# Effect of Landscape Elements on the Symmetry and Variance of the Spatial Distribution of Individual Birds within Foraging Flocks of Geese

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Behavioural Instability

#### 1.2. Environmental Stressors of Geese

#### 1.3. Behavioural Instability of Symmetry

#### 1.4. Behavioural Instability of Variance

#### 1.5. Aims of the Investigation

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.2. Data Extraction

#### 2.3. Data Analysis

^{2}), the slope and the intercept of all LRDs and LRRs have been estimated as well as significance for each slope (later noted as asterisks; *: p < 0.05, **: p < 0.01, ***: p < 0.001).

## 3. Results

#### 3.1. Correlation between Distance to Landscape Elements and Behavioural Instability of Symmetry (BSYM)

#### 3.1.1. Wind Turbines

^{2}= 20.53%) *** and (r

^{2}= 10.51%) *** respectively (Table 1 and Figure 2a,d). The greylag geese showed the same trend, but the regression was not significant (r

^{2}= 0.45%, p > 0.05) (Table 1 and Figure 2g).

#### 3.1.2. Roads

^{2}= 8.08%) *** (Table 1 and Figure 2h). Whereas, barnacle geese and pink-footed geese showed (with r

^{2}< 5%) the opposite trend with a significant decrease of BSYM with decreasing distance to the roads (r

^{2}= 0.04%) *** and (r

^{2}= 1.01%) *** respectively (Table 1 and Figure 2b,e).

#### 3.1.3. Hedgerows

#### 3.2. Correlation between Distance to Landscape Elements and Behavioural Instability of Variance (BVAR)

#### 3.2.1. Wind Turbines

^{2}= 14.69%) *** and (r

^{2}= 22.18%) *** respectively (Table 1 and Figure 3a,d). Whereas, the greylag geese showed (with r

^{2}< 5% and p > 0.05) the opposite trend with a decrease of BVAR with decreasing distance to the wind turbines (Table 1 and Figure 3g).

#### 3.2.2. Roads

^{2}= 10.67%) *** (Table 1 and Figure 3h). Whereas, barnacle geese and pink-footed geese showed a significant increase (with r

^{2}< 5%) increase of BVAR with decreasing distance to the roads (r

^{2}= 2.35%) *** and (r

^{2}= 2.64%) *** respectively (Table 1 and Figure 3b,e).

#### 3.2.3. Hedgerows

^{2}= 5.20%) ***, (Table 1 and Figure 3c). Whereas, pink-footed geese showed a significant (with r

^{2}< 5%) increase of BVAR with decreasing distance to the hedgerows (r

^{2}= 2.74%) ***, (Table 1 and Figure 3f).

## 4. Discussion

^{2}< 5%), for negative slopes of the linear regression of density (LRD), which indicates an increasing BSYM with decreasing distance to the landscape elements (Table 1 and Figure 2). There is also a clear tendency with few exceptions (with r

^{2}< 5%) for a negative slope of the linear regression of residuals (LRRs), which means an increasing BVAR with decreasing distance to the landscape elements (Table 1 and Figure 3). Thus, both indices show asymmetry of spatial distribution, implying environmental stress in flocks of geese induced by foraging near the studied landscape elements, which indicates these measurements to be useful tools for monitoring environmental stress. We have chosen the 5% threshold arbitrarily; however, it is also notable that the same negative trends were observed for other LRD and LRR although with r

^{2}below 5% (Figure 2 and Figure 3). However, such relatively weak trends might not be of biological importance and should thus be interpreted with caution. Additionally, p-values also should be evaluated cautiously as the large sample size increases the significance of the indices even with low r2 as seen in both indices (Table 1). These relatively low r

