Ecological Systems as Complex Systems

8/10/2019 Ecological Systems as Complex Systems

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Diversity 2010, 2, 395-410; doi:10.3390/d2030395

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diversityISSN 1424-2818

www.m dpi.co m /journal/diversit

Article

Ecological Systems as Complex Systems: Challenges o! an

Eme!ging Science

"a#h$! Anan#1%

&% An#!e' (on)ale)2% *!+#+!ic ($icha!#

2% ,$!e .olasa

/an# ael Pa!!ott

4

1

!c"ool o# $nvironmental !ciences, %niversit o# &uelp", &uelp", 'ntario, (1& 2)1, *anada2+epartment o# iolo, c&ill %niversit, ontral ueec, 3 11, *anada;

$-ails: andrew.onalem cill.ca6.&.7; #red.uic"ard m cill.ca68.&.73

+epartment o# iolo, caster %niversit, amilton, 'ntario, ! 41, *anada;

$-ail:


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Diversity 2010, 2 140

1 Int!o#$ction

!ince seminal pulications on t"e suject D1,2E, t"e stud o# Fecoloical compleBitG "as ained

momentum. $Bamples o# t"is trend can e #ound in recent oo


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power-laws D15E. !imple measures suc" as t"ese can e used to distinuis" a random or "omoenous

ecoloical pattern #rom a compleB one and ma serve as dianostic tools to detect c"anes in t"e state

o# an ecosstem D1IE, as we s"all illustrate in suseJuent sections.

*ig$!e 1 @emporal, spatial and structural sinatures o# simple ordered and disorderedsstems versus a compleB sstem. 3a !inusoidal time series; ordered spatial pattern;

reular networE.

owever, application o# *!! to ecolo reJuires t"at compleB sinatures distinuis" random #rom

non-random ecoloical processes. @"is can e seen comparin 8iure 1 and 1c, in particular t"e

temporal, spatial or structural sinatures s"own in t"e last column. @"us, o# interest to *!! are patterns

and structures t"at arise #rom non-random processes. @"is points to anot"er major contriution o# *!!

to ecolo: t"e oservation t"at simple models, wit" certain


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well-de#ined, unc"anin spatiotemporal environments. @"e use o# simple models can improve our

understandin o# ecoloical dnamics and t"e mec"anistic oriins o# oserved patterns D1E. *lassical

models #rom *!! emp"asie t"e importance o# local interactions etween t"e MparticlesN #or t"e

#ormation o# sel#-oranied structure at larer scales D19E, and indeed t"ese tpes o# models "ave een

ale to eBplain t"e eBistence o# surprisin ecoloical patterns D20-22E.

Hn t"e #ollowin susections, we elaorate on "ow simple measures and models #rom *!! "ave

improved our understandin in t"ree important areas o# ecolo, namel #ood wes, patc" dnamics

and population #luctuations.

2-2- ood ebs

8ood we t"eories "ave traditionall emp"asied t"e stud o# stailit and compleBit in relation to

t"e structure o# trop"ic interactions. Oecent researc" in rap" t"eor and networ,2E and t"e prediction o# patterns o# coeBtinction D29E. !uc" results are re-#uelin t"e

deate aout w"et"er ecoloical communities assemle towards structures t"at #avor persistence and

dnamic stailit D30,31E.

)"ile t"e aove researc" "as contriuted to t"e c"aracteriation o# t"e static structures o# #ood

wes, new dnamic models o# population dnamics #rom *!! "ave s"ed li"t on t"e stud o# "ow

#ood we structures assemle and c"ane over time D32-3IE. @"ese models reproduce man

p"enomena oserved in empirical data suc" as power law scalin o# speciation and eBtinction events,

non-random 6ut not scale-#ree7 networ< structure and relativel s"ort #ood c"ain lent"s. !imilar to

traditional otE. Hn t"ese models, species are represented diital

FenomesG. ow levels o# mutation durin reproduction allow a speciesN enome to evolve, enalin a

species to adapt its interaction strent"s and ot"er parameters. !uc" dnamic models enerate

spatio-temporal data on interaction wes 6not just predator-pre networ


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Diversity 2010, 2 14/

creatin new avenues o# researc" in ecolo, suc" as studies o# species co-evolution and t"e #ormation

o# ecoloical communities, suc" models ma enale ecoloists to draw parallels etween t"e dnamics

o# ecoloical networ


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variationG in population densities D50,51E is a sinature o# a power law relations"ip etween t"e

