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\begin{document}

\title{Habitat geometry rather than visual acuity limits the visibility of a
ground-nesting bird's clutch to terrestrial predators.}



\author[1]{George Hancock}%
\author[2]{Lizzie Grayshon}%
\author[3]{Ryan Burrell}%
\author[4]{Andrew Hoodless}%
\author[5]{Innes Cuthill}%
\author[6]{Jolyon Troscianko}%
\affil[1]{University of Exeter College of Life and Environmental Sciences}%
\affil[2]{Game and Wildlife Conservation Trust}%
\affil[3]{Bournemouth University}%
\affil[4]{The Game \& Wildlife Conservation Trust}%
\affil[5]{University of Bristol}%
\affil[6]{University of Exeter}%


\vspace{-1em}



  
  \date{May 10, 2024}


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\selectlanguage{english}
\begin{abstract}
The nests of ground-nesting birds rely heavily on camouflage for their
survival, and predation pressures, often linked to human activity, are a
major source of mortality. Numerous ground-nesting bird populations are
in decline, so understanding the effects of camouflage on their nesting
behaviour is of relevance to their conservation concern. Habitat
three-dimensional (3D) geometry together with predator visual abilities,
viewing distance, and viewing angle determine whether a nest is either
visible, occluded or too far away to detect. While this link is
intuitive, few studies have investigated how fine-scale geometry is
likely to help defend nests from different predator guilds. We
quantified nest visibility based on 3D occlusion, camouflage, and
predator visual modelling in northern lapwing, Vanellus Vanellus, on
different land management regimes. Lapwings selected local backgrounds
that had a higher 3D complexity at a spatial scale greater than their
entire clutches compared to nearby control sites. Importantly, our
findings show that habitat geometry -- rather than predator visual
acuity restricts nest visibility to terrestrial predators, and that an
open field would actually be perceived as a closed habitat to a
terrestrial predator searching for nests on the ground. Taken together
with lapwings' careful nest site selection, our findings highlight the
importance of considering habitat geometry for understanding the
evolutionary ecology and management of conservation sites for
ground-nesting birds.%
\end{abstract}%



\sloppy


\textbf{Habitat geometry rather than visual acuity limits the visibility
of a ground-nesting bird's clutch to terrestrial predators.}

\textbf{Authors:} George R.A. Hancock*\textsuperscript{1}, Lizzie
Grayshon\textsuperscript{2}, Ryan Burrell\textsuperscript{3}, Innes
Cuthill\textsuperscript{4}, Andrew Hoodless\textsuperscript{2}, Jolyon
Troscianko\textsuperscript{1}

*Corresponding author: ghancockzoology@gmail.com

1. Centre for Ecology \& Conservation, University of Exeter, Penryn,
TR10 9FE, UK

2. Game \& Wildlife Conservation Trust, Fordingbridge, SP6 1EF, UK

3. Faculty of Science and Technology, Bournemouth University, Fern
Barrow, Poole, Dorset, BH12 5BB, UK

4. School of Biological Sciences, University of Bristol, Woodland Road,
Bristol BS8 1UG, UK

\subsection*{Key Words}

{\label{key-words}}

Camouflage, 3D Scanning, Occlusion, Ground-nesting Birds, Lapwing

\section*{Abstract}

{\label{abstract}}

The nests of ground-nesting birds rely heavily on camouflage for their
survival, and predation pressures, often linked to human activity, are a
major source of mortality. Numerous ground-nesting bird populations are
in decline, so understanding the effects of camouflage on their nesting
behaviour is of relevance to their conservation concern. Habitat
three-dimensional (3D) geometry together with predator visual abilities,
viewing distance, and viewing angle determine whether a nest is either
visible, occluded or too far away to detect. While this link is
intuitive, few studies have investigated how fine-scale geometry is
likely to help defend nests from different predator guilds. We
quantified nest visibility based on 3D occlusion, camouflage, and
predator visual modelling in northern lapwing, Vanellus Vanellus, on
different land management regimes. Lapwings selected local backgrounds
that had a higher 3D complexity at a spatial scale greater than their
entire clutches compared to nearby control sites. Importantly, our
findings show that habitat geometry -- rather than predator visual
acuity restricts nest visibility to terrestrial predators, and that an
open field would actually be perceived as a closed habitat to a
terrestrial predator searching for nests on the ground. Taken together
with lapwings' careful nest site selection, our findings highlight the
importance of considering habitat geometry for understanding the
evolutionary ecology and management of conservation sites for
ground-nesting birds.

