A framework for quantifying the relationship between intensity and severity of impact of disturbance across types of events and species.

Understanding the impacts of natural disturbances on wildlife populations is a central task for ecologists; in general, the severity of impact of a disturbance (e.g., the resulting degree of population decline) is likely to depend primarily on the disturbance intensity (i.e., strength of forcing), type of disturbance, and species vulnerability. However, differences among disturbance events in the physical units of forcing and interspecific differences in the temporal variability of population size under normal (non-disturbance) conditions hinder comprehensive analysis of disturbance severity. Here, we propose new measures of disturbance intensity and severity, both represented by the return periods. We use a meta-analysis to describe the severity-intensity relationship across various disturbance types and species. The severity and the range of its 95% confidential interval increased exponentially with increasing intensity. This nonlinear relationship suggests that physically intense events may have a catastrophic impact, but their severity cannot be extrapolated from the severity-intensity relationship for weak, frequent disturbance events. The framework we propose may help to clarify the influence of event types and species traits on the severity-intensity relationship, as well as to improve our ability to predict the ecological consequences of various disturbance events of unexperienced intensity.

Supplementary File S1| Detailed description of methods

Time series of abundance Sources of time series of abundance
To quantify the severity of the impact of various disturbance events with an intensity return period of ≥20 years on various species, we obtained primary time series for the abundance of populations affected by such an event during the study period from three sources: (1) Google Scholar (GS); (2) the Global Population Dynamics Database (GPDD, ver. 2); and (3) our research project along a rocky intertidal shore (RPRI).
When searching GS, to gather primary literature by authors self-identifying and reporting the effects of disturbance events on populations we used a keyword search for each of the following terms or their combinations: ("abundance" OR "population size") AND ("natural disturbance" OR "catastrophic event" OR "extreme climate") AND ("impact" OR "decrease" OR "damage"), ("long term"), ("large scale" OR "region*"), ("pre and post" OR "before and after"). We finished conducting our search on 24 December 2014; the search yielded 2940 hits. GPDD is the largest database of population time series and includes >10-year time series for nearly 5000 populations of 1800 species (24 classes, including terrestrial plants, e.g., Dicotyledoneae; terrestrial and aquatic invertebrates, e.g., Insecta and Bivalvia; terrestrial and aquatic vertebrates, e.g., Mammalia and Osteichthyes; and unicellular organisms, e.g., Dinophyceae and Bacillariophyceae) across the globe. In the case of the abundance data obtained from GS and GPDD, we examined whether the time series met requirements for analysis by reading the original papers or books in the subsequent selection processes; we excluded time series for which the literature was not available. RPRI provided 12 years of time series for hundreds of populations of sessile organisms on rocky intertidal shores (e.g., algae, barnacles, and bivalves) in six regions along the Pacific coast of Japan. Within each region (>10 km 2 ) we chose five shores along the coastline. Within each shore, we established five census plots. Each plot was 50 cm wide by 100 cm high, and the mean tidal level corresponded to the vertical midpoint of the plot on steep rock walls. Detailed descriptions of the study sites and biogeographic features of the area can be found in previous reports 1,2 .

Pre-processing of the resulting time series of abundance
The resulting time series of abundance were pre-processed, as needed, to provide a single time series of population abundance that included data measured regularly at 1year or shorter intervals for each species in each study. If the time series of abundance was represented as plots or graphs, we measured values from the figure by applying quantitative methods to highly magnified images using GSYS2.4 (www.jcprg.org/gsys/2.4/index-j.html). If there were multiple census points within the study site, we used the average abundance across the site. If the recording periods differed among the census points within the study site, we used the data in the period for which (1) the census was conducted at multiple census points and (2) the combination of the census points was consistent.
Quality assessment of the pre-processed time series of abundance and selection of the target species To extract the time series of abundance that satisfied the basic requirement for use in the analysis, we selected relevant time series from the pre-processed ones on the basis of (1) quality assessment of the time series of abundance and (2) selection of the target species. Quality of the time series was assessed on the basis of the purpose of the study, the resolution of the census, the measurement of abundance, the temporal trend of abundance, the spatial scale of the time series, and the length of the time series (Supplementary Table S3-i online). Target species were selected on the basis of the absence of seasonal migration and on generation time (Supplementary Table S3-ii online). The generation time condition for analysis was determined by the temporal scale of the disturbance. We identified disturbance events with a ≥20-year return period with regard to intensity, so we used species with generation times of ≤10 years, because an event that occurs less than once in two generations can be assumed to be a deviation from the usual environmental fluctuation. Although it would be ideal to equalize the relative length of the return period to the generation time of each species, we could not do this owing to the lack of information on the exact generation times of some species and the limited sample numbers.  When the time series of force-strength measurement was reported in the original literature ( Fig. S2-I, A), we estimated the distribution of the occurrence probability of the force-strength measurement and then identified the physical intensity of the focal disturbance event reported in the original literature. Next, we estimated the return period of the disturbance intensity as the inverse of the occurrence probability of the focal disturbance event per year. Finally, if the return period of the intensity of the focal disturbance event was ≥20 years, we selected the disturbance event for analysis.

