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Spatio-Temporal Ecological and Evolutionary Dynamics in Natural Butterfly Populations (2015 Field Season)
The study of evolution in natural populations has advanced our understanding of the origin and maintenance of biological diversity. For example, long term studies of wild populations indicate that natural selection can cause rapid and dramatic changes in traits, but that in some cases these evolutionary changes are quickly reversed when periodic variation in weather patterns or the biotic environment cause the optimal trait value to change (e.g., Reznick et al. 1997, Grant and Grant 2002). In fact, spatial and temporal variation in the strength and nature of natural selection could explain the high levels of genetic variation found in many natural populations (Gillespie 1994, Siepielski et al. 2009). Long term studies of evolution in the wild could also be informative for biodiversity conservation and resource management, because, for example, data on short term evolutionary responses to annual fluctuations in temperature or rainfall could be used to predict longer term evolution in response to directional climate change. Most previous research on evolution in the wild has considered one or a few observable traits or genes (e.g., Kapan 2001, Grant and Grant 2002, Barrett et al. 2008). We believe that more general conclusions regarding the rate and causes of evolutionary change in the wild and selectionâs contribution to the maintenance of genetic variation could be obtained by studying genome-wide molecular evolution in a suite of natural populations. Thus, in 2012 we began a long term study of genome-wide molecular evolution in a series of natural butterfly populations in the Greater Yellowstone Area (GYA). This study will allow us to quantify the contribution of environment-dependent natural selection to evolution in these butterfly populations and determine whether selection consistently favors the same alleles across space and through time
Assessing Functional Role and Community Dynamics of Whitebark Pine at Alpine Treeline, Grand Teton National Park
Whitebark pine (Pinus albicaulis) is a keystone and foundation tree species in high elevation ecosystems of the Rocky Mountains. At alpine treelines along the eastern Rocky Mountain Front and in the Greater Yellowstone Ecosystem, whitebark pine often initiates tree islands through facilitation, thereby shaping vegetation pattern. This role will likely diminish if whitebark pine succumbs to white pine blister rust infection, climate change stress, and mountain pine beetle infestations. Here, we established baseline measurements of whitebark pineâs importance and blister infection rates at two alpine treelines in Grand Teton National Park. Our specific objectives were to: 1) examine the potential relationship between whitebark pine establishment and krummholz tree island formation at the upper alpine treeline ecotone in GTNP; 2) characterize blister rust infection rate and intensity at two treeline study areas and in whitebark pine growing both solitarily and within tree islands; and 3) characterize the biophysical environments a) where whitebark pine is/is not a majority tree island initiator, and b) with varying blister rust infection rates in treeline whitebark pine. In July 2015, we field-sampled treeline composition and blister rust infection in all krummholz whitebark pine in a total of 40 study plots. Preliminary results reveal: 1) that whitebark pine is a substantial component of treeline ecosystems, but is not a significant majority tree island initiator, and 2) blister rust infection levels for both study areas combined is 15.65%. Blister rust and mountain pine beetle interactions were not evident at the two study areas. This work provides important baseline measurements for understanding how community structure and composition may be altered given infestation by pathogens and pests in GTNP, especially in light of changing climate regimes
Glacier Monitoring Internship Report: Grand Teton National Park, 2015
The small glaciers of Grand Teton National Park (GTNP) are iconic landmarks, enhancing the experience of millions of visitors to the park each year. They are valuable far beyond their beauty, and play a critical role in the parkâs unique high-elevation ecosystems
A bound for condition numbers of matrices
Let A be a diagonalizable matrix; so there is an invertible matrix T and a normal matrix Dˆ, such that T −1AT = Dˆ.A sharp bound for the constant κT = ∥T∥∥T −1∥ is suggested. Some applications of the obtained bound are also discussed
On Kronecker Quotients
Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663–688, 2005.]. This article considers the basic properties that a Kronecker quotient should satisfy and additional properties which may be satisfied. A class of Kronecker quotients for which these properties have a natural description is completely characterized. Two examples of types of Kronecker quotients are described
The norm of the k-the derivative of the Chi-symmetric power of an operator
In this paper, the exact value for the norm of directional derivatives, of all orders,for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained