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
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$1000
$200
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$1000
$200
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= 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
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 50 500 0 0 0 0 0 2000 2004 2008 2000 2004 2008 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
21 − Epibulus insidiator 22 − Scarus niger 23 − Hemigymnus fasciatus 24 − Hemigymnus melapterus 50 25 − Scarus frenatus 40 50 100 30 30 30 30 20 60 20 Abundance Abundance Abundance Abundance Abundance 10 10 10 10 20 0 0 0 0 0 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
26 − Chlorurus microrhinos 50 27 − Scarus chameleon 28 − Plectropomus leopardus 29 − Pomacentrus lepidogenys 30 − Ctenochaetus spp 60 60 300 30 40 40 1000 200 Abundance Abundance Abundance Abundance Abundance 20 20 500 100 10 0 0 0 0 0 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
31 − Chlorurus sordidus 32 − Neopomacentrus azysron 33 − Acanthochromis polyacanthus 34 − Pomacentrus moluccensis 35 − Scarus psittacus 150 600 4000 1500 300 100 400 2000 Abundance Abundance Abundance Abundance Abundance 50 200 500 100 0 0 0 0 0 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
36 − Chum salmon 37 − Chinook salmon 38 − Atlantic salmon 39 − Pink salmon, even years 40 − Pink salmon, odd years 4000 1400000 6e+05 1000000 1.0e+07 Returns Returns Returns 2000 3e+05 Adult returns 600000 400000 0 0 0 Adult production numbers
1965 1975 1985 1995 19500e+00 1970 1990 2010 1970 1980 1990 2000 1980 1985 1990 1995 1965 1975 1985 1995 0.0e+00 Years Years Years Years Years 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 50 500 0 0 0 0 0 2000 2004 2008 2000 2004 2008 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
21 − Epibulus insidiator 22 − Scarus niger 23 − Hemigymnus fasciatus 24 − Hemigymnus melapterus 50 25 − Scarus frenatus 40 50 100 30 30 30 30 20 60 20 Abundance Abundance Abundance Abundance Abundance 10 10 10 10 20 0 0 0 0 0 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
26 − Chlorurus microrhinos 50 27 − Scarus chameleon 28 − Plectropomus leopardus 29 − Pomacentrus lepidogenys 30 − Ctenochaetus spp 60 60 300 30 40 40 1000 200 Abundance Abundance Abundance Abundance Abundance 20 20 500 100 10 0 0 0 0 0 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 Years Years Years Years Years
31 − Chlorurus sordidus 32 − Neopomacentrus azysron 33 − Acanthochromis polyacanthus 34 − Pomacentrus moluccensis 35 − Scarus psittacus 150 600 4000 1500 300 100 400 2000 Abundance Abundance Abundance Abundance Abundance 50 Data from various sources including: 200 500 100 0 0 0 0 0 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010 1995 2000 2005 2010Dorner1995 et al.2000 2008,2005 CJFAS2010 Years Years Years Years Years
36 − Chum salmon 37 − Chinook salmon 38 − Atlantic salmon 39 − Pink salmon, even years Rothamsted40 − Pink salmon, Insect odd years Survey 4000 1400000 6e+05 1000000 Australian Institute of Marine Science 1.0e+07 Returns Returns Returns 2000 3e+05 Adult returns 600000 400000 0 0 0 Adult production numbers
1965 1975 1985 1995 19500e+00 1970 1990 2010 1970 1980 1990 2000 1980 1985 1990 1995 1965 1975 1985 1995 0.0e+00 Years Years Years Years Years ● Mean−variance PE Average−CV PE 1 Crustacean larvae (1.8) ● 2 Ground beetles (2.0) ● 3 Karner blue butterflies (2.3) ● 4 Copepods (2.6) ● 5 Feathered thorn moth (1.5) ● 6 Heart & dart moth (1.5) ● 7 Common footman moth (1.6) ● 8 December moth (1.6) ● 9 Common swift moth (1.7) ● 10 Yellow−line quaker moth (1.7) ● 11 Ingrailed clay moth (1.7) ● 12 Mottled umber moth (1.7) ● 13 Brown silver−lines moth (1.7) ● 14 Square−spot rustic moth (1.7) ● 15 Common emerald moth (1.7) ● 16 Common quaker moth (1.8) ● 17 The magpie moth (1.9) ● 18 Chaetodon trifasciatus (1.0) ● 19 Gomphosus varius (1.1) ● 20 Chaetodon plebeius (1.1) ● 21 Epibulus insidiator (1.1) ● 22 Scarus niger (1.2) ● 23 Hemigymnus fasciatus (1.2) ● 24 Hemigymnus melapterus (1.2) ● 25 Scarus frenatus (1.3) ● 26 Chlorurus microrhinos (1.3) ● 27 Scarus chameleon (1.3) ● 28 Plectropomus leopardus (1.5) ● 29 Pomacentrus lepidogenys (1.5) ● 30 Ctenochaetus spp (1.5) ● 31 Chlorurus sordidus (1.5) ● 32 Neopomacentrus azysron (1.5) ● 33 Acanthochromis polyacanthus (1.6) ● 34 Pomacentrus moluccensis (1.6) ● 35 Scarus psittacus (1.7) ● 36 Chum salmon (1.5) ● 37 Chinook salmon (1.6) ● 38 Atlantic salmon (1.6) ● ● 39 Pink salmon, even years (1.7) ● ● 1 Coho salmon (2.4) a ● Mean−variance PE 40 Pink salmon, odd years (1.7) ● 2 Pink salmon, odd years (2.3) ● Average−CV PE 41 Chum salmon (1.9) ● 3 Sockeye salmon (2.2) ● 42 Chinook salmon (1.9) ● 434 SocChinookkeye salmon (2.0)(2.1) ● 5 Pink salmon,44 Chum odd salmon years (2.0)(2.1) ● ● Metapopulation 456 Soc Atlantickeye salmon (2.0)(2.1) ● ● Subpopulations 467 Pink Pink salmon, salmon, even odd yearsyears (2.0)(2.1)Mean-variance PE● ● Average-CV PE 8 Pink 47salmon, Sockeye even salmon years (2.0) ● ● ● ● 48 Pink salmon,9 Sock eevenye salmon years (2.0) ● ● Salmon 1 Coho salmon (2.4) a ● Mean−variance PE 1049 Pink Pink salmon, salmon, e oddven yearsyears (2.1)(2.0) ● ● 2 Pink salmon, odd years (2.3) ● bAverage−CV PE 5011 Sockeye Atlantic salmon (2.1)(2.0) ● ● 3 Sockeye salmon (2.2) ● 51 Pink salmon, odd years (2.1) ●● 412 Soc Chumkeye salmon (2.0)(2.1) ● 52 Sockeye salmon (2.1) ● ● 5 Pink13 salmon, Chinook odd salmon years (2.0)(2.1) ● Metapopulation 53 Sockeye salmon (2.2) ● 146 SocChinookkeye salmon (1.9)(2.1) ● ● Subpopulations 54 Pink salmon, odd years (2.3) ● 7 Pink salmon,1555 ChumCoho odd salmon years (2.4)(1.9)(2.1) ● ● 168 Pink Pink salmon, salmon, e oddven years (1.7)(2.0) ● ● ● 17 Pink salmon,9 Sock eeyMothveen salmon y earsRE mean (1.7)(2.0) ● Salmon 10 Pink salmon,18Reef Atlantic efishesven salmon y earsRE mean (1.6)(2.0) ● ● ID: 10 ● b 1911 Chinook AtlanticSalmon salmon RE mean (1.6)(2.0) ● z = 2.1 All2012 populations Chum salmon RE mean (1.5)(2.0) ● ● 13 Chinook salmon (2.0) ● 2114 The Chinook magpie salmon moth (1.9) 0.5● 1 ● 2 5 10 22 Common quaker moth (1.8) ●● 15 Chum salmon (1.9) Portfolio effect (PE) 2316 CommonPink salmon, eme oddrald ymothears (1.7) ● ● Moths 2417 Square−spotPink salmon, reusticven ymothears (1.7) ● ● 25 Brown18 sil Atlanticver−lines salmon moth (1.6)(1.7) ●● c ID: 10 ● 26 Mottled19 Chinook umber salmon moth (1.7)(1.6) ● z = 2.1 27 Ing20railed Chum cla salmony moth (1.5)(1.7) ● ● ●
28 Yellow−line quaker moth (1.7) iance) ● r 2921 Common The magpie swift moth (1.7)(1.9) ● a 22 Common30 December quaker moth (1.6)(1.8) ●● v ● ● 2331 Common emefootmanrald moth (1.6)(1.7) log( ● Moths 24 Square−spot32 Heart & rustic dart moth (1.5)(1.7) ● ID: 34 33 Feathered thorn moth (1.5) ● ● 25 Brown silver−lines moth (1.7) c z = 1.6 26 Mottled umber moth (1.7) ● 2734 Ing Scarailedrus cl psittacusay moth (1.7) ●● 35 Pomacentrus moluccensis (1.6) ● ●
28 Yellow−line quaker moth (1.7) iance) 36 Acanthochromis polyacanthus (1.6) ● ● r 29 Common swift moth (1.7) a 37 Neopomacent30 Decemberrus azysron moth (1.6)(1.5) ● ● v Reef fishes 38 Chlorurus sordidus (1.5) ● ●
31 Common footman moth (1.6) log( 3932 CtenochaetusHeart & dart moth spp (1.5) ● ● d ● ID: 34 40 P33omacent Featheredrus lepidoge thorn mothnys (1.5) ● 41 Plectropomus leopardus (1.5) ● z = 1.6 4234 Sca Scarusrus chameleon psittacus (1.7)(1.3) ● ● 35 P43omacent Chlorurrusus moluccensis microrhinos (1.6)(1.3) ● ● 36 Acanthochromis44 Sca polrusyacanthus frenatus (1.3)(1.6) ● ● 3745 Neopomacent Hemigymnus rmelapteus azysronrus (1.5)(1.2) ● ● Reef fishes 46 Hemigymnus fasciatus (1.2) ● ● 38 Chlorurus sordidus (1.5) ID: 51 39 Ctenochaetus47 Scarus niger spp (1.2)(1.5) ● ● d 40 Pomacent48 Epirusbulus lepidoge insidiatornys (1.1)(1.5) ● ● z = 1.2 41 Plectropo49 Chaetodonmus leopardus plebeius (1.1)(1.5) ● ● ● log(mean) 5042 GomphosusScarus chameleon varius (1.1)(1.3) ● 5143 ChaetodonChlorurus microrhinos trifasciatus (1.0)(1.3) ● ● 44 Scarus frenatus (1.3) ● 45 HemigymnusSalmon melapte RErus mean (1.2) ● 46 HemigymnusMoth fasciatus RE mean (1.2) ● Reef47 Sca fishesrus niger RE mean (1.2) ● ID: 51 48 Epibulus insidiator (1.1) ● z = 1.2 49 Chaetodon plebeius (1.1) ● 50 Gomphosus varius (1.1) 0.5 ●1 2 5 10 log(mean) 51 Chaetodon trifasciatus (1.0) ● Portfolio effect (PE) Salmon RE mean Moth RE mean Reef fishes RE mean
