This thesis investigates the relationships between mercury (Hg) and stable isotope of carbon (δ13C) in marine pelagic zooplankton (Calanus spp., Themisto spp. and Euchaeta spp.) with water mass characteristics in the North Water Polynya (NOW) and in the Mackenzie shelf – Amundsen Gulf area. Two ship based sampling field expeditions were carried out in late summer of 2005 and 2006 in both regions on board the CCGS Amundsen. In the North Water (NOW) polynya, higher levels of water Hg, depleted δ18O, lower salinity and lower nitrate levels were measured at sampling locations near the Prince of Wales glacier (POW) on the eastern coast of Ellesmere Island in the Smith Sound area. These results suggest that the glacier may be a source of Hg to this region which, in turn, is responsible for the correspondingly high concentrations of THg and MMHg measured in Calanus spp. and Euchaeta spp. at the same locations. The Mackenzie shelf – Amundsen Gulf region was characterized by fresher surface water properties (low salinity and depleted δ18O) in the western part and was strongly linked to the influence of the Mackenzie River. Higher THg concentrations in zooplankton were associated with larger fractions of both meteoric water and sea-ice melt. These findings suggest that in the western Arctic, inorganic Hg uptake in zooplankton via-absorption near surface water was highly driven by freshwater inputs into the system. Based on the analysis of three main genus Calanus spp. (mostly adult females Calanus hyperboreus), Euchaeta spp. and Themisto spp. (mostly adult Themisto libellula), THg and MMHg concentrations were the highest in the carnivorous copepod Euchaeta spp. in the North Water polynya followed by the omnivorous hyperiid amphipod Themisto spp. The herbivorous copepod Calanus spp. had both the lowest THg and MMHg concentrations in the Eastern and the Western Arctic. In addition, the Western Arctic is the area in which each zooplankton genus had the most depleted carbon and the most enriched nitrogen. The highest concentrations of THg in Calanus spp., Euchaeta spp. and Themisto spp. were measured in the Western Arctic as well as the highest MMHg in Calanus spp. and Themisto spp. The highest %MMHg was calculated in the Archipelago for Themisto spp., in the Eastern Arctic for Euchaeta spp. and in the Western Arctic for Calanus spp. The relationships observed between THg, MMHg, %MMHg and δ13C in all three major zooplankton taxa and water mass properties were in agreement with what have been previously described in the literature. Our findings suggested that both Hg and δ13C can be used as tracers to help understand zooplankton vertical distribution, feeding ecology and ultimately to predict climate changes impact at lower trophic level in the pelagic food web. The implications for marine mammals foraging in these regions are also discussed. / October 2008

Nitrogen (N) contained in roots and rhizodeposits represents a significant input of crop residue-N into soil that is often unaccounted, despite its contribution to the total N budget and its influence on soil nutrient cycling. Utilizing 15N-labeling methodologies under controlled conditions, the goal of this research was to quantify the input of belowground N (BGN), including rhizodeposits and roots, to soil and to investigate the influence of BGN on soil N cycling processes from the major pulse and oilseed crop grown across the Canadian prairies—namely, field pea and canola, respectively. Using continuous 15N2 labeling, the input of fixed-N to rhizosphere soil from pea plants amounted to less than 2% of the total plant N assimilated via fixation. Nodulation and root 15N enrichment were positively related to rhizosphere 15N enrichment, suggesting that the relatively low input of fixed-N to soil was due to low N fixation in this system. Shoot 15N-labeling techniques enabled a higher 15N enrichment in roots; as a result, rhizodeposition was detected in the rhizosphere as well as the surrounding bulk soil. Rhizodeposition accounted for 7.6 and 67% of plant N and BGN, respectively, in mature pea. Temporal changes in the pattern of rhizodeposition were detected as evidenced by differing 15N enrichment in rhizosphere versus bulk soils. In comparison to pea, a higher proportion of BGN contributed to the total residue-derived N from canola. The higher quantity of N rhizodeposition by canola was related to greater root biomass. However, pea rhizodeposition contributed more to soil inorganic N pools; this was sustained over time, as a higher proportion of pea BGN contributed to the growth of a subsequent wheat crop. In addition, wheat uptake of residue-derived N was twice as much from belowground compared to straw residues. Whereas the abundance of denitrifying bacterial communities in the rhizosphere was uncoupled from rhizodeposition and denitrification enzyme activity (DEA), root-derived 15N correlated with DEA in pea and canola. This research highlights the importance of belowground inputs from differing crop species on N budgets and soil N cycling.

