The physiology and biomechanics of avian flight at high altitude

Many birds fly at high altitude, either during long-distance flights or by virtue of residence in high-elevation habitats. Among the many environmental features that vary systematically with altitude, five have significant consequences for avian flight performance: ambient wind speeds, air temperature, humidity, oxygen availability, and air density. During migratory flights, birds select flight altitudes that minimize energy expenditure via selection of advantageous tail- and cross-winds. Oxygen partial pressure decreases substantially to as little as 26% of sea-level values for the highest altitudes at which birds migrate, whereas many taxa reside above 3000 meters in hypoxic air. Birds exhibit numerous adaptations in pulmonary, cardiovascular, and muscular systems to alleviate such hypoxia. The systematic decrease in air density with altitude can lead to a benefit for forward flight through reduced drag but imposes an increased aerodynamic demand for hovering by degrading lift production and simultaneously elevating the induced power requirements of flight. This effect has been well-studied in the hovering flight of hummingbirds, which occur throughout high-elevation habitats in the western hemisphere. Phylogenetically controlled studies have shown that hummingbirds compensate morphologically for such hypodense air through relative increases in wing size, and kinematically via increased stroke amplitude during the wingbeat. Such compensatory mechanisms result in fairly constant power requirements for hovering at different elevations, but decrease the margin of excess power available for other flight behaviors

Kinematics of hovering hummingbird flight along simulated and natural elevational gradients

Hovering flight is one of the most energetically demanding forms of animal locomotion. Despite the cost, hummingbirds regularly hover at high elevations, where flight is doubly challenging because of reduced air density and oxygen availability. We performed three laboratory experiments to examine how air density and oxygen partial pressure influence wingbeat kinematics. In the first study, we experimentally lowered air density but maintained constant oxygen partial pressure. Under these hypodense but normoxic conditions, hummingbirds increased stroke amplitude substantially and increased wingbeat frequency slightly. In the second experiment, we maintained constant air density but decreased oxygen partial pressure. Under these normodense but hypoxic conditions, hummingbirds did not alter stroke amplitude but instead reduced wingbeat frequency until they could no longer generate enough vertical force to offset body weight. In a final combined experiment, we decreased air density but increased oxygen availability, and found that the wingbeat kinematics were unaffected by supplemental oxygen. We also studied hovering and maximally loaded flight performance for 43 hummingbird species distributed along a natural elevational gradient in Peru. During free hovering flight, hummingbirds showed increased stroke amplitude interspecifically at higher elevations, mirroring the intra-individual responses in our first laboratory experiment. During loaded flight, hummingbirds increased both wingbeat frequency and wing stroke amplitude by 19% relative to free-flight values at any given elevation. We conclude that modulation of wing stroke amplitude is a major compensatory mechanism for flight in hypodense or hypobaric environments. By contrast, increases in wingbeat frequency impose substantial metabolic demands, are only elicited transiently and anaerobically, and cannot be used to generate additional sustained lift at high elevations

Developments in the Khintchine-Meinardus probabilistic method for asymptotic enumeration

A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler's generating function $\prod_{k=1}^\infty S(z^k)$ for partitions, where $S(z)=(1-z)^{-1}$. By applying a method due to Khintchine, we extend Meinardus' theorem to find the asymptotics of the coefficients of generating functions of the form $\prod_{k=1}^\infty S(a_kz^k)^{b_k}$ for sequences $a_k$, $b_k$ and general $S(z)$. We also reformulate the hypotheses of the theorem in terms of generating functions. This allows us to prove rigorously the asymptotics of Gentile statistics and to study the asymptotics of combinatorial objects with distinct components.Comment: 28 pages, This is the final version that incorporated referee's remarks.The paper will be published in Electronic Journal of Combinatoric

