Metapopulations operate in a complex spatial framework that potentially affects organism dispersal patterns, isolation of habitats and metapopulation dynamics. Small-world network theory provides an approach to model complex spatial pattern and may be valuable to models of complex metapopulations: it has been used to describe systems as diverse as rivers, the world-wide-web, and protein interactions, but has not been used as an experimental treatment for metapopulation dynamics. Small-world networks are characterized in their extremes as scale-free or single-scale, where a distribution of connections among sites follows a power law in scale-free networks but follows a normal distribution in a single-scale network. Scale-free networks should be sensitive to attack on highly-connected sites, whereas single-scale networks should be sensitive to random attacks. We tested the effects of network architecture (scale-free vs. single-scale) on simulated metapopulations with different population growth rates and dispersal patterns (unidirectional, bidirectional, or random). We also tested response of these networks to different attacks (targeted to highly-connected sites or random), and attack severity (0, 5, 10, 20, or 40% attacked populations). We recorded metapopulation size and inter-population variance (CV) in a simulated system designed to be relevant to conservation biology and ecology.
Results/Conclusions
As expected, metapopulation size and inter-population variance were strongly affected by combinations of dispersal pattern and growth rate (prior to attack). Network architecture strongly affected metapopulation size and CV, especially given unidirectional dispersal and low growth rate, which were also important to the effects of attack on networked metapopulations. Metapopulation size decreased as the attack severity increased in unidirectional and random dispersing populations in both scale-free and single-scale networks. However, scale-free and single-scale networks did not differ in response to random or targeted attacks, in contrast to expectations from network theory that focus on network architecture. This study focused instead on metapopulation parameters, and results suggest that population growth rate and dispersal direction are more important to metapopulation dynamics than fragmentation type in networked metapopulations. Low connectivity and other experimental assumptions of our simulations must be evaluated further, but our results indicate that metapopulations operating in small-world spatial networks may differ in response to fragmentation type than expected from network theory focused on network architecture.
