Limits...
Temporal development and collapse of an Arctic plant-pollinator network.

Pradal C, Olesen JM, Wiuf C - BMC Ecol. (2009)

Bottom Line: The network does not reach an equilibrium state (as defined by our model) before the collapse set in and the season is over.We have shown that the temporal dynamics of an Arctic plant-pollinator network can be described by a simple mathematical model and that the model allows us to draw biologically interesting conclusions.Our model makes it possible to investigate how the network topology changes with changes in parameter values and might provide means to study the effect of climate on plant-pollinator networks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Bioinformatics Research Centre, Aarhus University, C, F, Mollers Alle 8, Building 1110, DK-8000 Aarhus C, Denmark.

ABSTRACT

Background: The temporal dynamics and formation of plant-pollinator networks are difficult to study as it requires detailed observations of how the networks change over time. Understanding the temporal dynamics might provide insight into sustainability and robustness of the networks and how they react to environmental changes, such as global warming. Here we study an Arctic plant-pollinator network in two consecutive years using a simple mathematical model and describe the temporal dynamics (daily assembly and disassembly of links) by random mechanisms.

Results: We develop a mathematical model with parameters governed by the probabilities for entering, leaving and making connections in the network and demonstrate that A. The dynamics is described by very similar parameters in both years despite a strong turnover in the composition of the pollinator community and different climate conditions, B. There is a drastic change in the temporal behaviour a few days before the end of the season in both years. This change leads to the collapse of the network and does not correlate with weather parameters, C. We estimate that the number of available pollinator species is about 80 species of which 75-80% are observed in each year, D. The network does not reach an equilibrium state (as defined by our model) before the collapse set in and the season is over.

Conclusion: We have shown that the temporal dynamics of an Arctic plant-pollinator network can be described by a simple mathematical model and that the model allows us to draw biologically interesting conclusions. Our model makes it possible to investigate how the network topology changes with changes in parameter values and might provide means to study the effect of climate on plant-pollinator networks.

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Empirical and fitted distributions, 1996. Dynamic features of the 1996 network and the associated distributions. a) Number of pollinators entering the network each day fitted to a Poisson distribution, b) Number of pollinators leaving the network each day fitted to a binomial distribution with sigmoid-shaped parameter, c) Number of links assigned to pollinators when they enter the network. Here fitted to a modified geometric distribution, d) Number of links added or removed each day from pollinators in the network. The model is a geometric distribution for the added links and a binomial distribution with a sigmoid-shaped parameter for the removed ones. See Additional file 5 for 1997.
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Figure 3: Empirical and fitted distributions, 1996. Dynamic features of the 1996 network and the associated distributions. a) Number of pollinators entering the network each day fitted to a Poisson distribution, b) Number of pollinators leaving the network each day fitted to a binomial distribution with sigmoid-shaped parameter, c) Number of links assigned to pollinators when they enter the network. Here fitted to a modified geometric distribution, d) Number of links added or removed each day from pollinators in the network. The model is a geometric distribution for the added links and a binomial distribution with a sigmoid-shaped parameter for the removed ones. See Additional file 5 for 1997.

Mentions: Once in the network, pollinators can keep the same number of links - which is the most frequent situation; 65% (resp. 75%) of the cases in 1996 (resp. 1997) - get one or more additional links or loose one or more links each day. For the addition of links we fit a geometric distribution and for the loss of links a binomial distribution. The loss of links is more pronounced at the end of the season and we allowed a sigmoid form of the parameter again. All the computed parameters, and results of the tests for the chosen distributions are gathered in Table 2, Figure 3 (year 1996) and Additional file 5 (year 1997).


Temporal development and collapse of an Arctic plant-pollinator network.

Pradal C, Olesen JM, Wiuf C - BMC Ecol. (2009)

Empirical and fitted distributions, 1996. Dynamic features of the 1996 network and the associated distributions. a) Number of pollinators entering the network each day fitted to a Poisson distribution, b) Number of pollinators leaving the network each day fitted to a binomial distribution with sigmoid-shaped parameter, c) Number of links assigned to pollinators when they enter the network. Here fitted to a modified geometric distribution, d) Number of links added or removed each day from pollinators in the network. The model is a geometric distribution for the added links and a binomial distribution with a sigmoid-shaped parameter for the removed ones. See Additional file 5 for 1997.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2800837&req=5

Figure 3: Empirical and fitted distributions, 1996. Dynamic features of the 1996 network and the associated distributions. a) Number of pollinators entering the network each day fitted to a Poisson distribution, b) Number of pollinators leaving the network each day fitted to a binomial distribution with sigmoid-shaped parameter, c) Number of links assigned to pollinators when they enter the network. Here fitted to a modified geometric distribution, d) Number of links added or removed each day from pollinators in the network. The model is a geometric distribution for the added links and a binomial distribution with a sigmoid-shaped parameter for the removed ones. See Additional file 5 for 1997.
Mentions: Once in the network, pollinators can keep the same number of links - which is the most frequent situation; 65% (resp. 75%) of the cases in 1996 (resp. 1997) - get one or more additional links or loose one or more links each day. For the addition of links we fit a geometric distribution and for the loss of links a binomial distribution. The loss of links is more pronounced at the end of the season and we allowed a sigmoid form of the parameter again. All the computed parameters, and results of the tests for the chosen distributions are gathered in Table 2, Figure 3 (year 1996) and Additional file 5 (year 1997).

Bottom Line: The network does not reach an equilibrium state (as defined by our model) before the collapse set in and the season is over.We have shown that the temporal dynamics of an Arctic plant-pollinator network can be described by a simple mathematical model and that the model allows us to draw biologically interesting conclusions.Our model makes it possible to investigate how the network topology changes with changes in parameter values and might provide means to study the effect of climate on plant-pollinator networks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Bioinformatics Research Centre, Aarhus University, C, F, Mollers Alle 8, Building 1110, DK-8000 Aarhus C, Denmark.

ABSTRACT

Background: The temporal dynamics and formation of plant-pollinator networks are difficult to study as it requires detailed observations of how the networks change over time. Understanding the temporal dynamics might provide insight into sustainability and robustness of the networks and how they react to environmental changes, such as global warming. Here we study an Arctic plant-pollinator network in two consecutive years using a simple mathematical model and describe the temporal dynamics (daily assembly and disassembly of links) by random mechanisms.

Results: We develop a mathematical model with parameters governed by the probabilities for entering, leaving and making connections in the network and demonstrate that A. The dynamics is described by very similar parameters in both years despite a strong turnover in the composition of the pollinator community and different climate conditions, B. There is a drastic change in the temporal behaviour a few days before the end of the season in both years. This change leads to the collapse of the network and does not correlate with weather parameters, C. We estimate that the number of available pollinator species is about 80 species of which 75-80% are observed in each year, D. The network does not reach an equilibrium state (as defined by our model) before the collapse set in and the season is over.

Conclusion: We have shown that the temporal dynamics of an Arctic plant-pollinator network can be described by a simple mathematical model and that the model allows us to draw biologically interesting conclusions. Our model makes it possible to investigate how the network topology changes with changes in parameter values and might provide means to study the effect of climate on plant-pollinator networks.

Show MeSH