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UNIVERSIDADE FEDERAL DE GOIÁS
INSTITUTO DE CIÊNCIAS BIOLÓGICAS
PROGRAMA DE PÓS-GRADUAÇÃO EM ECOLOGIA E EVOLUÇÃO
UM MODELO ESTOCÁSTICO DE COEXTINÇÕES EM REDES MUTUALÍSTICAS
Marcos Costa Vieira
Goiânia Maio de 2014
iii
UNIVERSIDADE FEDERAL DE GOIÁS
INSTITUTO DE CIÊNCIAS BIOLÓGICAS
UM MODELO ESTOCÁSTICO DE COEXTINÇÕES EM REDES MUTUALÍSTICAS
Marcos Costa Vieira
Orientador: Dr. Mário Almeida-Neto Co-orientador: Dr. Marcus Vinicius Cianciaruso
Dissertação apresentada à Universidade
Federal de Goiás como parte das exigências do
Programa de Pós-graduação em Ecologia e
Evolução para obtenção do título de Magister
Scientiae.
__________________________________ Dr. Dilermando Pereira Lima Jr.
__________________________________ Dr. Paulo De Marco Jr.
____________________________________ Dr. Mário Almeida Neto (Orientador)
Goiânia – GO Abril de 2014
v
His resuls, brought about by the very soul and essence
of method, have, in truth, the whole air of intuition.
(Edgar Allan Poe, emThe Murders in the Rue Morgue)
vi
AGRADECIMENTOS
Pelo apoio, pessoal e intelectual, e pelo amor de sempre, sou grato à minha família.
Pelo companheirismo incondicional e pela paciência infinita, agradeço à Rachel.
Pelo ambiente ao mesmo tempo intelectualmente desafiador e pessoalmente acolhedor,
sou grato aos professores do Programa de Pós Graduação em Ecologia e Evolução,
especialmente ao Mário, ao Marcus, ao Paulo, ao Adriano e ao Zé Alexandre.
Pelos dias de realidade paralela vividos na Amazônia e na Mata Atlântica, sou grato aos
amigos que fiz durante os cursos de campo, especialmente aos Paulinhos, ao Zé Luís e
ao Glauco, aos meus amigos e colegas de monitoria Thiago e Carol, que atendem pelos
nomes de guerra “Xexéu” e “Valdyrenne”, e a minha grande amiga e “monissora”
Laura.
Este estudo sobre interações ecológicas jamais teria sido possível sem a extensa rede de
interações de amizade e companheirismo que eu e os meus colegas da EcoEvol
construímos ao longo dos últimos dois anos. Assim, eu agradeço por tudo a Tati,
Douglas e Batata (que atendem ambos pelo nome científico de Lucas), Daniel, Cris,
Tailise, Albert, Nelson, Zé Hidasi, Raísa, e Dinei. Pela quantidade infinita de risadas,
bobagens, cerveja, aventuras e histórias para contar, sou grato especialmente a Paola,
Carol, Macaxeira e Luciano.
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SUMÁRIO
RESUMO .................................................................................................................... 1
INTRODUÇÃO GERAL ............................................................................................ 2
CAPÍTULO 1 .............................................................................................................. 7 ABSTRACT ............................................................................................................. 8
INTRODUCTION ................................................................................................... 9
MATERIAL AND METHODS ............................................................................. 12
RESULTS .............................................................................................................. 16
DISCUSSION ........................................................................................................ 20
ACKNOWLEDGEMENTS .................................................................................. 24
REFERENCES ...................................................................................................... 25
CAPÍTULO 2 ............................................................................................................ 28 ABSTRACT ........................................................................................................... 29
INTRODUCTION ................................................................................................. 30
MATERIAL AND METHODS ............................................................................. 32
RESULTS .............................................................................................................. 39
DISCUSSION ........................................................................................................ 42
ACKNOWLEDGMENTS ..................................................................................... 48
REFERENCES ...................................................................................................... 50
SUPPLEMENTARY MATERIAL ....................................................................... 54
CONCLUSÃO GERAL ............................................................................................ 63
1
RESUMO
A compreensão dos processos de extinção e coextinção das espécies, bem como a
capacidade de prever esses eventos, são objetivos fundamentais da ecologia moderna.
No caso de espécies ligadas entre si por interações mutualísticas, as coextinções tem
sido tradicionalmente estudadas utilizando-se modelos simples baseados na topologia
das redes de interação. Aqui, apresentamos um modelo estocástico de coextinções em
redes mutualísticas que incorpora duas fontes importantes de variação biológica
previamente ignoradas pelos modelos existentes: variação na dependência intrínseca das
espécies em relação ao mutualismo, e variação no peso das interações entre uma espécie
e seus diferentes parceiros mutualistas. Nosso modelo estocástico permite a simulação
de cascatas de extinção muito mais complexas do que aquelas geradas pelos modelos
topológicos. Simulações realizadas em redes mutualísticas empíricas mostraram que a
frequência e o tamanho das cascatas de extinção aumentam conforme a dependência
intrínseca das espécies em relação à interação mutualística. Além disso, os resultados
sugerem uma relação negativa entre a fragilidade e a conectância das redes
mutualísticas, o que contrasta com resultados anteriores. Por fim aplicamos o modelo
para estudarmos o declínio da diversidade funcional e filogenética das comunidades
vegetais sob um cenário de extinção dos seus polinizadores.
2
INTRODUÇÃO GERAL
Apresentação
As ideias desta dissertação de mestrado são aqui apresentadasde uma maneira linear que
não coincide com a trajetória convoluta que as ideias geralmente percorrem na mente
dos autores – ou dos cientistas em geral – ao longo do tempo. De saída, nos debruçamos
sobre um problema relativamente específico, interessados em entender as consequências
das extinções e coextinções das espécies sobre duas dimensões fundamentais da
biodiversidade: a diversidade filogenética, definida pelo volume de história evolutiva
representada em uma comunidade de espécies; e a diversidade funcional, definida pela
variedade de estratégias ecológicas ali reunidas. Embora esteja na origem desta
dissertação,esse problema é tratado aqui no segundo e último capítulo. Na tentativa de
abordá-lo, percebemos que os modelos utilizados para simular os processos de extinção
e coextinção em comunidadesnaturais de espécies ligadas por interações mutualísticas
eram excessivamente simples e otimistas. Ao questionarmos os pressupostos ecológicos
responsáveis pela simplicidade e otimismo excessivo dos modelos tradicionais, os
modelos de coextinção passaram de ferramenta à condição de peça central da nossa
pesquisa. Portanto, o desenvolvimento e a exploração de um modelo de coextinção mais
geral, capaz de incorporar propriedades ecológicas e biológicas das interações
mutualísticas entre as espécies, são os temas do primeiro capítulo.
De posse de um modelo mais poderoso, pudemos não apenas retomar o problema
original relativo às consequênciasdas coextinções, mas também investigar as
propriedades das comunidades que tornam tais coextinções mais prováveis. O resultado
é uma pequena contribuição para o tradicional debate sobre a relação entre a
complexidade e a estabilidade das comunidades ecológicas, conforme discutido no
3
Capítulo 1. Em termos mais gerais, esperamos ter contribuído para o esforço de integrar
processos biológicos aos modelos que, utilizados hoje na Ecologia, foram originalmente
desenvolvidos no contexto da teoria de redes por físicos e matemáticos. Uma vez
reformulados em termos biológicos, tais modelos deverão ser capazes de gerar
estimativas mais acuradas da resistência das comunidades à perda de espécies, bem
como previsões mais realistas a respeito das consequências do colapso das comunidades
para a biodiversidade e os serviços ecossistêmicos.
Interações mutualísticas sob a perspectiva de redes
Nosso estudo se debruçou sobre extinções de espécies em decorrência da perda de
outras espécies com as quais elas mantém interações mutualísticas. Interações
mutualísticas são aquelas que resultam em um efeito líquido positivo para todas as
espécies envolvidas (Stachovicz 2001). Os exemplos mais discutidos entre os ecólogos
atualmente são os mutualismos de polinização e de dispersão de sementes (Bascompte
& Jordano 2007).
A maior parte das espécies de plantas da Terra necessita, em maior ou menor grau, da
ação de animais para transportar pólen entre diferentes indivíduos e,dessa
maneira,garantir a fecundação cruzada. (Ollerton et al. 2011). Embora diversas espécies
de plantas sejam capazes de realizar autofecundação em diferentes níveis, mesmo essas
espécies tendem a se beneficiar do aumento da variabilidade genética e da diminuição
na frequência de anomalias genéticas resultantes da fecundação cruzada promovida pela
ação de polinizadores animais. De maneira semelhante ao que acontece com a dispersão
do pólen, muitas espécies de plantas requerem o auxílio de animais na dispersão das
suas sementes. A dispersão eficiente das sementes favorece a sobrevivência da prole ao
reduzir a competição por recursos entre a planta-mãe e a prole que se desenvolve a
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partir das suas sementes. Em ambos os casos, os animais envolvidos beneficiam-se da
interação ao obter alimento das plantas: recursos florais (e.g. néctar), no caso dos
polinizadores, e frutos, no caso dos frugívoros dispersores de sementes.