\section*{1 INTRODUCTION}

{\label{introduction}}

Camouflage is one of the most common anti-predator strategies exhibited
by animals, as reducing the ability of predators to detect or
distinguish a target from its background reduces the risk of predation
(Cott, 1940; Cuthill, 2019; Endler, 1981). Ground-nesting birds are no
exception to this, with many of their species exhibiting camouflage at
various phases in their life history (Stevens et al., 2017, 2017;
Stoddard et al., 2016). One notable phase where camouflage has evolved
is that of the egg (Kilner, 2006; Westmoreland, 2008). The comparative
openness and accessibility of ground-nesting wader nests, such as
coursers (Cursoriinae) and plovers (Charadriinae), renders them
particularly vulnerable to predation. When predators approach, adults
abandon their nests (Blumstein, 2003; Wilson-Aggarwal et al., 2016),
relying on the patterns of their eggs to camouflage them while the
parent(s) harass or distract the predator (Armstrong, 1954; Simmons,
1951). The nests of species that rely more on the parents' plumage for
camouflage have been shown to have less camouflaged eggs. Whereas in
other ground-nesting species the eggs can be occluded by either burying
them, or by relying on vegetation from surrounding hedgerows, scrub or
forest understory (Bravo et al., 2022; Masero et al., 2012; Stevens et
al., 2017; Stoddard et al., 2011; Troscianko et al., 2016a). Occlusion
by natural structures is arguably one of the most effective forms of
camouflage (Troscianko et al., 2016a). Partial occlusion can mask
important visual cues for detection and recognition such as an object's
outline, size and identifiable morphological features (limbs, eyes, etc)
(DiPietro et al., 2002; Sharman et al., 2018; Sovrano and Bisazza, 2008;
Tvard\selectlanguage{ngerman}íková and Fuchs, 2010). While total occlusion forces observers to
rely on other sensory cues to detect the occluded object, providing that
the source of occlusion isn't also recognisable e.g., nesting material
or incubating parent (Bailey et al., 2015; Broughton and Parry, 2019;
Stevens et al., 2017).

Occlusion isn't without costs. The openness of the nests of
ground-nesting birds is thought to be a balance between multiple
trade-offs. Nest predation, parent predation, thermoregulation and both
habitat and nesting material availability all contribute to the
appearance of ground-nesting bird nests (Gillis et al., 2012; Kubelka et
al., 2019; Mainwaring et al., 2014; Stevens et al., 2017; Swaisgood et
al., 2018). Local vegetation height has been shown to influence nest
site selection and predation risk of ground-nesting birds; taller
vegetation results in shorter flushing distances, higher nest survival
and greater parent predation risk (Bertholdt et al., 2017; Gómez-Serrano
\& López-López, 2014). A study using periscopes to assess the visibility
of dogs and humans from the perspective of nesting Kentish plovers
(\emph{Charadrius alexandrines)} showed that sites selected by parents
offered greater predator visibility at the cost of increased nest
predation risk (Gómez-Serrano and López-López, 2014).

When measuring nest camouflage, the visual ecology of the observing
parents and predators should be considered. Visual modelling using
colour-calibrated images has increasingly been used to assess animal
camouflage from different visual systems, accounting for differences in
observer colour reception and spatial acuity (Caves et al., 2018; Maia
et al., 2013; van den Berg et al., 2020). These measures have been used
to show that camouflage from local background pattern match can predict
nest survival in ground-nesting birds (Troscianko et al., 2016b).
However, an aspect of visual ecology rarely considered is predator
height in combination with distance and habitat structure. The height of
an animal's eye relative to its object of interest changes the angles
and distances required for the object to be occluded by surrounding
structures (Martin, 2011). A nest that appears exposed from a human
height may be undetectable to a smaller mammalian predator even at
closer distances, while an avian predator excluded to the edge of a
field by harassing parents may be at too great a distance to detect a
clutch of eggs (Gómez-Serrano and López-López, 2014). Microhabitat
selection likely helps balance the trade-offs between predator and nest
visibility (Gómez-Serrano and López-López, 2014; Lovell et al., 2013;
Stoddard et al., 2016). By selecting areas of surrounding local
elevation ground-nesting birds should be able to increase visibility of
predators. Combined with the depression of the scrape, local elevation
should paradoxically decrease nest visibility; requiring a greater
viewing angle to be seen unobstructed by approaching predators.

Ground-nesting waders are in decline across their range due to habitat
loss, agricultural intensification, reduced prey availability and
elevated predation risk from mesopredators, such as foxes, mustelids,
corvids and raptors (Evans, 2004; Galbraith, 1988; Roos et al., 2018;
Vickery et al., 2004). Consequently, mechanisms of further understanding
the habitat features that both encourage nesting and minimise predation
are of increasing conservation interest, as predation is typically the
leading cause of nest mortality (Baines, 1990; Ricklefs, 1969; Teunissen
et al., 2008). Just as camera quality has advanced colour analyses of
visual scenes, increasing accessibility of terrestrial and aerial 3D
scanners allow for the measurement of topography and vegetation
structure at different spatial scales (de Vries et al., 2021; Hill et
al., 2014; Li et al., 2022). Terrestrial scanners have even been used to
compare the volume and shape of bowl nesting birds, though these were
taken \emph{in vitro} (Simonov and Matantseva, 2020). 3D scanning allows
for a more complete measure of local 3D composition than more
traditional chart and ruler based measurements of vegetation height and
cover (Gómez-Serrano and López-López, 2014; Gregg, 1991; Pendleton and
Nickerson, 1951).

In this study, we used hand-held 3D scanners and colour-calibrated
images to measure the shape and appearance of northern lapwing
(\emph{Vanellus vanellus} ) nests in pastoral, arable and wet grassland
sites. The goal was to investigate how the 3D and colour environment
influences lapwing nesting decisions. The methods of habitat management
and local variation should also influence the colour and 3D composition
of the habitat, changing the occlusion of nests, the number of
distractive structures with similar 3D shape to the nests and the colour
match of the nests. We hypothesised that lapwing should favour
backgrounds of higher local elevation, greater surrounding 3D variation
at scales relative to the size of their nests, and which are more
obstructed from the perspectives of their predators. We also compared
the distances where modelled occlusion and acuity influence
detectability by predators and investigated whether background match and
occlusion predict predation in lapwing. A full breakdown of the 3D
scanning methods and scripts required is provided within our
supplementary material, including methods for using photogrammetry
generated point clouds in place of 3D scanners.

\section*{2 MATERIALS AND METHODS}

{\label{materials-and-methods}}

\subsection*{Study System:}

{\label{study-system}}

The northern lapwing (\emph{Vanellus vanellus} ) is a ground-nesting
wader that commonly breeds in lowland wet grassland and arable sites
across temperate Eurasia (Cramp and Brooks, 1992). The species is of
conservation concern in the UK and mainland Europe as their populations
have been in decline since the 1970s (Wilson et al., 2001).
Unsustainable nest predation is cited as a barrier to population
recovery (Evans, 2004; Laidlaw et al., 2021; Roos et al., 2018).Northern
lapwing nests comprise shallow scrapes in bare ground or short mixed
vegetation, lined with varying amounts of dead plant matter (Kubelka et
al., 2019). Their nests are defended from predators by using a
combination of mobbing, distractive displays, behavioural crypsis and
egg camouflage (Salek and Cepáková, 2006). While positioning away from
trees and around waterbodies also protects nests (Eglington et al.,
2009; Kaasiku et al., 2022).

We sampled lapwing nests from sites in two separate locations monitored
by the Game and Wildlife Conservation Trust (GWCT); the Avon Valley in
Hampshire and Burpham in Sussex. The Avon Valley sites included a
variety of habitats, predominantly under UK agri-environment schemes,
such as wet grassland, marshland, pasture, and a restored ex-gravel
quarry. Conversely, the Sussex sites consisted of arable fields in
various stages of rotation between plough, spring cereal, and fallow.
Predation was monitored at the sites using iButton (Thermochron iButton,
Maxim Integrated Products, Inc., Sunnyvale, CA) nest temperature loggers
and weekly nest checks (Hartman and Oring, 2006). Nest outcomes
(hatched, abandoned, flooded, trampled and predated) were determined by
both interpretation of nest temperature logger plots and accepted
in-field techniques (Hartman \& Oring, 2006; Sheldon et al., 2010). All
sites utilised some form of predator control or management to protect
wading birds. These varied in intensity and included deterrents such as
electric fences and crow scarers and removal methods such as Larsen
traps, tunnel traps, and shooting (Fletcher et al., 2010; Laidlaw et
al., 2021; Malpas et al., 2013).

\subsection*{Ethics Statement:}

{\label{ethics-statement}}

Corresponding permissions were granted as part of a collaboration with
the GWCT and were approved by the University of Exeter Ethics Committee.

