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32 plant-pollinator dynamics: stability reconsidered pollinators A j (with α ij = 1 and α kj = 0) and A l (with α il = 0 and α kl = 1). Here, even with niche differentiation of the two plant species and no interspecific competition between pollinators for food resources, the presence of P i has an indirect effect on the pollinator of P k : The higher the relative abundance of plant species i, the more time do pollinators of species l need to spend searching for their preferred plant species k. Thus, if the relative abundance of plant i increases, the nectar intake rate of pollinator l may fall to a level where its birth rate cannot compensate its mortality. In that case, A j will decline and may become extinct if its birth rate at low density is still not high enough to balance its death rate. Increasing the amount of nectar per plant or the conversion rate of nectar to pollinator offspring, or decreasing pollinator mortality, allows a pollinator of a rarer plant species to survive under conditions that would otherwise result in its extinction. As long as the plant niches are sufficiently separated and b veg is large enough to maintain a plant population in the absence of pollinators, plant species k will survive even if its pollinator dies out. On the other hand, if plant competition for space is strong, plant k may not be able to compete with plant i in the absence of its pollinator, and may therefore also become extinct. However, our measure of local stability does not distinguish between these two cases. As we have now identified the degree of plant niche overlap and the three parameters affecting pollinator growth rates as the most important factors that determine the effect of plantpollinator interactions on plant coexistence, it is clear that empirical estimates of these parameters are needed in order to draw conclusions about the stability of real plant-pollinator systems. As for plant niche overlap, very few studies provide experimentally derived estimates of Lotka-Volterra competition coefficients (Goldberg & Barton, 1992; Silvertown, 2004), a fact that may partly be due to the lack of a mechanistic basis of the Lotka-Volterra model (Chesson, 2000; Dormann & Roxburgh, 2005). However, since resource requirements and mode of resource use of different plant species within communities such as a meadow are often strikingly similar, it seems likely that levels of plant niche overlap close to one are the norm rather than the exception in natural plant communities. Consequently, there is an ongoing debate about the question whether differential resource use alone can explain coexistence of diverse plant communities even in the absence of a minority disadvantage mediated through pollination (e.g. Bell, 2001; Silvertown, 2004; Leibold & McPeek, 2006; Levine & HilleRisLambers, 2009). This raises the question whether growth rate parameters of real pol-
2.5 discussion 33 linator populations are such that stable coexistence in plantpollinator systems is possible even at high degrees of plant niche overlap. Rather than trying to find estimates for each parameter separately, it may be helpful to consider the fact that all three parameters affect the ratio of pollinators per plant at the coexistence equilibrium. To our knowledge, no estimates of this ratio have been published, but in a few cases the amount of flower resources required to rear a bee larva has been quantified (Müller et al., 2006, and references therein). These studies seem to indicate that the number of flowers needed to raise one bee varies widely, from less than one flower head of Helianthus annuus (Asteraceae) to several dozen flowers of Campanula rapunculus (Campanulaceae). Therefore, it may well be that the effect of interactions with pollinators on plant coexistence varies from one community to the other. In conclusion, our analysis of population dynamics in plantpollinator systems has shown that interactions with pollinators may impede or facilitate plant coexistence, and identified a number of parameters that influence the stability of plant and pollinator communities. However, apart from the task of finding empirical estimates for these parameters, our approach has its limitations and several open questions remain. For example, the measure of community stability applied here is just one of several possible choices (Grimm & Wissel, 1997), and one that is only based on a system’s behaviour in the immediate vicinity of an equilibrium state. It would not be surprising if a measure that accounts for the effects of larger perturbations produced a different relationship between pollinator specialisation and stability. Moreover, niche differentiation of plant species is by no means the only mechanism that may induce stable coexistence in plant-pollinator systems. From the literature, a number of other potentially stabilising mechanisms are known that are not specific to plant-pollinator interactions, but can contribute to species coexistence in a variety of ecological contexts (Chesson, 2000). Likewise, competition between pollinators could be modelled differently. In the current model, pollinators do not compete for resources other than nectar. Thus, the strength of interspecific competition solely depends on the probability that two pollinators of different species visit the same flower. Inclusion of pollinator competition for other resources, e.g. nesting sites for bees or larval host plants for butterflies, could affect the stability properties of the system in several ways. Niche differentiation of pollinator species with respect to these other resources could have a stabilising effect similar to that produced by plant niche differentiation. However, while popula-
Page 1: L I N K I N G S P E C I A L I S AT
Page 5: E R K L Ä R U N G gemäß § 4 Abs
Page 9 and 10: D A N K S A G U N G Zuallererst mö
Page 14 and 15: xiv contents 3.3 The Model 43 3.3.1
Page 17 and 18: 1 I N T R O D U C T I O N “Es ist
Page 19 and 20: 1.3 ecological stability 3 vegetabl
Page 21 and 22: 1.3 ecological stability 5 tions an
Page 23 and 24: 1.4 specialisation 7 tween the fund
Page 25 and 26: 1.4 specialisation 9 may be promote
Page 27 and 28: 1.4 specialisation 11 ogy through h
Page 29 and 30: 1.4 specialisation 13 tionships bet
Page 31 and 32: 1.5 outline of this thesis 15 1.5.1
Page 33: 1.5 outline of this thesis 17 2007)
Page 36 and 37: 20 plant-pollinator dynamics: stabi
Page 55 and 56: 3 C A N P L A N T- P O L L I N AT O
Page 57 and 58: 3.2 introduction 41 the maximum num
Page 59 and 60: 3.3 the model 43 certain types of r
Page 61 and 62: 3.3 the model 45 time unit, summed
Page 63 and 64: 3.3 the model 47 Figure 3.1: Illust
Page 65 and 66: 3.4 results 49 difference in evenne
Page 67 and 68: 3.5 discussion 51 abundance 150 100
Page 69 and 70: 3.5 discussion 53 seed numbers betw
Page 71 and 72: 3.6 appendix 55 Despite the existen
Page 73 and 74: 3.6 appendix 57 mean number of visi
Page 75 and 76: 3.6 appendix 59 Table 3.2: Plant di
Page 77: 3.6 appendix 61 proportional differ
Page 80 and 81: 64 contrasting specialisation-stabi
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82 contrasting specialisation-stabi
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84 the importance of being synchron
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100 the importance of being synchro
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S Y N T H E S I S 6 The previous fo
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6.1 mechanisms of diversity mainten
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6.2 consequences of climate change
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S U M M A RY For most angiosperm pl
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summary 123 veloped in chapter 2. O
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summary 125 and intensity of extrem
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128 zusammenfassung ten der Erhaltu
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130 zusammenfassung wir den Zusamme
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R E F E R E N C E S Abrams, P.A. (2
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eferences 135 R., Thomas, C.D., Set
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eferences 137 Clavel, J., Julliard,
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eferences 139 role of trade-off str
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eferences 141 Gomez, J.M., Abdelazi
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eferences 143 Ives, A.R. & Carpente
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eferences 145 Leibold, M. & McPeek,
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eferences 147 Moonen, A. & Barberi,
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eferences 149 Pielou, E.C. (1975).
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eferences 151 Schemske, D.W., Mitte
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eferences 153 Visser, M.E. & Hollem
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L I S T O F P U B L I C AT I O N S
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