Individual-scale inference to anticipate climate-change vulnerability of biodiversity

Abstract

Anticipating how biodiversity will respond to climate change is challenged by the fact that climate variables affect individuals in competition with others, but interest lies at the scale of species and landscapes. By omitting the individual scale, models cannot accommodate the processes that determine future biodiversity. We demonstrate how individual-scale inference can be applied to the problem of anticipating vulnerability of species to climate. The approach places climate vulnerability in the context of competition for light and soil moisture. Sensitivities to climate and competition interactions aggregated from the individual tree scale provide estimates of which species are vulnerable to which variables in different habitats. Vulnerability is explored in terms of specific demographic responses (growth, fecundity and survival) and in terms of the synthetic response (the combination of demographic rates), termed climate tracking. These indices quantify risks for individuals in the context of their competitive environments. However, by aggregating in specific ways (over individuals, years, and other input variables), we provide ways to summarize and rank species in terms of their risks from climate change.

Figure 1.

(a) Examples of (i) negative and (ii) positive interactions when input variables are scaled to (0,1) (equation 2.10). Contours and shading indicate magnitude of the response. Strong interactions (thick arrows) cross many contours, weak interactions (thin arrows) cross few contours. Negative interactions indicate a large response to one input when the other is low, and vice versa. (b–d) Fraxinus interactions are positive for adult and juvenile growth and negative for fecundity. The distribution of data (size of circles proportional to magnitude of response) helps evaluate parameter space where observations are insufficient. (e–g) Sensitivity to light for Fraxinus depends on the summer drought experienced by each tree in each year (dots).

Figure 2.

Sensitivities differ for each species to each climate variable in each of three (a) fecundity, (b) mature growth and (c) mature survival demographic rates. Species are ordered by sensitivity to winter temperature (w_j,t). A second sensitivity is also shown for each species, the one that is largest. Variables are listed in table 1.

Figure 3.

Predictive means and 95% predictive intervals (red lines) for individuals selected at random for (a) Fraxinus, (b) Tsuga and (c) Liquidambar in response to summer drought. The true values are in black. The lower panels show the median and 95% of the individual deviations , i.e. they summarize the population.

Figure 4.

Predictive loss for PDSI at each individual tree-year for Fraxinus P(q) = G(q) + V(q) decrease with (a) increasing light, (b) PDSI and (c) local moisture. PDSI is tracked more closely on average (low G(q)) and with greater confidence (low V(q)) when resources are high. (d–f) predictive means and (g–i) standard deviations plotted against actual inputs x_ij,t(q) for all Fraxinus tree-years. The 1 : 1 line for predictive means indicates agreement.

Figure 5.

Fraxinus showing 1/MSPE for summer PDSI at a site on the Piedmont plateau. Large circles indicate close tracking of PDSI on dry sites at this site.