Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

Geochemical variation among small eruptive centers in the central SVZ of the Andes: An evaluation of subduction, mantle and crustal influences

Subduction zone magmatism is an important and extensively studied topic in igneous geochemistry. Recent studies focus on from where arc magmas are generated, how subduction components (fluids or melts) are fluxed into the source of the magmas, and whether or how the subduction components affect partial melting processes beneath volcanic arcs at convergent boundaries. ^ At 39.5°S in the Central Southern Volcanic Zone of the Andes, Volcano Villarrica is surrounded by a suite of Small Eruptive Centers (SEC). The SECs are located mostly to the east and northeast of the stratovolcano and aligned along the Liquine-Ofqui Fault Zone, the major fracture system in this area. Former studies observed the geochemical patterns of the SECs differ distinctively from those of V. Villarrica and suggested there may be a relationship between the compositions of the volcanic units and their edifice sizes. This work is a comprehensive geochemical study on the SECs near V. Villarrica, using a variety of geochemical tracers and tools including major, trace and REE elements, Li-Be-B elements, Sr-Nd-Pb isotopes and short-lived isotopes such as U-series and 10Be. In this work, systematic differences between the elemental and isotopic compositions of the SECs and those of V. Villarrica are revealed and more importantly, modeled in terms of magmatic processes occurring at continental arc margins. Detailed modeling calculations in this work reconstruct chemical compositions of the primary magmas, source compositions, compositions and percentages of different subduction endmembers mixed into the source, degrees of partial melting and different time scales of the SECs and V. Villarrica, respectively. Geochemical characteristics and possible origins of the two special SECs—andesitic Llizan, with crustal signatures, and Rucapillan, to the northwest toward the trench, are also discussed in this work. ^

Estimation of average annual daily traffic (AADT) using geographically weighted regression (GWR) method and geographic information system (GIS)

Annual average daily traffic (AADT) is important information for many transportation planning, design, operation, and maintenance activities, as well as for the allocation of highway funds. Many studies have attempted AADT estimation using factor approach, regression analysis, time series, and artificial neural networks. However, these methods are unable to account for spatially variable influence of independent variables on the dependent variable even though it is well known that to many transportation problems, including AADT estimation, spatial context is important. ^ In this study, applications of geographically weighted regression (GWR) methods to estimating AADT were investigated. The GWR based methods considered the influence of correlations among the variables over space and the spatially non-stationarity of the variables. A GWR model allows different relationships between the dependent and independent variables to exist at different points in space. In other words, model parameters vary from location to location and the locally linear regression parameters at a point are affected more by observations near that point than observations further away. ^ The study area was Broward County, Florida. Broward County lies on the Atlantic coast between Palm Beach and Miami-Dade counties. In this study, a total of 67 variables were considered as potential AADT predictors, and six variables (lanes, speed, regional accessibility, direct access, density of roadway length, and density of seasonal household) were selected to develop the models. ^ To investigate the predictive powers of various AADT predictors over the space, the statistics including local r-square, local parameter estimates, and local errors were examined and mapped. The local variations in relationships among parameters were investigated, measured, and mapped to assess the usefulness of GWR methods. ^ The results indicated that the GWR models were able to better explain the variation in the data and to predict AADT with smaller errors than the ordinary linear regression models for the same dataset. Additionally, GWR was able to model the spatial non-stationarity in the data, i.e., the spatially varying relationship between AADT and predictors, which cannot be modeled in ordinary linear regression. ^

Relating precipitation and water management to nutrient concentrations in the oligotrophic ‘‘upside-down’’ estuaries of the Florida Everglades

We present 8 yr of long-term water quality, climatological, and water management data for 17 locations in Everglades National Park, Florida. Total phosphorus (P) concentration data from freshwater sites (typically ,0.25 mmol L21, or 8 mg L21) indicate the oligotrophic, P-limited nature of this large freshwater–estuarine landscape. Total P concentrations at estuarine sites near the Gulf of Mexico (average ø0.5 m mol L21) demonstrate the marine source for this limiting nutrient. This ‘‘upside down’’ phenomenon, with the limiting nutrient supplied by the ocean and not the land, is a defining characteristic of the Everglade landscape. We present a conceptual model of how the seasonality of precipitation and the management of canal water inputs control the marine P supply, and we hypothesize that seasonal variability in water residence time controls water quality through internal biogeochemical processing. Low freshwater inflows during the dry season increase estuarine residence times, enabling local processes to control nutrient availability and water quality. El Nin˜o–Southern Oscillation (ENSO) events tend to mute the seasonality of rainfall without altering total annual precipitation inputs. The Nin˜o3 ENSO index (which indicates an ENSO event when positive and a La Nin˜a event when negative) was positively correlated with both annual rainfall and the ratio of dry season to wet season precipitation. This ENSO-driven disruption in seasonal rainfall patterns affected salinity patterns and tended to reduce marine inputs of P to Everglades estuaries. ENSO events also decreased dry season residence times, reducing the importance of estuarine nutrient processing. The combination of variable water management activities and interannual differences in precipitation patterns has a strong influence on nutrient and salinity patterns in Everglades estuaries.

Development of an integrated surface and subsurface model of Everglades National Park

An integrated surface-subsurface hydrological model of Everglades National Park (ENP) was developed using MIKE SHE and MIKE 11 modeling software. The model has a resolution of 400 meters, covers approximately 1050 square miles of ENP, includes 110 miles of drainage canals with a variety of hydraulic structures, and processes hydrological information, such as evapotranspiration, precipitation, groundwater levels, canal discharges and levels, and operational schedules. Calibration was based on time series and probability of exceedance for water levels and discharges in the years 1987 through 1997. Model verification was then completed for the period of 1998 through 2005. Parameter sensitivity in uncertainty analysis showed that the model was most sensitive to the hydraulic conductivity of the regional Surficial Aquifer System, the Manning's roughness coefficient, and the leakage coefficient, which defines the canal-subsurface interaction. The model offers an enhanced predictive capability, compared to other models currently available, to simulate the flow regime in ENP and to forecast the impact of topography, water flows, and modifying operation schedules.

Phosphorus Availability and Salinity Control Productivity and Demography of the Seagrass Thalassia testudinum in Florida Bay

Biomass, net primary productivity (NPP), foliar elemental content, and demography of Thalassia testudinum were monitored in populations from five sites across Florida Bay beginning in January 2001. Sites were selected to take advantage of the spatial variability in phosphorus (P) availability and salinity climates across the bay. Aboveground biomass and NPP of T. testudinum were determined five to six times annually. Short-shoot demography, belowground biomass, and belowground NPP were assessed from a single destructive harvest at each site and short-shoot cohorts were estimated from leaf scar counts multiplied by site-specific leaf production rates. Biomass, relative growth rate (RGR), and overall NPP were positively correlated with P availability. Additionally, a positive correlation between P availability and the ratio of photosynthetic to non-photosynthetic biomass suggests that T. testudinum increases allocation to aboveground biomass as P availability increases. Population turnover increased with P availability, evident in positive correlations of recruitment and mortality rates with P availability. Departures from seasonally modeled estimates of RGR were found to be influenced by salinity, which depressed RGR when below 20 psu or above 40 psu. Freshwater management in the headwaters of Florida Bay will alter salinity and nutrient climates. It is becoming clear that such changes will affect T. testudinum, with likely feedbacks on ecosystem structure, function, and habitat quality.