Locally Self-Adjusting Skip Graphs

We present a distributed self-adjusting algorithm for skip graphs that minimizes the average routing costs between arbitrary communication pairs by performing topological adaptation to the communication pattern. Our algorithm is fully decentralized, conforms to the $\mathcal{CONGEST}$ model (i.e. uses $O(\log n)$ bit messages), and requires $O(\log n)$ bits of memory for each node, where $n$ is the total number of nodes. Upon each communication request, our algorithm first establishes communication by using the standard skip graph routing, and then locally and partially reconstructs the skip graph topology to perform topological adaptation. We propose a computational model for such algorithms, as well as a yardstick (working set property) to evaluate them. Our working set property can also be used to evaluate self-adjusting algorithms for other graph classes where multiple tree-like subgraphs overlap (e.g. hypercube networks). We derive a lower bound of the amortized routing cost for any algorithm that follows our model and serves an unknown sequence of communication requests. We show that the routing cost of our algorithm is at most a constant factor more than the amortized routing cost of any algorithm conforming to our computational model. We also show that the expected transformation cost for our algorithm is at most a logarithmic factor more than the amortized routing cost of any algorithm conforming to our computational model

Foundation species enhance food web complexity through non-trophic facilitation

Food webs are an integral part of every ecosystem on the planet, yet understanding the mechanisms shaping these complex networks remains a major challenge. Recently, several studies suggested that non-trophic species interactions such as habitat modification and mutualisms can be important determinants of food web structure. However, it remains unclear whether these findings generalize across ecosystems, and whether non-trophic interactions affect food webs randomly, or affect specific trophic levels or functional groups. Here, we combine analyses of 58 food webs from seven terrestrial, freshwater and coastal systems to test (1) the general hypothesis that non-trophic facilitation by habitat-forming foundation species enhances food web complexity, and (2) whether these enhancements have either random or targeted effects on particular trophic levels, functional groups, and linkages throughout the food web. Our empirical results demonstrate that foundation species consistently enhance food web complexity in all seven ecosystems. Further analyses reveal that 15 out of 19 food web properties can be well-approximated by assuming that foundation species randomly facilitate species throughout the trophic network. However, basal species are less strongly, and carnivores are more strongly facilitated in foundation species' food webs than predicted based on random facilitation, resulting in a higher mean trophic level and a longer average chain length. Overall, we conclude that foundation species strongly enhance food web complexity through non-trophic facilitation of species across the entire trophic network. We therefore suggest that the structure and stability of food webs often depends critically on non-trophic facilitation by foundation species

Foundation species enhance food web complexity through non-trophic facilitation

Food webs are an integral part of every ecosystem on the planet, yet understanding the mechanisms shaping these complex networks remains a major challenge. Recently, several studies suggested that non-trophic species interactions such as habitat modification and mutualisms can be important determinants of food web structure. However, it remains unclear whether these findings generalize across ecosystems, and whether non-trophic interactions affect food webs randomly, or affect specific trophic levels or functional groups. Here, we combine analyses of 58 food webs from seven terrestrial, freshwater and coastal systems to test (1) the general hypothesis that non-trophic facilitation by habitat-forming foundation species enhances food web complexity, and (2) whether these enhancements have either random or targeted effects on particular trophic levels, functional groups, and linkages throughout the food web. Our empirical results demonstrate that foundation species consistently enhance food web complexity in all seven ecosystems. Further analyses reveal that 15 out of 19 food web properties can be well-approximated by assuming that foundation species randomly facilitate species throughout the trophic network. However, basal species are less strongly, and carnivores are more strongly facilitated in foundation species’ food webs than predicted based on random facilitation, resulting in a higher mean trophic level and a longer average chain length. Overall, we conclude that foundation species strongly enhance food web complexity through non-trophic facilitation of species across the entire trophic network. We therefore suggest that the structure and stability of food webs often depends critically on non-trophic facilitation by foundation species.</p