THE ROLE OF PLANT TRAITS

Transcription

1 THE ROLE OF PLANT TRAITS IN THE REGULATION OF DIVERSITY - A MODELLING STUDY - DE ROL VAN PLANTENEIGENSCHAPPEN IN DE REGULATIE VAN DIVERSTEIT - EEN MODELSTUDIE - (met een samenvatting in et Nederlands) Proefscrift Ter verkrijging van de graad van doctor aan de Universiteit van Utrect o gezag van de Rector Magnificus, Prof. Dr. W.H. Gisen, ingevolge et besluit van et College voor Promoties in et oenbaar te verdedigen o maandag 8 maart 24 des middags te 6.5 uur door Teresia Elisabet Pronk geboren o 2 maart 976 te Amersfoort

2 Promotor: Prof. Dr. M.J.A. Werger Co-romotor: Dr. F. Scieving Plant Ecology Grou, Faculty of Biology Utrect University T.E. Pronk Te role of lant traits in te regulation of diversity ISBN Keywords: lant traits, ontogeny, allocation attern, eigt growt, reroduction, cometition, fitness, coeistence, diversity, mecanistic model, game teory Coyrigt 24 T.E. Pronk All rigts reserved.

3 VOOR MIJN OUDERS Te fact tat organisms living in different laces are different is easy to elain by Wallacian forces. Te question of ow so many sorts of organisms are able to ersist togeter in te same lace is muc more difficult to answer, is muc more interesting; it demands a biotic interretation and a Darwinian solution. Harer (977 : 75)

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5 CONTENTS: Cater General Introduction 7 Cater 2 A mecanistic model for te simulation of growt and fitness of annual lants 7 Tessa E. Pronk, Feike Scieving Cater 3 Eloring eigt growt traits as a mecanism for coeistence 37 Tessa E. Pronk, Feike Scieving, Marinus J.A. Werger Cater 4 Plant games wit eigt 59 Tessa E. Pronk, Heinjo J. During, Feike Scieving, Marinus J.A. Werger Cater 5 Seed mass investment as a mecanism for coeistence 79 Tessa E. Pronk, Feike Scieving, Heinjo J. During Cater 6 Effects of disersal distance on te coeistence of lants differing in cometitive strengt 3 Tessa E. Pronk Cater 7 Te role of crown sae in lant growt and cometition 29 Tessa E. Pronk, Feike Scieving Cater 8 Summary and General discussion 5 Cited references 57 Samenvatting 7 Nawoord 74 Curriculum vitae 75

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7 CHAPTER GENERAL INTRODUCTION Processes accounting for te maintenance of diversity Te issue of secies diversity is an intriguing toic. Since long it as become a central question in community ecology ow large numbers of cometing secies can coeist. Gause (934) first formulated te classic teory on te relation between cometition and diversity. Tis teory was based on a model made by Lotka (925) and Volterra (928). Tis model was te basis for many later models on cometition. Lotka (925) and Volterra (928) sowed tat, wen two secies cometed for similar resources in a similar way, one would always be te suerior cometitor and eventually outcomete te weaker secies. Te teory was suorted by observations in eerimental settings. Later tis was called te cometitive eclusion rincile (Hardin, 96). Considering tat lants in a community can artition te available resources, te teory was generalised by stating tat te number of secies in a community could not eceed te number of limiting resources (e.g. McArtur & Levins, 964). Plants in general need te same resources, te most imortant being ligt, water and nitrogen. If tese are te only imortant limiting factors, it seems to contrast wit te large diversity observed in many natural systems, suc as troical rain forests or calk grasslands. Since te formulation of Gause s cometitive eclusion rincile, teories ave been develoed tat try to solve te arado of diversity. Palmer (994) distinguised no less tan 2 ublised teories. Tese teories can rougly be categorised by teir focus on mecanisms tat avoid, delay or disrut cometitive eclusion (Palmer, 994). Avoid cometitive eclusion Wen a secies in a community increases in abundance it can lead to te etinction of oter secies in te community. However, it does not always come to tat. In some cases, te rocess can be ut to a alt by stabilising mecanisms suc as negative density or frequency deendence. For instance, ig densities of a secies can be more suscetible to secies-secific ests. Tis will revent te secies from being very abundant. Also, as frequency increases, intra-secific cometition can reduce a secies vigour. Accordingly, Lotka -Volterra models redict tat secies can coeist if intra-secific cometition is larger tan inter-secific cometition. Tese kind of self-limitations can also occur less deterministic. A recently emerging teory is tat of cometitive caos (Huisman & Weissing, 2; Roelke et al., 23). Little canges in initial conditions can ut a system onto a comletely different trajectory of develoment, and te develoment in itself can be caotic. Predicting te outcome of cometition in tese systems can be etremely difficult, or even imossible. 7

