Flock Patterns When Pigeons Fly over Terrain with Different

Properties

Margarita Zaleshina

and Alexander Zaleshin

Moscow Institute of Physics and Technology, Moscow, Russia

Keywords: Pigeon Flocks, Spatial Navigation, Collective Motion.

Abstract: The way in which flocks are organized affects the ability of birds to perceive the landscape over which they

fly: if the pattern of the flock changes, then the generalized perception of the terrain over which birds fly

will also change. In this paper the features of dynamic spatial organization of pigeons in a flock during

flights over landscapes with different characteristics were studied based on the analysis of GPS tracks of

birds. The ways of group flight were revealed for typical situations, such as survey of unfamiliar terrain or

flight home from remote sites. The spatial distribution of distances between pairs of individual birds and

directions of movement were calculated, and then related to the features of terrain over which flights were

occurred. The data analysis was performed based on comparison of flock patterns during group flights over

terrain of distinct types (sea coast, urban and countryside terrain, and natural landscape). The spatial data

was processed using the geographic information system QGIS.

1 INTRODUCTION

This paper considers pigeons' collective behaviour

during flight over mixed terrain. The aim of this

work is to reveal the relationship between changes in

flight trajectories and the distribution of birds in the

flock, depending on the terrain over which the flight

takes place. Studying the spatial organization of

birds in the flock reveals features of group

coordination of birds while surveying unfamiliar

terrain, returning home from a remote point,

foraging or migrating over long-distances. It should

be noted that the arrangement of birds in the flock is

directly associated with the terrain over which they

fly. Reflexively, birds adapt their flight in the flock

to the tasks to be solved. Based on the flock

configuration at any moment, assumptions can be

made about the problem solved by the birds.

Flock spatial structure is determined by the

organization of birds within a group, i.e. by their

location relative to each other, and by the direction

of movement of both individual birds and the whole

flock. The individual arrangement of birds changes

dynamically during the flight. However, some

characteristics of the spatial distribution of birds in

the flock can remain steady for long periods of time

– such as typical distances between the birds or

specific flock patterns.

The coordination of bird trajectories is evident in

the adjustment of individual birds to the general

direction of flight. Spatial distribution within the

flock can change the features of aggregate terrain

perception; when changing their distribution

parameters during the flight, birds adapt to the new

tasks to be solved. For example, a high density of

birds in the flock will contribute to multiple

observations of one and the same terrain point; a

flock pattern with large coverage area will allow

simultaneous perception of a large area of terrain. In

flocking, there are sets of options for the

arrangement of birds, which allow their group

observation of visually related elements of the

landscape over which the flight takes place. In

addition, there are options for the arrangement of

birds at nodes and reference points, from which the

birds can observe (as a whole) the boundaries and all

the nearby points on the terrain with similar

attributes. The main parameters of flocks of pigeons

are shown in Figure 1.

In this paper, we calculated basic flight

parameters from records of GPS tracks of different

pigeon flocks: pairwise distances between pigeons,

flight directions of pigeons and standard deviations

for these parameters, measured at the same time. In

334

Zaleshina, M. and Zaleshin, A.

Flock Patterns When Pigeons Fly over Terrain with Different Properties.

DOI: 10.5220/0007255703340341

In Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2019), pages 334-341

ISBN: 978-989-758-351-3

addition, variation in these parameters was

calculated for the intervals +/- 10 seconds.

Figure 1: Main parameters of flock of pigeons: general

flight direction, individual pigeon's flight direction, and

pairwise distance. On the terrain over which the pigeons

fly, it is possible to distinguish surfaces with different

types of coverage, such as forest and ground area, as well

as to select extended objects, such as roads or rivers.

The obtained flight characteristics of the flock were

compared at the moments of flight of the flock over

extended visually perceived elements of the terrain,

such as rivers, roads, and boundaries between

different visually homogeneous textures, which were

identified via remote sensing data from open

sources. The special points that were identified

reflect the relationship between fast events (about a

second) and long-term changes in flight parameters

(about 10 seconds).

Figure 2: Model of the ‘stimulus-reaction’ relationship for

flight of a flock.

It can be assumed that the biological analogue of

such a relationship is a ‘stimulus-response’

phenomenon (Figure 2), where ‘stimulus’ is either

the specific behaviour of the flock or a special event

in the landscape, and the ‘response’ is the variation

in the measured parameters in 10-second interval

before and after the stimulus. The analysis of mean

value and standard deviation (SD) in distances

between pigeons and in flight directions made it

possible to identify the relationships between flock

structures, and to determine the typical response to

external, visually noticeable spatial landmarks.

