Simon Labouesse
email: simon.labouesse@gmail.com

Jérôme Idier
email: jerome.idier@ls2n.fr

Anne Sentenac
email: anne.sentenac@fresnel.fr

Marc Allain
email: marc.allain@fresnel.fr

Proof of the resolution-doubling of Random Illumination Microscopy using the variance of the speckled images 1 st

Keywords: Computational imaging, Quadratic inverse problems, Multi-illumination imaging, Super-resolution, Cutoff frequency, Second-order statistics, Variance, Optical microscopy

Owing to minor modifications of the optical setup, Random Illumination Microscopy (RIM) surpasses the resolution limit of a standard fluorescence microscope. RIM uses speckle illuminations of the sample to derive a single variance image from the resulting diffraction-limited acquisitions. Variancematching iterations then produce a super-resolved estimate of the sample. Here, we demonstrate that in the noiseless case, variancematching yields a unique solution for the set of spatial frequencies corresponding to a doubled resolution limit. A similar result was already proven for covariance-matching, but covariancebased iterations are not implementable in practice, due to the huge size of the covariance matrix and to the induced numerical complexity. Our new identifiability result is a strong theoretical evidence supporting the super-resolution capability of the variance-matching version of RIM.

I. INTRODUCTION

Fluorescence microscopy is an indispensable tool in cell biology but its lateral resolution, limited by diffraction to about 300 nm for the best set-ups, remains generally insufficient for following the dynamic interplay of the cell constituents. Several super-resolution (SR) microscopy approaches have been proposed in the last twenty years [START_REF] Schermelleh | Super-resolution microscopy demystified[END_REF] to tackle this issue, among which the best compromise between high resolution and practical in-vivo imaging is Structured Illumination Microscopy (SIM) [START_REF] Heintzmann | Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating[END_REF], [START_REF] Gustafsson | Doubling the lateral resolution of wide-field fluorescence microscopy using structured illumination[END_REF]. SIM consists in recording several

The authors acknowledge partial financial support for this paper from the Agence Nationale de la Recherche under Grant ANR-12-BS03-0006 and the ITMO Cancer of the 'Plan Cancer 2014-2019'. low-resolution images of the sample under different positions and orientations of a known periodic illumination. The role of the periodic illumination is to down-modulate previously inaccessible sample high spatial frequencies into the Fourier support of the observation Point Spread Function (PSF). After some straightforward manipulations, a correspondence can be found between SIM low-resolution images and the spatial frequencies of the sample over an enlarged Fourier support which can reach twice that of a widefield fluorescence microscope. Yet, this identifiability requires the knowledge and thus a tight control of the illumination patterns which limits SIM application to weakly scattering samples and complexifies the experimental set-up [START_REF] Demmerle | Strategic and practical guidelines for successful structured illumination microscopy[END_REF].

In order to release this major constraint, it has been proposed to replace the periodic illumination of SIM by random uncontrolled speckles [START_REF] Mudry | Structured illumination microscopy using unknown speckle patterns[END_REF], [START_REF] Labouesse | Joint reconstruction strategy for structured illumination microscopy with unknown illuminations[END_REF]. A speckle is the light pattern formed when a coherent beam (laser) is reflected or transmitted by a random diffusive medium. The key property of random speckle illumination is that its statistics (average and covariance) are perfectly known and, furthermore, insensitive to aberrations and scattering. Random Illumination Microscopy (RIM) is thus expected to be easier to use than SIM, as it does not require the control of the illumination, with an extended application domain, as it is insensitive to aberrations on the excitation side. Yet, contrary to SIM, the ability to extract the spatial frequencies of the sample over an enlarged Fourier support from the low-resolution speckled images of RIM is not a straightforward issue.

Recently, we have shown mathematically that, provided the frequency support of the speckle patterns is similar to that of the PSF, the theoretical SR capacity of RIM is identical to that of SIM [START_REF] Idier | On the super-resolution capacity of imagers using unknown speckle illuminations[END_REF]. Our demonstration exploited the statistical covariance matrix of the recorded speckled images, which was shown to depend quadratically on the sample fluorescence and on the known speckle covariance and PSF. Yet, although theoretically appealing, this approach could not be transformed into a realistic numerical scheme as images of 1000 × 1000 pixels generate a covariance matrix of size 10 6 × 10 6 which is not tractable on modern computer systems.