8 CHAPTER Anoter elanation for observed small-scale diversity is te teory of nice differentiation. In 975, Diamond formally formulated te nice differentiation yotesis. Tis states tat secies will -in order to avoid cometition- secialise (or be forced) on a secific combination of resources. As a consequence, te number of available nices will be te uer limit of te number of secies in a community. Tere are many interretations on te nature of tese nices. Nices can reresent different resource requirements or different a-biotic conditions in te microabitat (Leibold, 995), bot available as temoral or satial windows of oortunity for secies to secialise on. Related to tis teorem is te resource ratio yotesis (Tilman, 985) tat suoses tat secies need secific quantities and combinations of resources. Te cange in relative availabilities of limiting resources troug time or sace will result in diversity of secies. A recent teory on te regulation of diversity is te romoting role of diversity on itself: Diversity begets diversity. It argues tat diversity gives rise to many different conditions in sace and time, roviding nices for additional secies (Palmer & Maurer, 997; Franzen, 2). In tis case te question is not wy tere are so many secies coeisting, but rater wy tere are not more secies coeisting. Variation in life-istory teory can also account for coeistence. Cometitioncolonisation models elain coeistence of secies tat sow a trade-off in cometitive ability versus disersal. Te teory states tat te most cometitive secies is a oor diserser and is tus unable to occuy all sites, and te secies tat is te least cometitive is te most likely to reac an emty site. Many secies differing in cometitive ability were found to be able to coeist as redicted by tis teorem. Tilman (994) even sowed tat an unlimited amount of secies could coeist. Continuous creation of emty atces by disturbance or mortality and consequent establisment of lants erein is te key rocess for attaining diversity along te rules of tis teorem. Oter trade-offs, suc as seed size and number (Turnbull et al., 999), cometitive ability and mortality (Adler, 999), or a sift in cometitive interactions during life istorystages (Goldberg et al., 2), can in teory lead to coeistence of lants. Delay cometitive eclusion A contrasting elanation for te coeistence of secies is te suggestion tat differences between secies are in fact negligible. Te more similar secies are, te less tey will differ in fitness and te longer it will take for te eclusion of one secies by te oter. Random and neutral rocesses will dictate te comosition of lant communities rater tan differences between secies. Te teory of island biogeogray (McArtur & Wilson, 967) is based on tis assumtion. In tis teory it is argued tat secies essentially are equivalent in cometitive ability, lifesan and reroduction. Site occuation is random. Te model was later etended by Hubbel (2). Te teory also bears resemblance to te secies-ool model (Eriksson, 993). In tis model te comosition is determined by te regional secies ool and inter-secific interactions lay minor roles. Also te carousel model (van der Maarel & Sykes, 993) is related. It is stated in tis teory tat all lants in a similar abitat, for eamle a grassland, ave te 8

9 CHAPTER same abitat nice and all lants can find some window of oortunity to establis or reestablis in te community by local lant mortality and ig secies mobility. Satial attern as also roven a factor in delaying cometitive eclusion. As a result of a sort disersal distance, secies tend to form mono-secific aggregates. On average, te inter-secific interactions are reduced. Tis will be advantageous for weaker cometitors because on average te cometitive ressure of stronger secies is less witin tese aggregates. On te oter and, for strong cometitors te cometition is more intense because tey eerience more con-secific interactions. As a consequence te cometitive dislacement of weak secies is delayed (Pacala & Levin, 997; Cave & Levin, 22). Disrut cometitive eclusion In te absence of disturbance, ecosystems tend to sow a succession towards vegetation dominated by a few secies. Local disturbance as been regarded as one of te driving factors beind te maintenance of diversity. Disturbance removes art of te vegetation. In tose disturbed atces oter conditions revail, for instance caused by relieve of cometitive ressure. Secies tat would be outcometed at undisturbed atces can establis and grow. Later tese disturbed atces again become filled wit more cometitive secies. Local disturbance can tus create a mosaic of different successional stages in communities (Sousa, 984). At a larger scale, secies from different successional stages togeter will score a ig secies diversity. Tis view of lant communities consisting of mosaics of atces is resent in a wole range of different teories (see Wu & Levin, 994). Under some kind of disturbance, like mowing or grazing, te dominant secies will suffer most. Tis can be because te dominant secies are affected disroortionately, for instance because of a tall stature or ig alatability. Subordinate secies can erform relatively well under suc circumstances. By grazing or mowing regimes, several secies can eist alongside (Bobbink & Willems, 993). A need for mecanisms All above teories attemt to elain observed atterns of diversity in communities. So far it as been common ractice to simlify a system to suc an etent tat it can ardly be elained eactly wy observed atterns occur. Agnew et al. stated in 993: We ave not reaced te state were we can understand vegetation dynamics by describing mecanisms. In many cases we can at best describe and quantify rocesses, wic later ave to be understood by finding underlying mecanisms. Esecially cometition as te otential to strongly influence te community structure (Grace & Tilman, 99; Goldberg & Barton, 992). Te lack of insigt in te mecanisms beind cometition as amered rogress in te understanding of lant cometition (Scwinning & Weiner, 998; Berntson & Wayne, 2). Increasing tis understanding will aid to build a coerent 9

10 CHAPTER teory on lant cometition and its role in dynamics, structure and evolution of lant communities (Connoly et al., 2). In te cometition for ligt, lants interact by modifying te available ligt. Witin te vegetation, te different leaf layers in te canoy intercet ligt, creating a vertical ligt climate. It will deend on te develoing ligt gradient and te osition of te lant erein, ow it will erform. Plant eigt and leaf area are te most imortant traits determining te strengt of te interactions between lants, as tey determine te amount of ligt interceted by a lant itself, as well as affect te quality and quantity of ligt tat is available for neigbouring lants. Heigt and leaf area traits are te result of caracteristics of allocation and growt. Consequently, wen studying interactions between lants in a canoy, te investment attern sould be elicitly included. Plants can (or be forced to-) alter teir eigt and leaf area growt in resonse to te resence of neigbours (Weiner & Tomas, 992). Cometition tus triggers te lant to alter its leaf area and eigt growt and tis affects teir cometitive interactions. Traits associated wit leaf area are, amongst oters, secific leaf area, leaf angle, leaf turnover, individual leaf size, leaf nitrogen content, and evaoration of water. Traits associated wit eigt growt are, for instance, stem diameter and te distribution and density of suortive tissue. Canges in tese traits can reflect on te root system as well. For lants wit a limited lifesan it is not enoug to simly witstand cometition. During a lifetime, investments ave to be made in reroduction to ensure future generations. Secies can differ in teir timing, etent and duration of investments in reroduction. As one investment goes at te disadvantage of te oter, lants ave to find te combination of different traits tat ensures teir erseverance in te vegetation over te years. Wit so many interacting traits, wic also interact wit te environment, it is very difficult to distinguis between te influences of different traits on lant erformance. Mecanistic models can be of great el to assess te role of traits in cometition. A model system allows singling out te effect of a secific trait searate from oter traits or environmental variation. A mecanistic aroac is essential for te understanding of observed atterns of lant beaviour. We could simly describe rocesses involved at eac searate scale and use te emirical model for te simulation of lant or oulation growt. Tis ractice owever gives no elanation as to ow or wy te variables act to affect growt (Tilman, 99; Weiner, 995b; Jarvis, 995). As cometition determines te eclusion of tyes according to te cometitive eclusion rincile, tis will give insigt in te develoment of te diversity of communities. We develoed a model to investigate cometitive interactions between lants tat ossess a variety of traits. We included mecanisms at te lant and organ scale in te simulations of rocesses at oulation or community scale. In tis way we acieved self-assembling communities witout inserting community-level secifications (Colisanti et al., 2). Te community structure we obtained is truly a result of underlying mecanisms. In tis tesis, we will try to formulate general statements on te influence of investment atterns on cometition, oulation develoment and coeistence, indeendent of variation in eternal factors for growt.

