A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a pa... more A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a parametric analysis of stability properties of dynamics on the system in which the functional response is a function of the ratio of prey to predator. It is shown that incorporating of Allee effect on prey equation significantly modifies the dynamics of the original system, as the modified model involves other non-topological equivalent behaviors. We prove the existence of a parameter subsets for which the system can have a Hopf bifurcation, a Bogdanov-Takens bifurcation, and showing the existence of separatrix curves in the phase plane determining that the long-term dynamics of the system is high sensitivity to initial conditions.
1. Earlier studies used static models to evaluate the responses of mutualistic networks to extern... more 1. Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web. 2. In this study, we model the temporal evolution of three empirical plant-pollination networks incorporating both population and topological dynamics. We test the hypothesis that topological plasticity, realized through the ability of animals to rewire their connections after depletion of host abundances, enhances tolerance of mutualistic networks to species loss. We also compared the performance of various rewiring rules in affecting robustness. 3. The results show that topological plasticity markedly increased the robustness of mutualistic networks. Our analyses also revealed that network robustness reached maximum levels when animals with less host plant availability were more likely to rewire. Also, preferential attachment to richer host plants, that is, to plants exhibiting higher abundance and few exploiters, enhances robustness more than other rewiring alternatives. 4. Our results highlight the potential role of topological plasticity in the robustness of mutualistic networks to species extinctions and suggest some plausible mechanisms by which the decisions of foragers may shape the collective dynamics of plant-pollinator systems.
1. Earlier studies used static models to evaluate the responses of mutualistic networks to extern... more 1. Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web. 2. In this study, we model the temporal evolution of three empirical plant–pollination networks incorporating both population and topological dynamics. We test the hypothesis that topological plasticity, realized through the ability of animals to rewire their connections after depletion of host abundances, enhances tolerance of mutualistic networks to species loss. We also compared the performance of various rewiring rules in affecting robustness. 3. The results show that topological plasticity markedly increased the robustness of mutualistic networks. Our analyses also revealed that network robustness reached maximum levels when animals with less host plant availability were more likely to rewire. Also, preferential attachment to richer host plants, that is, to plants exhibiting higher abundance and few exploiters, enhances robustness more than other rewiring alternatives. 4. Our results highlight the potential role of topological plasticity in the robustness of mutualistic networks to species extinctions and suggest some plausible mechanisms by which the decisions of foragers may shape the collective dynamics of plant–pollinator systems.
Pollination systems are recognized as critical for the maintenance of biodiversity in terrestrial... more Pollination systems are recognized as critical for the maintenance of biodiversity in terrestrial ecosystems. Therefore, the understanding of mechanisms that promote the integrity of those mutualistic assemblages is an important issue for the conservation of biodiversity and ecosystem function. In this study we present a new population dynamics model for plant–pollinator interactions that is based on the consumer–resource approach and incorporates a few essential features of pollination ecology. The model was used to project the temporal dynamics of three empirical pollination network , in order to analyze how adaptive foraging of pollinators (AF) shapes the outcome of community dynamics in terms of biodiversity and network robustness to species loss. We found that the incorporation of AF into the dynamics of the pollination networks increased the persistence and diversity of its constituent species, and reduced secondary extinctions of both plants and animals. These findings were best explained by the following underlying processes: 1) AF increased the amount of floral resources extracted by specialist pollinators, and 2) AF raised the visitation rates received by specialist plants. We propose that the main mechanism by which AF enhanced those processes is (trophic) niche partitioning among animals, which in turn generates (pollen vector) niche partitioning among plants. Our results suggest that pollination networks can maintain their stability and diversity by the adaptive foraging of generalist pollinators.
Human activities have led to massive influxes of pollutants, degrading the habitat of species and... more Human activities have led to massive influxes of pollutants, degrading the habitat of species and simplifying their biodiversity. However, the interaction between food web complexity, pollution and stability is still poorly understood. In this study we evaluate the effect exerted by accumulable pollutants on the relationship between complexity and stability of food webs. We built model food webs with different levels of richness and connectance, and used a bioenergetic model to project the dynamics of species biomasses. Further, we developed appropriate expressions for the dynamics of bioaccumulated and environmental pollutants. We additionally analyzed attributes of organisms' and communities as determinants of species persistence (stability). We found that the positive effect of complexity on stability was enhanced as pollutant stress increased. Additionally we showed that the number of basal species and the maximum trophic level shape the complexity– stability relationship in polluted systems, and that in-degree of consumers determines species extinction in polluted environments. Our study indicates that the form of biodiversity and the complexity of interaction networks are essential to understand and project the effects of pollution and other ecosystem threats.