Em parte por influência de Darwin, que estudou os mecanismos extremamente
especializados de polinização em orquídeas, os biólogos durante muito tempo
enxergaram no mutualismo um exemplo extremo de especialização ecológica (Waser &
Ollerton 2006).Segundo essa visão, cada espécie de planta, por exemplo, seria visitada
por um único polinizador, ou por muito poucos, que por sua vez visitariam aquela única
espécies de planta, ou muito poucas espécies além dela. Essa visão mudou gradualmente
conforme os estudos de interações mutualísticas passaram a considerar não apenas
pequenas escalas (por exemplo, uma única espécie de planta e seus polinizadores ou
dispersores), mas também o padrão de interações mutualísticas na comunidade como
um todo(Jordano 1987, Memmott 1999). Esses estudos revelaram que interações
altamente especializadas, envolvendo pares de espécies interagindo exclusivamente
entre si, eram relativamente raras, enquanto interações envolvendo espécies mais
generalistas eram a regra. Dessa forma, as interações mutualísticas pareciam envolver
em uma única rede inúmeras espécies conectadas entre si direta ou indiretamente
(Bascompte & Jordano 2007).
Coextinções em redes mutualísticas
A constatação de que interações mutualísticas conectavam inúmeras espécies em
comunidades ecológicas sugeriu imediatamente que a dinâmica populacional e a
sobrevivência de uma determinada espécie sofrem influência, em maior ou menor grau,
da dinâmica populacional não apenas dos seus parceiros mutualistas imediatos, mas
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também das espécies às quais ela se conecta indiretamente na rede (Memmott et al.
2004). Assim, da mesma maneira que a extinção de uma presa ou hospedeiro poderia
levar à coextinção de um predador ou parasita, a extinção de um polinizador ou
dispersor importante poderia levar, direta ou indiretamente, a coextinções de plantas (e
vice-versa) que dependem das interações mutualísticas que estabelecem com esses
animais.
O processo de coextinção, quer envolvendo interações mutualísticas, quer outros tipos
de interação, tem sido extremamente difícil de se estudar empiricamente, e
pouquíssimos exemplos de coextinções foram efetivamente documentados (Dunn
2009). Assim, modelos de simulação que consideram a estrutura empírica das redes
ecológicas têm sido uma ferramenta essencial no estudo das coextinções (Bascompte &
Stouffer 2009, Colwell et al. 2012). Tais modelos, próximos ao paradigma das redes
complexas tradicionalmente estudadas na física e na matemática, são facilmente
aplicáveis a comunidades com grande riqueza de espécies, ao contrário dos modelos
clássicos baseados nas equações de Lotka-Volterra. Modelos de coextinção baseados
em redes ecológicas têm sido usados para avaliar a robustez das redes mutualísticas à
perda de espécies, bem como para investigar o efeito de diferentes fatores sobre
variações na robustez das comunidades(Memmott et al. 2004, 2007; Rezende et al.
2007; Kaiser-Bunbury et al. 2010; Mello et al. 2011). Dessa maneira, o uso desses
modelos produziu avanços importantes na nossa compreensão da dinâmica de redes
mutualísticas. Entretanto, conforme argumentamos no Capítulo 1, a transposição desses
modelos para a ecologia a partir da teoria de redes não incluiu propriedades biológicas
importantes das interações mutualísticas entre as espécies. Tais propriedades incluem a
variação na importância de diferentes parceiros mutualistas, bem como a variação na
dependência intrínseca das espécies em relação à interação mutualística em si. Incluir
6
tais propriedades em um modelo de coextinção, conforme demonstramos no Capítulo 1,
não apenas adiciona realismo biológico ao modelo, como também resulta em dinâmicas
de coextinção mais complexas e em previsões diferentes a respeito da probabilidade e
da ocorrência das coextinções.
REFERÊNCIAS
Bascompte, J. & Jordano, P. (2007). Plant-Animal Mutualistic Networks: The architecture of Biodiversity. Annu. Rev. Ecol. Evol. Syst., 38, 567–593.
Bascompte, J. & Stouffer, D.B. (2009). The assembly and disassembly of ecological networks. Philos. Trans. R. Soc. Lond. B. Biol. Sci., 364, 1781–7.
Colwell, R.K., Dunn, R.R. & Harris, N.C. (2012). Coextinction and persistence of dependent species in a changing World. Annu. Rev. Ecol. Evol. Syst., 43, 183–203.
Dunn, R.R. (2009). Coextinction: anecdotes, models and speculation. In: Holocene Extinctions (ed. Turvey, S.T.). Oxford University Press, New York, pp. 167 – 180.
Jordano, P. (1987). Patterns of mutualistic interactions in pollination and seed dispersal: connectance, dependence asymmetries, and coevolution. Am. Nat., 129, 657–677.
Kaiser-Bunbury, C.N., Muff, S., Memmott, J., Müller, C.B. & Caflisch, A. (2010). The robustness of pollination networks to the loss of species and interactions: a quantitative approach incorporating pollinator behaviour. Ecol. Lett., 13, 442–52.
Mello, M.A.R., Marquitti, F.M.D., Guimarães, P.R., Kalko, E.K.V., Jordano, P. & Aguiar, M.A.M. (2011). The missing part of seed dispersal networks: structure and robustness of bat-fruit interactions. PLoS One, 6, e17395.
Memmott, J. (1999). The structure of a plant-pollinator food web. Ecol. Lett., 2, 276–280.
Memmott, J., Craze, P.G., Waser, N.M. & Price, M. V. (2007). Global warming and the disruption of plant-pollinator interactions. Ecol. Lett., 10, 710–7.
Memmott, J., Waser, N.M. & Price, M. V. (2004). Tolerance of pollination networks to species extinctions. Proc. R. Soc. London Ser. B, 271, 2605–11.
Rezende, E.L., Lavabre, J.E., Guimarães, P.R., Jordano, P. & Bascompte, J. (2007). Non-random coextinctions in phylogenetically structured mutualistic networks. Nature, 448, 925–8.
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Stachowicz, J.J. (2001). Mutualism, Facilitation, and the Structure of Ecological Communities. Bioscience, 51, 235.
Waser, N.M. & Ollerton, J. (eds.) (2006). Plant-pollinator interactions: from specialization to generalization. University of Chicago Press, Chicago.
CAPÍTULO 1
A STOCHASTIC MODEL FOR COEXTINCTIONS IN MUTUALISTIC NETWORKS
Manuscritoa ser submetido à revista Ecology Letters
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ABSTRACT
Understanding and predicting species extinctions and coextinctions is a major goal of
ecological research in face of a biodiversity crisis. Ecologists have used simple models
based on network topology to simulate coextinctions in mutualistic networks. Such
models have so far neglected two kinds of biological variation in species interactions:
variation in the intrinsic dependence of species on the mutualism, and variation in the
relative importance of each interacting partner. By incorporating both axes of variation,
we developed a stochastic coextinction model capable of producing extinction cascades
far more complex than those produced by previous topological models. By simulating
coextinctions in empirical mutualistic networks, we show that topological models may
either underestimate or overestimate the number and likelihood of coextinctions,
depending on the intrinsic dependence of species on the mutualism. Also, contrary to
the topological model, our stochastic model predicts extinction cascades to be more
likely in highly connected mutualistic communities.
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INTRODUCTION
Anthropogenic modification of natural habitats across the globe and its past and
predicted effects on living species have led to the recognition of a global biodiversity
crisis (Pimm et al. 1995; Hooper et al. 2012). Current rates of species loss are higher
than the background rates inferred from the fossil record by two to three orders of
magnitude (Barnosky et al. 2011) and are predicted to remain high during the 21st
century (Pereira et al. 2010). Understanding and predicting the process of extinction is
thus a major topic of current ecological research. Because species depend on each other
for resources such as food and shelter and for processes such as breeding and dispersal,
the loss of a single species may drive the coextinction of other species which depend on
it (Dunn 2009; Colwell et al. 2012). However, most of the studies that have examined
the magnitude of species extinctions, as well as their causes and consequences, have not
taken into account that primary extinctions are likely to lead to further extinctions.
Taking such coextinction events into account when assessing the magnitude of the
current biodiversity crisis leads to higher estimated past and future extinction rates (Koh
et al. 2004).