11 CHAPTER Te model system Te multitude of traits in lants and teir intricate beaviour makes tem esecially interesting to study. However, it makes tem difficult to study as well. As already stated, model studies rovide a way to disentangle te secific roles tat traits lay in determining lant beaviour. In tis tesis, a closer look is taken on te role of investment in eigt growt, crown arcitecture, seed roduction and disersal in determining growt, cometition and coeistence between lants. It is imortant to look at mecanisms at least one scale below te rocess of interest. Usually, scientists coose one secific scale on wic tey ut teir focus. For tis scale, only te average of variables is taken into account, not te variation witin, for tis variation would find its origin in a lower scale. Te iger scale variables are taken omogeneous (Rietkerk et. al., 22). However, by re-setting te scale of interest, imortant asects of te system as a wole can easily be overlooked because results are not emerging from underlying mecanisms. Terefore we focus on te influence of mecanisms at lower scales on iger scale rocesses. We start by formulating investment strategies, evaluate imlications tereof for cometition and subsequently evaluate te effect of cometition on oulation develoment and community develoment. Wen building a model system, simlifications ave to be introduced. If too little simlifications are made, te tractability and interretation of model results will be difficult. It is ossible tat wit many arameters, te model will become overly sensitive to canges in te inut values because many arameters may interact. Also, a lot of data will ave to be gatered for arameterisation. On te oter and, using a lot of restricting assumtions can make te model infleible (Snowling & Kramer, 2). Wile sufficient detail sould be built into a model, it sould not become too comle. A solution is to only include tose traits tat are imortant to gain understanding of a articular rocess. Wen modelling te effect of lant sae in an environment were ligt is te single limiting factor, ligt-arvesting traits like eigt and leaf area growt will obviously ave to be incororated in te basic model. Oter factors, for instance nitrogen, also lay a crucial role in lant growt. But, because in our case te focus is not on below ground rocesses or lant ysiology, introducing nitrogen as a factor will only confound te effects of traits directly related to ligt. Hence, in te case of nitrogen, its availability sould be set constant. Eventually, wen a simle basic model is constructed, oter factors affecting lant growt sould referably be introduced one at te time. No new factor sould be introduced until te effect of an earlier included factor is clear. Te evaluated factor can consequently be removed, or set to a constant. In tis way we are building u an understanding of te intertwining effects of different sets of traits. In tis tesis we sow tat wit a simle basic model and a few varying factors er simulation, an ecologically meaningful, comreensible and interretable result will follow. As a consequence of tis aroac, te model lants described in tis tesis lack quite a number of functional traits. Plants in a real-life situation ave more comle caracteristics and strategies, involving many traits tat can ave differential effects on te erformance and fitness. In addition, tese real-life lants are subject to muc more

12 CHAPTER diverse influences from te environment. Te final enotye or a real-life lant is a comromise between a myriad of selection ressures (Roff, 98). Te urose of a teoretical study suc as tis one is terefore not to make accurate redictions on te erformance of any articular real-life lant. Rater, it is intended as a generator of new insigts and ideas about te role of articular traits in te atterns of erformance of lants growing in isolation or cometition. We tink tat te bottom u aroac from a combination of a more mecanistic basis for te simulation of larger scale rocesses as te otential for revealing muc about te ow and wy of many of tese rocesses. So far studies wit suc an aroac are few. Otimisation in an evolutionary contet We discussed te need for a mecanistic basis to understand te origin of iger-level rocesses suc as oulation growt and community diversity. To evaluate te erformance of a secies, a measure of fitness as to be assigned. To maintain a simle system, we focus our investigations on lants wit a single growing season. Because we are interested in te erformance on longer time-scales, a fitness measure tat as value only over a single growing season (like biomass) is not sufficient. One way for a lant to maintain itself in a community is to divert resources to roduce offsring. We assume tat, te iger te lifetime roduction of offsring, te iger te fitness. It is logical to assume tat a secies tat roduces more offsring in its lifetime tan oter secies increases faster in abundance. Terefore, a secies adoting a new trait tat enances its fitness, or canges te value of a trait to increase fitness, will readily become abundant in a community. Individuals lacking te trait will get relatively less abundant. Otimisation teory seeks to find tose (values of-) traits tat give te lant maimum fitness (Levin & Muller Landau, 2). Te fitness will deend on te environment and te restrictions tat te lant meets in arcitecture or trade-offs. For a given environment it can be calculated or simulated wic (value of a-) trait results in te igest fitness. Tis will give a rediction of or an elanation for wic value of a trait will be most widesread in a community. Researc as for eamle been done on otimal root-soot ratios (Hilbert, 99; Reynolds & Cen, 996) timing of reroduction (Coen, 97; Iwasa, 2) leaf nitrogen distribution (Hirose & Werger, 987) and many oter tings. Otimisation teory owever always assumes tat te environment is comletely redictable for te lant. It is of course unrealistic to assume tat lants can foresee te environmental conditions over a growing season (Reynolds & Cen, 996). Te ligt climate, for instance, is influenced not only by te growt of te lant itself but also by te arcitecture and growt traits of cometitors. If conditions cange, te value of te otimal resonse will cange. In a cometitive environment, te question wic trait value is otimal in resonse to te environment is not valid. A more aroriate question is wat value of a trait is otimal in resonse to lants wit oter traits tat interfere wit conditions constantly. 2

