MODULARITY BASED FUZZY COMMUNITY DETECTION IN SOCIAL NETWORKS

Fuzzy community detection is to identify fuzzy communities in a network, which are groups of vertices in the network such that the membership of a vertex in one community is in [0,1] and that the sum of memberships of vertices in all communities equals to 1. Fuzzy communities are pervasive in social networks, but only a few works have been done for fuzzy community detection. Recently, a one-step forward extension of Newman’s Modularity, the most popular quality function for disjoint community detection, results into the Generalized Modularity (GM) that demonstrates good performance in finding well-known fuzzy communities. Thus, GMis chosen as the quality function in our research. We first propose a generalized fuzzy t-norm modularity to investigate the effect of different fuzzy intersection operators on fuzzy community detection, since the introduction of a fuzzy intersection operation is made feasible by GM. The experimental results show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure. Then, we focus on how to find optimal fuzzy communities in a network by directly maximizing GM, which we call it Fuzzy Modularity Maximization (FMM) problem. The effort on FMM problem results into the major contribution of this thesis, an efficient and effective GM-based fuzzy community detection method that could automatically discover a fuzzy partition of a network when it is appropriate, which is much better than fuzzy partitions found by existing fuzzy community detection methods, and a crisp partition of a network when appropriate, which is competitive with partitions resulted from the best disjoint community detections up to now. We address FMM problem by iteratively solving a sub-problem called One-Step Modularity Maximization (OSMM). We present two approaches for solving this iterative procedure: a tree-based global optimizer called Find Best Leaf Node (FBLN) and a heuristic-based local optimizer. The OSMM problem is based on a simplified quadratic knapsack problem that can be solved in linear time; thus, a solution of OSMM can be found in linear time. Since the OSMM algorithm is called within FBLN recursively and the structure of the search tree is non-deterministic, we can see that the FMM/FBLN algorithm runs in a time complexity of at least O (n2). So, we also propose several highly efficient and very effective heuristic algorithms namely FMM/H algorithms. We compared our proposed FMM/H algorithms with two state-of-the-art community detection methods, modified MULTICUT Spectral Fuzzy c-Means (MSFCM) and Genetic Algorithm with a Local Search strategy (GALS), on 10 real-world data sets. The experimental results suggest that the H2 variant of FMM/H is the best performing version. The H2 algorithm is very competitive with GALS in producing maximum modularity partitions and performs much better than MSFCM. On all the 10 data sets, H2 is also 2-3 orders of magnitude faster than GALS. Furthermore, by adopting a simply modified version of the H2 algorithm as a mutation operator, we designed a genetic algorithm for fuzzy community detection, namely GAFCD, where elite selection and early termination are applied. The crossover operator is designed to make GAFCD converge fast and to enhance GAFCD’s ability of jumping out of local minimums. Experimental results on all the data sets show that GAFCD uncovers better community structure than GALS.

The effect of long-term water table manipulations on vegetation, pore water, substrate quality, and carbon cycling in a Northern poor fen peatland

Northern peatlands are large reservoirs of soil organic carbon (C). Historically peatlands have served as a sink for C since decomposition is slowed primarily because of a raised water table (WT) that creates anoxic conditions. Climate models are predicting dramatic changes in temperature and precipitation patterns for the northern hemisphere that contain more than 90% of the world’s peatlands. It is uncertain whether climate change will shift northern peatlands from C sequestering systems to a major global C source within the next century because of alterations to peatland hydrology. This research investigated the effects of 80 years of hydrological manipulations on peatland C cycling in a poor fen peatland in northern Michigan. The construction of an earthen levee within the Seney National Wildlife Refuge in the 1930’s resulted in areas of raised and lowered WT position relative to an intermediate WT site that was unaltered by the levee. We established sites across the gradient of long-term WT manipulations to examine how decadal changes in WT position alter peatland C cycling. We quantified vegetation dynamics, peat substrate quality, and pore water chemistry in relation to trace gas C cycling in these manipulated areas as well as the intermediate site. Vegetation in both the raised and lowered WT treatments has different community structure, biomass, and productivity dynamics compared to the intermediate site. Peat substrate quality exhibited differences in chemical composition and lability across the WT treatments. Pore water dissolved organic carbon (DOC) concentrations increased with impoundment and WT drawdown. The raised WT treatment DOC has a low aromaticity and is a highly labile C source, whereas WT drawdown has increased DOC aromaticity. This study has demonstrated a subtle change of the long-term WT position in a northern peatland will induce a significant influence on ecosystem C cycling with implications for the fate of peatland C stocks.

