years 1976 and 1978: before and after the drought. Confidence intervals were used as they also provided information about the direction of change.

Results

Hypothesis testing

The null hypothesis is that there was no significant change in mean beak depths between the year 1976 and 1978. The alternative hypothesis is that mean beak depth has increased between the year 1976 and 1978. A linear regression line was plotted and presents beak depth change between the years (Fig 2). A weak positive correlation can be seen between beak depth and year. As the 95% confidence interval for the slope of the regression line, does not include zero as shown in the confidence interval table (Table 1) and graph (Fig 3), we can reject the null hypothesis. Furthermore, as the upper and lower bounds of the confidence interval are positive, we can assume there has been a significant increase in beak depth between 1976 and 1978.

Figure 2: Linear regression of beak depth versus year, including 95% confidence interval
                   2.5 %       97.5 %
(Intercept) -935.6062223 -366.4881597
Year           0.1903349    0.4782044

Table 1: 95% confidence interval of intercept and slope of linear regression

Figure 3: 95% confidence interval of slope of linear regression

Assumption testing

A normal Q-Q plot was done to test if the assumption of normality for a linear model was met (Fig 4A). Most of the values lie around the dashed line, apart from a few outliers at the lower end. The assumption is mostly met and due to the robustness of the model and the large sample number, a linear model still seems to be a good fit. A graphical assessment of the homoscedasticity of residuals was also performed (Fig 4b). The data points in 1976 were slightly more spread out around the mean. There were also lower end outliers in both years, but as they were present in both their effect on the model is likely minimal. Overall, the distribution of residuals was fairly similar in both years, leading to the conclusion that the assumption of homoscedasticity of residuals was met for the linear model analysis.

Figure 4A: Normal Q-Q plot of residuals

Figure 4B: Test for homoscedasticity of residuals

Conclusions

The statistical analysis supports the hypothesis that natural selection acted upon the G. fortis population to increase beak depth in response to drought. A larger, thicker beak likely allow birds to more efficiently access the most abundant food source after a drought: large, tough seeds. There were some outliers, especially in 1978 that had smaller beaks than expected. Furthermore, the correlation between year and beak size was quite weak. This could be due to other seeds starting to become available after the period of drought, facilitating smaller beak. The weak correlation could also be explained by other phenotypic markers that are also beneficial in drought diminishing the direct action of natural selection on beak depth. One limitation of this study is that individual birds were randomly sampled, leading to potential repeated sampling of the same bird. Mortality rates during this period however were quite high3, potentially mitigating this limitation. Overall, this data shows that natural selection acts quickly in response to drastic changes in the environment, significantly influencing the average phenotype of the G. fortis population in the span of a couple years.

References

1.Grant, P. Ecology and Evolution of Darwin’s Finches. Princeton University Press, Princeton, NJ. (1986)

2.Ramsey, F.L. & Schafer, D. W. The Statistical Sleuth- A Course in Methods of Data Analysis (3rd ed). Cengage Learning. (2013)

3.Gibbs, H. L. & Grant, P. R. Adult Survivorship in Darwin’s Ground Finch (Geospiza) Populations in a Variable Environment. The Journal of Animal Ecology 56, 797 (1987)