13 CHAPTER Taking te reasoning a level iger, we can state tat fitness is also not static over te course of years. Fitness will deend on te canging frequency and abundance of cometitors, wic temselves are subject to te canging conditions. Additionally, it migt not even be necessary for a lant to resond otimally. If te resonse is suc tat it is fitter tan te cometitors, it will erform better. Calculations on te erformance of individuals or grous of lants ossessing a articular trait value in tis kind of cometitive setting are generally referred to as game teory. Game teoretic metods are a owerful way of assessing te fitness of individuals in an environment consisting of many different secies (Levin & Muller Landau, 2). It is tus suitable to address te question of maintenance of diversity. In Cater 4 and 5 (and less elicitly, Cater 6) of tis tesis we make use of game teory to assess te erformance of lants ossessing certain traits. Terefore we give a sort overview of te develoment and teory, elaining terms tat will be used furter on in tis tesis. Game teory as a tool An early alication of game teory to biology is by Maynard Smit & Price (973). His game consists of two tyes of layers, Hawk and Dove, wic comete for a resource. In tis game, eac layer gets some secified roortion of te resource, deending on te oonent tey encounter. Te roortion of resource tat is acquired in te encounter is te ay-off of te encounter. Te ay-off is assigned er game of cometing Hawk- Hawk, Hawk-Dove or Dove-Dove. It deends on te strategy adoted by te oonent wic strategy can best be adoted by te layer. Traditionally in game teory, a value or measure of success is assigned to te benefits received from laying a articular strategy. Te ay-off of a layer is assigned wit a function, to cover all otential situations (Vincent & Cressman, 2) or assigned er game like Maynard Smit and Price did (Riecert & Hammerstein, 983). Because in te cometition for ligt te dynamics of interacting lants are asymmetric and tus nonlinear, it is nearly imossible to catc te beaviour of te system in one single ay-off function or a simle value. A ossibility to overcome tis limitation is to numerically calculate te ay-off of lants laying a game instead of assigning a simle function or value. Tis way te mecanisms tat determine te beaviour of te system wit its comle a-symmetric connections can be included. We tus link te dynamics of ligt cometition to game-dynamic calculations. Lewontin (96) first elicitly introduced frequency dynamics for game teory, giving rise to evolutionary game teory. In evolutionary game teory, as oosed to classic game teory, layers ave fied strategies rater tan being able to coose (a set of-) strategies. Te success of a strategy is defined in terms of te number of coies tat a strategy will leave of itself to lay in te games of succeeding generations. Te strategies temselves are terefore te layers, and te games tey lay are dynamic rater tan static (Ross, 23). Wit evolutionary game teory, te time course and outcome of cometitive interactions can be determined over more tan one generation. Players wit a large ay- 3

14 CHAPTER off relative to te oter layers will increase in number. Consequently, te frequency at wic tey occur in te community will increase. Tis cange in te comosition of te community will alter te influence of te community as a wole on te ay-off of a single layer. If eventually te community comes into equilibrium, tere is no cange in te frequencies of te layers involved. One ossibility is tat tere is a monomoric equilibrium. In tis case only one strategy is left. Anoter ossibility is tat tere are more strategies tat ave an equal fitness at equilibrium. Tis would mean tat te equilibrium is olymoric. Anoter ossibility is tat tere are alternating winning strategies and te system never reaces equilibrium. Tis can occur wen te winning strategy deends igly on te comosition of te community and tis comosition continuously canges during successive calculations. Te strategy (or strategies) tat as maimised fitness given te oonents is te Nas solution. A strategy tat is resent at Nas equilibrium is an evolutionary stable strategy (ESS) if no individual can imrove its fitness by canging te value of its trait and tus no mutant strategy can invade te oulation (Maynard Smit, 982). Outline of tis tesis In tis tesis, we try to slowly build u an understanding of te role of a limited set of lant traits in te cometition between lants, oulation growt, and finally, te comosition of te community.in Cater 2, we describe a basic mecanistic lant growt model. Te driving forces beind lant growt in tis model are ligt availability, lant arcitecture, otosyntesis and allocation. Wit tis model as a basis, secific growt strategies of lants are elicitly incororated in later caters. Subsequently growt and fitness of lants are simulated, for single lants as well as lants in a cometitive contet. In Cater 3, we elore coeistence ossibilities for airs of lant tyes differing in te investment in eigt growt. In tese tyes, te investment in eigt growt trades off wit leaf area investment. We investigate weter tyes wit different eigt investment can gain similar fitness in a cometitive contet. Furtermore, te role of frequency deendent rocesses on coeistence between two lant tyes is studied. In Cater 4, we elore te ESS eigt investment in various environments and for lant tyes wit various traits. Te influence of density, season lengt, lasticity and distribution of leaf area over eigt on te ESS eigt investment is investigated. Tis is done in a game-teoretic framework. At te same time, we investigate te ossibilities for coeistence for tese various tyes in te different environmental conditions. Finally we elore te role of elicit sace for te coeistence of different eigt investment tyes. In Cater 5, we investigate te adative value for different seed allocation strategies, also in a game-teoretic framework. Plant tyes differ in teir timing of a switc from vegetative to seed roduction. Tere is tus a clear trade-off in fecundity and cometitive strengt. Also, te effect of reintroduction of etinct tyes is studied. In Cater 6, we investigate te effect of disersal distance on te cometitiveness of lant tyes. Te tyes differ in cometitive strengt as a result of a 4

