Core Network Compartments: Relative importance of ecosystems players in moving energy through the system

Transcription

1 Internatonal Envronmental Modellng and Software Socety (EMSs) 2012 Internatonal Congress on Envronmental Modellng and Software Managng Resources of a Lmted Planet, Sxth ennal Meetng, Lepzg, Germany R. Seppelt, A.A. Vonov, S. Lange,. ankamp (Eds.) Core Network Compartments: Relatve mportance of ecosystems players n movng energy through the system Ursula M. Scharler a, ran. ath b,c a School of Lfe Scences, Unversty of KwaZulu Natal, South Afrca emal: scharler@ukzn.ac.za b ology epartment, Towson Unversty, Towson, USA c Advanced Systems Analyss Program, IIASA, Laxenburg, Austra Abstract: Ecosystems that are depcted as nodes (speces groups) and lnks (trophc transfers) encompass well defned roles n terms of ther trophc structure. Some are prmary producers and furnsh the system wth newly bound energy or nutrents, whereas others dvde themselves over varous trophc levels creatng a herarchy of energy use and reuse. All waste and mortalty products of nodes comprse the non-lvng envronment of ecosystems, often supportng a consderable part of the system as detrtus. All food sources are n general used, but are so to varable extents. Some lnks are always among the maor lnks, e.g. flows from detrtus or remneralsaton from bactera. Smlarly, flows nto and from hgh turnover nodes, whch are ether small speces wth hgh turnover rates, or those wth dsproportonal hgh standng stock play an mportant role n shuntng energy through the system. Ecosystem ndces calculated from weghted ecologcal networks descrbng the patterns of energy flow through an ecosystem are often appled to emprcal data n order to categorse the system as an effcent or neffcent energy user. We calculated flow dversty (as Shannon s Index) and average mutual nformaton (AMI, as the degree of flow constrant) accordng to the method of Ulanowcz (1986). Specal attenton was gven to the contrbuton of each system part to the overall holstc property. A comparson of several, manly estuarne, ecosystems, shows that t s mostly flows nvolvng the same speces groups contrbutng to the bulk to the ndex value. These were flows from detrtus, bactera, and prmary producers. The relatve mportance of flows from heterotrophc groups (e.g., speces and speces groups of macrozoobenthos, meofauna, zooplankton, fsh) compared to that of the man groups was comparatvely mnor. Keywords: Ecologcal network analyss; Communty Modules, Estuarne ecosystems, Speces Identfcaton; Ascendency; low versty 1 INTROUCTION In ecosystem level studes, the ecosystem s charactersed ether n terms of ts behavour as a unt, or that of speces and speces groups wthn the context of the entre system. In ths paper, we nvestgate trophc connectvty between speces and the resultng patterns of nteractons n the context of the entre system. To descrbe patterns of energy flows n ecosystems, ndces such as Ascendency and evelopment Capacty have been used (Ulanowcz 1986; Ulanowcz et al. 2009). These are proposed to descrbe ecosystem behavour n terms of flow constrants (Ascendency (A), Average Mutual Informaton (AMI)) and the dversty of trophc flows (evelopment Capacty (C), low dversty (H)) from the

