Appendix B. Sensitivity analysis of critical habitat size.

Sensitivity analysis of critical habitat size

Female fitness in 2008–2009.

<p>Spatial distribution of host plants of bagworms, <i>Thyridopteryx ephemeraeformis</i>, sampled in Indiana and south Michigan to determine the presence or absence of bagworms (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014166#pone-0014166-t003" target="_blank">table 3</a>). For comparison, the effect of latitude (x) on female reproductive output (y, in mg eggs; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014166#pone-0014166-t001" target="_blank">Table 1</a>) is depicted in 2008 (<i>y</i> = 4059−96.1 <i>x</i>, <i>r²</i> = 0.662, <i>P</i><0.0001, <i>N</i> = 61 sites) and 2009 (<i>y</i> = 4612−110.0 <i>x</i>, <i>r²</i> = 0.652, <i>P</i><0.0001, <i>N</i> = 50 sites).</p

Extinction of bagworm populations.

<p>Probability of extinction of populations of <i>Thyridopteryx ephemeraeformis</i> during the winter of 2008–2009 as a function of latitude and reproductive output of females in parental generation.</p>t<p>Values of 0 are indicative of complete reproductive failure of females, whereas values >1 indicate that at least some females successfully reproduced.</p

Source of variation.

<p>Partition of variance evaluating the variance component associated with latitude, longitude (both classified as one degree bands), and host plant (arborvitae or juniper) for different parameters of fitness. For all parameters, the highest variance component value was standardised as 1.000, to facilitate comparison of variance effects across fitness parameters.</p

Appendix A. Comparison of critical patch sizes from the implicit and explicit models.

Comparison of critical patch sizes from the implicit and explicit models

Female fitness in 2009.

<p>Spatial distribution of host plants of bagworms, <i>Thyridopteryx ephemeraeformis</i>, sampled in Indiana to determine multiple components of female fitness during the 2009 bagworm generation (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014166#pone-0014166-t001" target="_blank">Table 1</a>). Latitude (x) significantly affected proportions of pupal survival [linear model with 50 sites, <i>y</i> = 4.33−0.086 <i>x</i>, <i>r²</i> = 0.257, <i>P</i> = 0.0002] and of mated females [linear model with 50 sites, <i>y</i> = 12.2−0.29 <i>x</i>, <i>r²</i> = 0.655, <i>P</i><0.0001], as well as fecundity [linear model with 49 (excluding one site with no egg mass sampled), <i>y</i> = 2315−50.8 <i>x</i>, <i>r²</i> = 0.305, <i>P</i><0.0001].</p

Appendix B. Derivations of the distributions of the estimated parameters.

Derivations of the distributions of the estimated parameters

Appendix A. Survivorship data for the 58 mammal species considered in survivorship analysis.

Survivorship data for the 58 mammal species considered in survivorship analysis

Supplement 1. S-PLUS code for estimating parameters and calculating risk metrics from a time series.

<h2>File List</h2><blockquote> <p> S-Plus code: </p> <p> <a href="DHMethod.txt">DHMethod.txt</a><br> <a href="riskmetrics.txt">riskmetrics.txt</a><br> </p> <p> All files are in ASCII text. </p> </blockquote><h2>Description</h2>Following are S-Plus files (in ascii format) to estimate parameters and risk metrics from a time series using the Dennis-Holmes method. <p> The file DHMethod.txt contains code to estimate -- IMAGE: Please see in attached file. -- using running sums and -- IMAGE: Please see in attached file. --² using the slope method from a time series of counts.</p> <p> The file riskmetrics.txt contains code to estimate risk metrics given estimates of -- IMAGE: Please see in attached file. -- and -- IMAGE: Please see in attached file. --². The following metrics are calculated: confidence intervals on -- IMAGE: Please see in attached file. --, probability of extinction with 95% confidence intervals, probability of decline with 95% confidence intervals, probability of observing extinction, and probability of observing a given decline. </p

Appendix C. Derivation of the distributions for cross-validating parameter estimates.

Derivation of the distributions for cross-validating parameter estimates