15 CHAPTER trade-off between vegetative growt and seed roduction. Tyes diserse and grow in a satially elicit area. We elore te influence of disersal distance on oulation develoment of tyes of equal strengt and different strengt. Also, te effect of clustering on te oulation develoment is studied. Finally, we ceck if coeistence by means of a cometition/colonisation trade-off is ossible for tese tyes, witout additional disturbances. In Cater 7, we study te effect of te vertical distribution of leaf area on te erformance of te lant, in isolation or cometition. Plants in tis cater can bring teir leaf area to iger ositions along teir stem (e.g. cange teir crown sae) under te influence of sade. Plants can differ in te rate wit wic tey can cange te sae of teir crown, and te etent. In contrast wit te former caters, lants grow according to a ie teory model. Stem volume is not determined by an allometric function, but by te leaf area and its distribution along te eigt of te lant. In Cater 8 we discuss and summarize te results tat were obtained in te revious caters. We also discuss te ossible influence of omitted traits and oter factors tat were not treated in te various caters, wic could romote coeistence. 5

16 6 CHAPTER

17 CHAPTER 2 A MECHANISTIC MODEL FOR THE SIMULATION OF GROWTH AND FITNESS OF ANNUAL PLANTS Summary Altoug in many models te relation between life-istory traits is imlicitly assumed to result from alternative allocation of resources, elicit mecanistic models of tis allocation rocess are few. We describe a dynamic mecanistic simulation model, suitable for te simulation of growt of cometing annual lants in mied stands. Most imortant features of tis model are:. Te secific attern of allocation er lant. 2. Growt according to a strict carbon balance. 3. Te inclusion of crown arcitecture. Te model is based on te rocess of otosyntesis. Plants comete in a defined sace, wit comlete miing of leaves. Heigt, leaf area and leaf distribution arameters secify te sae of te lant. Te fitness of individuals is measured as te amount of carbon investment in seed at te end of a defined growing eriod. Model assumtions include lastic allocation atterns as a resonse to te local ligt climate, wic is influenced by te caracteristics of te lant itself and neigbouring lants. Te model will allow for te evaluation of te fitness value of searate traits in te cometition for ligt, ontogenetic investment atterns and lasticity. In addition, it can be used for evaluation of te fitness of trait combinations. Keywords: crown arcitecture, carbon balance, allocation attern, mecanistic model, dynamic, lant growt 7

18 CHAPTER 2 Introduction Cometition for ligt can be a major factor in determining secies erformance in dense stands. It is quite obvious tat in te direct cometition for ligt, te ligt caturing ability of lants will be of te utmost imortance. Plant arcitecture will be one of te most imortant features tat determine ligt caturing ability of a lant (Skalova et al., 999). Numerous studies ave tried to assess te role of different lant arcitecture caracteristics for ligt acquisition under cometitive circumstances (e.g. Mitcley, 988; Teugels et al., 995; Hirose & Werger, 995; Scwinning & Weiner, 998; Aerts, 999; Anten & Hirose, 999; Werger et al., 22). Tese studies agree tat ligt-caturing ability of individuals is determined in articular by two caracteristics. Firstly, leaf area determines te surface wit wic te lant can cature ligt. Secondly, ositions of te leaves in te vertical ligt gradient determine wat ligt intensity leaves eerience. Tis is secified by te eigt of te lant and te vertical distribution of leaf area over te eigt. To imrove ligt cature in a crowded vegetation, secies migt allocate more of teir currently acquired carboydrates to eiter eigt or leaf area growt. A secies may be lastic or rigid in tis allocation. Many studies sow tat lants alter teir allocation attern as a resonse to te environment tey eerience, in order to reduce or avoid cometitive suression (Scmitt, 997; Scwinning & Weiner, 998; Dorn et al., 2; Weinig, 2). As secies allocate teir biomass and grow, te available ligt in te vegetation canges. Tis cange affects not only te total ligt availability but also te ligt available in te different layers of te vegetation. Te adequacy of allocation strategies to imrove ligt cature may vary under tis vertical and temoral variation of te ligt climate. Tus, besides leaf area and te osition of te leaf area over te eigt of te stand, te lifetime attern of allocation to ligt arvesting caracteristics is an imortant feature of overall lant cometitive ability. To gain insigt on te limits and ossibilities of sae and allocation strategies of lants, a modelling aroac is suitable. Models can reresent a well-defined system in wic questions can strategically be tested. Is te set of lant sae caracteristics and lastic resonses beneficial for te given secies? Wat is te range of circumstances in wic a certain strategy is most effective? Te questions become more comle wen satial and temoral dynamics are taken into account. For gaining insigt in te above questions, a descritive model is insufficient. We focus on elanatory models because a non-deterministic nature of links between lant arcitectural traits, cost and benefits is essential to acieve an understanding of ow and wy rocesses and traits interact (Tilman, 99). For tis urose, rocesses on at least one ierarcical level deeer tan te resonse described sould be included (Jarvis, 995). Tree elements are imortant for a concise simulation of mecanistic lant growt under ligt limiting conditions. Te first imortant asect is an elicit arcitecture. Tis will determine te eact ligt intercetion of lants in relation to neigbouring lants. Secondly, an elicit lifetime allocation attern to different lant functions is needed. Tirdly, tese two caracteristics sould be linked troug a carbon balance. Te carbon balance includes elements suc as 8