In this letter, we prove a new result about RIM that reconciles the theoretical SR capacity and an affordable computational burden. Indeed, under fairly realistic assumptions, we mathematically show that the statistical variance of the recorded images is sufficient to recover an image of the sample with the same SR factor as covariance-based RIM.

Second-order statistics being quadratic functions of the unknown sample, the issue of retrieving spatial frequency components of the latter from either the variance or the covariance of the speckle images belongs to the family of quadratic inverse problems (QIP) [START_REF] Beinert | Non-convex regularization of bilinear and quadratic inverse problems by tensorial lifting[END_REF]. As a consequence, it is substantially more difficult to formally characterize the SR capacity of RIM, compared to SIM.

Let us also mention that variance-based microscopy using speckle illuminations has been already proposed, either for its sectioning properties [START_REF] Ventalon | Quasi-confocal fluorescence sectioning with dynamic speckle illumination[END_REF], or in the context of superresolution [START_REF] Oh | Sub-Rayleigh imaging via speckle illumination[END_REF]. However, to our best knowledge, our contribution is the first one to mathematically characterize the super-resolution property of variance-based RIM.

In Section II, we introduce a mathematical description of the image model. For sake of self-consistency, we also recall known results for covariance-based RIM. Our novel result concerning variance-based RIM is presented in Section III, and elements of discussion are given in Section IV.

II. PHYSICAL ASSUMPTIONS AND KNOWN RESULTS

A. Imaging model

For the sake of clarity, we restrict ourselves to the case of two-dimensional samples, and we formulate the problem in a fully discrete setting, where both the recorded images and the sample are represented on fine grids, with a sampling rate common to both. RIM images can then be modelled by:

z m = y m + m , (1)
with

y m = H (ρ • I m ) , (2)
where m is a random variable modeling an additive noise, y m is a vectorized image corresponding to the mth speckle illumination I m , H a convolution matrix corresponding to a convolution by the Point Spread Function (PSF) h of the microscope, ρ the fluorescence density map to recover, and • the Hadamard (i.e., entrywise, or Schur) matrix product [START_REF] Horn | Matrix analysis[END_REF]Chapter 5].

When the speckle illuminations are fully developed, the speckle covariance Cov(I m ) = C is a known convolution operator [START_REF] Goodman | Statistical optics[END_REF]. Then, the covariance matrix of z m reads

Γ z (ρ) = Γ y (ρ) + Γ , (3)
with

Γ y (ρ) = HDiag(ρ)CDiag(ρ)H t . (4)
The variance identifies with the diagonal of the covariance matrix v z (ρ) = diag(Γ z ). Assuming the noise covariance Cov( m ) = Γ is known, the knowledge of v z is thus equivalent to that of

v y = diag(Γ y ). (5)
Hereafter, we refer to v y and Γ y as v and Γ, respectively.

In this document, we assume that the illumination and observation of the sample are performed through a perfect optical mounting so that H and C are nonnegative definite convolution operators defined by the Airy functions h and c [13, Sec. 4.4.2] with frequency cut-off f PSF = 2NA obs /λ obs and f spec = 2NA ill /λ ill respectively, with NA obs(ill) the numerical aperture of the observation (illumination) objective and λ obs(ill) the emission (excitation) wavelength.

Since our goal is to demonstrate a factor two in terms of super-resolution, the sampling rate of the object must be at least four times the cutoff frequency imposed by the PSF. In the rest of this document, we make use of the following notations: f PSF ≤ 1/4 denotes the normalized cutoff frequency imposed by the PSF, and

G = ν ∈ R d , ν ∞ < 1/2 ∩ n/N, n ∈ Z d
denotes the d-dimensional normalized frequency grid limited by the Nyquist frequency (d = 2 for 2D imaging). Here, we assume that RIM acquisitions z m are made of N = n d elements. Then each of them can be decomposed over the set of discrete frequencies D PSF = D(f PSF ), where D(f ) is a generic notation for the "discrete interior" of a ball of radius f :

D(f ) = {ν ∈ G, ν < f }.