^{2}values might be caused by noise from other factors influencing the density of bird flocks, masking the disturbing effects of the landscape elements. Such factors might include flock size [11] as well as food and water distribution [12], which are both known to affect the density and spatial distribution of bird flocks. Especially BVAR might have been affected by variations in flock size as flocks of different size prioritise anti-predation behaviour and foraging beneficial behaviour differently. A study by Lazarus [11], who examined the influence of flock size on the vigilance of white-fronted geese (Anser albifrons), noted that the percentage of vigilant birds in a flock would decrease steeply at flock sizes above 200–300 individuals [11]. Hence, larger flocks might prioritise foraging beneficial behaviour while smaller flocks prioritise anti-predator behaviour through the dilution effect [7,11,13,14]. However, trends were still observed for both BSYM and BVAR that prove that both methods can be applied to wildlife behaviour with multiple random influences, as long as the factor of interest is measured across a correlated variable.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Pertoldi, C.; Bahrndorff, S.; Novicic, Z.K.; Rohde, P.D. The Novel Concept of “Behavioural Instability” and Its Potential Applications. Symmetry
**2016**, 8, 135. [Google Scholar] [CrossRef] - Rees, E.C. Impacts of wind farms on swans and geese: A review. Wildfowl
**2012**, 62, 37–72. [Google Scholar] - Madsen, J. Impact of Disturbance on Field Utilization of Pink-footed Geese in West Jutland, Denmark. Biol. Conserv.
**1985**, 33, 53–63. [Google Scholar] [CrossRef] - Larsen, J.K.; Madsen, J. Effects of wind turbines and other physical elements on field utilization by pink-footed geese (Anser brachyrhynchus): A landscape perspective. Landsc. Ecol.
**2000**, 15, 755–764. [Google Scholar] [CrossRef] - Chudziǹska, M.E.; van Best, F.M.; Madsen, J.; Nabe-Nielsen, J. Using habitat selection theories to predict the spatiotemporal distribution of migratory birds during stopover—A case study of pink-footed geese Anser brachyrhynchus. Oikos
**2015**, 124, 854–860. [Google Scholar] [CrossRef] - Harrison, A.L.; Petkov, N.; Mitev, D.; Popgeorgiev, G.; Gove, B.; Hilton, G.M. Scale-dependent habitat selection by wintering geese: Implications for landscape management. Biodivers. Conserv.
**2018**, 27, 167–188. [Google Scholar] [CrossRef] - Hötker, H. Birds: Displacement. In Wildlife and Wind Farms, Conflicts and Solutions; Volume 1 Onshore: Potential Effects; Perrow, M.R., Ed.; Pelagic Publishing: Exeter, UK, 2017; pp. 119–154. [Google Scholar]
- Roberts, G. Why individual vigilance declines as group size increases. Anim. Behav.
**1996**, 51, 1077–1086. [Google Scholar] [CrossRef] [Green Version] - Bech-Hansen, M.; Kallehauge, R.M.; Lauritzen, J.M.S.; Sørensen, M.H.; Pertoldi, C.; Bruhn, D.; Laubek, B.; Jensen, L.F. Evaluation of disturbance effect on geese and swans (Anserinae) caused by an approaching unmanned aerial vehicle. Bird Conserv. Int. under review.
- Silverman, B. Density Estimation for Statistics and Data Analysis; Chapman & Hall: London, UK, 1986; pp. 9–13. [Google Scholar]
- Lazarus, J. Vigilance, flock size and domain of danger size in the White-fronted Goose. Wildfowl
**1978**, 29, 135–145. [Google Scholar] - Gill, J.A. Habitat Choice in Pink-Footed Geese: Quantifying the Constraints Determining Winter Site Use. J. Appl. Ecol.
**1996**, 33, 884–892. [Google Scholar] [CrossRef] - Black, M.J.; Carbone, C.; Wells, R.L.; Owen, M. Foraging dynamics in goose flocks: The cost of living on the edge. Anim. Behav.
**1992**, 44, 41–50. [Google Scholar] [CrossRef] - Carbone, C.; Thompson, W.A.; Zadorina, L.; Rowcliffe, J.M. Competition, predation risk and patterns of flock expansion in barnacle geese (Branta leucopsis). J. Zool. Lond.
**2003**, 259, 301–308. [Google Scholar] [CrossRef] - Palmer, A.R.; Strobeck, C. Fluctuating asymmetry: Measurement, analysis, patterns. Annu. Rev. Ecol. Syst.
**1986**, 17, 391–421. [Google Scholar] [CrossRef] - Pertoldi, C.; Kristensen, T.N.; Andersen, D.H.; Loeschcke, V. Developmental instability as an estimator of genetic stress. Heredity
**2006**, 96, 122–127. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Overview of behavioural instability indices used to monitor one flock of pink-footed geese foraging near a road: (

**a**) Aerial photos of a flock of individual geese are georeferenced in geographic information systems (GIS) and geographic positions of individual geese are geotagged (illustrated as circles). Flock density is quantified by Kernel density estimates using the geographic positions of identified birds. Kernel density estimates are illustrated as white (low density) to dark red (high density); (

**b**) Density estimates of individuals as a function of distance to the nearest landscape element, in this case, roads. The mean distance is illustrated as a red vertical line. A linear regression of density (LRD): Density Estimate = a × Distance + b (illustrated as a grey line) is fitted to measure behavioural instability through asymmetry of density between distances left and right of the mean distance. Symmetrical density would result in a non-significant slope (a = 0). Contrarily, an anti-predator behaviour induced by the road would yield a negative slope (a < 0). Residual distances between observed densities and LRD is illustrated as blue lines; (

**c**) Residual distances of density (Figure 1b) as a function of distance to the nearest landscape elements, in this case roads. A linear regression of residuals (LRR): Residual = a × Distance + b (illustrated as a grey line) is fitted to measure behavioural instability through asymmetry of variance in density between distances left and right of the mean distance. A constant variance in density across distance would result in a non-significant slope (a = 0). Contrarily, increased variance would yield a negative slope (a < 0).