Species coextinctions are difficult to document and investigate empirically, which
makes the use of modeling approaches highly relevant to advance our ability to predict
future extinction rates (Colwell et al. 2012). A long-standing line of research in
community ecology has focused on the effects of structural properties of model
interaction networks on community stability as well as the number of coextinctions and
their distribution among trophic levels (e.g. Pimm 1979; Borrvall et al. 2000; Eklof &
Ebenman 2006). Such approach usually employs dynamical models based on
generalized Lotka-Volterra equations, in which primary extinctions lead to both direct
and indirect additional extinctions through complex extinction cascades. However,
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much effort has recently been devoted to analyzing the structure of empirical interaction
networks and modeling their dynamics (Bascompte et al. 2003; Montoya et al. 2006;
Bascompte & Stouffer 2009). Because dynamical models are computationally intensive
and difficult to parameterize, attempts of modeling coextinctions in real, species-rich
interaction networks are usually based on topological models of coextinction (Solé &
Montoya 2001; Dunne et al. 2002; Memmott et al. 2004; Kaiser-Bunbury et al. 2010;
Pocock et al. 2012).
Topological models do not consider population dynamics explicitly and are based on
the architecture of species interaction networks (i.e. their topology). Such models
remove species from the network and assume that a coextinction occurs when a species
has no surviving prey, host, or mutualistic partner (e.g. Dunne et al. 2002; Memmott et
al. 2004). The assumption that the coextinction of a species requires the loss of all the
species on which it depends places a severe constraint on the complexity of extinction
cascades under topological models. In mutualistic networks, a species that suffers
coextinction due to the loss of a partner has, by definition, no other partners left.
Therefore, its loss cannot lead to additional extinctions. While species in real
mutualistic networks are connected with varying strength to their different partners
(Vázquez et al. 2005, 2012), this assumption also implies that a species can persist even
if only a minor, weakly-interacting partner is present. Relaxing the assumption that
coextinctions require the loss of all mutualistic partners allows for complex extinction
cascades in which primary extinctions in one trophic level indirectly lead to additional
extinctions in the same trophic level (i.e. ‘horizontal cascades’; Sanders et al. 2013). For
example, the coextinction of a plant species following the primary loss of a key
pollinator species might lead to the extinction of additional pollinator species that
depend strongly on the plant, which might in turn lead to the extinction of other plant
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species, and so on. Horizontal extinction cascades have been observed empirically in
host-parasitoid systems (Sanders et al. 2013).
In addition to neglecting variation in the interaction strengths of mutualistic partners,
current topological models of coextinctions in mutualistic networks also ignore
variation in the intrinsic dependence of species on the given mutualism for survival. In
the case of plant-pollinator networks, for example, topological models do not take into
account that plant species vary in the extent to which they are able to self-pollinate
successfully without the aid of an animal pollinator (Bond 1994), or that pollinators
often feed on resources other than floral nectar (Blüthgen 2010). Such variation in
species dependence on mutualisms may also occur at the scale of entire assemblages
(Kissling et al. 2009; Ollerton et al. 2011). Relaxing this second assumption may reduce
the expected number of coextinctions in some situations and lead to different
conclusions regarding which species are most sensitive to coextinctions. In turn, this
could change predictions about the order in which species are lost.
One straightforward consequence of the traditional topological approach to modeling
coextinctions in ecological networks is that primary extinctions in highly connected
networks are less likely to produce coextinctions, so that increased network connectance
should lead to increased robustness to extinctions (Dunne et al. 2002). This is a
necessary consequence of the assumption that coextinctions require the loss of all
interacting partners, since such total loss becomes more unlikely as species tend to have
more connections. However, one could alternatively argue that extinction cascades
triggered by primary extinctions should propagate more easily in highly connected
networks, so that increased connectance should lead to decreased robustness to
extinctions. Secondary extinctions under the traditional topological approach cannot
trigger additional extinctions in mutualistic networks. Thus, the positive relationship
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between network connectance and robustness predicted by the traditional topological
model may simply result from the combination of an excessively optimistic assumption
assumption and the model’s neglect of complex extinction cascades.
Here, we describe and evaluate a stochastic model of coextinctions in mutualistic
networks (hereafter stochastic coextinction model) which allows for complex extinction
cascades and is easily applicable to empirical interaction networks. Our model
incorporates variation in the dependence of species on the mutualistic interaction in
order to persist. In addition, by considering the variation in the mutual dependence
between every species and each of its mutualistic partners, the model relaxes the
assumption that the coextinction of a species requires the loss of all of its mutualistic
partners. By contrasting the stochastic coextinction model to the traditional topological
model, we demonstrate that the topological model may either underestimate or
overestimate the number and likelihood of coextinctions depending on the overall
intrinsic dependence of species on the mutualism. Also, while the topological model
suggests a positive relationship between network connectance and robustness to species
extinctions, the stochastic coextinction model predicts an opposite relationship in which
highly connected networks are more susceptible to coextinction cascades following
primary extinctions.
MATERIAL AND METHODS
A stochastic coextinction model for mutualistic networks
We developed a stochastic simulation model of coextinctions in mutualistic networks
based on the intrinsic dependence of species on the mutualism and the dependence of
species on each of their mutualistic partners. Previously, we briefly presented the model
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and used it to explore the functional and phylogenetic consequences of plant-pollinator
coextinctions (Vieira et al. 2013). Here, we provide a more formal presentation of the
model followed by a detailed exploration of its properties.
Let A and B be two sets of species (hereafter “trophic levels”) so that every species in A
has mutualistic interactions with one or more species in B, and vice versa. We assume
that no direct interactions occur between species in the same trophic level. We let Pij =
Ri dijbe the probability of species i going extinct following the extinction of a
mutualistic partner species j. Dependence of i on j (dij) is defined as the strength of the
interaction between i and j divided by the sum of interaction strengths between i and all
of its partners. Empirically, dij may be estimated as the number of interactions recorded
between species i and j divided by the total number of interactions involving species i
(Bascompte et al. 2006), which is easy to calculate from empirical quantitative
interaction matrices. Note that it is not necessary to have dij = dji. Ri is assumed constant
for each species and reflects the intrinsic demographic dependence of species i on the
mutualism in question. For example, if species i is a plant, Ri may reflect the extent to
which its seed set is limited by cross-pollination (allogamy) and might be inversely
related to its degree of self-compatibility or to its ability to reproduce asexually. Since
pollinators need not be restricted to consuming floral resources, Ri may also reflect the
intrinsic dependence of a pollinator on nectar. This dependence on floral resources for
food could be estimated empirically, for example by calculating the proportion of floral
resources in the animal’s diet. The same approach could be applied to fruiting plants
and seed dispersers. In this last case, plants depend on the animals for having their seeds
spread, which increases the survival of their offspring, whereas animals depend on fruits
as food resource.
14
Simulated extinction cascades in the stochastic coextinction model begin with a single
primary extinction in a given trophic level (say, trophic level A). Following the primary
extinction, all species from trophic level B have a probability of suffering coextinction
according to the equation Pij = Ri dij. For each coextinction in B, if any, all species in A
have a probability of going extinct themselves, and so on. Whenever coextinctions lead
to no additional extinctions, we assume that the community has reached equilibrium. As
the extinction cascade goes on, the dependences dij are recalculated. For example,
species i has dependence dij = 1 when j is its last surviving partner, regardless of the
initial value of dij (as long as it was not zero). Note that, since Pij may be less than 1
when species j is the last surviving partner of species i, species i may persist even if it
has lost all of its partners.
We define the degree of an extinction cascade as the number of extinction episodes,
with each episode involving one or more species, summed across both tropic levels. For
example, if the primary loss of a pollinator species leads to the extinction of two plant
species, which in turn leads to the loss of four additional pollinator species, we define
this event as a third-degree extinction cascade. Note that the degree does not necessarily
correspond to the total number of species lost in the extinction cascade (which is seven
in the example above).
Simulations on empirical data
In order to explore the behavior of our model by applying it to empirical data, we
compiled data on 27 quantitative mutualistic networks (14 pollination and 13 seed
dispersal networks) from a variety of biomes and geographic regions. A quantitative
mutualistic network is described by an interaction matrix whose entries aij contain the
15
number of times animal species i was recorded interacting with plant species j.
Interaction frequency can be used as a surrogate for the total effect of each mutualistic
interaction on the interacting pair of species (Vázquez et al. 2005). We obtained the data
from previous compilations by Rezende et al. (2007) and by Vieira et al. (2013) (see
table S1 for details and sources).
We simulated extinction cascades on the empirical mutualistic networks according to
our model. In each simulation, the original network was subjected to a single extinction
cascade in which the initial, primarily extinct species was chosen randomly from either
trophic level and coextinctions occurred according to the equation Pij = Ri dij.. Starting
dij values were calculated from the original interaction matrices. Ri was assumed equal
for all species and was uniformly sampled in each simulation from three intervals
representing low (0 <Ri ≤ 0.3), intermediate (0.3 <Ri ≤ 0.6) and high (0.6 <Ri ≤ 1)
intrinsic demographic dependence on the mutualistic interaction for persistence. For
each network, we performed 104 simulations for each interval of Ri and constructed
empirical frequency distributions for the total number of extinctions in an extinction
cascade. We also quantified the degree of each extinction cascade and constructed its
corresponding frequency distribution. From this frequency distribution, we calculated,
for each network and Ri level, the probability that a primary extinction would result in
second-, third- and fourth-degree-or-higher extinction cascades.