2 BACKGROUND AND RELATED

WORKS

2.1 Characteristics of Birds during

Their Flight in a Flock

Flying in a flock allows joint, coordinated spatial

migration of birds. The birds gather in flocks to

increase their feeding efficiency or decrease their

vulnerability to predators (Morse, 1977). Besides,

flying in flocks can improve joint spatial orientation

during long-distance migrations and enable more

exact orientation on the terrain. The coordination of

birds during changes in flight direction or height is

apparent in the flock pattern and in the distance

between birds. The joint flight of the flock of birds is

controlled by visual perception and acoustic signals.

In ecology, many types of flock patterns are

described, such as “straight front”, “regiment of

starlings”, “wedge of geese”, and so on.

The structure of pigeon flocks was considered in

paper (Mehlhorn and Rehkaemper, 2016). The

authors remark that pigeons form flocks with a

flexible structure and without any strict hierarchy.

During pigeon migrations both single flights and

flights in pairs as well as in flocks are possible. The

efficiency of flight in the flock differs from that of

individuals or pairs of pigeons, and, on the whole, it

depends on the number of pigeons flying in the

flock.

Research on the behaviour of flocks has been

carried out through analysis of GPS tracks. In

publication (Dell’Ariccia et al., 2008), comparison

of GPS tracks of individual pigeons and pigeons

flying in flocks demonstrated that grouping changes

flock navigational behaviour. Based on investigation

of groups of six pigeons, the authors hold that

‘group cohesion facilitates a shift towards more

efficient homing strategies: individuals prefer

navigating by familiar landmarks, while flocks show

a compass orientation’.

Coordination of birds during flights, including

typical inter-individual distances, has also been

investigated using GPS tracks. Based on this type of

Flock Patterns When Pigeons Fly over Terrain with Different Properties

335

data, birds’ behaviour during circular movement was

investigated for small flocks in publications (Nagy et

al., 2013; Yomosa et al., 2015; Chen et al., 2017). In

publication (Nagy et al., 2013), track data was

recorded using GPS loggers and the leader-follower

relationships in the flock were analysed. In

publication (Chen et al., 2017), it was found out that

pigeons in small flocks coordinate their behaviour

with that of their nearest neighbours, which can

change during the flight. Pigeons can be considered

as flying in a pair if the distance between them is

three to four metres less than the average distance

between pigeons in the flock.

Grouping of birds within the flock was studied in

paper (Ballerini et al., 2008). The authors measured

the three-dimensional positions of individual birds in

compact flocks of up to 2,600 European Starlings

(Sturnus vulgaris) in the field. Based on analysis of

bird flocks flying above Rome, from pictures taken

at an average distance of a hundred metres,

aggregation in the combined flock is maintained

through the formation of multiple groups of seven to

eight birds with a topological interaction.

2.2 Characteristics of the Terrain over

which Pigeons Fly

Visual perception of terrain during the flight of birds

is based on reflexes. During changes in the observed

surroundings, rapid adjustment of the flight

trajectory to the terrain occurs. Importantly, the birds

perceive not individual objects but consolidated data

from the distinct visual elements and attributes of

the terrain. These can include the attributes of

textures, boundaries and distinct areas.

In landscape perception there is a set of visually

connected terrain elements, besides which there is an

opportunity for interpolation between sets of data on

the terrain with similar and dissimilar attributes.

While flying over the terrain it is possible to be

guided by elements with previously known

attributes. Although birds can see places that they

have never seen before, these sites often have

already known characteristics, or are simply part of

an extended area (e.g. road section, river bank, forest

strip). The perceptible elements with well-known

attributes (‘nodes’ or ‘reference points’) dynamically

form the basis for interpolation of spatial data in the

area over which movement of the flock occurs. It

helps orientation both in a situation that is not well

enough known and one in which there is excessive

information.

Multi-scale integration of perception is also

based on the aggregate interpolation of visual

attributes. Distances between flowers, or trees, or

shades can set the different scales for spatial data

generalization. Simplification to single-scale

perception can occur after a reduction from a multi-

scale integration of perception.

2.3 Correlation of Bird Flock Flight

and Terrain Characteristics

The role of visual reference points for pigeons in

getting around terrain is considered in paper (Mann

et al., 2011). The authors have found that the most

informative elements of flight trajectories coincide

with landscape features that have previously been

suggested to form important components of the

homing task.

Perception of the surrounding landscape during

the flight and the influence of landscape on way-

finding and training of pigeons during the flight was

studied in (Guilford and Biro, 2014), and the authors

demonstrated that memorised guidance control is

likely to relate to geocentrically fixed, local features

of the landscape. However, in the case of a familiar

route, the importance of snapping to the reference

points on the terrain may decrease. Nevertheless,

route memorizing depends on the terrain type: ‘birds

follow single memorised routes more readily, or

more faithfully, over some landscape types than

others’.