In this thesis, we study the behaviour of Lovasz and Schrijver's lift-and-project operators N and N_0 while being applied recursively to the fractional stable set polytope of a graph. We focus on two related conjectures proposed by Liptak and Tuncel: the N-N_0 Conjecture and Rank Conjecture. First, we look at the algebraic derivation of new valid inequalities by the operators N and N_0. We then present algebraic characterizations of these valid inequalities. Tightly based on our algebraic characterizations, we give an alternate proof of a result of Lovasz and Schrijver, establishing the equivalence of N and N_0 operators on the fractional stable set polytope. Since the above mentioned conjectures involve also the recursive applications of N and N_0 operators, we also study the valid inequalities obtained by these lift-and-project operators after two applications. We show that the N-N_0 Conjecture is false, while the Rank Conjecture is true for all graphs with no more than 8 nodes.

Stable isotope analysis is a tool employed in ecological studies to provide information on the movement of elements and energy through a system. The stable carbon and nitrogen isotope analysis of aquatic organisms has been commonly used to address questions related to energy transfer between organisms and to identify the reliance of aquatic organisms on different sources of organic matter within the system. Within the rivers, stable isotope analysis has been used to describe food webs and connect conditions within the watershed with the river. The Grand River watershed is a predominantly agricultural watershed which receives inputs from ~26 MWWTP and is managed for flow by multiple large reservoirs and weirs. The stable isotope values of aquatic organisms within this watershed were analyzed from samples collected between May and September, 2007. Sites were selected in relation to three different municipal waste water treatment plants (MWWTP) in the centre of the watershed and along a 200 km stretch of the main stem of the Grand River. Results show that stable isotope analysis can be used to differentiate organisms collected from different sites and which represent different trophic levels within the river system under select conditions. Sites which are influences by inputs from organic matter or nutrients within distinct isotope values can be distinguished easily if the input is large and the isotope values are significantly distinct from background values. For smaller inputs changes in stable isotope values were not observed relative the background variability in the system. In this case, sites should be selected to allow for the characterization the variation in isotope values already occurring within the river. Samples collected later in the growing seasons have more distinctive isotope values are between sites. At sites where seasonal variation is greater, the organisms collected may not show a clear separation between trophic levels. A lack of knowledge regarding the time period represented by the tissues of the organisms challenges interpretation these results. It is concluded that stable isotope values of aquatic organisms reflected the condition of this watershed. For nitrogen increasing loads from point sources were accompanied by increasing isotope values. Stable isotope values decreased over the river reach where recovery in river condition occurs as a result of ground water inputs. The influence of individual large MWWTP and reservoirs was observable and the management of the MWWTP and reservoir appears to affect the changes in isotope values which are observed.

Vehicular ad hoc networks (VANETs) have emerged as an area of interest for both industry and research scholars because they have become an essential part of intelligent transportation systems (ITSs). Many applications in VANET require sending a message to certain or all vehicles within a region, called geocast. Sometimes geocast requires that the message be kept alive within the region for a period of time. This time-stable geocast has a vital role in some ITS applications, particularly commercial applications. This study presents a novel time-stable geocast protocol that works well even in too sparse networks. Moreover, since commercial applications sometimes make it necessary to change the duration of the stable message within the region, the dynamic nature of a geocast protocol should allow this time to be extended, reduced, or canceled without any additional cost. Therefore, we call it a dynamic time-stable geocast, DTSG, protocol. It works in two phases (the pre-stable period and the stable period), and the simulation results show that it works well in its performance metrics (delivery ratio and network cost). In addition, these results validate the protocol prediction of its performance metrics. Moreover, with the informed time of zero, all the intended vehicles will be informed as soon as they enter the region. The fact that the protocol is independent of the networks’ density, the vehicles’ speed, and the vehicles’ broadcasting range, makes it more robust than others that fail in sparse networks or in high-speed nodes.

