The Distribution of Length and Components of the Sum of $n$ Random Unit Vectors

Greenwood, J. Arthur; Durand, David

doi:10.1214/aoms/1177728540

Cited by 187 publications

(78 citation statements)

References 8 publications

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“…In all ordinations, the understorey data were transformed into presence/absence values and species occurring in less than 5% of the plots in a given catchment omitted. To test whether temporal changes had a common direction in the ordination spaces, or whether the directions of the temporal trajectories connecting the two surveys of the same plot were randomly distributed, Rayleigh's R statistic was used (Greenwood and Durand 1955). Changes in the cover of individual species between the two surveys were assessed using Wilcoxon's matched pairs test (Zar 1999).…”

Section: Statistical Analysesmentioning

confidence: 99%

Understorey Vegetation Stability and Dynamics in Unmanaged Boreal Forests Along a Deposition Gradient in Sweden

Grandin

2011

AMBIO

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The aims of this study were to investigate spatial patterns and temporal changes in understorey vegetation at four forest catchments forming a depositional gradient. Inventories of the bottom and field layers were carried out in the 1990s and repeated after 5-14 years, depending on catchment. It was hypothesized that changes and patterns in ground vegetation would be related to changes and patterns in N and S deposition. The data were analyzed using Ellenberg indices and multivariate methods. All catchments showed temporal changes in species composition. Analyses of the bottom layer were confounded by a change of field staff, but after accounting for this observer effect, differences in species composition between the catchments remained. Within catchments, the changes in species composition were unrelated to N or S deposition. Relationships between environmental factors, expressed as Ellenberg indices, and compositional patterns differed between catchments although Ellenberg indices showed small temporal changes.

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Section: Statistical Analysesmentioning

confidence: 99%

Understorey Vegetation Stability and Dynamics in Unmanaged Boreal Forests Along a Deposition Gradient in Sweden

Grandin

2011

AMBIO

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“…The distributions of the initial food-unloading angles and dance angles were analyzed by first determining which distributions were significantly non-random (Raleigh test, Greenwood and Durand 1955). For each non-random distribution, I tested if the direction of the mean vector equaled 0° or 180°, as appropriate, with Stephens' (1962a) "polar vector" test.…”

Section: Analysis Of Turn Angles Angular Velocity and Average Velocitymentioning

confidence: 99%

The food recruitment dance of the stingless bee, Melipona panamica

Nieh

1998

Behavioral Ecology and Sociobiology

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Foragers of the stingless bee Melipona panamica can communicate the location of a good food source to nestmates and evidently communicate part of this information inside the nest. However there is no careful description of within-nest recruitment behavior for this species or for any other stingless bee. Therefore the goal of this paper is to provide a detailed description of the behaviors of recruiting M. panamica foragers within the nest. A recruiting forager enters the nest, begins producing pulsed sounds as food-unloading bees collect her food (unloading phase), and then performs a dance by rapidly executing clockwise and counterclockwise turns while continuing to produce sound pulses (dance phase). To investigate whether directional information is encoded in the dance, I alternately recorded the behavior of foragers trained to two food sources, each 175 m from the colony but in opposite directions (north and south). I examined the following parameters and found no differences between the dances of foragers feeding in opposite directions: (1) order of clockwise and counterclockwise turns, (2) turn direction, (3) angular start position, (4) angular stop position, (5) turn magnitude, and (6) turn angular velocity. Foragers recruiting for a rich food source (2.5 M) initially unloaded food with their bodies oriented 180° from the entrance. They began turns at random orientations, but tended to end these turns facing the nest entrance (0°). Dancers for poor food sources (1.0 M sucrose solution) turned at significantly lower velocities than dancers for good food sources (2.5 M sucrose solution), and exhibited random initial, start-turn, and stop-turn orientations. Throughout her stay inside the nest, the recruiting forager produced sounds. During sound production, her folded wings vibrated dorsoventrally over her abdomen and she attracted the attention of follower bees who J.C. Nieh Department of Organismic and Evolutionary Biology, MCZ Labs, Harvard University, Cambridge, MA 02138, USA positioned their antennae closely around her body. Foragers recruiting for 1.0 M and 2.5 M food sources attracted the same number of food-unloading bees, but 1.0 M recruiters attracted significantly fewer followers around their abdomens.

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“…These orientation azimuths were then treated as a circular distribution and the following parameters obtained for each observation time (Batschelet, 1965;Greenwood and Durand, 1955): (1) mean orientation direction (0); (2) a grouping factor (r) indicating the extent to which the butterfly azimuths for an observation were concentrated about the 0 for that observation; (3) an angular deviation (AD) for 0; and (4) the probability (P) of r occurring by chance. Computer plots were made for 0 and the sun azimuth values as a function of time of day.…”

Section: Psychementioning

confidence: 99%

The Orientation of Migrant and Non‐Migrant Monarch Butterflies,Danaus Plexippus (L.)

Kanz

1977

Psyche: A Journal of Entomology

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The Distribution of Length and Components of the Sum of $n$ Random Unit Vectors

Cited by 187 publications

References 8 publications

Understorey Vegetation Stability and Dynamics in Unmanaged Boreal Forests Along a Deposition Gradient in Sweden

Understorey Vegetation Stability and Dynamics in Unmanaged Boreal Forests Along a Deposition Gradient in Sweden

The food recruitment dance of the stingless bee, Melipona panamica

The Orientation of Migrant and Non‐Migrant Monarch Butterflies,Danaus Plexippus (L.)

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