In publication (Pearce et al., 2014) it was

demonstrated that terrain perception cannot depend

directly on the distribution of pigeons in the flock,

but, for dense flocks, it plays an immediate role in

the joint perception of the terrain. The behaviour of

birds is specific to the density of flock, and

observations of real bird flocks show that a bird

usually reacts to six to seven of its nearest

neighbours.

2.4 Mathematical Simulation of

Behaviour in Flocks

The distribution of directions and, in a similar way,

distribution of velocities can be characterised in a

similar way to spatial distribution, by finding out the

common, regular factors. For each individual, the

spatial characteristics and direction of movement are

determined at a specified moment and compared

with the average parameters of the flock.

A typical mathematic model (‘Boids algorithm’)

of bird behaviour in a flock was suggested by Craig

Reynolds (Reynolds, 1987). Firstly, each bird in the

model aimed to avoid collisions with the other birds.

Secondly, each bird moved in the same direction as

ICPRAM 2019 - 8th International Conference on Pattern Recognition Applications and Methods

336

the nearby birds. Thirdly, each bird aimed to move

at the same distance from other birds. The flock size

is insignificant for the model.

The ‘Vicsek Model’ (Vicsek et al., 1995) is

used to describe large flocks, and demonstrates how

individual birds in the flock adjust their movement

in the presence of noise depending on location of

their neighbours. Allocation of aggregated data is

presented in publication (Topaz, Ziegelmeier and

Halverson, 2015) using simulation snapshots of the

‘Vicsek Model’.

Models for explaining and predicting pigeon

flock flights in real-time mode (‘Pigeon Model’)

were suggested in publication (Wallentin and Oloo,

2016), where the authors used specific algorithms to

identify an optimal range of parameters that can be

used to reproduce realistic navigation paths of

homing pigeons. In (Oloo and Wallentin, 2017) the

authors combined an agent-based model of social

pigeon flights with a simulated data stream from

recorded GPS tracks.

Directions were calculated for individuals in

schools of fish to analyse joint behaviour in

publication (Jolles et al., 2017) based on the

example of free-swimming three-spine stickleback

shoals (Gasterosteus aculeatus).

3 MATERIALS AND METHODS

3.1 Materials

In this work the behaviour of pigeon flocks –

consisting of three to eight birds – during flights

over unfamiliar heterogeneous terrain was studied.

During the investigation, calculations were carried

out based on data on pigeon flights published in

open repositories (Dryad Digital Repository and

Movebank Data Repository). The calculations were

made for six flocks.

The first three flocks (data package from

https://datadryad.org/resource/doi:10.5061/dryad.f9n

8t, paper (Watts et al., 2016)) flew over mixed

terrain near the seashore: sea coast, urban terrain and

agricultural fields. The specific distance between the

individual values of coordinates for pigeon GPS

tracks is presented within the range of three to five

metres. Measurements of coordinates between

separate points of GPS tracks were taken five times

per second. The number of pigeons in the first,

second and third flock were four, five, and three,

respectively.

The other three flocks (data package from

www.datarepository.movebank.org/handle/10255/m

ove.365, paper (Santos et al., 2014)) flew over the

mixed terrain in the foothills: natural forests,

populated countryside and agricultural fields The

specific distance between the individual values of

coordinates for pigeon GPS tracks is presented

within the range of three to six metres.

Measurements of coordinates between individual

points of GPS tracks were taken four times per

second. The number of pigeons in the fourth, fifth

and sixth flock were eight, seven and eight

respectively.

Earth remote sensing data – satellite images – in

the form of OpenLayers (http://openlayers.org) were

applied as a source of information about terrain

surfaces. The coordinate system for the project was

WGS 84/Pseudo-Mercator (EPSG:3857).

3.2 Methods

To determine how the behaviour of each flock

changed – in response to changes in the terrain over

which it flew – pigeon GPS tracks were analysed

and characteristics of the movements of individual

Figure 3: Points at which the flock flew apart, according to

the local maximums of pairwise distances between

pigeons at the same time. Dotted points show the

trajectories of individual pigeons, the circle is a special

point.

Flock Patterns When Pigeons Fly over Terrain with Different Properties

337

birds during their flight in the flock and the

aggregated parameters of the flock were calculated.

The analysis was made for all flight trajectories

for each of the six flocks specified in subsection 3.1

and for all periods of time during which the flights

of these flocks were performed. The distance

between the departure and destination points for all

six flock flights was about ten kilometres.