0.5 1 2 5 10 Portfolio effect (PE) 1 Coho salmon (2.4) a ● ● Mean−variance PE 2 Pink salmon, odd years (2.3) ● Average−CV PE 3 Sockeye salmon (2.2) ● 4 Sockeye salmon (2.1) ● 5 Pink salmon, odd years (2.1) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) ● 8 Pink salmon, even years (2.0) ● 9 Sockeye salmon (2.0) ● Salmon 10 Pink salmon, even years (2.0) ● b 11 Atlantic salmon (2.0) ● 12 Chum salmon (2.0) ● 13 Chinook salmon (2.0) ● 14 Chinook salmon (1.9) ● 15 Chum salmon (1.9) ● 16 Pink salmon, odd years (1.7) ● 17 Pink salmon, even years (1.7) ● 18 Atlantic salmon (1.6) ● ID: 10 19 Chinook salmon (1.6) ● z = 2.1 20 Chum salmon (1.5) ●
21 The magpie moth (1.9) ● 22 Common quaker moth (1.8) ● 23 Common emerald moth (1.7) ● Moths 24 Square−spot rustic moth (1.7) ● 25 Brown silver−lines moth (1.7) ● c 26 Mottled umber moth (1.7) ● 27 Ingrailed clay moth (1.7) ● ●
28 Yellow−line quaker moth (1.7) iance) ● r
29 Common swift moth (1.7) a 30 December moth (1.6) ● v ●
31 Common footman moth (1.6) log( ● 32 Heart & dart moth (1.5) ID: 34 33 Feathered thorn moth (1.5) ● z = 1.6 34 Scarus psittacus (1.7) ● 35 Pomacentrus moluccensis (1.6) ● 36 Acanthochromis polyacanthus (1.6) ● 37 Neopomacentrus azysron (1.5) ● Reef fishes 38 Chlorurus sordidus (1.5) ● 39 Ctenochaetus spp (1.5) ● d 40 Pomacentrus lepidogenys (1.5) ● 41 Plectropomus leopardus (1.5) ● 42 Scarus chameleon (1.3) ● 43 Chlorurus microrhinos (1.3) ● 44 Scarus frenatus (1.3) ● 45 Hemigymnus melapterus (1.2) ● 46 Hemigymnus fasciatus (1.2) ● 47 Scarus niger (1.2) ● ID: 51 48 Epibulus insidiator (1.1) ● z = 1.2 49 Chaetodon plebeius (1.1) ● 50 Gomphosus varius (1.1) ● log(mean) 51 Chaetodon trifasciatus (1.0) ● Salmon RE mean Moth RE mean Reef fishes RE mean
0.5 1 2 5 10 Portfolio effect (PE) 1 Coho salmon (2.4) a ● ● Mean−variance PE 2 Pink salmon, odd years (2.3) ● Average−CV PE 3 Sockeye salmon (2.2) ● 4 Sockeye salmon (2.1) ● 5 Pink salmon, odd years (2.1) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) ● 8 Pink salmon, even years (2.0) ● 9 Sockeye salmon (2.0) ● Salmon 10 Pink salmon, even years (2.0) ● b 11 Atlantic salmon (2.0) ● 12 Chum salmon (2.0) ● 13 Chinook salmon (2.0) ● 14 Chinook salmon (1.9) ● 15 Chum salmon (1.9) ● 16 Pink salmon, odd years (1.7) ● 17 Pink salmon, even years (1.7) ● 18 Atlantic salmon (1.6) ● ID: 10 19 Chinook salmon (1.6) ● z = 2.1 20 Chum salmon (1.5) ●
21 The magpie moth (1.9) ● 22 Common quaker moth (1.8) ● 23 Common emerald moth (1.7) ● Moths 24 Square−spot rustic moth (1.7) ● 25 Brown silver−lines moth (1.7) ● c 26 Mottled umber moth (1.7) ● 27 Ingrailed clay moth (1.7) ● ●
28 Yellow−line quaker moth (1.7) iance) ● r
29 Common swift moth (1.7) a 30 December moth (1.6) ● v ●
31 Common footman moth (1.6) log( ● 32 Heart & dart moth (1.5) ID: 34 33 Feathered thorn moth (1.5) ● z = 1.6 34 Scarus psittacus (1.7) ● 35 Pomacentrus moluccensis (1.6) ● 36 Acanthochromis polyacanthus (1.6) ● 37 Neopomacentrus azysron (1.5) ● Reef fishes 38 Chlorurus sordidus (1.5) ● 39 Ctenochaetus spp (1.5) ● d 40 Pomacentrus lepidogenys (1.5) ● 41 Plectropomus leopardus (1.5) ● 42 Scarus chameleon (1.3) ● 43 Chlorurus microrhinos (1.3) ● 44 Scarus frenatus (1.3) ● 45 Hemigymnus melapterus (1.2) ● 46 Hemigymnus fasciatus (1.2) ● 47 Scarus niger (1.2) ● ID: 51 48 Epibulus insidiator (1.1) ● z = 1.2 49 Chaetodon plebeius (1.1) ● 50 Gomphosus varius (1.1) ● log(mean) 51 Chaetodon trifasciatus (1.0) ● Salmon RE mean Moth RE mean Reef fishes RE mean