\subsection*{3D Scanning \& Calibrated
Photography:}

{\label{d-scanning-calibrated-photography}}

From March to Mid-June of 2021 and 2022, we photographed, and 3D scanned
83 lapwing nests. Each nest was scanned with an ASUS Zenfone AR using
the Matterport Scenes app from a height of 1.2m (Shults et al., 2019).
Phone 3D scanners provides a cheap and relatively easy method for
capturing 3D point clouds using triangulation from an structured light
time-of-flight sensor (Froehlich et al., 2017). Scans were taken from a
height of 1.2 metres at a flat 90\textsuperscript{o} polar (vertical)
angle from the ground. Each scan taking 7 seconds to complete. ~For each
nest, an additional nest-less photo and scan were taken at a distance of
1-2 metres (4 paces) from the nest, by backtracking in the direction of
the approach to avoid further trampling the surrounding area. These
additional photos and scans were used as a paired null for each nest.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. Framework for 3D analyses of ground-nesting bird nests.
Example images are from an agri-environment scheme site (left-blue) and
spring-cereal arable site (right-yellow). A) Photograph of nest taken
with colour calibrated Sony camera. B) 3D scan nests with ASUS phone and
upload the point cloud into Matterport scenes for standardisation of
formatting. C) Import and label point clouds in ImageJ. D) Run nest 3D
energy and visibility transect analysis scripts.

Photographs of the nests and nulls were taken using a MICA
colour-calibrated Sony A6000 with a baader venus-u 52mm UV filter and
the camera's own visible light filter (Moher Alsady et al., 2016). A 7\%
and 93\% uniform (\selectlanguage{greek}λ \selectlanguage{english}200-700nm) reflectance standard was placed in situ
for each photograph (Troscianko et al., 2016b). Standards were created
using Zenith Polymer sintered PTFE sheets. As the lighting environment
was highly variable with weather conditions, all photos were taken with
a 1m\textsuperscript{2} pop-out NEEWER diffuser sheet at times greater
than 2 hours from dawn and dusk (Duarte et al., 2018; Troscianko et al.,
2016b). Photographs were calibrated and converted to multispectral
images using the MICA toolbox v2.2.2 for ImageJ (Schneider et al., 2012;
Troscianko and Stevens, 2015; van den Berg et al., 2020).

\subsection*{Constructing Height Maps:}

{\label{constructing-height-maps}}

The 3D scans were processed using the open-source program MeshLab
v.2022.02 (Visual Computing Lab -- ISTI -- CNR,
http://meshlab.sourceforge.net/), to extract only the height data and
export the scans as .ply files (Simonov and Matantseva, 2020). These
files were then imported into ImageJ, using a custom script, to create
images containing each nest's X, Y, and Z (height) coordinates, with 1
pixel representing 1mm (Schneider et al., 2012). Missing Z values
(0.07\% of pixel values) were filled with the mean background value.
Finally, ImageJ was used to label the different parts of each scan,
including the clutch (area around all the eggs), the nest (area around
the scrape), the background (non-blank parts of the scan), and the
individual eggs (group of regions of interest around each egg), see
Figure 1. Instructions can be found within our supplementary material
and on our GitHub.

\subsection*{Nest 3D Measures:}

{\label{nest-3d-measures}}

Cross-section maps of each nest were constructed by creating a circle
selection (radius=300mm) centred on the clutch ROI. At each integer
distance (radius = 0-300mm), the mean Z-value was measured and
translated either to the minimum of the clutch (nest-normalised) or the
surrounding background (radius-normalised) (see supplemental material).
These cross-sections allowed for comparisons of the scans' peak nest,
peak clutch and trough heights and calculation of the nest's slope.

To quantify how rough or smooth the terrain at nest locations was at
different spatial scales, we used methods similar to those used for 2D
pattern analysis. We measured the `energy' (SD) of the Z value at
different spatial scales relative to the mean wavelength of the clutches
( \(\sqrt{\text{clutch}}\ area=86mm\)), in the following octaves (1/8, 1/4, 1/2, 1, 2, 4)
(Lindeberg, 2015; Michalis et al., 2017). Energy maps for each spatial
scale were made using difference of Gaussians (DoG); subtracting each
octave by 1.6x the same scale (Figure 2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\par\null

Figure 2. 3D scan energy at different spatial scales relative to clutch
size: x1/8, x1/4, x1/2, x1, x2, x4. The left-hand side shows the
original height map and associated ROIs: eggs, clutch, rim and
background. More elevated (positive) regions are shown as lighter, while
less elevated regions are shown as darker. The right-hand images show
the separated spatial scales with the position of the clutch marked by a
black arrow. The eggs are most visible at x1/4 scale, the scrape at x1
scale and the nest elevation at x4 scale.