Spatial and temporal patterns in ungulate-ecosystem interactions

Ungulates are important components of a variety of ecosystems worldwide. This dissertation integrates aspects of ungulate and forest ecology to increase our understanding of how they work together in ways that are of interest to natural resource managers, educators, and those who are simply curious about nature. Although animal ecology and ecosystem ecology are often studied separately, one of the general goals of this dissertation is to examine how they interact across spatial and temporal scales. Forest ecosystems are heterogeneous across a range of scales. Spatial and temporal habitat use patterns of forest ungulates tend to be congregated in patches where food and/or cover are readily available. Ungulates interact with ecosystem processes by selectively foraging on plants and excreting waste products in concentrated patches. Positive feedbacks may develop where these activities increase the value of habitat through soil fertilization or the alteration of plant chemistry and architecture. Heterogeneity in ecosystem processes and plant community structure, observed at both stand and local scales, may be the integrated outcome of feedbacks between ungulate behavior and abiotic resource gradients. The first chapter of this dissertation briefly discusses pertinent background information on ungulate ecology, with a focus on white-tailed deer (Odocoileus virginianus) in the Upper Great Lakes region and moose (Alces acles) in Isle Royale National Park, Michigan, USA. The second chapter demonstrates why ecological context is important for studying ungulate ecology in forest ecosystems. Excluding deer from eastern hemlock (Tsuga canadensis) stands, which deer use primarily as winter cover, resulted in less spatial complexity in soil reactive nitrogen and greater complexity in diffuse light compared to unfenced stands. The spatial patterning of herbaceous-layer cover was more similar to nitrogen where deer were present, and was a combination of nitrogen and light within deer exclosures. This relationship depends on the seasonal timing of deer habitat use because deer fertilize the soil during winter, but leave during the growing season. The third chapter draws upon an eight-year, 39-stand data set of deer fecal pellet counts in hemlock stands to estimate the amount of nitrogen that deer are depositing in hemlock stands each winter. In stands of high winter deer use, deer-excreted nitrogen inputs consistently exceeded those of atmospheric deposition at the stand scale. At the neighborhood scale, deer-excreted nitrogen was often in excess of atmospheric deposition due to the patchy distribution of deer habitat use. Spatial patterns in habitat use were consistent over the eight-year study at both stand and neighborhood scales. The fourth chapter explores how foraging selectivity by moose interacts with an abiotic resource gradient to influence forest structure and composition. Soil depth on Isle Royale varies from east to west according to glacial history. Fir saplings growing in deeper soils on the west side are generally more palatable forage for moose (lower foliar C:N) than those growing in shallower soils on the east side. Therefore, saplings growing in better conditions are less likely to reach the canopy due to moose browsing, and fir is a smaller overstory component on the west side. Lastly, chapter five focuses on issues surrounding eastern hemlock regeneration failure, which is a habitat type that is important to many wildlife species. Increasing hemlock on the landscape is complicated by several factors including disturbance regime and climate change, in addition to the influence of deer.

IMPACTS OF CLIMATE CHANGE ON SOIL MICROORGANISMS IN NORTHERN HARDWOOD FORESTS

As global climate continues to change, it becomes more important to understand possible feedbacks from soils to the climate system. This dissertation focuses on soil microbial community responses to climate change factors in northern hardwood forests. Two soil warming experiments at Harvard Forest in Massachusetts, and a climate change manipulation experiment with both elevated temperature and increased moisture inputs in Michigan were sampled. The hyphal in-growth bag method was to understand how soil fungal biomass and respiration respond to climate change factors. Our results from phospholipid fatty acid (PLFA) analyses suggest that the hyphal in-growth bag method allows relatively pure samples of fungal hyphae to be partitioned from bacteria in the soil. The contribution of fungal hyphal respiration to soil respiration was examined in climate change manipulation experiments in Massachusetts and Michigan. The Harvard Forest soil warming experiments in Massachusetts are long-term studies with 8 and 18 years of +5 °C warming treatment. Hyphal respiration and biomass production tended to decrease with soil warming at Harvard Forest. This suggests that fungal hyphae adjust to higher temperatures by decreasing the amount of carbon respired and the amount of carbon stored in biomass. The Ford Forestry Center experiment in Michigan has a 2 x 2 fully factorial design with warming (+4-5 °C) and moisture addition (+30% average ambient growing season precipitation). This experiment was used to examine hyphal growth and respiration of arbuscular mycorrhizal fungi (AMF), soil enzymatic capacity, microbial biomass and microbial community structure in the soil over two years of experimental treatment. Results from the hyphal in-growth bag study indicate that AMF hyphal growth and respiration respond negatively to drought. Soil enzyme activities tend to be higher in heated versus unheated soils. There were significant temporal variations in enzyme activity and microbial biomass estimates. When microbial biomass was estimated using chloroform fumigation extractions there were no differences between experimental treatments and the control. When PLFA analyses were used to estimate microbial biomass we found that biomass responds negatively to higher temperatures and positively to moisture addition. This pattern was present for both bacteria and fungi. More information on the quality and composition of the organic matter and nutrients in soils from climate change manipulation experiments will allow us to gain a more thorough understanding of the mechanisms driving the patterns reported here. The information presented here will improve current soil carbon and nitrogen cycling models.