2 Scharler and ath / Core network compartments probabltes of occurrence of weghted trophc flows. A and C are equal to AMI and H scaled by the total system throughput, TST (AMI x TST = A; H x TST = C). The ndces, especally Ascendency (A) and evelopment Capacty (C) have been used to characterse the developmental state of ecosystems (e.g., Latham and Scully, 2002; Patríco et al., 2006), ether n relaton to envronmental changes, or to track changes n ecosystem status over tme. AMI s usually hgh f there are few pathways transportng the bulk of materal and at ts lowest f all nodes are fully connected and lnks transport an equal amount of materal. As such, the ecosystem ndex of AMI (AMI SYS ) mportantly gves an mpresson on the overall flow organsaton wthn an ecosystem n terms of ts connectvty and flow dstrbuton. H as an ecosystem ndex, on the other hand, gves an ndcaton on the complexty of the ecosystem and a hgh H s assocated wth hgh uncertanty, complexty and dversty of flows (Ulanowcz, 1986; Latham and Scully, 2002). The values of AMI and H depend on the magntude of flows and connectvty of the system. There are varous reasons why energy flows are unequally dstrbuted n ecosystems, and they depend on the turnover rate of speces, the unequal energy requrements of speces, the varous degrees of omnvory or the trophc specalsaton between speces, and the avalablty of prey. In addton to comparng whole ecosystem ndces, t may be of nterest to nvestgate the proportonal contrbuton of the ndvdual trophc flows to the ecosystem ndex and so ascertan the mportance of ndvdual lnks wthn the context of the ecosystem. If the resoluton of the network s hgh enough, then the mportance of lnks from ndvdual speces can be calculated (e.g., commercally mportant fsh, crabs, mgratng speces, etc.), or otherwse those from groups of speces (e.g., functonal groups). The whole system ndces (H SYS, AMI SYS ) represent the sum of the ndex calculated for each ndvdual flow n the system (AMI IN, H IN ). AMI IN and H IN therefore descrbe the extent to whch the ndvdual ndex contrbutes to AMI SYS and H SYS. A hgh AMI IN value denotes a sngle lnk between predator and prey for energy transfer, or the domnant lnk of multple flows from a predator to varous prey, whereas a low value denotes multple outgong lnks transportng a smlar amount of materal (.e., there s no domnant lnk). AMI IN thus denotes how specalsed and mportant the trophc lnk s n transportng energy between two nodes. AMI IN n relaton to AMI SYS shows how mportant the partcular trophc flow s wthn the context of all flows n the ecosystem n terms of the quantty of energy transported n relaton to other flows leavng the same prey. H IN, on the other hand, descrbes the contrbuton of a partcular flow to the complexty of the ecosystem (H SYS ). Sngle flow H IN s calculated from a combnaton of ts contrbuton to complexty due to ts occurrence (small or large transport along lnk n relaton to total systems throughput, expressed as p), and the frequency of ts occurrence. In order to ascertan the roles ndvdual speces, speces groups and abotc components play n the energy transfer n ecosystems, we use the AMI and H values of ndvdual trophc flows to frstly characterse maor pathways n terms of AMI and H orgnatng from prey. Secondly these pathways are compared for several estuarne ecosystems. Ths we hope to acheve by dentfyng those flows that contrbute most to the potental for development (H SYS ) as well as to the realsed developmental status (AMI SYS ) n terms of energy transfer effcency n emprcal networks. 2.0 MATERIAL AN METHOS The ndces for flow dversty (H IN ) and average mutual nformaton (AMI IN ) are calculated from trophc flows between prey and predator, or abotc source and

3 Scharler and ath / Core network compartments grazer or detrtus feeder. In the calculatons below, flows from and to the outsde of the system, as well as respraton flows are not consdered. 2.1 low versty (H): The calculaton of flow dversty s acheved through applyng Shannon s formula to ndvdual trophc flows. A trophc flow that s rare has a hgh potental to contrbute to complexty, but due to ts rare occurrence ts actual contrbuton to the system s comparatvely low. The actual contrbuton of each trophc flow, calculated by Shannon s formula as H K p log p, can be expressed as (Ulanowcz 1986): H IN T k T.. T log T.. Where T denotes a flow from compartment to compartment, and T.. the sum of all flows, over all and compartments. The low versty ndex for the entre ecosystem, H SYS, s taken as the sum of H IN over all flows. (1) 2.2 Average Mutual Informaton (AMI): The Average Mutual Informaton (AMI) ndex s used to calculate whether the trophc flow patterns n the ecosystem contrbute to ordered or random behavour of flows between sources and snks (Ulanowcz 1986). or example, f a node s a source to many other nodes, and energy s dstrbuted equally along all outgong pathways, there s hghest uncertanty about whch ones of the outgong pathways wll transport the quantum of energy from the orgnatng node. However, f there s a domnant pathway, there s a hgher probablty that the quantum of energy wll use the domnant pathway. To calculate the degree of constrant on a flow s acheved by quantfyng the nformaton gan from probabltes of flows occurrng. rstly, the uncertanty that an event (flow) occurs s calculated by H K log p( a ) Thereafter, the uncertanty that the same event occurs s calculated from the condtonal probablty by knowng, n addton to what enters, what leaves a tmestep earler: H K log p, (3) where p a b a b p a, b ) / p( a ) ( (2), (4) and p(a,b ) s the ont probablty of the flow from speces to speces and s denoted as T /T.., whereas p(a ) as T. /T... Then, the condtonal probablty s subtracted from the ntal probablty: I K log p ( a ) [ k log p a b ] I K log[ p a b / p( a )]. (5) Translated nto flows, the formula for gan of nformaton s as follows: TT I K log T. T... where T. enotes all flows leavng compartment and T. denotes all flows enterng compartment. The nformaton gan for each ndvdual flow s weghted by the frequency of the flow n order to become AMI IN :, or (6)