In this thesis, we study the behaviour of Lovasz and Schrijver's lift-and-project operators N and N_0 while being applied recursively to the fractional stable set polytope of a graph. We focus on two related conjectures proposed by Liptak and Tuncel: the N-N_0 Conjecture and Rank Conjecture. First, we look at the algebraic derivation of new valid inequalities by the operators N and N_0. We then present algebraic characterizations of these valid inequalities. Tightly based on our algebraic characterizations, we give an alternate proof of a result of Lovasz and Schrijver, establishing the equivalence of N and N_0 operators on the fractional stable set polytope. Since the above mentioned conjectures involve also the recursive applications of N and N_0 operators, we also study the valid inequalities obtained by these lift-and-project operators after two applications. We show that the N-N_0 Conjecture is false, while the Rank Conjecture is true for all graphs with no more than 8 nodes.

Stable isotope analysis is a tool employed in ecological studies to provide information on the movement of elements and energy through a system. The stable carbon and nitrogen isotope analysis of aquatic organisms has been commonly used to address questions related to energy transfer between organisms and to identify the reliance of aquatic organisms on different sources of organic matter within the system. Within the rivers, stable isotope analysis has been used to describe food webs and connect conditions within the watershed with the river. The Grand River watershed is a predominantly agricultural watershed which receives inputs from ~26 MWWTP and is managed for flow by multiple large reservoirs and weirs. The stable isotope values of aquatic organisms within this watershed were analyzed from samples collected between May and September, 2007. Sites were selected in relation to three different municipal waste water treatment plants (MWWTP) in the centre of the watershed and along a 200 km stretch of the main stem of the Grand River. Results show that stable isotope analysis can be used to differentiate organisms collected from different sites and which represent different trophic levels within the river system under select conditions. Sites which are influences by inputs from organic matter or nutrients within distinct isotope values can be distinguished easily if the input is large and the isotope values are significantly distinct from background values. For smaller inputs changes in stable isotope values were not observed relative the background variability in the system. In this case, sites should be selected to allow for the characterization the variation in isotope values already occurring within the river. Samples collected later in the growing seasons have more distinctive isotope values are between sites. At sites where seasonal variation is greater, the organisms collected may not show a clear separation between trophic levels. A lack of knowledge regarding the time period represented by the tissues of the organisms challenges interpretation these results. It is concluded that stable isotope values of aquatic organisms reflected the condition of this watershed. For nitrogen increasing loads from point sources were accompanied by increasing isotope values. Stable isotope values decreased over the river reach where recovery in river condition occurs as a result of ground water inputs. The influence of individual large MWWTP and reservoirs was observable and the management of the MWWTP and reservoir appears to affect the changes in isotope values which are observed.

Vehicular ad hoc networks (VANETs) have emerged as an area of interest for both industry and research scholars because they have become an essential part of intelligent transportation systems (ITSs). Many applications in VANET require sending a message to certain or all vehicles within a region, called geocast. Sometimes geocast requires that the message be kept alive within the region for a period of time. This time-stable geocast has a vital role in some ITS applications, particularly commercial applications. This study presents a novel time-stable geocast protocol that works well even in too sparse networks. Moreover, since commercial applications sometimes make it necessary to change the duration of the stable message within the region, the dynamic nature of a geocast protocol should allow this time to be extended, reduced, or canceled without any additional cost. Therefore, we call it a dynamic time-stable geocast, DTSG, protocol. It works in two phases (the pre-stable period and the stable period), and the simulation results show that it works well in its performance metrics (delivery ratio and network cost). In addition, these results validate the protocol prediction of its performance metrics. Moreover, with the informed time of zero, all the intended vehicles will be informed as soon as they enter the region. The fact that the protocol is independent of the networks’ density, the vehicles’ speed, and the vehicles’ broadcasting range, makes it more robust than others that fail in sparse networks or in high-speed nodes.