0.5 1 2 5 10 Portfolio effect (PE) 1 Coho salmon (2.4) a ● ● Mean−variance PE 2 Pink salmon, odd years (2.3) ● Average−CV PE 3 Sockeye salmon (2.2) ● 4 Sockeye salmon (2.1) ● 5 Pink salmon, odd years (2.1) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) ● 8 Pink salmon, even years (2.0) ● 9 Sockeye salmon (2.0) ● Salmon 10 Pink salmon, even years (2.0) ● b 11 Atlantic salmon (2.0) ● 12 Chum salmon (2.0) ● 13 Chinook salmon (2.0) ● 14 Chinook salmon (1.9) ● 15 Chum salmon (1.9) ● ● 1 Coho salmon (2.4)16 Pinka salmon, odd years● (1.7) ● Mean−variance PE ● 2 Pink salmon, odd years 17(2.3) Pink salmon, even● years (1.7) Average−CV PE 3 Sockeye salmon (2.2) 18 Atlantic salmon● (1.6) ● ID: 10 4 Sockeye salmon (2.1) 19 Chinook salmon● (1.6) ● z = 2.1 5 Pink salmon, odd years (2.1) 20 Chum salmon● (1.5) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) 21 The magpie● moth (1.9) ● 8 Pink salmon, even years (2.0)22 Common quaker● moth (1.8) ● 9 Sockeye salmon (2.0)23 Common emer●ald moth (1.7) ●Salmon Moths 10 Pink salmon, even years 24(2.0) Square−spot rustic ●moth (1.7) ●b 11 Atlantic salmon (2.0)25 Brown silver−lines● moth (1.7) ● c 12 Chum salmon (2.0)26 Mottled umber● moth (1.7) ● 13 Chinook salmon (2.0) 27 Ingrailed cla●y moth (1.7) ● ● ● 14 Chinook salmon (1.9)28 Yellow−line quaker moth (1.7) iance) ● ● r 15 Chum salmon (1.9)29 Common swift moth (1.7) a 30 December● moth (1.6) ● v 16 Pink salmon, odd y●ears (1.7) 1 Coho salmon (2.4) a ● ● Mean−variance PE ●
31 Common footman moth (1.6) log( 17 Pink salmon, even● years (1.7) 2 Pink salmon, odd years (2.3) 32 Heart & ●dartA mothverage−CV (1.5) PE ● ID: 10 18 Atlantic salmon● (1.6) ID: 34 3 Sockeye salmon (2.2) 33 Feathered tho●rn moth (1.5) ● 19 Chinook salmon● (1.6) z = 2.1 z = 1.6 4 Sockeye salmon (2.1) 20 Chum salmon (1.5) ● 5 Pink salmon, odd years (2.1) ● 34 Scarus psittacusMetapopulation (1.7) ● ● 6 Sockeye salmon (2.1) 35 Pomacentrus● moluccensisSubpopulations (1.6) ● 21 The magpie● moth (1.9) 7 Pink salmon, odd years (2.1) 36 Acanthochromis polyacanthus● (1.6) ● 22 Common quaker● moth (1.8) 8 Pink salmon, even years (2.0) 37 Neopomacentrus azysron● (1.5) ● Reef fishes 23 Common eme●rald moth (1.7) Moths 9 Sockeye salmon (2.0) 38 Chlorurus sordidusSalmon● (1.5) ● 24 Square−spot rustic● moth (1.7) 10 Pink salmon, even years (2.0) 39 Ctenochaetus● spp (1.5) ● c 25 Brown silver−lines● moth (1.7) b d 11 Atlantic salmon (2.0) 40 Pomacentrus lepidoge● nys (1.5) ● 26 Mottled umber● moth (1.7) 12 Chum salmon (2.0) 41 Plectropomus leopardus● (1.5) ● 27 Ingrailed cl●ay moth (1.7) 13 Chinook salmon (2.0) 42 Scarus chameleon● (1.3) ● 28 Yellow−line quaker● moth (1.7) iance) 14 Chinook salmon (1.9) ● ● r
43 Chlorurus microrhinos (1.3) a 29 Common swift● moth (1.7) 15 Chum salmon (1.9) 44 Scarus frenatus● (1.3) ● v 30 December● moth (1.6) 16 Pink salmon, odd years (1.7) 45 Hemigymnus melapte● rus (1.2) ● 31 Common footman● moth (1.6) log( 17 Pink salmon, even years (1.7) 46 Hemigymnus● fasciatus (1.2) ● 32 Heart &● dart moth (1.5) ● ID: 10 ● ID: 34 ID: 51 18 Atlantic salmon (1.6)33 Feathered thorn moth (1.5) 47 log(variance) Scarus niger (1.2) 19 Chinook salmon (1.6) ● 48 Epibulus insidiator (1.1) z = 2.1 ● z = 1.6 z = 1.2 ● 20 Chum salmon (1.5) 34 Scarus psittacus (1.7)49 Chaetodon plebeius● (1.1) ● 50 Gomphosus● varius (1.1) ● log(mean) 35 Pomacentr●us moluccensis (1.6) 21 The magpie moth (1.9) 51 Chaetodon● trifasciatus (1.0) ● 36 Acanthochromis polyacanthus● (1.6) 22 Common quaker moth (1.8) ● 37 Neopomacentrus azysron● (1.5) Reeflog(mean) fishes 23 Common emerald moth (1.7) Salmon●Moths RE mean 38 Chlorurus sordidus● (1.5) ● ● 24 Square−spot rustic moth (1.7) 1 Coho● salmon (2.4) a Mean−variance PE 39 Ctenochaetus spp (1.5) Moth RE mean ● ● 2 Pink salmon, odd years (2.3) d 25 Brown silver−lines moth (1.7) Reef fishesc● RE mean Average−CV PE 40 Pomacentrus lepidoge● nys (1.5) ● 26 Mottled umber moth (1.7) 3 Sock●eye salmon (2.2) 41 Plectropomus leopardus● (1.5) ● 27 Ingrailed clay moth (1.7) 4 Soc● keye salmon (2.1) 42 Scarus chameleon● (1.3) 5 Pink salmon, odd years (2.1) ● Metapopulation 28 Yellow−line quaker moth (1.7) ● iance) 0.5 1 2 5 10 43 Chlorurus microrhinos● (1.3) 6 Socr keye salmon (2.1) ● Subpopulations 29 Common swift moth (1.7) ● a 44 Scarus frenatus● (1.3) v ● 30 December moth (1.6) 7 Pink salmon,● odd years (2.1) Portfolio effect (PE) 45 Hemigymnus melapte● rus (1.2) 8 Pink salmon, even years (2.0) ●
31 Common footman moth (1.6) ● log( 46 Hemigymn●us fasciatus (1.2) ● Salmon 32 Heart & dart moth (1.5) 9 Soc● keye salmon (2.0) ID: 51 47 Sca● rus niger (1.2) ID: 34 ● 33 Feathered thorn moth (1.5) 10 Pink salmon,● even years (2.0) z = 1.2 48 Epibulus insidiator (1.1) z = 1.6 ● b 11 Atlantic● salmon (2.0) 49 Chaetodon● plebeius (1.1) ● 34 Scarus psittacus (1.7) 12● Chum salmon (2.0) log(mean) 50 Gomphosus● varius (1.1) ● 35 Pomacentrus moluccensis (1.6) ●13 Chinook salmon (2.0) 51 Chaetodon trifasciatus (1.0) ● 36 Acanthochromis polyacanthus (1.6) ● 14 Chinook salmon (1.9) 37 Neopomacentrus azysron (1.5) ● 15 ChumReef salmon fishes (1.9) ● Salmon RE mean ● 38 Chlorurus sordidus (1.5) ● 16 Pink salmon, odd years (1.7) Moth RE mean ● 39 Ctenochaetus spp (1.5) ● 17 Pink salmon, even years (1.7) Reef fishes RE mean d ● 40 Pomacentrus lepidogenys (1.5) ● 18 Atlantic salmon (1.6) ID: 10 41 Plectropomus leopardus (1.5) ● 19 Chinook salmon (1.6) ● z = 2.1 ● 42 Scarus chameleon (1.3) ● 0.5 20 Chum1 salmon2 (1.5)5 10 43 Chlorurus microrhinos (1.3) ● 44 Scarus frenatus (1.3) ● 21 ThePor tmagpiefolio eff ectmoth (PE) (1.9) ● 45 Hemigymnus melapterus (1.2) ● 22 Common quaker moth (1.8) ● 46 Hemigymnus fasciatus (1.2) ● 23 Common emerald moth (1.7) ● Moths 47 Scarus niger (1.2) ● 24 Square−spot rustic moth (1.7)ID: 51 ● 48 Epibulus insidiator (1.1) ● 25 Brown silver−lines moth (1.7)z = 1.2 ● c 49 Chaetodon plebeius (1.1) ● 26 Mottled umber moth (1.7) ● 50 Gomphosus varius (1.1) ● 27 Ingrailed claylog(mean) moth (1.7) ● ● ● 51 Chaetodon trifasciatus (1.0) 28 Yellow−line quaker moth (1.7) iance) ● r
29 Common swift moth (1.7) a Salmon RE mean 30 December moth (1.6) ● v ●
Moth RE mean 31 Common footman moth (1.6) log( ● Reef fishes RE mean 32 Heart & dart moth (1.5) ID: 34 33 Feathered thorn moth (1.5) ● z = 1.6 0.5 1 2 5 3410 Scarus psittacus (1.7) ● 35 Pomacentrus moluccensis (1.6) ● Portfolio effect36 (PE) Acanthochromis polyacanthus (1.6) ● 37 Neopomacentrus azysron (1.5) ● Reef fishes 38 Chlorurus sordidus (1.5) ● 39 Ctenochaetus spp (1.5) ● d 40 Pomacentrus lepidogenys (1.5) ● 41 Plectropomus leopardus (1.5) ● 42 Scarus chameleon (1.3) ● 43 Chlorurus microrhinos (1.3) ● 44 Scarus frenatus (1.3) ● 45 Hemigymnus melapterus (1.2) ● 46 Hemigymnus fasciatus (1.2) ● 47 Scarus niger (1.2) ● ID: 51 48 Epibulus insidiator (1.1) ● z = 1.2 49 Chaetodon plebeius (1.1) ● 50 Gomphosus varius (1.1) ● log(mean) 51 Chaetodon trifasciatus (1.0) ● Salmon RE mean Moth RE mean Reef fishes RE mean
0.5 1 2 5 10 Portfolio effect (PE) 1 Coho salmon (2.4) a ● ● Mean−variance PE 2 Pink salmon, odd years (2.3) ● Average−CV PE 3 Sockeye salmon (2.2) ● 4 Sockeye salmon (2.1) ● 5 Pink salmon, odd years (2.1) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) ● 8 Pink salmon, even years (2.0) ● 9 Sockeye salmon (2.0) ● Salmon 10 Pink salmon, even years (2.0) ● b 11 Atlantic salmon (2.0) ● 12 Chum salmon (2.0) ● 13 Chinook salmon (2.0) ● 14 Chinook salmon (1.9) ● 15 Chum salmon (1.9) ● ● 1 Coho salmon (2.4)16 Pinka salmon, odd y●ears (1.7) ● Mean−variance PE ● 2 Pink salmon, odd years 17(2.3) Pink salmon, even● years (1.7) Average−CV PE 3 Sockeye salmon (2.2) 18 Atlantic salmon● (1.6) ● ID: 10 4 Sockeye salmon (2.1) 19 Chinook salmon● (1.6) ● z = 2.1 5 Pink salmon, odd years (2.1) 20 Chum salmon● (1.5) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) 21 The magpie● moth (1.9) ● 8 Pink salmon, even years (2.0)22 Common quaker● moth (1.8) ● 9 Sockeye salmon (2.0)23 Common emer●ald moth (1.7) ●Salmon Moths 10 Pink salmon, even years 24(2.0) Square−spot rustic ●moth (1.7) ●b 11 Atlantic salmon (2.0)25 Brown silver−lines● moth (1.7) ● c 12 Chum salmon (2.0)26 Mottled umber● moth (1.7) ● 13 Chinook salmon (2.0) 27 Ingrailed cla●y moth (1.7) ● ● ● 14 Chinook salmon (1.9)28 Yellow−line quaker moth (1.7) iance) ● ● r 15 Chum salmon (1.9)29 Common swift moth (1.7) a 16 Pink salmon, odd years (1.7) 30 December● moth (1.6) ● v ● ●