\subsection*{Clutch Occlusion \&
Visibility:}

{\label{clutch-occlusion-visibility}}

For each depth map, occlusion maps were created for 16 different
observer orientations around the azimuth of the nest, from
0\textsuperscript{o}-337.5\textsuperscript{o}, in
22.5\textsuperscript{o} intervals. To calculate occlusion, for each
pixel in the clutch, the shallowest/minimum elevation angle (mA) that
allowed it to be un-occluded was calculated from each of the 16
bearings, given the 3D depth profile, see Figure 1. Elevation angles
above a pixel's mA allow that pixel to be visible. For observer
elevation angles between 0.5\textsuperscript{0} -
60\textsuperscript{0}we measured the visibility. The visibility at a
given polar angle was equal to the mean percentage of pixels un-occluded
across the 16 bearings. The distance required to achieve viewing angles
was calculated at fox height {[}0.4m{]} and a matrix of corvid flight
heights {[}1.6m, 3.2m, 6.4m, 12.8m, 25.6m{]}.

\subsection*{Colour Metrics:}

{\label{colour-metrics}}

Luminance \selectlanguage{greek}Δ\selectlanguage{english}S and colour \selectlanguage{greek}Δ\selectlanguage{english}S (JND) from the local (nest) and distal
(background) surrounding each clutch was modelled for corvid vision and
fox vision as a metric of camouflage, using the mica toolbox (Jacobs et
al., 1993; Martin, 2017; Moher Alsady et al., 2016; Vorobyev and Osorio,
1998). Where higher \selectlanguage{greek}Δ\selectlanguage{english}S values correspond with a poorer match. The
Siddiqi method was used for \selectlanguage{greek}Δ\selectlanguage{english}S luminance (Weber fraction 0.2) and RNL
model for \selectlanguage{greek}Δ\selectlanguage{english}S colour (Weber fraction of most abundant cone of 0.05) (Lind
et al., 2013; Moher Alsady et al., 2016; Pretterer et al., 2004; Siddiqi
et al., 2004; Vorobyev and Osorio, 1998). For each observer, we used the
most phylogenetically relevant systems known. These were the common
peafowl \emph{Pavo cristatus,} for the corvid vision, and the red
fox\emph{Vulpes vulpes} , for the fox vision (Jacobs et al., 1993;
Malkemper, 2014; Malkemper and Peichl, 2018; \selectlanguage{ngerman}Ödeen and Håstad, 2013).

\selectlanguage{greek}Δ\selectlanguage{english}S values were measured for images acuity corrected for the hypotenuse
distance required for a given series of polar viewing angles
{[}1.875\textsuperscript{o}, 2.5\textsuperscript{o},
3.75\textsuperscript{o}, 5\textsuperscript{o}, 7.5\textsuperscript{o},
10\textsuperscript{o}, 15\textsuperscript{o}, 20\textsuperscript{o},
30\textsuperscript{o} and 40\textsuperscript{o}{]}, when at the height
of the model observers (fox 0.4m, corvid 3.2m) (van den Berg et al.,
2020). The polar viewing angles for corvid vision were adjusted post-hoc
to the matrix of values used for clutch occlusion {[}1.6, 3.2, 6.4, 12.8
and 25.6 m{]}, by calculating the polar angle and horizontal distance
required to produce the same observer distance. Acuity correction was
carried out using the known peak resolving power, magpie \emph{Pica
pica} 33.33 cp/d and red fox \emph{Vulpes vulpes} 8 cp/d (Malkemper,
2014; Martin, 2017).

\emph{Statistical Analyses:}

Statistical analyses were performed using R, version 3.6.3 (Team, 2013).
The 3D energy metrics were treated as continuous variables and were
log-transformed so that residuals fitted a normal distribution. The
energy of the nest and null sites were compared at each spatial scale
with the lme4 package using linear mixed models derived from the
following formula:

\emph{lmer (log (Energy) \textasciitilde{}
poly(Scale,2)*ROI+(1\textbar{}Site)+(1\textbar{}ScanID)
+(1\textbar{}NestID) ) , where ROI specifies nest vs null measurement,
ScanID specifies the label for the individuals can and NestID is the
shared ID for the nest and its corresponding null.}

The influence of 3D energy and habitat type on visibility was also
assessed using linear mixed models, while visibility's effect on
predation was analysed using generalised mixed models with predation as
a binary (yes/no) variable. We also compared the effect of broad scale
(agri-environment and arable)) and fine-scale (wet grassland, gravel,
crop, fallow, cattle-grazed and sheep-grazed) on 3D energy using Tukey's
post-hoc tests.

\section*{3 RESULTS}

{\label{results}}

\subsection*{Nest Site 3D Background
Selection}

{\label{nest-site-3d-background-selection}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

As spatial scale increases, z energy increases following a quadratic
(scale\textsuperscript{2}, \selectlanguage{greek}β \selectlanguage{english}= -13.96, SE= 0.16, p \textless{}0.0001
\textbar{} scale, \selectlanguage{greek}β\selectlanguage{english}= 24.12, SE= 1.15, p\textless{}0.0001); see Figure 3.
Compared to the null scans, lapwing nest surrounds possessed higher 3D
variation across all spatial scales (nest, \selectlanguage{greek}β \selectlanguage{english}= 2.90, SE=0.12, p=0.00379)
and variation increased with spatial scale at a faster rate for nest
sites at the smaller spatial scales (nest:scale\textsuperscript{2}, \selectlanguage{greek}β \selectlanguage{english}=
2.621, SE=0.04, p= 0.0089 \textbar{} nest:scale, \selectlanguage{greek}β \selectlanguage{english}= -2.029, SE=0.13, p=
0.042). Post hoc comparison of site management strategies showed the
nests of sheep grazed fields had significantly lower 3D variation
compared to other sites, while wet grassland sites had significantly
higher 3D variation (see supplemental material) For scales below the
size of the clutch, 3D energy originates from deviation in height
between small vegetation (grasses) or from the substrate (large stones,
gravel). The 3D energy of pastoral nest sites at higher spatial scales
was more similar to those of the arable sites than their null sites,
except for at sheep grazed sites. At scales above the size of the nest,
high energy results from large clumps/mounds of weedy vegetation,
trampling and sloping terrain (hills). On average, clutches were
elevated 4.5cm above their local surroundings. There was no significant
difference between management type and nest elevation; nest elevation
was instead predicted by 3D energy of the surroundings (energy :
elevation, \selectlanguage{greek}β \selectlanguage{english}= 2.894, SE= 53.816, p = 0.00493).

\subsection*{Nest Predation}

{\label{nest-predation}}

Over the 2 years, we sampled the Avon Valley and Sussex Sites we
photographed 115 lapwing nests, 86 of which were scanned. Of the nests
found, 13 (8 in 2021, 5 in 2022) were predated. The proportion of nests
predated varied widely between county and site, with no predation events
of scanned nests recorded in the Sussex sites. Though nest predation of
unscanned nests did occur. Predation was the most common cause of nest
failure, followed by abandonment. On average, predated nests had poorer
colour matches and lower surrounding luminance complexity (SD). However,
no significant result was observed and none of the camouflage metrics
used were able to predict nest failure from predation (see supplementary
material).

\subsection*{Clutch Occlusion \&
Camouflage:}

{\label{clutch-occlusion-camouflage}}

The percentage visibility (un-occluded) of the clutch (eggs only)
increases with the observer viewing angle in a sigmoid fashion. On
average, a viewing angle of 15\textsuperscript{o} elevation (equivalent
Horizontal Distance: Fox 1.5m, corvid {[}6.0m, 11.9m, 23.9m, 47.8m,
95.5m{]}) is required for 25\% visibility and an angle of
27\textsuperscript{o} (Horizontal Distance: Fox 0.8m, corvid {[}3.14m,
6.2m, 12.6m, 25.1m, 50.2m{]}) to see 50\% (Figure 4). Increased 3D
energy across spatial scales increases nest occlusion at low viewing
angles (10 \textsuperscript{o} -30 \textsuperscript{o}), particularly at
spatial scales below the clutch size, with the lower scales to the
clutch having the largest effect (scale of grasses) on occlusion (See
Supplemental Material).

The JND colour and luminance difference of the clutches from the local
surround are in line with those of highly camouflaged animals (fox, lum
\selectlanguage{greek}Δ\selectlanguage{english}S \selectlanguage{greek}μ \selectlanguage{english}1.10 \selectlanguage{ngerman}± 0.02 SE \textbar{} col \selectlanguage{greek}Δ\selectlanguage{english}S \selectlanguage{greek}μ \selectlanguage{english}0.85 \selectlanguage{ngerman}± 0.02 SE) (Corvid, Lum \selectlanguage{greek}Δ\selectlanguage{english}S,
\selectlanguage{greek}μ \selectlanguage{english}0.9 \selectlanguage{ngerman}± 0.02SE \textbar{} Col \selectlanguage{greek}Δ\selectlanguage{english}S \selectlanguage{greek}μ \selectlanguage{english}1.58 \selectlanguage{ngerman}± 0.02 SE). Clutches were of a
better colour match to bare crop and fallow sites as opposed to
vegetated wet grassland sites for both visual systems (Sussex-Hampshire
: corvid colour \selectlanguage{greek}Δ\selectlanguage{english}S \selectlanguage{greek}β\selectlanguage{english}= -6.33, SE= 0.87, p \textless{} 0.0001)
(Sussex-Hampshire : fox colour \selectlanguage{greek}Δ\selectlanguage{english}S, \selectlanguage{greek}β\selectlanguage{english}= -7.43, SE= 0.80, p \textless{}
0.0001). \selectlanguage{greek}Δ\selectlanguage{english}S colour and \selectlanguage{greek}Δ\selectlanguage{english}S luminance follow a negative exponential with
increasing viewing angle (Figure 4). For a decrease in viewing angle to
drop \selectlanguage{greek}Δ\selectlanguage{english}S colour and/or \selectlanguage{greek}Δ\selectlanguage{english}S luminance by just 0.1 JND, the clutch would
already be 75\% occluded from most viewing heights. The exceptions were
for corvid vision from a height of 12.8m (22.5 \textsuperscript{o} for
-0.1 JND) and 25.6m (32.5 \textsuperscript{o} for -0.1 JND).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4 The effect of viewing angle on both the percentage of the
clutch un-occluded by surrounding structures (yellow curve, right hand
axis) and the \selectlanguage{greek}Δ\selectlanguage{english}S luminance (grey) / \selectlanguage{greek}Δ\selectlanguage{english}S colour (blue) (left hand axes)
from the perspectives of a red fox (height = 0.4 m) and magpie (height =
{[}1.6, 3.2, 6.4, 12.8, 14.6{]} m). The X axis shows both the viewing
angle and the hypotenuse distance required to be at that viewing angle
for the different heights. The dashed lines show the angle required for
25\% and 50\% of the nest to not be occluded.

\section*{4 DISCUSSION}

{\label{discussion}}

Here we provide one of the first empirical measures of animal occlusion
from different predator viewing angles and the first use of observer
height as a factor for acuity modelling. Measurements of camouflage from
arrays of different distances are increasingly being used in
publications on the functions of animal colour patterns (Caves et al.,
2018; Nokelainen et al., 2021). However, studies frequently fail to
account for occlusion in determining whether or not the viewing
distances used for visual models are biologically relevant. Our results
show that `openness' at a human scale does not reflect openness at
scales relative to the nests (Allen et al., 2011), with nest occlusion
being more likely to limit detection distance than visual acuity.
Especially when viewed at the height of terrestrial predators, where the
scales of the clutches and observers render the 3D scene more akin to a
closed habitat, the bowl shape of the nest occluding the clutches at low
angles. The ability to obtain a broader array of unobscured viewing
angles, independent of physical height and topography, is a likely
driver of the increased acuity of aerial predators. Short terrestrial
predators should not be under selection for visual acuities capable of
segmenting objects from further than they are capable of observing.
Previous work investigating the search behaviour of foxes and domestic
dogs trained to find nests have found them to possess a short
localisation distance, less than 2m, for nests. Previous work
investigating the search behaviour of foxes and domestic dogs trained to
find nests has found them to have a short localisation distance of
\textless{}2 metres (Seymour et al., 2003; Storaas et al., 1999). Both
our \selectlanguage{greek}Δ\selectlanguage{english}S measurements and occlusion measures support this observation.
Discrimination of the clutch outline at short distances is likely to be
the mechanism of egg detection for all, barring the few poorly
background-matching background matching clutches. Nests with greater
visibility (less vegetated) were also found to have better colour match
in the corvid visual model. Whether the increased differences were due
to higher selection intensity when less occluded or limitations in the
avian egg colour palette's ability to match live vegetation is difficult
to disentangle with our current dataset (Hanley et al., 2015).

