Profile Likelihood Surface for <i>G_NS</i> and <i>G_EW</i>

<p>The plus signs indicate locations where the likelihood was evaluated. The dark contour at −250 marks the −2 log-likelihood support region for the estimates of <i>G_NS</i> and <i>G_EW</i>.</p

The Dispersal Parameter σ as a Function of the Selection Intensity <i>s</i>

<p>The curves are drawn for the two MLEs of <i>R</i> and labeled accordingly. ¹Based on estimates in [<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030339#pbio-0030339-b02" target="_blank">2</a>] and [<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030339#pbio-0030339-b03" target="_blank">3</a>]. ²From <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030339#pbio-0030339-t001" target="_blank">Table 1</a> of [<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030339#pbio-0030339-b27" target="_blank">27</a>].</p

Profile Likelihood for <i>R</i>

<p>The grey line shows the log profile likelihood for <i>R</i> when selection is assumed to be uniform spatially (<i>G_NS</i> = <i>G_EW</i> = 0). The MLE of <i>R</i> in this case is 2.77 × 10⁵ with a log-likelihood of −263.0. The black line shows the profile likelihood when selection gradients are incorporated into the model (<i>G_NS</i> and <i>G_EW</i> are free parameters). The corresponding MLE of <i>R</i> is 1.03 × 10⁶ with a log likelihood of −247.7.</p

Shaded Contour Map of Δ32 Allele Frequency Data

<p>The sampling locations are marked by black points. The interpolation is masked in regions where data are unavailable.</p

An Example of the Allele Frequency Surface and Simulated Data

<div><p>(A) The underlying allele frequency surface generated by the PDE model using MLEs for the parameters. The coarseness of the surface and irregular coastlines are due to the resolution of the simulated habitat (see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030339#sg001" target="_blank">Figure S1</a>).</p> <p>(B and C) Two replicates of simulated data obtained using the same sampling locales and sample sizes as in the dataset and displayed using the same interpolation methods and contours as in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0030339#pbio-0030339-g001" target="_blank">Figure 1</a>. The results show that underlying smooth, unimodal allele frequency surfaces can give rise to irregular, multimodal observed allele frequency surfaces.</p></div

Likelihood Surfaces for the Origin of the Allele

<div><p>(A) Assuming selection intensity is uniform spatially (i.e., <i>G_NS</i> = <i>G_EW</i><b>=</b> 0).</p> <p>(B) Allowing for north–south and east–west spatial gradients in selection (i.e., <i>G_NS</i> and <i>G_EW</i> are free parameters).</p> <p>Likelihoods were calculated at each of the black points and the surface was obtained by interpolation.</p></div

Cumulative predictive distributions of <i>T</i>, the proportion of village residents with parasite count greater than <i>c</i> = 8000/ml, for the five randomly selected villages shown in Figs 3 and 5, based on the fitted model without covariates.

<p>Dashed vertical lines show the point predictions. Black horizontal lines show equal-tailed 95% plug-in predictive intervals. Red horizontal lines show the corresponding 95% confidence intervals for the true proportions based on the binomial sampling distribution of the observed numbers of individuals in each village with parasite count greater than <i>c</i> = 8000/ml.</p

Log-likelihood-ratio statistic <i>D</i> = 2(<i>L</i>_<i>w</i> − <i>L</i>_<i>g</i>), for 156 villages where <i>L</i>_<i>w</i> and <i>L</i>_<i>g</i> denote maximised log-likelihoods for Weibull and Gamma fits, respectively.

<p>Log-likelihood-ratio statistic <i>D</i> = 2(<i>L</i>_<i>w</i> − <i>L</i>_<i>g</i>), for 156 villages where <i>L</i>_<i>w</i> and <i>L</i>_<i>g</i> denote maximised log-likelihoods for Weibull and Gamma fits, respectively.</p

Map showing the locations of the 222 villages for which data are available.

<p>Map showing the locations of the 222 villages for which data are available.</p

Log-likelihood-ratio statistics, D, degrees of freedom, df, and p-values, p, for candidate covariates in univariable analysis.

<p>Log-likelihood-ratio statistics, D, degrees of freedom, df, and p-values, p, for candidate covariates in univariable analysis.</p