**Figure 2.**Linear regression of density (LRD) (illustrated as a red line), which regresses the density estimates of individual birds as a function of bird distances to the nearest landscape element. The following species were regressed: barnacle goose (BG), pink-footed goose (PINK), and Greylag goose (GREY). Distances from the landscape elements: wind turbines (dwi), roads (dro), and hedgerows (dhe). The r

^{2}values of LRD above 5% (r

^{2}> 5%) are in bold.

**Figure 3.**Linear regression of residuals (LRR) (illustrated as a red line), which regresses the absolute values of the residuals from LRD were regressed as a function of bird distances to the nearest landscape element. The following species were regressed: barnacle goose (BG), pink-footed goose (PINK), and greylag goose (GREY). Distances from the landscape elements; wind turbines (dwi), roads (dro), and hedgerows (dhe). The r

^{2}values of LRR above 5% (r

^{2}> 5%) are in bold.

**Table 1.**Species: Barnacle goose (BG), pink-footed goose (PINK), and greylag goose (GREY); distances from the landscape elements: wind turbines (dwi), roads (dro), and hedgerows (dhe), n = number of measurements. Coefficient of determination (r

^{2}) slope (a), intercept (b) and significance level (p) of both linear regression of density (LRD) (which regress the density estimates of individual birds as a function of bird distances to nearest landscape element) and of linear regression of residuals (LRR) (which regress the absolute values of residual distance from LRD as a function of bird distances to nearest landscape element). The r

^{2}values above 5% (r

^{2}> 5%) are in bold.

Species Dist. from Obstacles | n (Number of Measurements) | LRD r^{2} | LRD a & b | LRD p | LRR r^{2} | LRR a & b | LRR p | |||
---|---|---|---|---|---|---|---|---|---|---|

BG | dwi | 4872 | 20.53% | Slope a: Intercept b: | −0.052 34.182 | *** | 14.69% | Slope a: Intercept b: | −0.023 15.038 | *** |

dro | 18925 | 0.04% | Slope a: Intercept b: | 0.001 10.258 | ** | 2.35% | Slope a: Intercept b: | −0.004 5.394 | ** | |

dhe | 18925 | 1.46% | Slope a: Intercept b: | −0.007 11.610 | *** | 5.20% | Slope a: Intercept b: | −0.008 5.968 | *** | |

PINK | dwi | 4894 | 10.51% | Slope a: Intercept b: | −0.035 28.681 | *** | 22.18% | Slope a: Intercept b: | −0.026 17.196 | *** |

dro | 26394 | 1.01% | Slope a: Intercept b: | −0.008 8.744 | *** | 2.64% | Slope a: Intercept b: | −0.008 6.301 | *** | |

dhe | 26313 | 2.13% | Slope a: Intercept b: | 0.008 11.588 | *** | 2.74% | Slope a: Intercept b: | −0.005 5.734 | *** | |

GREY | dwi | 361 | 0.45% | Slope a: Intercept b: | −0.002 3.720 | n.s. | 0.65% | Slope a: Intercept b: | 0.001 1.090 | n.s. |

dro | 458 | 8.08% | Slope a: Intercept b: | −0.006 4.176 | *** | 10.67% | Slope a: Intercept b: | −0.004 1.910 | *** | |

dhe | 353 | 0.18 | Slope a: Intercept b: | 0.001 2.873 | n.s. | 0.46% | Slope a: Intercept b: | −0.001 1.22 | n.s. |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bech-Hansen, M.; M. Kallehauge, R.; Bruhn, D.; H. Funder Castenschiold, J.; Beltoft Gehrlein, J.; Laubek, B.; F. Jensen, L.; Pertoldi, C.
Effect of Landscape Elements on the Symmetry and Variance of the Spatial Distribution of Individual Birds within Foraging Flocks of Geese. *Symmetry* **2019**, *11*, 1103.
https://doi.org/10.3390/sym11091103

**AMA Style**

Bech-Hansen M, M. Kallehauge R, Bruhn D, H. Funder Castenschiold J, Beltoft Gehrlein J, Laubek B, F. Jensen L, Pertoldi C.
Effect of Landscape Elements on the Symmetry and Variance of the Spatial Distribution of Individual Birds within Foraging Flocks of Geese. *Symmetry*. 2019; 11(9):1103.
https://doi.org/10.3390/sym11091103

**Chicago/Turabian Style**

Bech-Hansen, Mads, Rune M. Kallehauge, Dan Bruhn, Johan H. Funder Castenschiold, Jonas Beltoft Gehrlein, Bjarke Laubek, Lasse F. Jensen, and Cino Pertoldi.
2019. "Effect of Landscape Elements on the Symmetry and Variance of the Spatial Distribution of Individual Birds within Foraging Flocks of Geese" *Symmetry* 11, no. 9: 1103.
https://doi.org/10.3390/sym11091103