Estimation of disturbance intensity
When the time series of force-strength measurement was not reported in the original literature ( Fig. S2-I, B), we used the following two procedures, depending on whether the focal disturbance was a climatic disturbance event ( Fig. S2-I, C) or an occasional or rare disturbance event ( Fig. S2-I, D). For a climatic disturbance event, we obtained the time series of the climatic parameter as the force-strength measurements recorded at the station nearest (<20 km distance) to the focal study site. In climatic disturbance events, the climatic parameter (e.g., snowfall for severe winters and wave height for storms) likely has values similar to those at the study site and the nearby station 3,4 . We selected and used the time series of the climatic parameter that had been recorded at stations with topographic and geographic conditions similar to those of the site (e.g., flatland or distance from the sea) and that covered the whole period for which the population abundance survey was conducted. If there were multiple available time-series data, we used their average value. After these procedures, we estimated the distribution of occurrence probabilities of the climatic parameter. We then identified the intensity of the disturbance event that occurred in the period when the population abundance survey was conducted and estimated the return period of the disturbance intensity. For an occasional or rare disturbance event, we obtained historical evidence of the focal disturbance event from other literature. We then estimated the return period of intensity of the disturbance event as the average interval of occurrence of such an event with equal or greater intensity. In both procedures, we selected for analysis those disturbance events with an intensity return period of ≥20 years.

II. Estimation of disturbance event intensity when no disturbance event was reported in the original literature (Fig. S2-II).
When a disturbance event was not reported in the original literature ( Fig. S2-II, A), we identified whether the time series of environmental parameters represented the forcestrength of the disturbance. In such cases, we estimated the distribution of occurrence probabilities of the force-strength measurements. We then estimated the force-strength of the disturbance for each year in the period when the population abundance survey was conducted. When the environmental parameters were ones that did not represent force-strength, we identified the main type of disturbance event for the focal species by reading the original report or other literature. When the focal disturbance event was climatic ( Fig. S2-II, C), before we estimated the distribution of occurrence probabilities of the force-strength measurement, we obtained the time series of climatic parameters measured at the station nearest to the study site. When the focal disturbance event was rare or occasional ( Fig. S2-II, D), before we estimated the return period of the disturbance intensity, we obtained historical evidence of the focal disturbance event from other literature. In both procedures, we selected for analysis those disturbance events with intensity return periods of ≥20 years.
If the time series of the environmental parameters had not been reported in the original literature ( Fig. S2-II, B), we identified the main type of disturbance event for the focal species by reading the original report or other literature. The following steps were the same as in Fig. S2-II, A and the subsequent procedure.

Estimation of disturbance severity
To estimate the severity of the impact of a disturbance, we first selected the time series of abundance that satisfied the minimum requirements for calculation of the severity (Table S3-iii). Next, we calculated the effect size representing the severity. Finally, we excluded those data for which the estimated effect size was positive, meaning that the annual population growth rate in the year of the disturbance event was higher than usual. The direct effect of a disturbance event cannot be an increase in population abundance, so a positive effect may indicate that the indirect effect of the event was too large to allow evaluation of the direct effect of the focal disturbance event.

a) Estimation of intensity
Supplementary Figure S1| Diagram of estimation of intensity and severity. (a) Intensity was estimated by two different methods depending on the type of disturbance event: climatic events and rare or occasional events. Intensity was represented by the return period, which was estimated as the inverse of the occurrence probability for climatic events and as the mean interval time of the focal disturbance event with equal or greater magnitude for rare or occasional events. (b) Severity estimation was based on the effect size, which was calculated by comparing the population growth rate between the year when the disturbance event occurred and under normal conditions. Severity was represented by the return period, which was estimated as the inverse of the occurrence probability of the effect size.  Two procedures used to estimate the intensity of the disturbance event that seemed to decrease the focal species abundance and occurred in the period of the study, for each time series: (I) when the disturbance event was reported in the original literature and (II) when no disturbance event was reported. Length of time series Exclusion Length less than twice the generation time To ensure accuracy of the population dynamics of the focal species and severity estimation by using sufficient length of time series relative to generation time of focal species [3] ii) Target species Seasonal migration Exclusion Observing migratory species Difficulty in specifying the place and timing of population decline and the factor(s) causing it