In addition to performing simulations under our stochastic topological model, we used
simulations to obtain the frequency distribution for the total number of extinctions
under the standard topological model, which constrains the coextinction of a species to
the loss of all of its mutualistic partners. From this distribution, we calculated the
probability that a primary extinction would result in a second-degree extinction cascade
under the topological model (note that third-degree-or-higher cascades are impossible
16
under this model). Finally, we assessed the relationship between network connectance
and the probability of a primary extinction resulting in additional extinctions (hereafter
the probability of an extinction cascade) for both models. We implemented all
simulations and analyses in R (R Development Core Team 2013). Code for the
simulations is available as supplementary material.
RESULTS
Probability and degree of extinction cascades
Frequency distributions of the total number of extinctions and the degree of extinction
cascades in empirical mutualistic networks are illustrated in Fig. 1 for the topological
model and the stochastic coextinction model.
Figure 1. Typical frequency distributions of the degree (a) and total number of extinctions (b) of extinction cascades simulated in an empirical mutualistic network using the topological model (gray bars) and the stochastic coextinction model (red bars). Red numbers indicate the number of observations for rare, extremely large degree values obtained under the stochastic coextinction model. The red arrow indicates large observed values of total number of extinctions that were omitted to improve visualization.
17
While the topological model is constrained to producing coextinction cascades with a
maximum degree of two (Fig. 1a), the stochastic coextinction model was able to
produce cascades of degree up to 7, 12 and 19, for low, medium and high values of the
R parameter, respectively. Under the stochastic coextinction model, the frequency
distribution of extinction cascade degrees was highly skewed, with most primary
extinctions leading to extinction cascade of degree one (i.e. no additional extinctions) or
two, and occasional primary extinctions leading to complex, high-degree extinction
cascades (Fig.1a).
Figure 2.Probability of extinction cascades (a) and their mean total number of extinctions (b) in 27 empirical mutualistic networks. Lines connect values obtained for the same network. Black: topological model. Red: Stochastic coextinction model. Triangles: low R. Crosses: Intermediate R. Open circles: high R.
The probability of an extinction cascade under our model is either lower or higher than
expected from the topological model, depending on the intrinsic demographic
dependence of species on the mutualistic interaction (i.e. the value of R) (Fig. 2a). For
most networks (74%) under low R, the probability of an extinction cascade was lower
under the stochastic coextinction model than under the topological model (Fig. 2a).
Under intermediate R, on the other hand, most networks (85%) had a higher probability
of suffering an extinction cascade under the stochastic coextinction model. For high
18
values of R, all mutualistic networks had a higher probability of suffering an extinction
cascade under the stochastic coextinction model (Fig. 2a). Averaging across all 27
empirical mutualistic networks on which we performed simulations, the probability that
a primary extinction would result in an extinction cascade was 0.15 ± 0.09 (mean ± S.D)
under the topological model. Under the stochastic coextinction model, extinction
cascades occurred on average with probabilities 0.10 ± 0.02, 0.23 ± 0.6 and 0.32 ± 0.10
for low, intermediate and high values of R, respectively. For three networks, the
probability of an extinction cascade under the topological model was zero; no single
primary extinction left any other species completely disconnected.
Figure 3.Probability of extinction cascades of second-(black), third-(red) and fourth-degree-or-higher (blue) under the stochastic coextinction model as a function of the Rparameter. Lines connect observations taken from the same mutualistic network.
Under the stochastic coextinction model, extinction cascades of second-, third-, and
fourth-degree or higher were increasingly likely to occur as the value or R increased
(Fig. 3). Extinction cascades of second-degree or higher were relatively common even
when Rwas low, and their probability of occurrence averaged across all 27 mutualistic
networks was about 0.1. However, they were on average about three times as likely to
19
occur for high values of R. This effect is even stronger for third- and fourth-degree-or-
higher cascades, which occur with negligible probability under low values of R but
become relatively common under high values of R(Fig. 3). High values of Rthus tend to
increase not only the likelihood of extinction cascades but also their complexity (in
terms of their degree).
Total number of extinctions
Under both models, the frequency distribution of the total number of extinctions per
primary extinction was highly skewed, with most primary extinctions leading to zero or
a few additional extinctions and occasional primary extinctions leading to a larger
number of extinctions (Fig. 1b). The mean number of extinctions per primary extinction
under the stochastic coextinction model is either lower or higher than expected from the
topological model, depending on the value of R (Fig. 2b). For low values of R, our
model predicted 3.5-27.1% less extinctions for most mutualistic networks (85%) and
4.7-18.5% more extinctions for the remaining three networks. On the other hand, for
intermediate and high values of R, our model predicted a higher number of extinctions
per primary extinction for all mutualistic networks (Fig. 2b). Under intermediate and
high values of R, the mean number of extinctions was respectively 1.06-1.77 and 1.65-
3.27 times the corresponding mean under the topological model.
Connectance vs. probability of extinction cascades
Under the topological model, highly connected networks had a lower probability of
suffering extinction cascades (rs = -0.35, one-tailed p = 0.036; Fig. 4). Under the
stochastic topological model, no relationship between network connectance and
probability of second-degree-or-higher extinction cascades was found for low values of
20
R (rs = 0.31, one-tailed p = 0.056; Fig. 5a). On the other hand, for intermediate and high
values of R, highly-connected networks had a higher probability of suffering extinction
cascades (intermediate R: rs = 0.38, one-tailed p = 0.025; high R: rs = 0.36, one-tailed p
= 0.032; Fig. 5b, c). The positive effect of connectance was even stronger and occurred
for all levels of R when only third-degree-or-higher cascades were considered (low R: rs
= 0.49, one-tailed p = 0.004; intermediate R: rs = 0.57, one-tailed p < 0.001; high R: rs =
0.53, one-tailed p = 0.002; Fig. 5 d-f).
Figure 4.Probability of extinction cascades under the topological model for 27 mutualistic networks as a function of network connectance.
DISCUSSION
The use of topological models to simulate the dynamics of mutualistic networks has
provided valuable insights into the effect of extinction scenarios (Memmott et al. 2004),
animal behavior (Kaiser-Bunbury et al. 2010) and climate change (Memmott et al.
2007) on the overall robustness of such networks to species extinctions. The traditional
topological approach has also been used to assess the consequences of the collapse of
mutualistic networks (Rezende et al. 2007). Here, we build on this approach by adding
two dimensions of biological realism previously neglected by topological models:
21
variation in the dependence of species on their different mutualistic partners
and variation in the degree to which species depend on the mutualism itself in
order to persist. By relaxing assumptions built into the earlier topological approach,
we developed a model
22
that allows for complex extinction cascades in which species losses in one trophic level
may lead to indirect additional losses of species in the same trophic level (i.e.
‘horizontal’ coextinctions; Sanders et al. 2013). This increase in model complexity
comes at a relatively low cost in terms of additional parameters. Dependence of species
on their different mutualistic partners (i.e. dijvalues) can be readily estimated from
quantitative interaction matrices, and the intrinsic demographic dependence on the
mutualistic interaction (i.e. the R parameter) might be estimated in many ways. Some
examples include using self-pollination indices to assess the dependence of plants on
animal pollination (Brys & Jacquemyn 2011), or estimating the level of frugivory in
seed dispersers such as bats to assess their dependence on fruiting plants (Kissling et al.
2009; Mello et al. 2011).
Differences between the traditional topological model and our stochastic topological
model must be interpreted in light of variation in the intrinsic demographic dependence
of species on a given type of mutualistic interaction (Bond 1994). Our results indicate
that, in addition to underestimating the complexity of extinction cascades, the
topological model may either underestimate or overestimate the expected number of
extinctions per primary extinction, depending on the intrinsic demographic dependence
of species on the mutualism. According to our stochastic coextinction model, when
species are highly dependent on pollination or seed dispersal interactions for
persistence, extinction cascades are more likely to occur, are often more complex and
tend to result in a larger number of extinctions. Because natural assemblages may vary
in the overall extent to which the species in it depend on mutualistic interactions in
order to persist (Kissling et al. 2009; Ollerton et al. 2011), estimating the community-
wide intrinsic dependence of species on mutualistic interactions for persistence is
23
imperative for assessing the relative robustness of different mutualistic communities to
species extinctions.
In this study, we considered variation in the intrinsic dependence on the mutualism only
at the scale of whole mutualistic networks. However, it is possible to obtain empirical
estimates for different species in the same community. In combination with data on the
relative dependence of species on each of their partners, this might allow us to estimate
the sensitivity of each species to coextinction due to the loss of its mutualistic partners.