4 Scharler and ath / Core network compartments AMI IN T TT K log T.. T. T... (7) AMI IN s hghest, f the flow T s the only flow leavng and the only flow enterng. Summng all AMI IN values over all trophc flows renders AMI SYS. H IN and AMI IN were calculated for three South Afrcan and three North Amercan estuarne ecosystems. The ndces were depcted for all flows n the system, and flows were grouped accordng to the dentty of the outgong node,.e. of the source. These ncluded Prmary Producers (), era (), Zooplankton (), Meofauna (), Macrozoobenthos (MZ), sh (), and etrtus (). The groups responsble for hgh H IN values contrbute most to the actual complexty of the system. Those responsble for hgh AMI IN values are constraned lnks between energy sources and snks. 3.0 RESULTS The dstrbuton of low dversty (H IN ) and Average Mutual Informaton (AMI IN ) are presented for trophc flows between all sources and snks n several estuarne ecosystems, and trophc groups contrbutng the bulk to H SYS and AMI SYS were dentfed. 3.1 low dversty (H): The H SYS ndces calculated for the ecosystems were, n general, very smlar (gure 1). The largest energy flows, T, when converted to H IN, contrbuted most to the whole systems ndex of H SYS. Ths same pattern was apparent for all ecosystems nvestgated, denotng the rsng H IN values wth ncreasng lnk weght. The same compartment types were responsble for formng the bulk of the H SYS value. These always ncluded detrtus, prmary producers and bactera, where detrtus provdes large amounts of energy to the ecosystems, and both prmary producers and bactera are charactersed by hgh turnover rates relatve to the remander of the system and are thus able to mantan relatvely hgh energy flows.

5 Scharler and ath / Core network compartments Sundays estuary Swartkops estuary H IN H IN MZ MZ Kromme estuary St. Marks estuary H IN MZ H IN MZ Narragansett estuary Chesapeake ay H IN H IN MZ MZ 0E-01 2E+05 4E+05 6E+05 8E+05 T (mgc/m 2 /y) 0 1E5 2E5 3E5 4E5 5E5 6E5 7E5 T (mgc/m 2 /summer) gure 1: H IN values of South Afrcan (Sundays, Swartkops, Kromme) and North Amercan (St. Marks, Narragansett, Chesapeake) estuarne ecosystems The proporton of trophc flows responsble for 80% of the contrbuton to H SYS values were between 11 and 16% of all flows. Consequently, 84-89% of the flows contrbute only 20% to the H SYS value n all emprcal networks. The nodes the flows were orgnatng from always ncluded varous forms of detrtus, bactera and prmary producers. In some cases, bulk detrtus feeders (e.g., depost feedng or suspenson feedng macrobenthos) or hghly aggregated groups (e.g., meofauna) that may have a large outflow due to the aggregaton are ncluded n the top 80%. The nodes wth the lowest contrbutons always nclude zooplankton and fsh groups, ncdental feedng lnks (e.g., those that feed on detrtus and ncdentally ngest bactera) or hghly dsaggregated groups that consequently have small flows.

6 Scharler and ath / Core network compartments 3.2 Average Mutual Informaton (AMI): Smlar to the H IN values, there are only few AMI IN values that consttute the bulk of the AMI SYS values (gure 2). Of the ca 100 to 270 trophc flows per system, between 4 and 10% contrbute 80% to the AMI SYS value. These lnks are thus contrbutng the bulk to the energy effcency of the entre system and are of utmost mportance n feedng avalable energy through the system. In general, the same nodes (manly detrtus, bactera, prmary producers), as for H IN, are part of the 4-10% of flows, and smlarly the hgher trophc levels contrbute very lttle to the system. Sundays estuary Swartkops estuary 10 8 AMI IN MZ AMI IN MZ Kromme estuary St. Marks estuary AMI IN MZ AMI IN MZ Narragansett estuary Chesapeake ay AMI IN E-01 2E+05 4E+05 6E+05 8E+05 T (mgc/m 2 /y) MZ AMI IN 0 1E5 2E5 3E5 4E5 5E5 6E5 7E5 T (mgc/m 2 /summer) gure 2: AMI IN values of South Afrcan (Sundays, Swartkops, Kromme) and North Amercan (St. Marks, Narragansett, Chesapeake) estuarne ecosystems. MZ