17 Pink salmon, even years (1.7)31 Common footman moth (1.6) log( ● ● 18 Atlantic salmon (1.6) 32 Heart & dart moth (1.5) ID: 10 ID: 34 33 Feathered tho●rn moth (1.5) ● 19 Chinook salmon (1.6) z = 2.1 z = 1.6 20 Chum salmon (1.5) ● 34 Scarus psittacus (1.7) ● 21 The magpie moth35 (1.9) Pomacentrus● moluccensis (1.6) ● 22 Common quaker 36moth Acanthochromis (1.8) polyacanthus● (1.6) ● ● 23 Common emerald moth37 (1.7) Neopomacentrus azysron● (1.5) Moths Reef fishes 24 Square−spot rustic moth (1.7) 38 Chlorurus sordidus● (1.5) ● 25 Brown silver−lines moth (1.7) 39 Ctenochaetus● spp (1.5) ● c d 26 Mottled umber moth40 (1.7) Pomacentrus lepidoge● nys (1.5) ● 27 Ingrailed clay moth (1.7)41 Plectropomus leopardus● (1.5) ● 42 Scarus chameleon● (1.3) ● 28 Yellow−line quaker moth (1.7) iance) ● ● r
29 Common swift moth (1.7)43 Chlorurus microrhinos (1.3) a 30 December moth (1.6) 44 Scarus frenatus● (1.3) ● v 45 Hemigymnus melapte● rus (1.2) ●
31 Common footman moth (1.6) log( 46 Hemigymnus● fasciatus (1.2) ● 32 Heart & dart moth (1.5) ID: 34 ID: 51 33 Feathered thorn moth (1.5) 47 Sca● rus niger (1.2) ● 48 Epibulus insidiator (1.1) ● z = 1.6 z = 1.2 34 Scarus psittacus (1.7)49 Chaetodon plebeius● (1.1) ● ● log(mean) 35 Pomacentrus moluccensis (1.6) 50 Gomphosus● varius (1.1) 36 Acanthochromis polyacanthus (1.6)51 Chaetodon● trifasciatus (1.0) ● 37 Neopomacentrus azysron (1.5) ● Reeflog(mean) fishes 38 Chlorurus sordidus (1.5) Salmon● RE mean 39 Ctenochaetus spp (1.5) Moth● RE mean d 40 Pomacentrus lepidogenys (1.5) Reef fishes● RE mean 41 Plectropomus leopardus (1.5) ● 42 Scarus chameleon (1.3) ● 43 Chlorurus microrhinos (1.3) ● 0.5 1 2 5 10 ● 44 Scarus frenatus (1.3) Portfolio effect (PE) 45 Hemigymnus melapterus (1.2) ● 46 Hemigymnus fasciatus (1.2) ● 47 Scarus niger (1.2) ● ID: 51 48 Epibulus insidiator (1.1) ● z = 1.2 49 Chaetodon plebeius (1.1) ● 50 Gomphosus varius (1.1) ● log(mean) 51 Chaetodon trifasciatus (1.0) ● Salmon RE mean Moth RE mean Reef fishes RE mean
0.5 1 2 5 10 Portfolio effect (PE) 1 Coho salmon ● 2 Pink salmon, odd years ● 3 Sockeye salmon ● 4 Sockeye salmon ● 5 Pink salmon, odd years ● 6 Sockeye salmon ● 7 Pink salmon, odd years ● 8 Pink salmon, even years ● 9 Sockeye salmon ● 10 Pink salmon, even years ● 11 Atlantic salmon ● 12 Chum salmon ● 13 Chinook salmon ● 14 Chinook salmon ● 15 Chum salmon ● 16 Pink salmon, odd years ● 17 Pink salmon, even years ● 18 Atlantic salmon ● 19 Chinook salmon ● 20 Chum salmon ●
21 The magpie moth ● 22 Common quaker moth ● 23 Common emerald moth ● 24 Square−spot rustic moth ● 25 Brown silver−lines moth ● 26 Mottled umber moth ● 27 Ingrailed clay moth ● 28 Yellow−line quaker moth ● 29 Common swift moth ● 30 December moth ● 31 Common footman moth ● 32 Heart & dart moth ● 33 Feathered thorn moth ●
34 Scarus psittacus ● 35 Pomacentrus moluccensis ● 36 Acanthochromis polyacanthus ● 37 Neopomacentrus azysron ● 38 Chlorurus sordidus ● 39 Ctenochaetus spp ● 40 Pomacentrus lepidogenys ● 41 Plectropomus leopardus ● 42 Scarus chameleon ● 43 Chlorurus microrhinos ● 44 Scarus frenatus ● 45 Hemigymnus melapterus ● 46 Hemigymnus fasciatus ● 47 Scarus niger ● 48 Epibulus insidiator ● 49 Chaetodon plebeius ● 50 Gomphosus varius ● 51 Chaetodon trifasciatus ●
1.0 1.5 2.0 2.5 3.0 z value 1.Mean-variance relationship 2.Number 3.Correlation 4.Evenness Mean−variance PE Average−CV PE Subpopulation unevenness Low Mid High Low Mid High (a) (b) (c) (j) (k) (l) R. fishes 30 Moths y y y y y Low Salmon 10 PE 5 (d) (e) (f) (m) (n) (o) 30 y y y y y Mid
10 x x x x x x 2 1 (g) (h) (i) (p) (q) (r)