#reJuenc and t"e variance o# population #luctuations. ore speci#icall, population #luctuations wit"

a 1/f

pattern "ave a variance 6power7 t"at is proportional to t"e reciprocal o# #reJuenc 6f7; t"e

dominance o# low #reJuencies enenders t"e propert o# increasin variance and a lon-term

autocorrelation in densities over time. Hn an analsis o# 544 lon-term population time series Hnc"austi

and alle #ound t"at t"e distriution o# spectral eBponents centered on a median value o# 1.0

indicatin t"at man populations "ave a 1/f distriution D52E. *!! "as paid special attention to 1/f

#luctuations, w"ere eta is eJual to one ecause t"is is indicative o# scale invariance, a propert tpical

o# man compleB p"enomena li


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current and #uture states. )e emp"asie t"e importance o# memor and environmental variailit

ecause t"ese are 1E. promisin measure o# compleBit re#lectin t"e

dnamics o# diversit 6dnamical entrop7, t"at eBplicitl eBamine t"e relations"ips etween diversit,

compleBit, perturation and stailit "as also een recentl proposed D>2E. Hnterestinl, a new

measure #ounded in "ierarc" t"eor D55E #inds t"at "i"est levels o# compleBit occur at intermediate

derees o# interation and low levels o# perturation. numer o# ot"er indicators "ave een

proposed, includin increasin variance and increasin autocorrelation in 3E. (ew measures w"ic" attempt to interate disturance and variailit, into classical

measures o# compleBit, will e o# particular dianostic value in studies o# loal ecoloical c"ane.8urt"ermore, approac"es t"at provide #urt"er understandin on t"e lin4,>5E.


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*ig$!e 2 n illustration o# t"e components o# ecoloical compleBit. *ompleB ecoloical

sstems 6e.., #orests4 are t"ose in w"ic" structure 6e.., ap-sie distriution7 and

dnamics 6e.., succession7 derive #rom memor-ased 6e.., previous tree #alls, seed

anIE. $Bamples include diapause es, seed an>,>E.

+isturance 6#ire, drou"t7 ma create "i"l persistent patterns at t"e landscape scale t"at ma entrain

#uture ecosstem processes D>I,>9,0E. emor implies t"at t"e sstem can draw upon past events toin#orm current and #uture e"aviour; t"is is tpicall t"e propert o# t"e oranism. 8or eBample, recent

results suest t"at oranisms can en"ance t"eir #itness drawin upon t"e memor o# past pre


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Jualit, or distriution, w"en #orain D1,2E. 8rom an oserverPs perspective, memor is mani#ested

a stron temporal dependence in t"e dnamics o# an ecoloical sstem D3E. odelin

memor-ased sstems can e ac"ieved incorporatin autocorrelation or a time-la into t"e model

structure D4E, ut it remains a c"allene et to e addressed man *!! models. @"e trend in

individual-ased models D5E 6H7 is to incorporate memor allowin FaentsG to ma


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rupture, and eart"JuaE and collapse dnamics can

more enerall e applied to wild#ires, disease and insect outrea


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@"is article was orn out o# an oranied oral session entitled FiocompleBit !calin: an

ecoloical perspectiveG at t"e 2004 nnual eetin o# t"e $coloical !ociet o# merica. @"e aut"ors

t"an< ndrea elrano, ai-ian i, t"e late $ri< Oauc" and +avid !c"neider #or also presentin

papers in t"e session and earlier discussions. 8undin is rate#ull ac


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1. &rimm, L.; Oevilla, $.; erer, %.; =eltsc", 8.; ooij, )..; Oailsac0-14>>.

2>. &irvan, .; (ewman, .$.=. *ommunit structure in social and ioloical networ21->2I.

2. rause, .$.; 8ran.

31. elian, *.=.; ascompte, =. *ompleB networ05->0.

32. )illiams, O.=.; artine, (.+. !imple rules ield compleB #ood wes. at"re 2000, 0,

10-13.33. Oi


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3. Karrott, .; o5-99.

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models.!roc- Roy- .oc- ondon .er- - 17, 231-1>3>.

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iol- 17, 1=9, 1>9-1I.

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compleBit.$col- ndic- 200, 9, >0->90.

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U 2010 t"e aut"ors; licensee olecular +iversit Kreservation Hnternational, asel, !witerland.

@"is article is an open-access article distriuted under t"e terms and conditions o# t"e *reative

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