19 CHAPTER 2 otosyntesis, growt and maintenance. Elicit calculations of resource cature and costs for growt and maintenance enable us to make sound comarisons between te erformances of lants wit different allocation strategies. For te simulation of lant growt and ligt intercetion, a myriad of models is available. A large art of tese models is descritive or artly descritive. Esecially leaf area is often modelled as a function of lant develomental stage or simly as an inut arameter (Marcelis et al., 998). Relatively few models ave an elicit leaf area distribution for lants (but see Liet & Reynolds, 988) and at te same time ave been alied to simulate ligt intercetion and otosyntesis in a mied stand (but see Tournebize & Sinoquet, 995; Anten & Hirose, 999; 23). Even rarer is te aliance of suc models in a dynamical setting, wic is necessary for understanding and assessing te imortance of different structures over te life-time erformance of a lant (but see Yokozawa & Hara, 992; Yokozawa et al., 996; Caton et al., 999; Sekimura et al., 2, Sciers & Kroff, 2). Models do not usually combine all elements. In te model develoed in tis cater, individuals grow mecanistically according to a carbon balance. Te lant growt is mecanistic in te way tat growt of lant organs is not suerimosed on te lant, but is determined by te allocation to tose organs and te costs and benefits tis incurs. In te model, it is ossible to assign a secies-secific allocation attern to eac individual. Plasticity in eigt growt is imlemented as a resonse to sading. Te etent to wic a lant is lastic can be adjusted. Plants in tis cater ave an elicit vertical distribution of leaves, so te quantity of otons interceted over te vertical ligt gradient relative to oter individuals can be calculated. Te model can be used to assess te role of secific traits in te cometition for ligt (Cater 3 and 7). Also, it can be etended towards oulation dynamics (Cater 4, 5 and 6) and can be made satially elicit (Cater 6). In te following sections in tis cater, te basic features of te model are described. In Section, te sae of te aboveground art is discussed. Te calculation of te ligt climate is dealt wit in Section 2. In Section 3, leaf and lant otosyntesis is secified. Te carbon balance is described elicitly in Section 4. In Section 5 te allocation rogram of te lant is elained.. Sae of te Model lant A lant is confined to grow in a redetermined surface area, referred to as a cell. More tan one lant can inabit tis cell. Horizontally, te lants in a single cell are erfectly mied. Obviously, in real vegetations, lants do not comletely overla eac oter. In te aroac taken ere, an overestimation is made on te etent of lant interaction. However, by taking te cell as unit in wic lants grow, and tus standardising te leaf area overla, we can make easy comarisons between cells. Tis eliminates te variation in cometitive ressure on individuals tat would oterwise be caused by different levels of overla between lants. For tat reason, it is a more insigtful way of interference analysis. 9

20 CHAPTER 2 Eac lant as a secified smoot distribution of infinitesimal small leaf elements over its eigt. Te descrition of leaf area distribution in a single formula allows for a strait forward calculation of te rate of cange in te sae of te curve. Te leaf area distribution in leaf area er unit eigt er cell basal area is described by te following formula (Caton et al., 999): Leaf area distribution 2 L t λ ( ) = (.) t t t in wic is te eigt of te lant at time t, L is leaf area inde at time t, is te eigt at wic te leaf density is calculated and,, 2 are sae arameters. By dividing te leaf area by te eigt of te lant, te leaf area distribution is made indeendent of lant eigt. I.e., by taking / t as, one can write for te total leaf area L t Total leaf area L t = t 2 d λ ( ) = L d ( ) (.2) t Hence te sae arameter is given in terms of and 2 by te integral Sae arameter (.3) = d ( ) 2 By canging te sae arameters and 2 different leaf area distribution curves can be acieved. See Figure 3 in Aendi for eamles. Te relation between eigt t and stem volume S t at time t is given by a standard allometric formula (Stearns, 992): Stem volume S t β t = α (.4) Here α and β are constants. Altoug a root system is resent in te model lant, it is not functional. It merely acts as a carbon sink for te carboydrates from otosyntesis. Te root weigt is a linear function of te leaf area: Root mass R = σ L (.5) t t 2

21 CHAPTER 2 2. Ligt climate We assume a ligt climate in te vegetation cell in wic te otons flow vertically downward. At eac det te intercetion of ligt by te lants is modelled by Beer s law (Monsi & Saeki, 953). Te ligt etinction rate at eigt is calculated from te leaf area, leaf inclination in te orizontal lane and absortion coefficient of leaves of all lants in te cell: Ligt etinction rate d i = i λ( ) cosα a (2.) alllants Here cos α is te leaf inclination and a is te absortion coefficient of leaves. By integration of 2., te orizontal ligt intensity i () is given for eac eigt in te cell: Ligt climate = v i ( ) i ( v ) e d λ( ) cosα a (2.2) alllants were i ( v ) is te orizontal ligt intensity above te vegetation and v is te eigt of te vegetation. It is assumed tat te cells receive an average ligt intensity over a season; in oter words it does not vary during te develoment of te lants. Tis assumtion will make model results simler to interret. Te influence of a seasonally variable ligt climate will be assessed in Cater 5. Te rate of oton absortion for te leaf elements at eigt is calculated from te ligt climate at eigt, te leaf inclination and absortion coefficient of a lant. It is given by Ligt intercetion i al ( ) = i ( ) cosα a (2.3) During a simulation of te growt of lants in an individual cell, te vertical ligt climate not necessarily as a smoot distribution over te eigt of te vegetation. Terefore, at eac time ste, te ligt climate is calculated wit te fourt order Runge-Kutta metod. Tis integration metod evaluates te rate of cange at several oints in eac ste and can aroimate te vertical ligt climate in an accurate way (Press et al., 989). 3. Leaf and lant otosyntetic rates Te leaf otosyntetic rate is calculated on te basis of te non- rectangular yerbolic relationsi between maimum otosyntetic caacity, ligt intercetion and quantum yield. Tis relationsi accurately reroduces te curve of otosyntetic caacity in actual lants (Marsal & Biscoe, 98). 2