30 Subpopulation correlation 1 Number of subpopulations y y y y y High 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Subpopulation extinction
Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Indicator: ↓ ↓ Subpopulation extinction
Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Indicator: ↑ ↓ Increased synchrony
Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Indicator: ↓ ↓ Small populations get smaller and large populations get larger
Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Indicator: ↓ ↓ z decreases
Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Indicator: ↓ — z increases
Mean−variance PE Average−CV PE
CVµ low CVµ mid CVµ high CVµ low CVµ mid CVµ high a b c j k l R. fishes 30 Moths y y y y y 1 Salmon r = 0 10 PE d e f m n o 5 30 y y y y y
10 2
x x x x x x r = 0.25 1 g h i p q r 1 30 1 Number of subpopulations y y y y y r = 0.5 10 x x x x x x 0.5 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 Taylor's power law z−value Indicator: ↓ ↑ 1 Coho salmon (2.4) a ● ● Mean−variance PE 2 Pink salmon, odd years (2.3) ● Average−CV PE 3 Sockeye salmon (2.2) ● 4 Sockeye salmon (2.1) ● 5 Pink salmon, odd years (2.1) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) ● 8 Pink salmon, even years (2.0) ● 9 Sockeye salmon (2.0) ● Salmon 10 Pink salmon, even years (2.0) ● b 11 Atlantic salmon (2.0) ● 12 Chum salmon (2.0) ● 13 Chinook salmon (2.0) ● 14 Chinook salmon (1.9) ● 15 Chum salmon (1.9) ● ● 1 Coho salmon (2.4)16 Pinka salmon, odd y●ears (1.7) ● Mean−variance PE ● 2 Pink salmon, odd years 17(2.3) Pink salmon, even● years (1.7) Average−CV PE 3 Sockeye salmon (2.2) 18 Atlantic salmon● (1.6) ● ID: 10 4 Sockeye salmon (2.1) 19 Chinook salmon● (1.6) ● z = 2.1 5 Pink salmon, odd years (2.1) 20 Chum salmon● (1.5) ● Metapopulation 6 Sockeye salmon (2.1) ● Subpopulations 7 Pink salmon, odd years (2.1) 21 The magpie● moth (1.9) ● 8 Pink salmon, even years (2.0)22 Common quaker● moth (1.8) ● 9 Sockeye salmon (2.0)23 Common emer●ald moth (1.7) ●Salmon Moths 10 Pink salmon, even years 24(2.0) Square−spot rustic ●moth (1.7) ●b 11 Atlantic salmon (2.0)25 Brown silver−lines● moth (1.7) ● c 12 Chum salmon (2.0)26 Mottled umber● moth (1.7) ● 13 Chinook salmon (2.0) 27 Ingrailed cla●y moth (1.7) ● ● ● 14 Chinook salmon (1.9)28 Yellow−line quaker moth (1.7) iance) ● ● r 15 Chum salmon (1.9)29 Common swift moth (1.7) a 16 Pink salmon, odd years (1.7) 30 December● moth (1.6) ● v ● ●
17 Pink salmon, even years (1.7)31 Common footman moth (1.6) log( ● ● 18 Atlantic salmon (1.6) 32 Heart & dart moth (1.5) ID: 10 ID: 34 33 Feathered tho●rn moth (1.5) ● 19 Chinook salmon (1.6) z = 2.1 z = 1.6 20 Chum salmon (1.5) ● 34 Scarus psittacus (1.7) ● 21 The magpie moth35 (1.9) Pomacentrus● moluccensis (1.6) ● 22 Common quaker 36moth Acanthochromis (1.8) polyacanthus● (1.6) ● ● 23 Common emerald moth37 (1.7) Neopomacentrus azysron● (1.5) Moths Reef fishes 24 Square−spot rustic moth (1.7) 38 Chlorurus sordidus● (1.5) ● 25 Brown silver−lines moth (1.7) 39 Ctenochaetus● spp (1.5) ● c d 26 Mottled umber moth40 (1.7) Pomacentrus lepidoge● nys (1.5) ● 27 Ingrailed clay moth (1.7)41 Plectropomus leopardus● (1.5) ● 42 Scarus chameleon● (1.3) ● 28 Yellow−line quaker moth (1.7) iance) ● ● r
29 Common swift moth (1.7)43 Chlorurus microrhinos (1.3) a 30 December moth (1.6) 44 Scarus frenatus● (1.3) ● v 45 Hemigymnus melapte● rus (1.2) ●
31 Common footman moth (1.6) log( 46 Hemigymnus● fasciatus (1.2) ● 32 Heart & dart moth (1.5) ID: 34 ID: 51 33 Feathered thorn moth (1.5) 47 Sca● rus niger (1.2) ● 48 Epibulus insidiator (1.1) ● z = 1.6 z = 1.2 34 Scarus psittacus (1.7)49 Chaetodon plebeius● (1.1) ● ● log(mean) 35 Pomacentrus moluccensis (1.6) 50 Gomphosus● varius (1.1) 36 Acanthochromis polyacanthus (1.6)51 Chaetodon● trifasciatus (1.0) ● 37 Neopomacentrus azysron (1.5) ● Reeflog(mean) fishes 38 Chlorurus sordidus (1.5) Salmon● RE mean 39 Ctenochaetus spp (1.5) Moth● RE mean d 40 Pomacentrus lepidogenys (1.5) Reef fishes● RE mean 41 Plectropomus leopardus (1.5) ● 42 Scarus chameleon (1.3) ● 43 Chlorurus microrhinos (1.3) ● 0.5 1 2 5 10 ● 44 Scarus frenatus (1.3) Portfolio effect (PE) 45 Hemigymnus melapterus (1.2) ● 46 Hemigymnus fasciatus (1.2) ● 47 Scarus niger (1.2) ● ID: 51 48 Epibulus insidiator (1.1) ● z = 1.2 49 Chaetodon plebeius (1.1) ● 50 Gomphosus varius (1.1) ● log(mean) 51 Chaetodon trifasciatus (1.0) ● Salmon RE mean Moth RE mean Reef fishes RE mean
