William F. Morris, Catherine A. Pfister, Shripad Tuljapurkar, Chirrakal V. Haridas, Carol L. Boggs, Mark S. Boyce, Emilio M. Bruna, Don R. Church, Tim Coulson, Daniel F. Doak, Stacey Forsyth, Jean-Michel Gaillard, Carol C. Horvitz, Susan Kalisz, Bruce E. Kendall, Tiffany M. Knight, Charlotte T. Lee, and Eric S. Menges. 2008. Longevity can buffer plant and animal populations against changing climatic variability. Ecology 89:19–25.

This appendix provides results of statistical tests and further results not presented in the main text.

TABLE C1. Results of Wilcoxon’s rank sum tests for between-group differences in the relative effect of variability. The first through third comparisons are illustrated in Fig. 1 in the main text.

FIG. C1. Relative effect of increasing variability for long-lived species from uncorrelated (IID) and autocorrelated (Markov) environments. Box plot features as in Fig. 1 in the text. Numbers at top in panel A give the number of species in each group. Results of tests for differences between groups are reported in Table C1.

Elasticities for size-classified species

Figure C2 shows the elasticities to the means and SDs of all vital rates for the species with size-based life history stages. Increasing the mean rate of growth into larger stages increases, and increasing the mean rate of reversion into larger stages decreases, the long-term rate of population growth (top panel), but the elasticities to the mean growth and reversion probabilities are generally of small magnitude relative to the elasticities to the mean survival and reproductive rates. For some species, increasing the SDs of the growth or reversion rates has an effect that is comparable or even greater in magnitude than is the effect of increasing the variability of survival and reproductive rates (bottom panel). However, the elasticities of the vital rate SDs for growth or reversion are generally less substantial overall than are those for the vital rate means (compare for each species the numbers above the bars in the top and bottom panels in Fig. C2).

Figure C3 compares the relative effect of variability in survival vs. growth/reversion rates as a function of life expectancy. The log-transformed absolute value of the relative effect of variability in survival is significantly negatively correlated with the log of life expectancy (Spearman’s r = -0.57; P from two-sided test = 0.021). The log-transformed absolute value of the relative effect of variability in growth/reversion rates is negatively correlated with log of life expectancy, but not significantly so (Spearman’s r = -0.35; n = 16; P from two-sided test = 0.18). The slope of the relationship between the relative effect of variability and life expectancy does not differ significantly for survival vs. growth/reversion rates (ANCOVA on log-transformed absolute value of relative effect of variability vs. log of life expectancy; interaction effect: F1,28 = 2.37, P = 0.14).

FIG. C2. Magnitudes of the elasticities for types of vital rates for species with size-based life history stages. Top panel: elasticities to changes in vital rate means; bottom panel: elasticities to changes in vital rate standard deviations. Each type of vital rate has a different color; if the sum of elasticities over a type of vital rate is positive, a brighter hue of the color is used (see legend). In each bar, the absolute values of the summed elasticities for types of vital rates are normalized so that they sum to 1; the actual sums are given at the top of each bar. Abbreviations: LA = long-lived animal; LP = long-lived plants; SP = short-lived plants. For LP, species are ordered from highest (at left) to lowest (at right) life expectancy. For species names, see Appendix A.

FIG. C3. Comparison of the relative effect of variability (log-transformed) in survival rates (triangles) vs. growth/reversion rates (circles) for size-classified species as a function of life expectancy (log-transformed). Effect of variability in growth/reversion is the absolute value of the sum of the elasticities of the growth and reversion rates. If the sum of the elasticities to the SDs of the relevant vital rates is positive, the marker is black; if the sum is negative, the marker is white. To emphasize trends, regression lines for survival (dashed line) and growth/reversion (solid line) are shown.

Sensitivities to means and standard deviations of vital rates

The elasticities discussed in the main text are proportional derivatives, and equal the sensitivity (i.e., the derivative of  with respect to a vital rate mean (or standard deviation)) multiplied by the mean (or standard deviation) and divided by . The summed absolute values of the elasticities to the standard deviation of a type of vital rate could be small for a long-lived species (see Fig. 2) because the standard deviations are small and/or because the sensitivities are small. In the right-hand plots in Fig. C4, we show that the summed absolute values of the sensitivities to the standard deviations of the survival rates, the reproductive rates, and all vital rates combined are negatively correlated with life expectancy, and in Table C2, we show that all three Spearman’s rank correlations are statistically significantly different from zero. The left-hand plots in Fig. C4 show that the summed sensitivities to mean survival rates are higher for short-lived than for long-lived species, as are the summed sensitivities to all vital rates combined (see test results in Table C2). The summed sensitivities to increasing the mean reproductive rates do not differ as a function of life expectancy. However, note that the sensitivities to mean survival are generally greater than the sensitivities to mean reproduction, especially for long-lived species. Thus, as is frequently true of deterministic sensitivities (Pfister 1998, Caswell 2001), long-lived species are more sensitive to a change in the (mean) survival rates than they are to a change in the (mean) reproductive rates.

FIG. C4. Absolute values of the summed sensitivities to vital rate means and standard deviations vs. life expectancy. Circles: animal species; triangles: plant species.

TABLE C2. Spearman’s rank correlations for the relationships between sensitivities and life expectancies illustrated in Fig. C4. P values are results from two-tailed tests of the hypothesis that the rank correlation is zero.

LITERATURE CITED

Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation. Second Edition. Sinauer Associates, Sunderland, Massachusetts, USA.

Pfister, C. A. 1998. Patterns of variance in stage-structured populations: evolutionary predictions and ecological implications. Proceedings of the National Academy of Sciences of the United States of America 95:213–218.