In turn, this would allow us to predict the likely order in which species would be lost
during the collapse of mutualistic networks and therefore the intensity of the
corresponding decline in biodiversity and ecosystem services (Rezende et al. 2007;
Vieira et al. 2013).
Applying the topological model to a large set of empirical food webs, Dunne et al.
(2002) have shown that high network connectance leads to high network robustness to
secondary species extinctions. Our results have extended that conclusion for mutualistic
networks under the topological model. However, when complex extinction cascades
were simulated according to our stochastic coextincion model, we found an opposite
relationship: primary extinctions were more likely to trigger extinction cascades in
highly-connected networks. Broadly, this adds to the complexity-stability debate (May
1973; Pimm 1984; McCann 2000; Rooney & McCann 2012). While theoretical work
supports the idea that high connectance decreases the population stability of ecological
communities to small perturbations (May 1973; Allesina & Tang 2012), food web
studies based on Lotka-Volterra models have found either negative (Pimm 1979) or
positive (Eklof & Ebenman 2006) effects of connectance on network robustness, in
terms of additional species extinctions, to large perturbations (e.g. primary extinctions).
Considering mutualistic networks and using a different, probabilistic approach, our
24
results suggest that high network connectance makes it easier for the effects of primary
extinctions to propagate across the network and lead to the extinction of species many
links away. Our stochastic coextinction model therefore predicts that highly connected
communities of mutualists are more likely to experience changes in species composition
following primary extinctions than less connected communities.
Topological criteria have been used to simulate extinction dynamics in other kinds of
interaction networks, such as predator-prey food webs (Solé & Montoya 2001; Dunne et
al. 2002; Petchey et al. 2008; Dunne & Williams 2009) as well as non-biological
networks such as the Internet and the World Wide Web (Albert et al. 2000). Recently,
Bayesian techniques have been proposed as a way to model complex dynamics in
empirical food webs while taking into account variation in species interaction strengths
and without the need to implement Lotka-Volterra dynamical models (Eklöf et al.
2013). However, while the Bayesian approach is elegant and computationally simpler
since it requires no replicated simulations, it cannot be applied to intrinsically cyclic
interaction networks such as mutualistic networks.
The stochastic coextinction model takes a first step towards incorporating complex
dynamics into models of network disassembly in natural, species-rich mutualistic
communities. Because it incorporates important features of the biological variation of
species interactions while retaining the conceptual and computational simplicity of
standard topological models, it represents a novel modeling paradigm to estimate the
robustness of mutualistic communities to species extinctions in both theoretical and
applied research.
ACKNOWLEDGEMENTS
The authors would like to thank Paulo De Marco Jr. for fruitful discussions during the
conception of this work. MCV is grateful to his colleagues in the Graduate Program in
25
Ecology and Evolution at UFG for discussions and support.MCV is supported by a
graduate scholarship from the Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq). MAN received research fellowships (306843/2012-9 and
306870/2012-6, respectively) from the CNPq.
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CAPÍTULO 2
PLANT-POLLINATOR COEXTINTIONS AND THE LOSS OF PLANT FUNCTIONAL AND PHYLOGENETIC DIVERSITY
Artigo publicado na revista PLoS One em Novembro de 2013
Vieira, M.C., Cianciaruso, M.V. & Almeida-Neto, M. (2013). Plant-pollinator coextinctions and the loss of plant functional and phylogenetic diversity. PLoS One, 8, e81242. doi:10.1371/journal.pone.0081242
29
ABSTRACT
Plant-pollinator coextinctions are likely to become more frequent as habitat alteration
and climate change continue to threaten pollinators. The consequences of the resulting
collapse of plant communities will depend partly on how quickly plant functional and
phylogenetic diversity decline following pollinator extinctions. We investigated the
functional and phylogenetic consequences of pollinator extinctions by simulating
coextinctions in seven plant-pollinator networks coupled with independent data on plant
phylogeny and functional traits. Declines in plant functional diversity were slower than
expected under a scenario of random extinctions, while phylogenetic diversity often
decreased faster than expected by chance. Our results show that plant functional
diversity was relatively robust to plant-pollinator coextinctions, despite the underlying
rapid loss of evolutionary history. Thus, our study suggests the possibility of uncoupled
responses of functional and phylogenetic diversity to species coextinctions, highlighting
the importance of considering both dimensions of biodiversity explicitly in ecological
studies and when planning for the conservation of species and interactions.
30
INTRODUCTION
Current rates of anthropogenic habitat alteration have raised awareness of a global
biodiversity crisis [1]. Declines in species numbers have been reported for a wide
variety of taxa [2,3], and extinction rates are expected to increase due to predicted
global changes [4]. In addition to direct effects on ecosystem services such as nutrient
cycling and primary production [5], species extinctions may lead to the loss of
interactions on which other species depend for food, shelter, dispersal and reproduction
[6,7]. That is the case for most flowering plants, which depend on animal pollinators for
reproduction [8]. While data on pollinator richness and abundance is scarce for many
parts of the globe, there is growing concern that pollinators may be declining due to
habitat fragmentation, invasion by alien species, use of pesticides and global warming
[9–11].
Disruption of pollination by animals may lead to decreased plant productivity and
reproductive success [12,13]. Eventually, pollinator extinctions may trigger coextinction
cascades in which secondary extinctions of plants cause further extinctions of
pollinators and so on [6,7]. Thus, predicted pollinator declines may ultimately lead to
the disruption of plant communities, which in turn leads to the collapse of the ecosystem
services they maintain [1,5]. Since plant functional diversity is strongly related to
ecosystem functioning [14,15], the intensity of the decline in ecosystem functioning will
depend partly on how quickly plant functional diversity decreases following plant-
pollinator coextinctions.
In parallel to declines in plant functional diversity, plant extinctions due to the loss of
their pollinators imply the loss of the phylogenetic diversity of the plant assemblage
[16,17]. Because functional traits are often similar among closely related species [18]
functional diversity should be strongly related to phylogenetic diversity, so that the
31
functional and phylogenetic consequences of plant-pollinator coextinctions should be
similar. However, some studies have shown that congruence between patterns of
functional and phylogenetic diversity does not always occur [19,20]. While simulated
coextinctions in mutualistic networks (including pollination networks) may lead to
relatively fast declines in phylogenetic diversity [17], the consequences of plant-
pollinator coextinctions to plant functional diversity remain to be investigated. If
functionally unique plant species are particularly prone to suffer coextinctions, then
plant functional diversity should decline rapidly following pollinator losses. On the
other hand, if functionally unique plant species are unlikely to suffer secondary
extinctions compared to more redundant species, plant functional diversity should be
robust to the disruption of pollination services.
Here, we investigated the loss of plant functional and phylogenetic diversity following
pollinator extinctions by simulating coextinctions in empirical, quantitative plant-
pollinator networks. We contrasted simulated declines in functional and phylogenetic
diversity under a realistic coextinction scenario with declines resulting from optimistic,
pessimistic and random scenarios for the loss of functional and phylogenetic diversity.
We also looked for possible relationships between species functional and phylogenetic
uniqueness and their susceptibility to coextinctions. Finally, we asked whether
functionally or phylogenetically similar plant species are at similar risk of being lost in
a plant-pollinator coextinction scenario.
32
MATERIAL AND METHODS
Compilation of plant-pollinator networks
We performed simulations on empirical, quantitative networks available in the literature
or requested directly to authors. A quantitative plant-pollinator network is described by
an interaction matrix whose entries aij contain the number of times pollinator species i
was recorded visiting plant species j. Thus quantitative interaction networks report a
reasonable estimate of the total effect of each mutualistic interaction on the interacting
pair of species [21], as well as total interaction frequency for each species. We assume
that recorded interactions between plants and insects are actual plant-pollinator
interactions; however, we note that many studies do not discriminate between
occasional flower visitors and actual pollinators [22]. Interaction frequencies were used
here to ascribe relative risks of primary and secondary extinction to species in
simulations. Since we were interested in plant functional and phylogenetic diversity, we
could only include quantitative networks for which information on both functional traits
and phylogeny was available for the plants. Simultaneous availability of both kinds of
information is scarce, so that our literature search, resulted in seven networks described
in northern and central Europe: Switzerland (Albrecht et al. 2010 [23], data for the 130-
year-old site), Scotland (Devoto et al. 2012 [24], old-growth site #30), England
(Memmott 1999 [25]; Dicks et al. 2002 [26], Hicking site; both available as
supplementary material in [19]), Norway (Hegland et al. 2010 [27], data for 2004), and
Germany (Junker et al. 2010 [28], network #1; Weiner et al. 2011 [29], available as
supplementary material therein). We refer to each dataset by the name of the respective
first author (see Table S1 in Supporting Information for information on network size
and connectance).