0.5 1 2 5 10 Portfolio effect (PE) 1 Salmon ● 2 ● 3 ● 4 ● 5 ● 6 ● 7 ● 8 ●
z = 2.4 z = 2.3 z = 2.2 z = 2.1 z = 2.1 z = 2.1 z = 2.1 z = 2.0 ● ● ● Subpopulation variance Subpopulation variance ● Subpopulation variance Subpopulation variance Subpopulation variance ● Subpopulation variance Subpopulation variance Subpopulation variance ● 9 10 11 ● 12 13 14 ● 15 16
Subpopulation meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance mean abundance z = 2.0 z = 2.0 z = 2.0 z = 2.0 z = 2.0 z = 1.9 z = 1.9 z = 1.8 ● ● ● Subpopulation variance 17 Subpopulation variance ● 18 Subpopulation variance ● 19 Subpopulation variance 20 Subpopulation variance 21 MothsSubpopulation variance 22 Subpopulation variance 23 Subpopulation variance ● 24 ● ●
Subpopulation meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance mean abundance z = 1.7 z = 1.6 z = 1.6 z = 1.5 z = 1.9 z = 1.8 z = 1.7 z = 1.7 ● ● ●
Subpopulation variance Subpopulation variance ● Subpopulation variance Subpopulation variance Subpopulation variance Subpopulation variance Subpopulation variance ● Subpopulation variance 25 26 ● 27 28 29 30 31 32 ● ●
Subpopulation meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance mean abundance
log(variance) z = 1.7 z = 1.7 z = 1.7 z = 1.7 z = 1.7 z = 1.6 z = 1.6 z = 1.5 ● ● ● Subpopulation variance 33 Subpopulation variance 34 Reef fishesSubpopulation variance 35 Subpopulation variance ● 36 Subpopulation variance 37 Subpopulation variance 38 Subpopulation variance 39 Subpopulation variance 40 ● ● ● ●
Subpopulation meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance mean abundance z = 1.4 z = 1.7 z = 1.6 z = 1.6 z = 1.6 z = 1.5 z = 1.5 z = 1.5
Subpopulation variance 41 Subpopulation variance ● 42 Subpopulation variance 43 Subpopulation variance 44 Subpopulation variance ● 45 Subpopulation variance 46 Subpopulation variance 47 Subpopulation variance ● 48 ● ● ● ● ●
Subpopulation meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance mean abundance z = 1.5 z = 1.3 z = 1.3 z = 1.2 z = 1.2 z = 1.2 z = 1.2 z = 1.1
Subpopulation variance 49 Subpopulation variance ● 50 Subpopulation variance ● 51 Subpopulation variance Subpopulation variance Subpopulation variance Subpopulation variance Subpopulation variance
● Subpopulation meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance meanSubpopulation abundance mean abundance z = 1.1 z = 1.1 z = 1.0 Subpopulation variance Subpopulation variance Subpopulation variance log(mean) Average−CV PE Mean−variance PE vg. a 1 atic r
Fig. 3a Linear detrended Loess detrended Fig. 3a Linear detrended Loess detrended Quad Quad.−linear PE 1 Alternative mean-variance fits 5 2 3 Extrapolation is suspect 4 5 6 7 8 Average−CV PE Mean−variance PE 2 9 1
10 1 11 vg.
Salmon 12 13 a 14 1 15
16 1 atic 17 r 18 19
20 Fig. 3a Linear detrended Loess detrended Fig. 3a Linear detrended Loess detrended Quad Quad.−linear PE 0.5 1 5 212 223 234 245 256 267 278 2 289 1 Moths 2910 1 3011
Salmon 3112 3213 3314 1 15 3416 3517 3618 3719 0.5 3820 39 4021 4122 4223 4324 4425 Reef fishes 4526 4627 4728 Moths 29 4830 4931 5032 5133 34 35 36 37 38 39 40 41 42 43 44 Reef fishes 45 46 47 48 49 50 51 Z Competition Measurement error Demographic stochasticity Z Hidden diversity (a) Partial-asset Grizzly Commercial Commercial Recreational investors bear fisher 1 fisher 2 fisher
Ecological Chum Chinook assets salmon salmon
(b) Whole-asset Fisheries management Conservation investors agency agency What to do?
It’s complicated. Maximilien Brice, CERN a bit of background
Metophor Metric Management Joel Sartore, National Geographic