Pollution represents a major threat to biodiversity. A wide class of pollutants tends to accumula... more Pollution represents a major threat to biodiversity. A wide class of pollutants tends to accumulate within organisms and propagate within communities via trophic interactions. Thus the final effects of accumulable pollutants may be determined by the structure of food webs and not only by the susceptibility of their constituent species. Species within real food webs are typically arranged into modules, which have been proposed to be determinants of network stability. In this study we evaluate the effect of network modularity and species richness on long-term species persistence in communities perturbed by pollutant stress. We built model food webs with different levels of modularity and used a bioenergetic model to project the dynamics of species. Further, we modeled the dynamics of bioaccumulated and environmental pollutants. We found that modularity promoted the stability of food webs subjected to pollutant stress. We also found that richer food webs were more robust at all modularity levels. Nevertheless, modularity did not promote stability of communities facing a perturbation that shared most features with the pollutant perturbation, but does not spread through trophic interactions. The positive effect of both modularity and species richness on species persistence was cancelled and even reversed when the structure of food web departed from a realistic body size distribution or a hierarchical feeding structure. Our results support the idea that modularity implies important dynamic consequences for communities facing pollution, highlighting a main role of network structure on ecosystem stability.
Research on ecological communities, and plantÁpollinator mutualistic networks in particular, has ... more Research on ecological communities, and plantÁpollinator mutualistic networks in particular, has increasingly benefited from the theory and tools of complexity science. Nevertheless, up to now there have been few attempts to investigate the interplay between the structure of real pollination networks and their dynamics. This study is one of the first contributions to explore this issue. Biological invasions, of major concern for conservation, are also poorly understood from the perspective of complex ecological networks. In this paper we assess the role that established alien species play within a host community by analyzing the temporal changes in structural network properties driven by the removal of non-native plants. Three topological measures have been used to represent the most relevant structural properties for the stability of ecological networks: degree distribution, nestedness, and modularity. Therefore, we investigate for a detailed pollination network, 1) how its dynamics, represented as changes in species abundances, affect the evolution of its structure, 2) how topology relates to dynamics focusing on long-term species persistence; and 3) how both structure and dynamics are affected by the removal of alien plant species. Network dynamics were simulated by means of a stochastic metacommunity model. Our results showed that established alien plants are important for the persistence of the pollination network and for the maintenance of its structure. Removal of alien plants decreased the likelihood of species persistence. On the other hand, both the full network and the subset native network tended to lose their structure through time. Nevertheless, the structure of the full network was better preserved than the structure of the network without alien plants. Temporal topological shifts were evident in terms of degree distribution, nestedness, and modularity. However the effects of removing alien plants were more pronounced for degree distribution and modularity of the network. Therefore, elimination of alien plants affected the evolution of the architecture of the interaction web, which was closely related to the higher species loss found in the network where alien plants were removed.
In the fragmented Maulino forest (in Central Chile), differences in the relative frequencies of s... more In the fragmented Maulino forest (in Central Chile), differences in the relative frequencies of species between seedlings and mature trees are strong indicators of a changing replacement dynamics in the community. Stationary Markov chain models predict that the future tree composition such Maulino forest fragments will differ from that of continuous, intact forest. We found that the persistence probability was highest for Aristotelia chilensis and lowest for Nothofagus glauca. These two tree species are the most affected by fragmentation, and changes in their abundances appear to be the main drivers of the long-term change in stand composition. The aim of our study was to test if the management of just these two species would be sufficient to avoid long-term changes in the composition of forest fragments or would recover their composition toward a state more similar to the continuous forest. For this purpose, we constructed a Markov matrix model from published information, and calculated the future stable stand composition under different management simulations: (1) reduction of A. chilensis recruitment, (2) increased recruitment of N. glauca, and (3) a combined treatment. To evaluate the effectiveness of management treatments, the future composition of fragments was compared with the composition expected for continuous (i.e., undisturbed) Maulino forest. We performed a sensitivity analysis of the stable composition in order to assess the intensity of changes in the future composition driven by the treatments, and to determine to what extend the recruitment of other coexisting species contributes to changes in relative frequencies of A. chilensis and N. glauca. The simulated management treatments reduced the predicted compositional divergence between fragments and continuous forest. The combined treatment was the most effective, increasing the frequency of N. glauca and reducing the frequency of A. chilensis, but none of the management strategies totally prevented compositional change of fragments in the long term. Nevertheless, a single intervention to reduce recruitment of A. chilensis reduced by a third the compositional divergence, and was the most cost effective method to manage forest fragments. Other species were identified as potential focus for conservation management, either because of their positive impact on N. glauca, or negative impact on A. chilensis.