33
Measuring plant functional and phylogenetic diversity
We estimated plant functional diversity using a suite of traits which capture broad-scale
variation in plant ecological strategies: specific leaf area (SLA), plant height and seed
mass (LHS scheme, [30]). Each one of these traits represents important trade-offs
controlling plant strategies [30] and are related to other important traits [31]. These
traits are also associated to plant responses to soil resources, competitive strength, and
effects on biogeochemical cycles and productivity [32–34]. Further, such traits are
easily measurable, which makes the LHS system broadly used in ecological studies [35–
37].
We searched the LEDA database (www.leda-traitbase.org) for data on specific leaf area
(SLA), canopy height and seed mass. We included only plant species with data for at
least two traits. We removed plants with information for less than two traits from the
interaction matrices prior to the simulations and removed any pollinators which had
zero interactions after removing such plants (see Appendix S1 in Supporting
Information for details on the compilation of trait data and the adjustment of interaction
matrices). This resulted in 0–9 plant species being removed (0-38%, median = 8.6%).
We built a functional dendrogram for the set of plant species in each network using a
Euclidean distance matrix and the UPGMA clustering algorithm. We obtained
phylogenies for the plant assemblages in each network using a recently published dated
phylogeny of European plants [38] encompassing all plant species found in the
pollination networks included in this study. For consistency, we removed those plants
with insufficient data on functional traits (as defined above and in Appendix S1) from
each phylogeny and from subsequent calculations of phylogenetic diversity.
34
We measured functional and phylogenetic diversity as the sum of branch lengths needed
to connect all non-extinct species in the corresponding functional dendrogram or
phylogenetic tree: FD and PD, respectively [16,39,40]. Note that FD for a single species
assemblage is defined as zero, whereas this is not the case for PD. Each functional
dendrogram and phylogenetic tree was built with the complete set of plant species in
each network (except for plants with missing traits as defined above) and was not
reconstructed during the simulated coextinction sequences.
To estimate the functional and phylogenetic uniqueness of each plant species in each
assemblage, we calculated their “originality” from the corresponding functional
dendrogram and phylogenetic tree [41]. Originality measures the relative contribution of
each species to the overall functional or phylogenetic diversity of the assemblage, such
that the values for all species add up to 1. Both functional and phylogenetic originality
of each plant species were based on the complete plant assemblage of the network and
thus were calculated prior to simulated extinctions. As alternative metrics for functional
and phylogenetic diversity, we used “total functional originality” and “total
phylogenetic originality”, the sum of functional and phylogenetic originality values
across all non-extinct plant species in each network. Since results were qualitatively
consistent, we present only the results for FD and PD in the main text.
Coextinction model and simulations
To investigate the impact of pollinator extinctions on the functional and phylogenetic
diversity of plant communities, we used a simulation approach based on the removal of
species from the observed interaction matrices. This is the standard method for
estimating the robustness of interaction networks to coextinctions [17,42–44]. However,
35
we acknowledge that this approach may produce biased results for rare species due to
undersampling of interactions [22].
We developed a stochastic model of coextinctions in mutualistic networks based on
network topology and interaction strengths. Contrary to other topological models of
coextinctions in ecological networks (e.g. [43]), it allows coextinction cascades
involving an indefinite number of species to occur following a single episode of primary
extinction. We briefly describe the model here in the context of pollination networks
and shall discuss its properties in detail elsewhere. A single event of coextinction is
modeled as follows. We let Pij = Ridij be the probability of species i suffering extinction
following the extinction of a mutualistic partner species j, where dij is the dependence of
species i on species j and Ri is a constant which reflects the intrinsic reproductive
dependence of species i on pollination (when i is a plant) or its intrinsic dependence on
floral resources for food (when i is a pollinator). We assumed R = 1 for all plants and
pollinators in this study. Thus, while simulation models usually assume that a species
goes extinct only after losing its last mutualistic partner, we relax such assumption in
our model. We assume, however, that species cannot establish new mutualistic
interactions after the extinction of their original mutualistic partners. Dependence of i
on j is calculated as the number of interactions recorded between that pair of species
divided by the total number of interactions of species i [45]. Thus an interaction matrix
of a animals and p plants results in two a x p dependence matrices which describe how
much each plant depends on each pollinator and how much each pollinator depends on
each plant.
For each pollination network, we simulated coextinction sequences involving primary
extinction episodes and possible coextinction cascades which occurred according to the
model described above. Each simulated extinction sequence proceeded until all species
36
had become extinct. A simulation step in each sequence involved the primary extinction
of a single pollinator species followed by the update of the interaction matrix and
possibly by a sequence of associated extinctions. Extinctions were represented in the
interaction matrix by setting all entries of a row (pollinator) or column (plant) to zero.
At the beginning of each step, a single pollinator species was chosen as a target for
primary extinction. All plant species then had a chance of suffering secondary
extinction according to the model described above: for each plant species, a value
between 0 and 1 was sampled from a uniform distribution, and a species was considered
extinct if such value was smaller than the species Pij value. If any plant species went
secondarily extinct, all of the surviving pollinator species in turn had a chance of going
extinct themselves, and so on until the sequence was interrupted by no further
extinctions occurring. Then we assumed the community reached equilibrium, calculated
FD and PD for the set of surviving plant species and moved on to the next primary
extinction episode. The algorithm updated the dependence matrix as the extinction
sequence moved forward. We quantified the persistence of a plant species in an
extinction sequence as the number of primary extinction episodes which occurred
before that species was lost.
Primary extinctions of pollinators at the beginning of each simulation step took place in
a realistic scenario in which pollinator species with lower total interaction frequencies
had a higher chance of suffering primary extinctions at each step. In pollination
networks total interaction frequency tends to be strongly correlated with abundance
[46,47], which is in turn a proxy to extinction risk. We assumed that the probability of
primary extinction for each pollinator species is proportional to the inverse of its total
interaction frequency. We ran 104 coextinction sequences and calculated the average
curve describing the decline in FD and PD for each network, as well as the average
37
persistence of each plant species. Each average curve describes the decline in functional
or phylogenetic diversity as a function of the proportion of plant species lost.
In order to provide a framework to interpret declines in plant functional and
phylogenetic diversity, we calculated a second set of curves for each network which
described the decline in FD and PD when plant species were lost independently of their
pollinators and according to three reference scenarios: (1) a best-case scenario in which
plants species were removed deterministically in increasing order of originality
(functional or phylogenetic, separately); (2) a worst-case scenario in which plants
species were removed deterministically in decreasing order of originality; and (3) a
random scenario (104 simulations). Best- and worst-case scenarios set boundaries
within which any decline in FD and PD should lie. We implemented all simulations in
R [48] using package ‘ade4’ to calculate originality [49] and package ‘picante’ to
calculate FD and PD [50].
Statistical analyses
We performed Spearman correlation tests to assess whether persistence was associated
with functional and phylogenetic originality. To assess the degree to which functionally
or phylogenetically similar plant species shared similar risk of suffering coextinction,
we performed autocorrelation analyses by calculating Moran’s correlograms for
persistence using distance matrices built from the functional dendrograms and
phylogenetic trees for each network [51]. Also, because coupled responses of functional
and phylogenetic diversity require functional traits to be conserved to some degree
along lineages, we quantified phylogenetic signal in the functional originality of species
by calculating phylogenetic correlograms for functional originality in each network. We
conducted all autocorrelation analyses in PAM v0.9 (Phylogenetic Analysis in
Macroecology; [52]).
39
RESULTS
Declines in FD and PD associated with simulated plant-pollinator coextinctions are
shown in Figs. 1 and 2 (see also Figs. S1 and S2 in Supporting Information for results
obtained using total functional and phylogenetic originality, respectively). In six out of
seven networks, FD decreased consistently more slowly than expected under a random
scenario (Figs. 1, 3A). In those cases, the relative extra amount of functional diversity
preserved in comparison with the random scenario ranged from 3.1% (Memmott
network; Figs. 1F, 3A) to 11.9% (Dicks network; Figs. 1C, 3A) at the point when 50%
of all plant species had been lost. In the Devoto network, however, FD decreased
consistently faster than expected under the random scenario (Fig. 1B) and was 22.9%
smaller than the random expectation at the point when 50% of plant species had been
lost (Fig. 3A).
In all networks except Devoto, PD decreased faster than FD when both were compared
to their respective random expectation (Fig. 3). In four networks (Albrecht, Devoto,
Dicks and Memmott), declines in PD were consistently faster than expected under the
random scenario of plant extinctions (Figs. 2A-C,F; Fig. 3B), so that PD was 3.0–14.2
% smaller than the random expectation at the point when 50% of plant species had been
lost. Consistently slower-than-random declines in PD occurred in only one network
(Junker), so that PD was 3.5% greater than expected under the random scenario
following the loss of 50% of plant species (Figs. 2E, 3B). The two remaining networks
exhibited slower-than-random declines in PD up to the point when about 55% (Weiner;
Fig. 2G) and 67% (Hegland; Fig. 2D) of plant species had suffered coextinction, and
negative deviations from the random curve after that point.