During analysis the following groups of data

were processed:

I) Analysis of trajectories of individual pigeons,

taking into account their collective behaviour in the

flock during the flight.

Figure 4: Points of breaks in direction (points of sharp

changes in flock direction during one second). Dotted

points show the trajectories of individual pigeons, the

circle is a special point.

The spatial distribution of distances between

pairs of individual birds and directions of movement

were determined during the analysis. The following

parameters were compared to determine:

 distance between pairs of individual birds in

the flock and standard deviation of distances

between pairs for all birds in the flock taken at

the same moment of measurement;

 directions of movement for each bird and

standard deviation of directions for all birds in

the flock taken at the same moment of

measurement.

Based on analyses of trajectories, special points

in six flock flights were calculated in coordinates

and in time:

 points at which the birds in the flock flew

apart, according to the local maximums of

distances between pairs of birds (Figure 3);

points of breaks in direction (points of sharp changes

in flock direction during one second) of the flock

trajectories, i.e. points corresponding to significant

changes in the standard deviation of directions (

 Figure 4).

II) Analysis of terrain over which the pigeon

flocks flew

Based on analyses of remote sensing data from

OpenLayers, the spatial locations of the visually

perceived terrain elements were determined. In order

to do this, terrain isolines were contoured along the

boundaries of distinct terrain textures. The isolines

revealed the significant extended objects on the

terrain, as well as the boundaries between territories

with different surface features.

Figure 5: Points of intersection of the flock flight

trajectories and the terrain isolines. Yellow lines indicate

the isolines identified on the surface. Dotted points show

the trajectories of individual pigeons. The circles indicate

special points of intersection.

ICPRAM 2019 - 8th International Conference on Pattern Recognition Applications and Methods

338

III) Comparison of characteristics of pigeon

flights and terrain features

Based on analyses of additional special points –

points of intersection of the flock flight trajectories

and the terrain isolines – were determined for

different types of surface (Figure 5).

3.3 QGIS Plugins

The data were processed using the open source

software program QGIS (http://qgis.org), including

additional analysis plugins: QGIS geoalgorithms and

GDAL tools (http://www.gdal.org) integrated into

QGIS. The source data layers were added using the

OpenLayers Plugin in QGIS, which allows to obtain

Google Maps, Bing Maps and another open layers.

Geographic information system QGIS allow to

process GPS data of the pigeons’ flight paths with

precise reference to the locations and terrain features:

 Create vector track lines by points of GPS

measurements.

 Calculate variation in directions of motion and

variation in distances by vector data.

 Build summary diagrams of the dependence of

different flight parameters with reference to

time and to coordinates along the flight

trajectories.

 Calculate the terrain features obtained from

remote sensing data, such as the boundaries

between different types of terrain, and select

contour isolines.

 Calculate the density of special lines on the

surface in the form of a ‘heat map’.

The applied QGIS tools and plugins are

presented in Table 1.

Table 1: Applied QGIS tools and external plugins.

Plugin

Description

OpenLayers Plugin:

https://github.com/so

urcepole/qgis-

openlayers-plugin

QGIS plugin embeds OpenLayers

(http://openlayers.org)

functionality.

It allows to obtain Google Maps,

Bing Maps, OpenStreetMap and

another open source layers.

Points2One:

http://plugins.qgis.or

g/plugins/points2one

Create lines and polygons from

vertices. Connects points in a

layer to form lines and polygons.

Line intersections:

https://www.qgis.org/

en/docs/index.html

Locate intersections between

lines, and output results as a point

shapefile.

Heatmap Plugin:

http://www.qgistutori

als.com/en/docs/creat

ing_heatmaps.html

Create a density raster of an input

point vector layer based on the

number of points in a location,

with larger numbers of clustered

points resulting in larger values.

4 RESULTS

In this work three types of special points were

calculated (points at which the birds in the flock

flew apart, points of breaks in direction with sharp

changes in flock direction during one second, points

of intersection of flock flight trajectories and terrain

isolines) for the flights of six flocks using three

different methods.

Based on special points, peri-stimulus

histograms were forming as histogram of flight

parameters around stimulus events – ‘triggers’. Peri-

stimulus histograms were plotted for: directions,

distances and deviations by direction and distances,

as well as detection of dependencies between flock

flight parameters and terrain properties. Peri-

stimulus histograms were constructed (using 200 or

250 ms bins) for the epoch between 10 seconds

before passing over a special point and 10 seconds

after passing over a special point (‘trigger

stimulus’). Typical phenomena occurring during the

flights of the flocks were analysed for points where:

 individual birds flew apart;

 there was sharp changes in flock direction;

 trajectories of pigeons crossed selected

isolines.