7 Scharler and ath / Core network compartments 4.0 CONCLUSION AN ISCUSSION rom the results above t s apparent that some nodes are more mportant than others n contrbutng to the energy effcency and the potental to develop wthn the framework of the gven amount of energy of a gven ecosystem. These ncluded manly the lower trophc levels, both abotc components as well as those convertng abotc energy nto bomass (prmary producers, bactera). The hgher trophc levels (zooplankton, fsh) n general contrbuted very lttle to the overall system organsaton n terms of energy flows. The bulk of the ndces that descrbe the potental for development are thus those that provde hgh energy flows relatve to the other nodes of the system, ether due to ther hgh bomass or hgh turnover rate. In addton, the way networks are ntally bult plays a strong role n the magntude of the ndces. Ths has prevously been demonstrated for Ascendency (Ulanowcz and Abarca-Arenas, 1997; Allesna et al., 2005). In ths study, hghly aggregated nodes whch had an ncreased energy flow due to aggregaton, also contrbuted more to the H SYS and AMI SYS values compared to f they had been dsaggregated nto speces or smaller speces groups. The consequence from ths fndng s that the ongong dscusson on trends and comparablty of Ascendency and evelopment Capacty (Ulanowcz, 1986) between ecosystems s thus also applcable to the AMI SYS and H SYS values, as well as H IN and AMI IN. A hgher degree of aggregaton wll ncrease the contrbuton of the flow values to the system value, whereas the resoluton n the assgnment of feedng lnks wll have an effect on the number of lnks makng a small or large contrbuton. Ths effect s apparent from the networks analysed for ths study, and t s typcal of many ecologcal networks, n that ndvdual fsh speces are assgned a node, whereas prmary producers, detrtus, zooplankton and benthc nvertebrates are mostly grouped nto functonal or speces groups wth few exceptons. Consequently, t s of mportance that n addton to the comparson of A and C, as well as AMI SYS and H SYS values, the contrbuton of ndvdual lnks s nvestgated. Ecosystems may thrve purely on prmary producers bndng energy, on detrtus and ther man consumers (e.g., bactera). Other trophc groups, although mportant for humanknd, may, purely n terms of energy flow, not be of great mportance to an ecosystem. However, f H s nterpreted as provdng room for development, ths may be the room created for hgher trophc levels whch, after all, are of hgher mportance n terms of sustanablty of ecosystems for humanknd. uture studes based on ths ntal nvestgaton can nvestgate further the trophc groups and ther rankng n the H IN and AMI IN values, to establsh clear preferences of certan nodes n certan postons. Secondly, ths method s useful when comparng tme seres of networks of the same system. Tme seres are perhaps better study obects snce they are n general bult n the same way and mssng nodes or lnks reflect real changes rather than the method of the researcher. Consequently, the change n the AMI SYS and H IN values can be tracked and the change n poston of ndvdual nodes over tme n the mportance of the system ascertaned. REERENCES Allesna, S., C. ondavall, and U. Scharler, The consequences of the aggregaton of detrtus pools n ecologcal networks. Ecologcal Modellng 189, , 2005.

8 Scharler and ath / Core network compartments Latham, L.G., and E.P. Scully, Quantfyng constrant to assess development n ecologcal networks. Ecologcal Modellng 154, 25 44, Patríco, J., R.E. Ulanowcz, M.A. Pardal, and J.C. Marques, Ascendency as Ecologcal Indcator for Envronmental Qualty Assessment at the Ecosystem Level: A Case Study. Hydrobologa 555, 19 30, Ulanowcz, R.E. Growth and evelopment. Sprnger Verlag, New York, 1986 Ulanowcz, R.E., and L.G. Abarca-Arenas, An nformatonal synthess of ecosystem structure and functon. Ecologcal Modellng 95, 1 10, Ulanowcz, R.E., S. Goerner,. Letaer, and R. Gomez, Quantfyng sustanablty: Reslence, effcency and the return of nformaton theory. Ecologcal Complexty 6, 27 36, 2009.