40
Species functional originality showed strongly asymmetric frequency distributions in all
pollination networks, with most plant species having very low functional originality and
single species accounting for 17.0–41.1% of the total (Fig. S3). We found no correlation
Figure 1. Declines in functional diversity (FD) following simulated plant-pollinator coextinctions in seven pollination networks (A-G).Circles: declines following plant-pollinator coextinctions. Dotted lines: declines following random plant extinctions in the absence of coextinctions. Solid lines above and below the dotted lines represent best- and worst-case scenarios, respectively.
between species persistence and species functional originality in any of the networks
(Fig. S3; Table S2). Phylogenetic originality was more evenly distributed across plant
species in pollination networks, with the single most phylogenetically original species
in each network accounting for 10.3–24.5% of total phylogenetic originality. We also
41
found no correlation between species phylogenetic originality and species persistence in
6 out of 7 networks (Fig. S4; Table S1). In the Devoto network, species with high
phylogenetic originality had lower persistence and thus higher risk of suffering
coextinction (rs = -
Figure 2. Declines in phylogenetic diversity (PD) following simulated plant-pollinator coextinctions in seven pollination networks (A-G). Circles: declines following plant-pollinator coextinctions. Dotted lines: declines following random plant extinctions in the absence of coextinctions. Solid lines above and below the dotted lines represent best- and worst-case scenarios, respectively.
0.643; p = 0.028). Overall, functionally similar or phylogenetically close plant species
had no tendency to have similar persistence to coextinctions (Fig 4A-B, Table S3).
Also, phylogenetically close plant species had no tendency to have similar functional
originality (Fig. 4C, Table S3), which suggests no overall phylogenetic signal in the set
of functional traits used.
42
Figure 3. Relative declines in FD and PD. Relative difference between declines in FD (A) and PD (B) under a plant pollinator coextinction scenario and declines under a random scenario of plant extinctions in the absence of coextinctions. Positive and negative deviations from the random expectation are shown in green and red, respectively. Closed squares = Albrecht, closed triangles = Devoto, closed circles = Dicks, crosses = Hegland, open triangles = Junker, open circles = Memmott, diamonds = Weiner. Vertical dotted line indicates values when 50% of plant species have been lost
DISCUSSION
Overall, coextinction trajectories led to slower declines in plant functional diversity than
expected under a scenario in which plant functional diversity was lost at random. In
contrast, phylogenetic diversity decreased faster than functional diversity in all
networks except one, and faster-than-random declines in phylogenetic diversity
occurred in four of them. Thus, our results show that the loss of plant functional
diversity is not necessarily coupled with the decline in plant phylogenetic diversity
following the loss of their pollinators. While the absence of phylogenetic signal in
functional traits would by itself suggest that functional diversity might not track
43
phylogenetic diversity in its faster decline, our results show that declines in functional
diversity may actually deviate from
44
Figure 4. Autocorrelation analyses. (A) Autocorrelation in persistence among plant species close to each other in the functional dendrogram. (B) Autocorrelation in persistence among phylogenetically close plant species. (C) Autocorrelation in functional originality among phylogenetically close plant species. Moran’s I values were calculated with respect to the first distance class in the correlogram.
45
the random expectation in the opposite direction. Thus, we confirm the previous finding
that phylogenetic diversity is often lost rapidly following coextinctions in mutualistic
networks [17], and we also show that plant functional diversity is relatively robust to
pollinator extinctions despite a relatively faster underlying loss of plant evolutionary
history.
The possibility of uncoupled functional and phylogenetic consequences of plant-
pollinator coextinctions highlights the importance of taking functional diversity
explicitly into account in ecological studies and when planning for the conservation of
species and their interactions, instead of simply taking phylogenetic diversity as a
proxy. Previous work has found mismatches between functional and phylogenetic
diversity in their spatial distribution [19,20] and in the extent to which they are
represented by indicator groups in a conservation context [53]. Our results further
suggest that, even when functional and phylogenetic diversity do exhibit congruence in
space, such local congruence may eventually be lost due to uncoupled responses to
species coextinctions. Consequently, because functional rather than phylogenetic
diversity is an ultimate driver of ecosystem functioning [54,55], predicting declines in
ecosystem functioning from declines in phylogenetic diversity may lead to erroneous
conclusions if both dimensions of biodiversity respond in different ways.
Non-random loss of functional diversity and ecosystem function in plant communities
under non-random extinction scenarios has been demonstrated before in computer
simulations [39,56] and experimentally [57,58]. Those studies have explored different
classes of realistic extinction scenarios, such as due to climate change or different
management and harvesting strategies of plant communities, and then simulated plant
extinctions based on traits likely to be associated with extinction risk in each scenario
[39,56,57] or on observed nested patterns of species occurrence [58]. We propose the
46
modeling of mutualistic coextinctions, previously used to study the loss of plant
phylogenetic diversity [17], as an additional strategy for building realistic scenarios
aimed at exploring the functional consequences of plant extinctions. Extinction risk in
this type of scenario is linked to the architecture of species interactions instead of being
directly linked to morphological or physiological traits, and realism can be achieved by
considering the empirical pattern of interactions described in mutualistic networks.
Although non-random declines in functional and phylogenetic diversity occurred, we
found no relationship between the functional and phylogenetic uniqueness of plant
species and their risk of suffering coextinction, nor did we find any tendency for
functionally of phylogenetically similar plant species to have similar coextinction risk.
It is possible that non-random declines result from one or a few plant species in each
network contributing disproportionately to the functional and phylogenetic diversity of
the plant assemblage. Because the loss of those highly unique species is associated with
the loss of large amounts of functional and phylogenetic diversity, overall declines in
those variables may be effectively determined by the particular persistence of those
species. For example, in the only network which exhibited a faster-than-random decline
in functional diversity under the coextinction scenario (Devoto network), two of the
three most sensitive species accounted for more than 60% of total functional originality.
In contrast, the single most persistent species accounted for about 40% of total
originality in the Junker network, in which functional diversity decreased more slowly
than the random expectation. Since the overall pattern seems to be slower-than-random
declines in functional diversity, our results suggest that plant species which contribute
disproportionately to functional diversity are relatively well-protected against the loss of
pollinators, even if no general relationship can be found among the whole plant
assemblage. On the other hand, since phylogenetic diversity decreased faster than
47
functional diversity, and often faster than expected under the random scenario, it
appears that highly phylogenetically unique plant species are often sensitive to the loss
of their pollinators.
While we provide a first assessment of the functional consequences of coextinctions in
mutualistic networks, the effect of predator-prey coextinctions on the functional
diversity of food webs has been investigated before. It has been shown that simulated
coextinctions lead to greater-than-random loss of total trophic diversity in model and
natural food webs [59]. In contrast, while we did find non-random declines in the
functional diversity of pollination networks, they were mainly in the opposite direction.
Also, we found no association between functional uniqueness and probability of
coextinction among plant species, while in food webs more functionally unique species
seem to have higher interaction frequencies [60] and higher probability of suffering
secondary extinctions [59]. While such food web studies focused on traits involved in
the realization of the predator-prey interactions, we estimated functional diversity by
considering non-reproductive traits related to broad variation in plant strategies and
related to ecosystem functions such as nutrient cycling and productivity. Thus, it is
possible that functional and phylogenetic diversity show coupled responses to plant-
pollinator coextinctions if functional diversity is estimated using reproductive (e.g.
floral, phenological) traits linked to pollination interactions and to the structure of
pollination networks.
It remains to be investigated whether similar results are to be found when considering
plant-pollinator communities from different regions of the globe. Different patterns of
decline in functional diversity might arise since, for example, structural properties of
mutualistic networks have been shown to vary along latitudinal and altitudinal gradients
[61,62]. Whether the degree of uncoupling between functional and phylogenetic
48
diversity varies geographically and can be predicted on the basis of network properties
is also open to investigation. Also, we do not know whether coextinctions due to the
loss of other kinds of mutualistic partners would produce similar impacts on plant
functional diversity. Seed dispersers such as birds, for example, are endangered due to
threats similar to those faced by pollinators [63], and the architecture of seed dispersal
networks is generally similar to that of pollination networks [47]. Finally, pollinator
behavior may influence the persistence of plant species since pollinators may switch to
new plant species following declines in the abundance of their original partners [64]. If
the probability of a plant species being visited by additional pollinator species is
correlated to its functional and phylogenetic originality, the effect of plant-pollinator
coextinctions on plant functional and phylogenetic diversity may differ from what is
suggested by our results.
In conclusion, our results point towards distinct consequences of mutualistic
coextinctions to the functional and phylogenetic diversity of plant assemblages.
Investigating the causes of such uncoupling, in terms of network structure, and its
implications, in terms of predicting community and ecosystem responses to
environmental change, can improve our understanding of the consequences of species
extinctions.
