My ventures are not in one bottom trusted, Nor to one place; nor is my whole estate Upon the fortune of this present year: Therefore my merchandise makes me not sad. Shakespeare, Merchant of Venice, 1598 False prophets? The challenges of quantifying ecological portfolios Sean C. Anderson with: Nick Dulvy and Andy Cooper (Simon Fraser University) thanks also to: Trevor Branch, Jon Moore, Branch lab $2881 $2174 $1000 $200 $1751 $1000 $2881 $2174 $1000 $200 $1751 $1000 $2881 $2174 $1000 $200 $1751 $1000 = = Diversified portfolio Single asset portfolio single asset CV portfolio CV Single asset Diversified portfolio Frank Angelo, 1922 Journal of Animal Blackwell Publishing Ltd Ecology 2007 Obituary: Roy (L. R.) Taylor (1924–2007) 76, 630–631 birthday and originally trained as bombardier; he was reassigned and retrained as a radar technician. Roy entered the war only after D-Day, serving first in Belgium and then in India installing air defence systems. In India, where he spent his off-duty time collecting butterflies, the enormous diversity of insect life further stimulated his childhood hobby, leading him to seek employment in entomology on his return to England in 1947. Roy applied for and was offered the position of Experimental Officer at Rothamsted Experimental Station to work with C. B. Williams and C. G. Johnson, who were investigating the population biology of insects of agricultural importance. Roy’s experience in the air force was instrumental in the development with ‘Johnny’ Johnson of very large insect samplers hoisted aloft by barrage balloons at RAF Cardington to determine the density of aphids (important carriers of plant viruses) in the atmosphere. It was while analysing these data of aphid abundance that Roy discovered that statistical distributions of insect abundance have ‘fat tails’ characteristic of power Taylor 2007, J. Anim. Ecol. law scaling relationships. This discovery was to have a profound impact on Roy’s career. It brought him to Roy (L. R.) Taylor (1924–2007) the attention of agricultural scientists in the USA and the US National Science Foundation. Awarded one L. R. Taylor, past President (1984–85) and editor of of NSF’s first Senior Foreign Fellowships in 1964, Roy the Journal of Animal Ecology (1976–89), died on 26 spent a sabbatical year at Kansas State University, the January 2007 at his home in Devon after a prolonged first of three visiting professorships he was awarded; illness. He will be remembered by ecologists and agri- the others at Queen Elizabeth College, London and cultural scientists around the world for his many The Ohio State University. contributions to insect ecology and his commitment to In 1960, Roy resumed sampling moths at Rothamsted agricultural entomology. But it is Taylor’s Power Law – with Williams’ light traps, followed soon after by light the power law scaling relationship that describes the traps at other experimental stations around the country. ‘fat tails’ of the distribution of abundance of nearly all This was the beginning of the Rothamsted Insect organisms – that is the contribution for which he will Survey. In 1963, the government, concerned over pes- be remembered by scientists in many disciplines. ticides in the environment, made funds available for The power law is one of several fundamental scaling research in what we now call integrated pest manage- relationships in ecology. The 1961 Nature publication ment. Taking advantage of this initiative, Roy proposed announcing the discovery is one of the most widely a feasibility study for an early warning system for cited publications in all of ecology and agriculture. It migratory aphid pests that could be sampled in the air has generated considerable discussion as to its origins, before they reached epidemic proportions in the field. its generality, which seems to be very wide, and what When the pest is a migrant capable of being monitored exactly it describes. It has defied satisfactory derivation before it reaches the crop, it is possible to reduce the and placement in population ecology theory, but has number of applications, and therefore the environmen- proven to be very useful both in basic ecology and in tal exposure to pesticides, by applying insecticides at agriculture and statistics, providing a powerful means the time most likely to be effective in protecting the for making data obey the mathematical assumptions crop. Taylor’s solution, literally sketched on the back underlying statistical analysis. of a postcard, was to establish a network of traps to Born on 14 December 1924, only child of Ethel and sample the air for aphids, the largest homogeneous Leslie, Roy showed a keen interest in natural history group of insect pests in northern Europe. A far-sighted from a very early age. He collected butterflies and Agricultural Research Council gave the scheme funds moths, and learned to rear them in his parents’ terraced that eventually permitted the entire British Isles to be © 2007 The Author. house in Manchester. He joined the RAF on his 17th Journal compilation sampled. Using the techniques pioneered by Roy’s © 2007 British mentors, Williams and Johnson, the Rothamsted Insect Ecological Society Correspondence: R. A. J. Taylor. E-mail: [email protected] Survey was conceived to tackle complex questions about Taylor’s power law z variance = c . mean PE data PE calculation (a) Metapopulation (portfolio) (c) Average-CV PE (b) Subpopulations (assets) Mean-variance PE undance (d) b A PE ) ( log Slope = z Time log(μ) 1000 ● ? 