Basic flight parameters and calculated results are

presented in Table 2 (SD - standard deviation).

Table 2: Basic flight parameters and calculated results.

Dryad Digital Repository

Flock number

Number of pigeons

Time interval between GPS

measurements, ms

200

Number of GPS

measurements

5395

3685

480

Mean SD of pairwise

distances, m

10.8

9.4

8.6

Mean SD of flight directions,

degrees

5.8

5.6

5.5

Isoline contour accuracy, m

Movebank Data Repository

Flock number

Number of pigeons

Time interval between GPS

measurements, ms

250

Number of GPS

measurements

3501

384

Mean SD of pairwise

distances, m

3.8

6.8

Mean SD of flight directions,

degrees

3.9

4.0

4.2

Isoline contour accuracy, m

Flock Patterns When Pigeons Fly over Terrain with Different Properties

339

The typical histograms for the different cases are

shown in the Figures below.

4.1 Results of Data Processing by

Distance

Figure 6: Histogram of distance deviations, in relation to

the moments when the flock crossed the isolines. The x

axis shows the timescale in relation to events ‘isoline’, s.

The y axis shows standard deviation of the distances

between pairs of pigeons, m.

Figure 7: Histogram of distance deviations, in relation to

the moments of break in flock direction. The x axis shows

the timescale in relation to events ‘breakpoint’, s. The y

axis shows standard deviation of the distances between

pair of pigeons, m.

4.2 Results of Data Processing by

Directions

Figure 8: Histogram of direction deviations, in relation to

the moment at which the flock flew apart. The x axis

shows the timescale in relation to events ‘flock flying

apart’, s. The y axis shows standard deviation of the

direction of pigeons, deg.

Figure 9: Histogram of direction deviations, in relation to

the moments when the flock crossed the isolines. The x

axis shows the timescale in relation to events ‘isoline’, s.

The y axis shows standard deviation of the direction of

pigeons, deg.

5 DISCUSSION AND

CONCLUSIONS

The aim of this work was to reveal the flight

properties of a small flock (three to eight

indistinguishable pigeons tracked using GPS

loggers) over homogeneous and combined

homogeneous and heterogeneous terrain. The paper

discusses typical flock behaviour related to specifics

of the terrain over which birds fly. Specific features

of the flight, revealed during turns of the flock, and

changes in the terrain colour characteristics or

lighting condition in landscape, presented the

principle interest for this study.

Reflexively, the pigeons arrange themselves

within the flock over the terrain. Moreover, part of

visual data about landscape, perceived by the

pigeons, forms the basic points and areas that

determine both continuity and change in pigeon

trajectories during flights (flight along the river

maintains consistency of trajectories, and flying out

of the forest into the fields can cause the flock to

turn around). With that, other visual data may be not

perceived as significant for navigation during the

flight (for example, a particular house among the

abundance of single houses in low-rise built-up

area), in such case no behavioural response is

associated with changing trajectories.

The pigeons can fly over heterogeneous and

homogeneous terrain. The scope of navigation tasks

solved by the pigeons when flying over

homogeneous terrain with a small number of

reference points is also limited and generally stable.

The arrangement of pigeons in the flock and their

flight trajectories will be maintained during the

whole flight over homogeneous terrain. The pigeons

pay attention to a limited and fixed number of

objects – for example, the river bank along which

ICPRAM 2019 - 8th International Conference on Pattern Recognition Applications and Methods

340

the flight occurs. Repetition of terrain textures and

structures enables stable behaviour and does not

require additional attention of pigeons. Any changes

or additional information – changes in weather

conditions or light, or the appearance of a predator –

may result in changes in the pigeons’ arrangement in

the flock and trajectories. In contrast to individual

birds, the flock perceives the terrain jointly and in

coordination and responds to changes in terrain

cooperatively – with changes not only in trajectories

but also in the flock structure itself.

During a flight over heterogeneous terrain, a

great amount of diverse information is observed.

This information can be generalized and become

typical. Sets of data are extracted from it and can be

applied even when the birds have become

accustomed to operating in other situations.

Accordingly, the responses to similar sets of data

will be alike. This promotes both fast and consistent

responses during flight over similar terrain and

adaptation during flight over different terrain. When

current situation change, the sets of reference points

and regions also change.

Generally, pigeons prefer to fly over already

familiar terrain, gradually extending the survey

areas. But even well-known territories can change –

at different times of day and seasons of the year –

and therefore flock navigational strategies can

change completely, and the flock can even fly away

from previously interesting terrain.

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