ACKNOWLEDGMENTS
We thank Mariano Devoto, Matthias Albrecht, Robert Junker and Stein Hegland for
kindly providing original interaction matrices describing plant-pollinator networks, and
Ignasi Bartomeus and an anonymous reviewer for helpful suggestions on the
manuscript.MCV is supported by a graduate scholarship from the Conselho Nacional de
49
Desenvolvimento Científico e Tecnológico (CNPq). MVC and MAN received research
fellowships (306843/2012-9 and 306870/2012-6, respectively) from the CNPq.
50
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SUPPLEMENTARY MATERIAL
Appendix S1 – Compilation of trait data and adjustment of interaction matrices
We searched the LEDA database (www.leda-traitbase.org) for information on
specific leaf area (SLA), canopy height and seed mass for the plant species in all seven
pollination networks. We obtained raw data from the database between March and
August 2012. We pooled pre-aggregated entries for each species according to the
following criteria: for SLA, we averaged all entries coming from measurements
performed on adult individuals following rehydration (for plant species in all networks
except Albrecht), in accordance with a protocol proposed by Cornelissen et al. (2003).
For plant species in the Albrecht network, we averaged all entries performed on adult
individuals without prior rehydration, since measurements following rehydration were
missing for many species. For canopy height, we averaged all entries for each species.
For seed mass, we averaged all entries for each species, except for entries coming from
measurements which reported the inclusion of seed appendages. Prior to coextinction
simulations, we removed plant species with information for less than two functional
traits from their respective networks, after checking whether data were available under
species synonyms (checked at www.theplantlist.org). This resulted in nine plant species
being removed from the Albrecht network (Cardamine resedifolia, Sempervivum
montanum, Trifolium pallescens, Laserpitium halleri, Campanula barbata, Galium
anisophyllon, Achillea erba-rota ssp. moschata, Taraxacum sp. and Hieracium
stacitifolium), two from Devoto (“unidentified Gramineae” and Plantago sp.), one from
Dicks (Taraxacum officinale), four from Hegland (Alchemilla sp., Euphrasia stricta,
Rosa sp. and Valeriana sambuccifolia), three from Junker (Erigeron anuus, “Rosa spec.
1” and Capsicum pubescens) and three from Weiner (Medicago varia, Orobranche sp.
and Taraxacum officinale). We also removed plants with zero interactions in the
original matrices provided by M. Albrecht (Albrecht network; Rumex scutatus,
Cardamine resedifolia, Rhododendron ferrugineum, Pyrola minor, Sempervivum
55
montanum, Sempervivum arachnoideum, Trifolium pratense, Trifolium pallescens,
Melampyrum silvaticum, Campanula barbata, Galium anisophyllon and Leontodon
helveticus) and obtained from Weiner et al. (2011) (Weiner network; Myosotris
sylvatica). We also removed any pollinators which had zero interactions following the
removal of plants: one from Devoto (pollinator #9) five from Albrecht (pollinators #15,
#18, #20, #23, #29); three from Hegland (Conops quadrifasciatus, Eristalis pertinax,
Opomyza petrei,); 13 from Junker (Tachinidae spp. 1 & 6, Vespidae spp. 3 & 4,
Chrysanelidae sp.1, Curculionidae sp.2, Dermaptera sp. 3, Heteroptera spp. 17, 22 & 30,
Ichneumonidae sp. 2, Melieria crassipennis and Thomisoidea sp. 1) and two from
Weiner (Megachile alpicola and Mechachile nigriventris).
Appendix S1 - References
Cornelissen, J.H.C., Lavorel, S., Garnier, E., Díaz, S., Buchmann, N., Gurvich, D.E., et
al. (2003). A handbook of protocols for standardised and easy measurement of
plant functional traits worldwide. Australian Journal of Botany, 51, 335–380.
Weiner, C.N., Werner, M., Linsenmair, K.E. & Blüthgen, N. (2011). Land use intensity
in grasslands : Changes in biodiversity , species composition and specialisation in
flower visitor networks. Basic and Applied Ecology, 12, 292–299.
56
Table S3. Results from autocorrelation analyses
Table references
1. Albrecht M, Riesen M, Schmid B (2010) Plant-pollinator network assembly along the chronosequence of a glacier foreland. Oikos 119: 1610–1624.
2. Devoto M, Bailey S, Craze P, Memmott J (2012) Understanding and planning ecological restoration of plant-pollinator networks. Ecology Letters: 319–328.
3. Dicks L V, Corbet SA, Pywell RF (2002) Compartmentalization in plant – insect flower visitor webs. Journal of Animal Ecology 71: 32–43.
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7. Weiner CN, Werner M, Linsenmair KE, Blüthgen N (2011) Land use intensity in
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Figure S1. Declines in total functional originality, following simulated plant-
pollinator coextinctions in seven pollination networks (A-G). Circles: declines
following plant-pollinator coextinctions. Dotted lines: declines following random plant
extinctions in the absence of coextinctions. Solid lines above and below the dotted lines
represent best- and worst-case scenarios, respectively.
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Figure S2. Declines in total phylogenetic originality, following simulated plant-pollinator coextinctions in seven pollination networks (A-G). Circles: declines following plant-pollinator coextinctions. Dotted lines: declines following random plant extinctions in the absence of coextinctions. Solid lines above and below the dotted lines represent best- and worst-case scenarios, respectively.
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Figure S3. Functional originality and ranked persistence values for plant species in the seven plant-pollinator networks (A-G).
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Figure S4. Phylogenetic originality and ranked persistence values for plant species in the seven plant-pollinator networks (A-G).
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CONCLUSÃO GERAL Apresentamos aqui um modelo estocástico de coextinções de espécies ligadas entre si
por interações mutualísticas. Ao incorporar diferentes propriedades biológicas e
ecológicas dessas interações, nosso modelo permite simular cascatas de extinção muito
mais complexas do que os modelos até então disponíveis para comunidades empíricas.
Esse aumento de complexidade se dá sem prejuízo da simplicidade conceitual e
computacional, grande virtude dos modelos anteriores.
Nosso modelo pode ser usado não apenas para investigar a resistência das comunidades
de mutualistas à perda de espécies, como também para estimarmos o risco de coextinção
para cada espécie em uma comunidade. Por sua vez, essa aplicação permite projetar
cenários para a ordem em que as espécies são perdidas durante o colapso das
comunidades e, consequentemente, prever o padrão de declínio da biodiversidade e dos
serviços ecossistêmicos. Ao aplicarmos o modelo para prever o impacto da perda de
polinizadores sobre as diversidades funcional e filogenética das comunidades vegetais,
sugerimos a possibilidade de que cada uma dessas dimensões da biodiversidade
responda de maneira diferente: enquanto a diversidade funcional tende a diminuir mais
lentamente do que esperado em um cenário de extinções aleatórias, sua contrapartida
filogenética diminui de maneira mais acelerada, por vezes mais acelerada do que a
expectativa aleatória. Nosso trabalho abre caminho para investigações mais gerais sobre
o efeito de coextinções envolvendo outras interações ecológicas, como a predação e o
parasitismo, sobre a perda de diversidade funcional e filogenética das comunidades.
Por fim, em termos mais gerais, nosso modelo representa um passo em direção à
incorporação de processos biológicos aos modelos ecológicos importados da teoria de
redes. Espécies biológicas ocorrem conectadas entre si por interações diversas, de
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maneira análoga ao que acontece com entidades não-biológicas. Computadores, por
exemplo, interagem uns com os outros em uma rede definida por conexões de Internet.
O modelo tradicional com que os ecólogos têm simulado o colapso de redes ecológicas
naturais é fundamentalmente idêntico ao modelo que foi originalmente aplicado por
físicos para simular o colapso da Internet. Entretanto, se por um lado está bem clara a
condição que caracteriza a “extinção” de um computador em termos práticos (a perda de
todas as suas conexões de internet), as condições para que uma espécie desapareça de
uma rede ecológica mutualística são mais complicadas e provavelmente não se
resumem à perda de todos os seus parceiros na rede. Diferentes parceiros têm diferentes
contribuições para a persistência das espécies, e a perda de um parceiro importante
poderia, em princípio, levar à extinção de uma espécie ainda que outros parceiros dela
persistam. Entretanto, é justamente a perda de todas as interações mutualísticas que
define a coextinção de uma espécie no modelo de coextinção tradicional. Nosso modelo
postula condições menos restritivas para a coextinção das espécies ao combinar a
variação na importância relativa dos diferentes parceiros com a variação na dependência
intrínseca das espécies em relação ao mutualismo. Embora desenvolvida no contexto de
interações mutualísticas, essa abordagem pode ser facilmente implementada para redes
definidas por outros tipos de interações ecológicas. Fazê-lo contribuiria para reformular,
em termos biológicos, os modelos que utilizamos em ecologia e que foram
desenvolvidos no contexto mais geral de redes não-biológicas.