500 200 ● ● 100 50 20log(variance) ● Variance 10 5 2 1 ● 2 5log(mean) 10 20 Mean Taylor’s power law z variance = c . mean Taylor’s power law 2 z variancesd = c . mean Frequency z value Taylor et al. 1982, J. Anim. Ecol. Portfolio effect Portfolio Tilman 1999, Ecology But what if you assume z = 2? PE data PE calculation (a) Metapopulation (portfolio) (c) Average-CV PE (b) Subpopulations (assets) Mean-variance PE undance (d) b A PE ) ( log Slope = z Time log(μ) Schindler et al. 2010, Nature CV Carlson et al. 2011, CJFAS Mean-variance portfolio effect Average-CV portfolio effect 1.How does the average-CV and mean- variance portfolio effect differ when applied to theoretical systems with varying z values? 2.How prevalent and strong is this difference across 51 metapopulations and 1070 subpopulations of salmon, moths, and reef fishes? 3.Despite its stronger theoretical foundations, is the mean-variance portfolio effect a reliable empirical metric of how population diversity benefits stability? (a) (b) Average−CV (c) z = 2 Mean−variance z = 1.75 1.8 z = 1.25 (a) (b) Average−CV (c) z = 2 1.4 Mean−variance z = 1.75 1.8 z = 1.25 1.0 (a) (b) effect Portfolio Average−CV (c) z = 2 1.4 Mean−variance z = 1.75 1.8 0.6 z = 1.25 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 1.0 1.4 effect Portfolio Number of subpopulations Correlation Unevenness 0.6 1.0 Portfolio effect Portfolio 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Number of subpopulations Correlation Unevenness 0.6 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Number of subpopulations Correlation Unevenness (a) (b) Average−CV (c) z = 2 Mean−variance z = 1.75 1.8 z = 1.25 z = 2 1.4 (a) (b) Average−CV (c) Mean−variance z = 1.75 1.8 z = 1.25 1.0 Portfolio effect Portfolio (a) (b) Average−CV (c) z = 2 1.4 Mean−variance z = 1.75 z = 1.25 1.80.6 2 4 81.0 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Portfolio effect Portfolio 1.4 Number of subpopulations Correlation Unevenness 0.6 1.0 Portfolio effect Portfolio 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Number of subpopulations Correlation Unevenness 0.6 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Number of subpopulations Correlation Unevenness (a) (b) Average−CV (c) z = 2 Mean−variance z = 1.75 1.8 z = 1.25 (a) (b) Average−CV (c) z = 2 1.4 Mean−variance z = 1.75 1.8 z = 1.25 1.0 Portfolio effect Portfolio (a) (b) Average−CV (c) z = 2 1.4 Mean−variance z = 1.75 z = 1.25 0.6 1.8 2 4 8 16 0.0 0.2 0.4 1.00.6 0.80.0 0.2 0.4 0.6 0.8 Portfolio effect Portfolio Number of subpopulations1.4 Correlation Unevenness 0.6 1.0 Portfolio effect Portfolio 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Number of subpopulations Correlation Unevenness 0.6 2 4 8 16 0.0 0.2 0.4 0.6 0.80.0 0.2 0.4 0.6 0.8 Number of subpopulations Correlation Unevenness 1 − Crustacean larvae 2 − Ground beetles 3 − Karner blue butterflies 4 − Copepods 5 − Feathered thorn moth 120 2500 100 120 80 8000 80 60 1500 Number Number 40 4000 40 Number caught Density per litre Density per litre 20 500 0 0 0 0 0 1984 1988 1992 1960 1965 1970 1975 2 4 6 8 10 12 14 1984 1988 1992 2000 2004 2008 Years Years Generations Years Years 250 6 − Heart & dart moth 7 − Common footman moth 8 − December moth 120 9 − Common swift moth 10 − Yellow−line quaker moth 200 80 80 600 60 150 100 40 40 Number caught Number caught Number caught Number caught Number caught 50 50 20 200 0 0 0 0 0 2000 2004 2008 2000 2004 2008 2000 2004 2008 2000 2004 2008 2000 2004 2008 Years Years Years Years Years 11 − Ingrailed clay moth 12 − Mottled umber moth 13 − Brown silver−lines moth 600 14 − Square−spot rustic moth 15 − Common emerald moth 150 300 400 400 600 100 200 200 200 50 100 Number caught Number caught Number caught Number caught Number caught 200 0 0 0 0 0 2000 2004 2008 2000 2004 2008 2000 2004 2008 2000 2004 2008 2000 2004 2008 Years Years Years Years Years 40 250 16 − Common quaker moth 17 − The magpie moth 18 − Chaetodon trifasciatus 19 − Gomphosus varius 20 − Chaetodon plebeius 60 20 30 15 40 1500 150 20 10 Abundance Abundance Abundance 20 10 5 Number caught Number caught