Previous research on landscape effects on lapwing nest success has shown
that increased proximity to taller ground vegetation, being at a greater
distance from the tree line and having surrounding bodies of water
decrease the risk of nest predations. The lapwings within our study
system were shown to nest preferentially in local habitats with higher
3D variation at scales above the size of the clutch. Habitats that
feature depressions and topography (plough, cattle and horse grazing)
with similar scales to their nests should decrease lapwing predation by
increasing the amount of noise at the scales relative to nests
(Swaisgood et al., 2018). Existing guidelines for creating suitable
lapwing nesting sites, promoted by the UK conservation organisations
(e.g., RSPB, BTO and GWCT), recommend fields with short patchy
vegetation in pastoral sites (Ausden and Hirons, 2002; Smart et al.,
2013). Analysis of lapwing habitat structure with our 3D scans supports
this preference for patchy local sites with 3D variation above the scale
of their nests. These results also emphasise previous work advising the
avoidance of grazing species that create homogenous and flat vegetation,
such as sheep (Winter et al., 2005). The null scans of the arable sites
were more similar to those of the nests than the pastoral sites. Chalk
arable sites offer both better colour match and local 3D variation match
to the lapwings' nests. While not significant, these sites had the
lowest proportion of predations, 0, but were also under intense predator
control. Northern lapwing populations have long been associated with
spring cropland throughout Eurasia (Galbraith, 1988; Salek and Cep\selectlanguage{ngerman}áková,
2006). Selection of these habitats has been thought to be and is likely,
driven by the large-scale match to the locally preferred background 3D
and colour features found naturally within wet grassland. Nesting
preference at these sites may be sub-optimal for survival at later
stages of their life history, acting as a sensory/ecological trap, with
higher chick predation and lower food availability present within these
sites (Baines, 1990; Schekkerman et al., 2009).

Modelling occlusion with handheld 3D scanners can be a useful tool for
estimating an object's visibility; however, it does not account for
taller features at greater distances. The nests of the sampled lapwing
were found in fields without much obstruction except at the boundaries
(hedgerows \& forests) (MacDonald \& Bolton, 2008). Other UK
ground-nesting waders, e.g., Eurasian curlew \emph{Numenius arquata} and
redshank \emph{Tringa totanus} , and populations of lapwing in more
forested areas are more likely to have visibility influenced by
structures further from the nest than in our 3D scans. Using large-scale
LIDAR scans in conjunction with fine scale scans could provide a broader
map of visibility and cover of nests (Lone et al., 2014). It is also
worth reminding that observing from lower visual angles will in of
itself influence the match to the surrounding background. Partial and
self-occlusion will reduce the visible area of the clutch and nesting
material and mask recognisable features such as the clutch's shadow and
edge (Lovell et al., 2013; Webster, 2015). Future work should consider
measuring camouflage in the presence of obstruction and/or from
different visual angles. In particular, experiments measuring the
survival of sedentary objects, such as eggs or model animal targets,
where object motion and changes in the local 3D environment are less
prevalent an issue. Using of 3D multispectral models or
colour-calibrated video cameras may also provide potential alternate
technological solutions to the challenges of measuring visibility from
multiple viewing angles (Miller et al., 2022; Vasas et al., 2022).
However, these methods are slower and more computationally expensive
than our 3D phone scans. Finally, our study serves as a reminder of how
occlusion is integral to understanding the distances with which visual
systems can interact with natural objects and the adaptations required
to break camouflage from biologically relevant distances.

\section*{Author Contributions}

{\label{author-contributions}}

The initial camouflage and 3D structure approach was conceived by JT and
AH and carried out by GRAH. Colour-calibrated photographs and 3D scans
were collected by GRAH, with nests located and monitored by LG and RB.
The code for converting .ply files to depth maps and for measuring the
difference of Gaussian energy was created by JT and modified by GRAH.
GRAH created the code for measuring occlusion. Manuscript and
supplementary guides were first written by GRAH, with subsequent edits
by all authors. GRAH performed data analyses with guidance from JT and
IC.

Acknowledgements.

NERC GW4+ NE/S007504/1 funded GRAH in a CASE partnership with the GWCT.
JT was funded by a NERC Independent Research Fellowship NE/P018084/1. We
thank the GWCT, and the landowners, gamekeepers and farmers involved
associated farming bodies for allowing us to carry out our research at
their field sites.

Conflict of Interest

The authors declare no conflict of interest.

Data Accessibility

{[}Data will be accessible from Dryad on publication, see attached
supplementary R folder, temporary link via dropbox
https://www.dropbox.com/s/e9kuk9g3x60si2r/R\_Code\_EE.zip?dl=0{]},
ImageJ scripts for running RNL and 3D analyses with the MICA toolbox can
be downloaded from our GitHub,
https://github.com/GeorgeHancock471/3D\_RNL\_Tools.

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