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Mutualism is an understudied phenomenon across taxa, but is important to the persistence and structure of communities. The role of positive interactions in supporting threatened species is critically important given that freshwater fish are extremely vulnerable due to the combined effects of climate change and habitat degradation. To disentangle complex positive multi-species interactions, I applied both Eltonian and Hutchinsonian niche approaches to the reproductive mutualism of leuciscids known as nest association, a form of alloparental care characterized by an adult of one species guarding the offspring of another. I conducted this study with the leuciscid community of Toms Creek in which Bluehead Chub Nocomis leptocephalus is the primary nest builder and nest associate species include Rosyside Dace Clinostomus funduloides, Rosefin Shiner Lythrurus ardens, Mountain Redbelly Dace Chrosomus oreas, Crescent Shiner Luxilus cerasinus, White Shiner Luxilus albeolus, Central Stoneroller Campostoma anomalum, Creek Chub Semotilus atromaculatus, and Blacknose Dace Rhinycthys atratulus. I applied Hutchinsonian niche theory with respect to hydrology and water temperature to define the reproductive phenology of each species involved in the reproductive mutualism, then used Eltonian niche theory to define the role of each species in parental and alloparental care. My dual niche theory approach elucidates the reproductive requirements of each species and quantifies the contribution of nest associates to alloparental care, which historically have not been included in definitions of nest association. My results show that Blacknose Dace Rhinichthys atratulus and Creek Chub Semotilus atromaculatus are not true nest associates of Bluehead Chub Nocomis leptocephalus based on their reproductive phenology and observed nesting behaviors. In contrast to previous work on nest association, most associate species did contribute to parental care through nest defense and vigilance behaviors, and their specific behaviors were influenced by morphology. By clearly defining the reproductive niches of these species, this study lays the groundwork for future investigation of how various climate scenarios may impact multi-species reproductive mutualisms. / Master of Science / Positive interactions are understudied throughout ecology, but are important to the persistence and structure of communities. The role of positive interactions in supporting threatened species is critically important given that freshwater fish are at high risk of extinction due to the combined effects of climate change and habitat degradation. To understand the complex positive interactions in freshwater fish, I applied both niche theory approaches to a mutualistic reproductive interaction known as nest association, where an adult of one species builds a nest on which it guards the offspring of other species (formally: a type of alloparental care). I conducted this study with the leuciscid (commonly known as minnow) community of Toms Creek in which Bluehead Chub Nocomis leptocephalus is the primary nest builder and nest associate species include Rosyside Dace Clinostomus funduloides, Rosefin Shiner Lythrurus ardens, Mountain Redbelly Dace Chrosomus oreas, Crescent Shiner Luxilus cerasinus, White Shiner Luxilus albeolus, Central Stoneroller Campostoma anomalum, Creek Chub Semotilus atromaculatus, and Blacknose Dace Rhinycthys atratulus. For each species involved in the reproductive mutualism, I defined the seasonal timing of reproduction with respect to hydrology and water temperature, then defined their role in parental and alloparental care. My approach clarifies the reproductive requirements of each species and establishes the contributions of associate species to alloparental care, which historically have not been included in definitions of nest association. My results show that Blacknose Dace Rhinichthys atratulus and Creek Chub Semotilus atromaculatus are not true nest associates of Bluehead Chub Nocomis leptocephalus based on their reproductive requirements and observed nesting behaviors. In contrast to historic descriptions of nest association, most associate species did contribute to parental care through nest defense and vigilance behaviors, and their specific behaviors were influenced by their size and physical adaptations. By clearly defining the reproductive needs and roles of these species, this study lays the groundwork for future investigation of how various climate scenarios may impact positive relationships among species.

Doctor of Philosophy / Department of Statistics / Paul I. Nelson / Rank based inference using independent random samples to compare K>1 continuous distributions, called the K-sample problem, based on precedence probabilities is developed and explored. There are many parametric and nonparametric approaches, most dealing with hypothesis testing, to this important, classical problem. Most existing tests are designed to detect differences among the location parameters of different distributions. Best known and most widely used of these is the F- test, which assumes normality. A comparable nonparametric test was developed by Kruskal and Wallis (1952). When dealing with location-scale families of distributions, both of these tests can perform poorly if the differences among the distributions are among their scale parameters and not in their location parameters. Overall, existing tests are not effective in detecting changes in both location and scale. In this dissertation, I propose a new class of rank-based, asymptotically distribution- free tests that are effective in detecting changes in both location and scale based on precedence probabilities. Let X_{i} be a random variable with distribution function F_{i} ; Also, let _pi_ be the set of all permutations of the numbers (1,2,...,K) . Then P(X_{i_{1}}<...<X_{i_{K}}) is a precedence probability if (i_{1},...,i_{K}) belongs to _pi_. Properties of these of tests are developed using the theory of U-statistics (Hoeffding, 1948). Some of these new tests are related to volumes under ROC (Receiver Operating Characteristic) surfaces, which are of particular interest in clinical trials whose goal is to use a score to separate subjects into diagnostic groups. Motivated by this goal, I propose three new index measures of the separation or similarity among two or more distributions. These indices may be used as “effect sizes”. In a related problem, Properties of precedence probabilities are obtained and a bootstrap algorithm is used to estimate an interval for them.