22 CHAPTER 2 Leaf Potosyntetic rate Wit ( + ) ( + ) 4 θ Pgl ( ) = Pml (3.) 2 θ Φ i = P al ml ( ) 2 Here P ml is te otosyntetic caacity of te leaves, Φ te quantum yield er unit absorbed ligt, θ a curvature factor and i al () is te rate of oton absortion of te leaves at eigt (see 2.4). It sould be noted tat for reasons of simlicity we assume tat caacity P ml, quantum yield Φ and curvature θ do not vary wit eigt. For eac lant te total otosyntetic rate is given by te integral over te lant s eigt, of te leaf otosyntetic rate times te leaf area. Tis gross otosyntesis is in µmol carbon er unit time. Plant Gross Potosyntetic rate P = d P ( ) λ ( ) (3.2) g Equation 3.2 is calculated using te Gaussian integration metod, wic is very accurate for smoot functions (Press et al., 989) suc as te leaf distribution formula. R m is te maintenance rate, wic is based on te carbon weigt of te lant arts. It is of te form gl Maintenance rate R m = r L + r S + r R (3.3) ml c ms c mr c in wic r ml, r ms, r mr are te maintenance resiration rates in gram carbon er unit carbon mass er unit time and L c, S c, R c are resectively te leaf, stem and root carbon masses at time t. Tese carbon masses are calculated wit el of conversion factors. Leaf carbon mass Stem carbon mass Root carbon mass L S R c c c = c L (3.4) l = c S (3.5) s = c R (3.6) r Here c l is in g carbon er m 2 leaf, c s is in g carbon er volume stem, c r is in g carbon er gram roots. In real systems, seeds are cast from te lant at some oint in time and are ten ysiologically indeendent from te lant. In tis model it is assumed tat after an initial 22

23 CHAPTER 2 investment, seeds no longer are an integral art of te lant. Terefore seed mass is not included in te calculation of te lant s maintenance resiration. Te calculation of te allocation rate of carbon to seed is treated in section Growt and te carbon balance Plant growt is calculated as te growt in stem, leaves and roots. A art of gross otosyntesis is allocated to seed. Seed mass can be seen as a fitness arameter, a measure of ow well te individual as erformed. Te lant allocates carbon to seed only if it is in reroductive mode. A fied ortion of carbon (f c ) from net otosyntesis is ten referentially allocated to seed mass roduction before te allocation to leaf, stem and root, but after te allocation to maintenance resiration. Wit te roduction of seed mass, a certain amount of carbon is resired in growt resiration. Te carbon consumtion rate for seed mass roduction F m is: Carbon consumtion for Seed mass C cf = ( c + r ) d F (4.) f f t m in wic c f is te carbon er gram seed mass and r f te growt resiration constant. It sould be noted tat, if net otosyntesis is negative or zero before allocation to seed, te allocation rate to seed is zero. Once generated, seed mass is assumed to no longer be an integrated art of te lant. Seeds need no additional carbon from net otosyntesis for e.g. maintenance resiration. Terefore seed mass is not taken into account in te carbon balance any furter. Te net otosyntesis considered in te remainder of tis cater is te net otosyntesis after allocation to seed: Net otosyntesis P n = P R ( c + r ) d F (4.2) g m f f t m At any time t, leaf area L and eigt togeter wit te constant sae arameter and 2 comletely determine te sae of te lant. If at any time te leaf area is equal to zero, te lant is considered dead. Growt of te lant in leaf area d t L and eigt d t is related to te consumtion and roduction rate of carboydrates. Growt is imosed on te lant according to its carbon balance. Tis means te net carbon consumtion rate of te lant as, at any time, to be equal to te rate of net otosyntesis. Te net carbon consumtion rate results from te carbon costs associated wit te roduction of stem volume and roduction or removal of leaf area and roots. Leaf and root elements are sed or roduced solely as a result of te carbon balance or a cange in sae. Leaf area and root roductions require two investments, te carbon invested in mass and te resiratory costs. Wen leaves or roots are sed, only a art of te reviously invested carbon can be retrieved. 23

24 CHAPTER 2 If te leaf area growt rate d t L is ositive, te associated carbon consumtion rate is Carbon consumtion rate for leaves C cl = ( c + r ) d L (4.3) l l t wit c l te carbon content of leaves in gram carbon er unit leaf area and r l te growt resiration costs in gram carbon er invested gram carbon. If te leaf area growt rate d t L is negative, te associated carbon roduction rate is Carbon roduction rate for leaves C l = c d L (4.4) rl t wit c rl te retrievable carbon in te leaves in gram carbon er gram of carbon in te leaves. In te case tat a lant seds its leaves, only a art of te carbon is recovered. Te rate of a cange in root mass d t R is a function of te cange in leaf area. Root growt rate d R = σ d L (4.5) t t wit σ te ratio wit wic leaf area and root mass cange. As can be derived from tis formula, we assume a balance between leaf and roots. Tis means tat sedding or growt of leaf elements is couled wit sedding or growt of root elements. Te associated carbon consumtion rate for roots if d t L > is Carbon consumtion rate for roots C cr = ( c + r ) σ d L (4.6) r r t wit r r te growt resiration costs in gram carbon er invested unit root carbon. If d t L < ten Carbon roduction rate for roots C r = c σ d L (4.7) rr t wit c rr te retrievable carbon in te roots in gram carbon er gram carbon in te roots. As is te case wit leaf area, only a art of te carbon invested in root mass can be recovered. If a lant grows in eigt wit rate d t tis requires an investment of carbon. Tis carbon investment consists of two arts. First, for te carbon consumtion rate associated wit te growt in stem volume (wic is equivalent to mass) we can write C consumtion rate C c = ( r + c ) d S = ( r + c ) d S d (4.8) s s t s s t 24

25 CHAPTER 2 Second, if a lant canges in sae by eiter eigt growt or canging te sae arameters and 2, leaf area as bot to be roduced and sed at a corresonding rate in order to maintain te sae of te lant (see Figure ). To find te region over wic te leaf area cange wit eigt d λ is ositive or negative, we determine te value of * at wic te leaf area cange rate is zero. For te calculation of *, see Aendi 2. Point of no leaf area cange + = d t (4.9) As can be seen in Figure, d λ is ositive above * and negative below * (rovided tat d t > ). Te ositive art of te function can be integrated to assess te total leaf area roduction rate wit eigt growt. Te negative art of te function can be integrated to assess te total rate of leaf area sedding wit eigt growt. Te integration is done wit el of te Gaussian integration metod. * * Heigt (m) ** Leaf area (m2/m) Figure. Te cange in lant sae wit eigt growt. Leaf area as to be redistributed in order to maintain te sae of te lant, as imosed on te lant by Formula.2. Te area indicated by * deicts te leaf area tat as to be newly roduced. Te area indicated by ** is te leaf area tat as to be cast away. Te oint at wic te leaf area cange is zero is deicted by *. In formal terms, if a lant grows in eigt wit a certain rate d t, te rate at wic leaf area L r is sed by te lant is calculated by integrating te negative rate of cange. Tis is given by 25