B. Covariance-based RIM

In the 2D case, [START_REF] Idier | On the super-resolution capacity of imagers using unknown speckle illuminations[END_REF] obtains that the knowledge of Γ allows to retrieve the frequency components of ρ within the ball D SR = D(2f spec ), provided that f spec ≤ f PSF . When f spec = f PSF , we have D SR = D(2f PSF ), which exactly corresponds to an SR factor equal to two. Theorem 1. Let ρ be any entrywise nonnegative vector of size N . For any entrywise nonnegative solution q to the quadratic system Γ(q) = Γ(ρ), the frequency components of q coincide with that of ρ in D SR .

Proof: The fact that all frequency components in D SR can be retrieved from Γ(ρ) is based on a unicity argument for the factorization. We recall that any nonnegative definite operator admits a unique, well-defined square root matrix and that H and C are nonnegative definite convolution operators while Γ(ρ) is a nonnegative definite operator. The covariance Γ (ρ) can be cast as

Γ(ρ) = H Diag(ρ) C Diag(ρ) H (6) = H Diag(ρ) √ C √ C Diag(ρ) H. (7)
If f spec ≤ f PSF , one can find a nonnegative convolution operator A such that AH = HA = √ C. Then, we can identify the square root of AΓ(ρ)A to

√ C Diag(ρ) √ C. Noting that diag( √ C Diag(ρ) √ C) = c 2 ρ
where is the convolution product, we conclude that the knowledge of Γ(ρ) uniquely determines the spectral components of ρ in D SR .

We also stress that this result is tight when f spec = f PSF (and in particular in the case H = C) since the frequency components of q outside D(2f PSF ) are not identifiable, according to the following proposition.

Proposition 1. Let ρ be any vector of size N . Then Γ(ρ+δ) = Γ(ρ) for any vector δ with no components in D(f PSF +f spec ).

Proof: For any vector δ with no components in D(f PSF + f spec ), each column of matrix Diag(δ)C has no frequency components in D PSF , so HDiag(δ)C = CDiag(δ)H = 0. As a consequence,

Γ(ρ + δ) = H Diag(ρ + δ) C Diag(ρ + δ) H = Γ(ρ) + Γ(δ) + H Diag(ρ) C Diag(δ) H + H Diag(δ) C Diag(ρ) H = Γ(ρ).

III. VARIANCE-BASED RIM

A. Super-resolution from variance equations

The quadratic system of Theorem 1 is made of 1 2 N (N + 1) real equations, for only M free real-valued variables, where M stand for the cardinality of D SR . Since M ≤ π 4 N in 2D (and M ≤ N in 1D), there is room left for a refined identifiability result, using a smaller number of equations.

Here, we show that the N variance equations are sufficient to uniquely determine the M frequency components in D SR , provided that ρ is an entrywise positive vector and that H = C. This last condition is satisfied if the illumination and observation are performed through the same objective and that the Stokes shift is neglected.

This important result is easily deduced from two technical results, Lemmas 1 and 2, which we derive first.

Let us define

M x = HDiag(x)H, B x = H • M x ,
In particular, for a given object ρ, the (noiseless) data variance vector ( 5) is given by v(ρ) = B ρ ρ according to the matrix identity [START_REF] Petersen | The Matrix Cookbook[END_REF]:

diag ADiag(x)B t = (A • B) x = (B • A) x. (8)
Lemma 1. For any two real solutions ρ and q to Eq. (5), we have ρq ∈ Ker(B ρ+q ) and ρ + q ∈ Ker(B ρ-q ).

Proof: Let us define the bilinear vector-valued function:

f (x, y) = diag HDiag(x)HDiag(y)H , (9)
so that f (x, y) = B x y = B y x (10)
and

v(ρ) = f (ρ, ρ). Each component of f is a symmetric form, since f (x, y) = f (y, x). Indeed, f (ρ + q, ρ -q) = f (ρ, ρ) -f (q, q) + f (q, ρ) -f (ρ, q) = v -v + f (q, ρ) -f (q, ρ) = 0. (11)
Combining Equations ( 10) and ( 11), we obtain

B ρ+q (ρ -q) = B ρ-q (ρ + q) = 0,
which proves the assertion.

