Abstract:Thiessen polygons are often used to model territory characteristics. However, information about the quality of Thiessen polygon-based estimates is currently lacking. We used published data to investigate the match between Thiessen polygons and mapped bird territories regarding territory size, shape and neighbourhood. Although territory sizes and the number of neighbours were strongly correlated between these two methods, both parameters were overestimated by the Thiessen polygons. Therefore, caution is require… Show more
“…An inherent assumption of this Thiessen polygon method is that competition with adjacent neighbours governs territory formation (Schlicht et al., 2014) but there are likely to be additional mechanisms involved that can transcend territory boundaries such as song production or individual movement. Also, in other areas of the wood with a low density of occupied nestboxes, this Thiessen polygon approach tends to overestimate territory size (Schlicht et al., 2014), leading to some unrealistically large territories. As a result, numerous associations in these networks seem rather improbable given the considerable distance between some nestboxes.Figure A2Comparison of male social networks in Wytham's great tit population generated using the (a) 5-nearest-neighbour method and (b) Thiessen polygon approach for a representative year (2006).…”
Section: Comparison Of Nearest-neighbour and Thiessen Polygon Networkmentioning
Animal personalities can influence social interactions among individuals, and thus have major implications for population processes and structure. Few studies have investigated the significance of the social context of animal personalities, and such research has largely focused on the social organization of nonterritorial populations. Here we address the question of whether exploratory behaviour, a well-studied personality trait, is related to the social structure of a wild great tit, Parus major, population during the breeding season. We assayed the exploration behaviour of wild-caught great tits and then established the phenotypic spatial structure of the population over six consecutive breeding seasons. Network analyses of breeding proximity revealed that males, but not females, show positive assortment by behavioural phenotype, with males breeding closer to those of similar personalities. This assortment was detected when we used networks based on nearest neighbours, but not when we used the Thiessen polygon method where neighbours were defined from inferred territory boundaries. Further analysis found no relationship between personality assortment and local environmental conditions, suggesting that social processes may be more important than environmental variation in influencing male territory choice. This social organization during the breeding season has implications for the strength and direction of both natural and sexual selection on personality in wild animal populations.
“…An inherent assumption of this Thiessen polygon method is that competition with adjacent neighbours governs territory formation (Schlicht et al., 2014) but there are likely to be additional mechanisms involved that can transcend territory boundaries such as song production or individual movement. Also, in other areas of the wood with a low density of occupied nestboxes, this Thiessen polygon approach tends to overestimate territory size (Schlicht et al., 2014), leading to some unrealistically large territories. As a result, numerous associations in these networks seem rather improbable given the considerable distance between some nestboxes.Figure A2Comparison of male social networks in Wytham's great tit population generated using the (a) 5-nearest-neighbour method and (b) Thiessen polygon approach for a representative year (2006).…”
Section: Comparison Of Nearest-neighbour and Thiessen Polygon Networkmentioning
Animal personalities can influence social interactions among individuals, and thus have major implications for population processes and structure. Few studies have investigated the significance of the social context of animal personalities, and such research has largely focused on the social organization of nonterritorial populations. Here we address the question of whether exploratory behaviour, a well-studied personality trait, is related to the social structure of a wild great tit, Parus major, population during the breeding season. We assayed the exploration behaviour of wild-caught great tits and then established the phenotypic spatial structure of the population over six consecutive breeding seasons. Network analyses of breeding proximity revealed that males, but not females, show positive assortment by behavioural phenotype, with males breeding closer to those of similar personalities. This assortment was detected when we used networks based on nearest neighbours, but not when we used the Thiessen polygon method where neighbours were defined from inferred territory boundaries. Further analysis found no relationship between personality assortment and local environmental conditions, suggesting that social processes may be more important than environmental variation in influencing male territory choice. This social organization during the breeding season has implications for the strength and direction of both natural and sexual selection on personality in wild animal populations.
“…The result is shown in Fig. 21, where we present nine slices at fixed values of m 2 (38) tend to overlap. We also observe that the boundary closer to the origin also seems to be singled out, especially at high values of m 2 .…”
Section: A Realistic Example With Tt Background and Combinatoricsmentioning
confidence: 91%
“…Voronoi tessellations For a basic introduction to Voronoi tessellations, see, e.g., [1] are useful in a wide variety of fields, from biology [2] to astronomy [3,4] to condensed matter physics [5]. In high energy physics, they have been used rather sporadically, e.g., as an optional approach to QCD jet-finding and area determination in FastJet [6] and in the model-independent definition of search regions in SLEUTH [7][8][9][10].…”
Section: Introductionmentioning
confidence: 99%
“…Since at hadron colliders the longitudinal momenta of the initial state partons are unknown, much effort went into the development of suitable "transverse variables" [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62], which are Lorentz-invariant under longitu-dinal boosts. 2 In principle, the optimal approach to a mass measurement is provided by the so-called "Matrix Element Method" (MEM), [67][68][69][70][71][72][73][74]. However, its use is often computationally prohibitive, especially when dealing with complicated final states and/or large reducible backgrounds.…”
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
“…, Schlicht et al . ), reports of overlapping home‐ranges (Engstrom & Sanders ) suggest the method could be flawed when applied to high‐density populations. We investigated RCW home‐range dynamics across a gradient of neighbouring group density conditions.…”
Information about how bird species respond to increasing density conditions through either space‐use sharing or increased territoriality, and how those changes affect fitness, is essential for effective conservation planning. We used a case study of endangered Red‐cockaded Woodpeckers Leuconotopicus borealis (RCW) to address these questions. We documented over 36 000 locations from 44 RCW groups in three density conditions on two sites in South Carolina, USA, between April 2013 and March 2015. The frequency of neighbouring group interactions differed among density conditions and was highest for high‐density groups. RCW home‐ranges and core‐areas were larger under low‐density conditions (x¯normalHome‐normalrange = 88.4 ha, x¯normalCore‐normalarea = 21.0 ha) than under medium (x¯normalHome‐normalrange = 68.29 ha, x¯normalCore‐normalarea = 16.6 ha) and high‐density (x¯normalHome‐normalrange = 76.3 ha, x¯normalCore‐normalarea = 18.6 ha) conditions. Neighbouring RCWs maintained overlapping home‐ranges with nearly exclusive core‐areas across density conditions, but overlap tended to increase as neighbouring group density increased. Under high‐density conditions, home‐range overlap correlated inversely with clutch size (β ± se = −0.19 ± 0.09), nestling production (β ± se = −0.37 ± 0.09) and fledgling production (β ± se = −0.34 ± 0.08). Our results indicate that RCWs dedicate more effort to territorial defence under high‐density conditions, potentially at the expense of greater foraging efficiency and time allocated to reproduction, as evidenced by reduced fitness. Large home‐range overlap indicated limited territoriality farther away from cavity trees, but the existence of exclusive core‐areas suggests that RCW groups defend habitat closer to cavity trees. Thiessen partitions used to allocate critical foraging habitat offered comprehensive habitat protection for RCW but appear flawed for spatially explicit habitat assessments because they do not accurately delineate space used by individual RCW groups.
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