This thesis documents a heavy-tailed analysis of stable portfolios. Stock market crashes occur more often than is predicted by a normal distribution,which provides empirical evidence that asset returns are heavy-tailed. The motivation of this thesis is to study the effects of heavy-tailed distributions of asset returns. It is imperative to know the risk that is incurred for unlikely tail events in order to develop a safer and more accurate portfolio. The heavy-tailed distribution that is used to model asset returns is the stable distribution. The problem of optimally allocating assets between normal and stable distribution portfolios is studied. Furthermore, a heavy-tail sensitivity analysis is performed in order to see how the optimal allocation changes as the heavy-tail coefficient is altered. In order to solve both problems, we use a mean-dispersion risk measure and a probability of loss risk measure. Our analysis is done for two-asset stable portfolios, one of the assets being risk-free, and one risky. The approach used involves changing the heavy-tail parameter of the stable distribution and finding the differences in the optimal asset allocation. The key result is that relatively more wealth is allocated to the risk-free asset when using stable distributions than when using normal distributions. The exception occurs when using a loss probability risk measure with a very high risk tolerance. We conclude that portfolios assuming normal distributions incorrectly calculate the risk in two types of situations. These portfolios do not account for the heavy-tail risk when the risk tolerance is low and they do not account for the higher peak around the mean when the risk tolerance is high.

An improved ability to assess whether individuals have been added through immigration or natality and lost through emigration or mortality could alleviate several problems in population ecology. Fortunately, advances in stable isotope techniques now allow the movements of individuals to be retraced from tissue values and provide an opportunity to link information about the origins of individuals with demographic rates so that questions about the significance of dispersal can be assessed. I used such an approach by combining feather isotope information with demographic rates derived from capture-mark-recapture of individual mallards (Anas platyrhynchos) breeding in the Canadian aspen parklands, at multiple spatiotemporal scales, to answer questions about population persistence, settling patterns by dispersers, and the fitness of immigrant birds relative to residents.<p> Feather isotope (ä34S, äD, ä15N, and ä13C) values from an independent sample of flightless mallard ducklings sampled from across the mid-continent breeding range was used to validate an existing model used for origin assignments. Spatial resolution analysis within the mid-continent mallard breeding range generally showed a loss in prediction when attempting to assign individuals to more narrowly separated geographic origins among boreal, aspen parkland and prairie regions. For feather äD, spatial resolution may be limited by temporal patterns of local climatic events that produce variability in consumer tissue values. Thus, the use of multiple feather isotope signals would provide more reliable information about the origin of individuals for addressing questions about long-distance dispersal in yearling mallards.<p> Demographic rescue in an apparent population sink near Minnedosa, Manitoba, Canada, was due to elevated survival rates from a highly productive group of nesting female mallards using nest tunnels (i.e., an artificial nesting structure) and recruitment of yearling females having natal origins within the aspen parklands. There was little evidence that immigration by yearling females dispersing long-distances was important to annual population growth rates. Consistently high annual survival rates of adult females using nest tunnels lowered the recruitment rates needed for population stability. While tunnel-origin and within-region recruitment of yearling females were nearly equally important to local population growth rate, fine-scale limitations of isotopic origin assignments prevented further assessment of where recruits originated from within the aspen parkland region.<p> Factors related to breeding area settling patterns of yearling females are not well understood despite implications to local population dynamics. The likelihood that immigrant yearling females would settle in a parkland breeding area was positively correlated with local breeding-pair density and the amount of perennial nest cover, but was negatively correlated with the amount of wetlands. Although these relationships were not well estimated, they are most consistent a hypothesis that females were attracted to breeding sites by conspecific cues rather than avoidance. Immigrants comprised an average of 9% (range: 0 39% over 22 sites) of yearling recruits; most had natal origins in the U.S. prairie pothole region but a non-trivial number originated from the boreal forest, indicating a high degree of connectedness among breeding regions resulting from long-distance natal dispersal.<p> One of the most frequent explanations for strong site fidelity in breeding female ducks is that females benefit from site familiarity. However, evidence for differential reproductive success between immigrant and resident yearling females was weak, On sites with favourable wetland conditions and low breeding-pair densities immigrant females were more likely to breed and nest successfully than were residents whereas under opposite wetland and pair conditions, resident females were favoured. Thus, the costs and benefits of a natal dispersal decision seemed to vary with social context and environmental conditions, and further work is needed to clarify these processes.