Accelerational Implications of Hummingbird Display Dives

Integrative Biolog

Patterns of Asexuality in the United States

In this paper we use data from the 2002 National Survey of Family Growth (NSFG) to ascertain and analyze patterns of asexuality in the United States. We endeavor to extend the earlier work of Bogaert (2004) on this topic, which focused on patterns of asexuality in Great Britain. Using a social constructionist perspective to study asexuality, we conceptualize and measure the phenomenon in several ways, according to behavior, desire, and self-identification. We use the NSFG respondent sampling weights to produce several sets of unbiased estimates of the percentages of persons in the U.S. population, aged 15-44, who are asexual; each set is based on one or more of the various definitions of asexuality. Finally, we describe some of the characteristics of the asexual population using multinomial logistic regression.self-identification, sexual behavior

Meinardus' theorem on weighted partitions: extensions and a probabilistic proof

We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types of decomposable combinatorial structures, which are called assemblies and selections. The results obtained are based on combining Meinardus' analytical approach with probabilistic method of Khitchine.Comment: The version contains a few minor corrections.It will be published in Advances in Applied Mathematic

Of hummingbirds and helicopters: Hovering costs, competitive ability, and foraging strategies

Wing morphology and flight kinematics profoundly influence foraging costs and the overall behavioral ecology of hummingbirds. By analogy with helicopters, previous energetic studies have applied the momentum theory of aircraft propellers to estimate hovering costs from wing disc loading (WDL), a parameter incorporating wingspan (or length) and body mass. Variation in WDL has been used to elucidate differences either among hummingbird species in nectar-foraging strategies (e.g., territoriality, traplining) and dominance relations or among gender-age categories within species. We first demonstrate that WDL, as typically calculated, is an unreliable predictor of hovering (induced power) costs; predictive power is increased when calculations use wing length instead of wingspan and when actual wing stroke amplitudes are incorporated. We next evaluate the hypotheses that foraging strategy and competitive ability are functions of WDL, using our data in combination with those of published sources. Variation in hummingbird behavior cannot be easily classified using WDL and instead is correlated with a diversity of morphological and physiological traits. Evaluating selection pressures on hummingbird wings will require moving beyond wing and body mass measurements to include the assessment of the aerodynamic forces, power requirements, and power reserves of hovering, forward flight, and maneuvering. However, the WDLhelicopter dynamics model has been instrumental in calling attention to the importance of comparative wing morphology and related aerodynamics for understanding the behavioral ecology of hummingbirds

Resolution of a paradox: Hummingbird flight at high elevation does not come without a cost

Flight at high elevation is energetically demanding because of parallel reductions in air density and oxygen availability. The hovering flight of hummingbirds is one of the most energetically expensive forms of animal locomotion, but hummingbirds are nonetheless abundant at high elevations throughout the Americas. Two mechanisms enhance aerodynamic performance in high-elevation hummingbirds: increase in wing size and wing stroke amplitude during hovering. How do these changes in morphology, kinematics, and physical properties of air combine to influence the aerodynamic power requirements of flight across elevations? Here, we present data on the flight performance of 43 Andean hummingbird species as well as a 76-taxon multilocus molecular phylogeny that served as the historical framework for comparative analyses. Along a 4,000-m elevational transect, hummingbird body mass increased systematically, placing further aerodynamic demands on high-elevation taxa. However, we found that the minimum power requirements for hovering flight remain constant with respect to elevation because hummingbirds compensate sufficiently through increases in wing size and stroke amplitude. Thus, high-elevation hummingbirds are not limited in their capacity for hovering flight despite the challenges imposed by hypobaric environments. Other flight modes including vertical ascent and fast forward flight are more mechanically and energetically demanding, and we accordingly also tested for the maximum power available to hummingbirds by using a load-lifting assay. In contrast to hovering, excess power availability decreased substantially across elevations, thereby reducing the biomechanical potential for more complex flight such as competitive and escape maneuvers

On Virtue and Peace: Creating a Workplace Where People Can Flourish

Nationbuilders in less developed countries need to understand how Western legal systems with "property" at their center have materially accounted for Western prosperity and liberty, but legal definitions of property are so abstruse that explication of this vital concept is made difficult. This paper finds an historical definitional essence to property in the right to exclude and maintains that liberty and property both share this essential meaning. The problems of corporate governance are then placed in the context of the exclusionary concept of property/liberty.