A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a pa... more A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a parametric analysis of stability properties of dynamics on the system in which the functional response is a function of the ratio of prey to predator. It is shown that incorporating of Allee effect on prey equation significantly modifies the dynamics of the original system, as the modified model involves other non-topological equivalent behaviors. We prove the existence of a parameter subsets for which the system can have a Hopf bifurcation, a Bogdanov-Takens bifurcation, and showing the existence of separatrix curves in the phase plane determining that the long-term dynamics of the system is high sensitivity to initial conditions.
1. Earlier studies used static models to evaluate the responses of mutualistic networks to extern... more 1. Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web. 2. In this study, we model the temporal evolution of three empirical plant-pollination networks incorporating both population and topological dynamics. We test the hypothesis that topological plasticity, realized through the ability of animals to rewire their connections after depletion of host abundances, enhances tolerance of mutualistic networks to species loss. We also compared the performance of various rewiring rules in affecting robustness. 3. The results show that topological plasticity markedly increased the robustness of mutualistic networks. Our analyses also revealed that network robustness reached maximum levels when animals with less host plant availability were more likely to rewire. Also, preferential attachment to richer host plants, that is, to plants exhibiting higher abundance and few exploiters, enhances robustness more than other rewiring alternatives. 4. Our results highlight the potential role of topological plasticity in the robustness of mutualistic networks to species extinctions and suggest some plausible mechanisms by which the decisions of foragers may shape the collective dynamics of plant-pollinator systems.
1. Earlier studies used static models to evaluate the responses of mutualistic networks to extern... more 1. Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web. 2. In this study, we model the temporal evolution of three empirical plant–pollination networks incorporating both population and topological dynamics. We test the hypothesis that topological plasticity, realized through the ability of animals to rewire their connections after depletion of host abundances, enhances tolerance of mutualistic networks to species loss. We also compared the performance of various rewiring rules in affecting robustness. 3. The results show that topological plasticity markedly increased the robustness of mutualistic networks. Our analyses also revealed that network robustness reached maximum levels when animals with less host plant availability were more likely to rewire. Also, preferential attachment to richer host plants, that is, to plants exhibiting higher abundance and few exploiters, enhances robustness more than other rewiring alternatives. 4. Our results highlight the potential role of topological plasticity in the robustness of mutualistic networks to species extinctions and suggest some plausible mechanisms by which the decisions of foragers may shape the collective dynamics of plant–pollinator systems.
Pollination systems are recognized as critical for the maintenance of biodiversity in terrestrial... more Pollination systems are recognized as critical for the maintenance of biodiversity in terrestrial ecosystems. Therefore, the understanding of mechanisms that promote the integrity of those mutualistic assemblages is an important issue for the conservation of biodiversity and ecosystem function. In this study we present a new population dynamics model for plant–pollinator interactions that is based on the consumer–resource approach and incorporates a few essential features of pollination ecology. The model was used to project the temporal dynamics of three empirical pollination network , in order to analyze how adaptive foraging of pollinators (AF) shapes the outcome of community dynamics in terms of biodiversity and network robustness to species loss. We found that the incorporation of AF into the dynamics of the pollination networks increased the persistence and diversity of its constituent species, and reduced secondary extinctions of both plants and animals. These findings were best explained by the following underlying processes: 1) AF increased the amount of floral resources extracted by specialist pollinators, and 2) AF raised the visitation rates received by specialist plants. We propose that the main mechanism by which AF enhanced those processes is (trophic) niche partitioning among animals, which in turn generates (pollen vector) niche partitioning among plants. Our results suggest that pollination networks can maintain their stability and diversity by the adaptive foraging of generalist pollinators.
Human activities have led to massive influxes of pollutants, degrading the habitat of species and... more Human activities have led to massive influxes of pollutants, degrading the habitat of species and simplifying their biodiversity. However, the interaction between food web complexity, pollution and stability is still poorly understood. In this study we evaluate the effect exerted by accumulable pollutants on the relationship between complexity and stability of food webs. We built model food webs with different levels of richness and connectance, and used a bioenergetic model to project the dynamics of species biomasses. Further, we developed appropriate expressions for the dynamics of bioaccumulated and environmental pollutants. We additionally analyzed attributes of organisms' and communities as determinants of species persistence (stability). We found that the positive effect of complexity on stability was enhanced as pollutant stress increased. Additionally we showed that the number of basal species and the maximum trophic level shape the complexity– stability relationship in polluted systems, and that in-degree of consumers determines species extinction in polluted environments. Our study indicates that the form of biodiversity and the complexity of interaction networks are essential to understand and project the effects of pollution and other ecosystem threats.
Pollution represents a major threat to biodiversity. A wide class of pollutants tends to accumula... more Pollution represents a major threat to biodiversity. A wide class of pollutants tends to accumulate within organisms and propagate within communities via trophic interactions. Thus the final effects of accumulable pollutants may be determined by the structure of food webs and not only by the susceptibility of their constituent species. Species within real food webs are typically arranged into modules, which have been proposed to be determinants of network stability. In this study we evaluate the effect of network modularity and species richness on long-term species persistence in communities perturbed by pollutant stress. We built model food webs with different levels of modularity and used a bioenergetic model to project the dynamics of species. Further, we modeled the dynamics of bioaccumulated and environmental pollutants. We found that modularity promoted the stability of food webs subjected to pollutant stress. We also found that richer food webs were more robust at all modularity levels. Nevertheless, modularity did not promote stability of communities facing a perturbation that shared most features with the pollutant perturbation, but does not spread through trophic interactions. The positive effect of both modularity and species richness on species persistence was cancelled and even reversed when the structure of food web departed from a realistic body size distribution or a hierarchical feeding structure. Our results support the idea that modularity implies important dynamic consequences for communities facing pollution, highlighting a main role of network structure on ecosystem stability.
Research on ecological communities, and plantÁpollinator mutualistic networks in particular, has ... more Research on ecological communities, and plantÁpollinator mutualistic networks in particular, has increasingly benefited from the theory and tools of complexity science. Nevertheless, up to now there have been few attempts to investigate the interplay between the structure of real pollination networks and their dynamics. This study is one of the first contributions to explore this issue. Biological invasions, of major concern for conservation, are also poorly understood from the perspective of complex ecological networks. In this paper we assess the role that established alien species play within a host community by analyzing the temporal changes in structural network properties driven by the removal of non-native plants. Three topological measures have been used to represent the most relevant structural properties for the stability of ecological networks: degree distribution, nestedness, and modularity. Therefore, we investigate for a detailed pollination network, 1) how its dynamics, represented as changes in species abundances, affect the evolution of its structure, 2) how topology relates to dynamics focusing on long-term species persistence; and 3) how both structure and dynamics are affected by the removal of alien plant species. Network dynamics were simulated by means of a stochastic metacommunity model. Our results showed that established alien plants are important for the persistence of the pollination network and for the maintenance of its structure. Removal of alien plants decreased the likelihood of species persistence. On the other hand, both the full network and the subset native network tended to lose their structure through time. Nevertheless, the structure of the full network was better preserved than the structure of the network without alien plants. Temporal topological shifts were evident in terms of degree distribution, nestedness, and modularity. However the effects of removing alien plants were more pronounced for degree distribution and modularity of the network. Therefore, elimination of alien plants affected the evolution of the architecture of the interaction web, which was closely related to the higher species loss found in the network where alien plants were removed.
In the fragmented Maulino forest (in Central Chile), differences in the relative frequencies of s... more In the fragmented Maulino forest (in Central Chile), differences in the relative frequencies of species between seedlings and mature trees are strong indicators of a changing replacement dynamics in the community. Stationary Markov chain models predict that the future tree composition such Maulino forest fragments will differ from that of continuous, intact forest. We found that the persistence probability was highest for Aristotelia chilensis and lowest for Nothofagus glauca. These two tree species are the most affected by fragmentation, and changes in their abundances appear to be the main drivers of the long-term change in stand composition. The aim of our study was to test if the management of just these two species would be sufficient to avoid long-term changes in the composition of forest fragments or would recover their composition toward a state more similar to the continuous forest. For this purpose, we constructed a Markov matrix model from published information, and calculated the future stable stand composition under different management simulations: (1) reduction of A. chilensis recruitment, (2) increased recruitment of N. glauca, and (3) a combined treatment. To evaluate the effectiveness of management treatments, the future composition of fragments was compared with the composition expected for continuous (i.e., undisturbed) Maulino forest. We performed a sensitivity analysis of the stable composition in order to assess the intensity of changes in the future composition driven by the treatments, and to determine to what extend the recruitment of other coexisting species contributes to changes in relative frequencies of A. chilensis and N. glauca. The simulated management treatments reduced the predicted compositional divergence between fragments and continuous forest. The combined treatment was the most effective, increasing the frequency of N. glauca and reducing the frequency of A. chilensis, but none of the management strategies totally prevented compositional change of fragments in the long term. Nevertheless, a single intervention to reduce recruitment of A. chilensis reduced by a third the compositional divergence, and was the most cost effective method to manage forest fragments. Other species were identified as potential focus for conservation management, either because of their positive impact on N. glauca, or negative impact on A. chilensis.
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Papers by Jose Flores