26 CHAPTER 2 Leaf area sed d L = d NEG( d λ ) d (4.) t r Te rate at wic leaf area L is ten roduced by te lant is calculated by integrating te ositive rate of cange. Tis is given by t Leaf area roduced d L = d POS( d λ ) d (4.) t Hence te value for te NEG art of te function is zero if te value is ositive, and d λ if negative. For POS, tis is te oter way around. In te case of mere reallocation of leaves (e.g. no cange in total leaf area) te leaf area tat is roduced is er definition always equal to te leaf area tat is sed, e.g. d t L r = d t L. Because te cost for roducing leaves is larger tan te carbon tat can be retrieved, te lant will ave to ay for te reallocation of te leaves. Te total carbon consumtion rate associated wit te leaf reallocation is t Leaf reallocation costs C λ = ( c + r ) d L c d L (4.2) c l l t rl t r It sould be noted tat rearrangement of leaf area does not involve any cange in te roots. Te leaf rearrangement is due to canges in te above ground lant sae and it is assumed to ave no consequences underground. To summarise te rocesses involved in te carbon balance: Te consumtion of carbon sould at any time be equal to te carbon gain from net otosyntesis P n. Heigt growt rate d t is always non-negative. Leaf area rate d t L can be eiter ositive or negative, deending on te carbon balance after eigt growt and reallocation of leaves. If root mass and leaf area are zero, te lant is considered dead. Te roduction rate of seed mass d t F m is not considered in te carbon balance. It is assumed tat, if te lant is in reroductive mode, te seed roduction occurs before growt of any oter lant structure. In case of a ositive leaf roduction rate (d t L > ) we write P n ( c = ( c l l + r ) l + r ) d L + c l t d POS( d s d λ) c S d rl t + ( c r r d NEG( d + r ) σ d L + λ) d t t (4.3) 26

27 CHAPTER 2 27 Rewriting tis gives [ ] t rl l l s t r r l l n d d NEG d c d POS d r c S d c L d r c r c P = ) ( ) ( ) ( ) ( ) ( λ λ σ (4.4) In case of a negative leaf roduction rate (d t L < ) we write t rl l l t rr t s t rl n d d NEG d c d POS d r c L d c d S d c L d c P = ) ( ) ( ) ( ) ( λ λ σ (4.5) Rewriting tis gives [ ] t rl l l s t rr rl n d d NEG d c d POS d r c S d c L d c c P = ) ( ) ( ) ( ) ( λ λ σ (4.6) From te equations 4.4 and 4.6 it is clear tat te sign of d t L is determined by te magnitudes of te term f (L, ) d t and te magnitude of te net otosyntetic rate. Tat is, we can write (as derived from 4.4 or 4.6): Leaf area cange n t t L P d L f L d L f + = ), ( ), ( (4.7) Tis means tat to find te elicit eression for d t L we must look at te eression for eigt growt rate d t. In te following section we will formulate ow te lant steers its growt rate in eigt. 5. Te allocation rogram of te lant Investments in lant organs are made in a ierarcical manner. Firstly, te lant allocates carbons to account for maintenance costs in our model. For annuals it is imortant to roduce seeds, for te lant does not survive until te net growing season. It can be assumed tat for annual lants, at some oint te allocation to reroduction will be referred over oter structures. Terefore, if te lant is in reroductive mode, te second riority is allocation to seed. After maintenance and seed investment, lants allocate

28 CHAPTER 2 biomass to different organs like leaves, root or stem. Because of te asymmetrical nature of te cometition for ligt, eigt will be imortant for a lant s cometitive status. Te riority of mass investment lies terefore wit stem investment. Finally, te lant invests watever is left from net otosyntesis in leaf area and roots. In Figure 2 te order of carbon allocation to various organs is deicted. Maintenance Gross otosyntesis Heigt LA/Root Reroduction Figure 2. Te allocation ierarcy of te model lants. From te ool of gross otosyntesis, carbon is allocated to: ) Maintenance 2) Reroduction, if te lant is in reroductive mode 3) Heigt 4) Leaf area and roots. Te allocation attern can be static, or cange over time deending on ontogenetic develoment or environmental conditions. In te latter case, te resonse of a lant is lastic. A well-known lastic resonse in lants is te sade avoidance resonse, wic is triggered by an altered red /far-red ratio and is mediated by te ytocrome (Ciollini & Scultz, 999). Inside a vegetation canoy, te sectral comosition of ligt is altered by absortion of ligt in te red region of te sectrum. By tis rocess, te red/far red ratio canges. Tese canges are reliably correlated wit te resence of neigbours (Scmitt, 997) and it is well known tat lants can detect tese canges in red/far red ratio. Plants will often sow an increased allocation to te stem art wen grown under suc an altered red/far red regime (Scmitt et al., 999). Te lant is tus able to grow taller and as a cance of reacing a better ligt climate. In tis way, lasticity allows to avoid ossible costs from sading by cometitors (Dorn et al., 2; Weinig, 2a). Te ratio of red to far-red wavelengts is an accurate signal of vegetation sade (Smit, 982). It is terefore assumed in tis model tat te red/far red signal for an individual lant scales directly wit te amount of ligt tat tis lant is derived from by surrounding leaves. Tis includes te lant s own leaves. 28