Comment on "Impacts of Biodiversity Loss on Ocean Ecosystem Services"

B. Worm et al., Science314, 787 (2006).

We staggered the start time of the time series to mimic staggered entry of fisheries, where 5% of the time series were started each year until all of the time series were active in year 20. If our analysis is scaled so that year 0 is 1950, the average start date of a fishery is 1960. Worm et al. (1) found that the average time of a fishery starting in their analysis was 1962.

Catch data are often log-normally distributed. Chesapeake Bay fisheries, for example, had a median CV of 82% (5), and the median CV for fisheries aggregated at the ocean level was 72% (6), which is probably low relative to the variability of catch in the large marine ecosystems analyzed by Worm et al. (1), because catches were aggregated over larger areas. Generally, most fish populations are not thought to vary naturally by this amount (i.e., CVs of abundance would generally be lower), and some of this variability may be due to trends in catch rather than randomness. Our simulations used a mean of 1000, but the mean does not affect the results. Similar increasing patterns in the proportion of time series below a fixed threshold were obtained with time series of independent observations and with normal distributions, but the magnitude of the increase in collapses over time depended on the distribution, CV, and autocorrelation coefficient, with higher CVs and lower autocorrelation coefficients having a higher rate of increase.

The cumulative distribution function (CDF) for the maximum of a series of independent, identically distributed (iid) random variables is F_max (y)= [F(y)]ⁿ, where F_max is the CDF of the maximum of a series of n iid random variables with a CDF F. For any specified F, the longer the time series and higher the CV, the higher the maximum is likely to be, making it more likely that much of the time series will be less than a fixed percentage of the maximum. This is why more time series are scored as collapsed under the scenario with a higher CV. The maximum of a stationary time series has an equal probability of occurring in any single year. The overall increasing trend in collapses is due to patterns of when the maximum occurs in each time series because, by their definition, collapses can only occur after the maximum has been reached. Therefore, the probability of scoring a time series as collapsed is much higher at the end of a time series than at the beginning.

National Oceanic and Atmospheric Administration Annual Commercial Landings Statistics, www.st.nmfs.gov/st1/commercial/landings/annual_landings.html.

United Nations Food and Agriculture Organization Fishery Information, Data and Statistics Unit (FAO-FIDI, Rome, 2004), Collation, Analysis and Dissemination of Global and Regional Fishery Statistics. FI Programme Websites. Updated Monday, Oct. 9, 09:51:18 CEST 2006. Available through the Fisheries Global Information System (FIGIS) from www.fao.org/figis/servlet/static?dom=org&xml=FIDI_STAT_org.xml.

We thank D. Secor, J. Bence, G. Nesslage, and two anonymous reviewers for comments that improved this manuscript. This is contribution number 4090 of the University of Maryland Center for Environmental Science Chesapeake Biological Laboratory.