Lemma 2. For any vector x with positive entries, Ker(B x ) is the linear span of frequency components outside D SR .

Proof: Let K min = min(x), so that x min = x -K min is entrywise nonnegative. We have Similarly, let K max = max(x), so that x max = K max -x is entrywise nonnegative. We have B x = K max G -B xmax , and B xmax and B x are both nonnegative definite. For all z ∈ Ker(G), z t B x z = -z t B xmax z, where the lhs and the rhs are nonnegative and nonpositive, respectively. We conclude that z t B x z = 0, so Ker(G) ⊂ Ker(B x ). Recalling that Ker(B x ) ⊂ Ker(G) we have demonstrated that Ker(B x ) = Ker(G). Now, matrix G is a convolution operator with kernel g = (h h)•h, with g = ( h• h) h the Fourier transform of g. The filter g has nonzero components for all spatial frequencies belonging to D SR . The kernel Ker(G) is the linear span of frequency components outside D SR .

B x = K min G + B xmin , with G = H 2 • H. For all z ∈ Ker(B x ), we have z t B x z = z t Gz + z t B xmin z = 0. Now,
Finally, let us consider two entrywise positive solutions ρ and q to Eq. ( 5). According to Lemma 1, we have ρq ∈ Ker(B ρ+q ), where ρ + q is entrywise positive. Therefore, we can conclude from Lemma 2 that ρq is in the linear span of frequency components outside D SR . Moreover, we know from Proposition 1 that the frequency components of q outside D SR have no impact on the data covariance, and hence on its diagonal. These results are summarized in the following theorem, providing the new identification result we aimed at.

Theorem 2. Let ρ be any entrywise positive vector of size N . For any entrywise nonnegative solution q to the quadratic system of N equations v(q) = v(ρ), the frequency components of q coincide with that of ρ in D SR , while the frequency components of q outside D SR remain arbitrary (up to the nonnegativity constraint on the entries of q). Several comments can be made about this variance-based result, compared to its covariance-based counterpart. First, we stress that Theorem 1 holds if f PSF = f spec whereas Theorem 2 requires that the matrices H and C are identical (for the matrix B x to be nonnegative definite) This condition is more stringent. Actually, we have found a small size counterexample with f PSF = f spec , and where the N variance equations admit two distinct entrywise positive solutions. This indicates that the assumptions of Theorem 2 are somewhat tight. A natural perspective would be to investigate if the identification result could be retrieved with H = C thanks to short-range correlations added to the variance.Note however that, if one has access to the raw images given by Eq. (2), it is always possible to filter the images such that H becomes C provided f PSF ≥ f spec .

Another important difference between Theorems 1 and 2 concerns the fact that strict positivity of the sample is needed in the latter case. We have some preliminary results showing that this condition could be relaxed, but the maximal number of zero entries allowing a provable super-resolution is currently indeterminate.

IV. CONCLUSION

This paper provides a mathematical proof that the superresolution capacity of random illumination microscopy still holds when only the statistical variance of the recorded lowresolution speckled images is considered instead of the full covariance. Such a theoretical result meets practical evidences recently obtained concerning 2D variance-based imaging applied to various types of biological samples [START_REF] Mangeat | Super-resolved live-cell imaging using Random Illumination Microscopy[END_REF].

As an important final remark, we note that a formal extension of our new identification result to the three-dimensional (3D) case is straightforward, with the benefit of an axial superresolution effect, on top of the lateral one obtained in 2D. Real-world applications would consist in recording multiple speckled images of the sample at different depths. This can be done in a sequential manner, by translating the sample through the focal plane, or simultaneously using a multifocus system [START_REF] Abrahamsson | Fast multicolor 3D imaging using aberration-corrected multifocus microscopy[END_REF]).

  the matrices G and B xmin , which are the Hadamard product between two nonnegative definite matrices, are also nonnegative definite according to the Schur product theorem [11, Theorem 5.2.1]. Therefore, Ker(B x ) = Ker(G) ∩ Ker(B xmin ) ⊂ Ker(G).


Tracey L Hammer
email: tracey.hammer@iphc.cnrs.fr

Pierre Bize

Claire Saraux

Benoit Gineste

Jean-Patrice Robin

René Groscolas

Vincent A Viblanc

Repeatability of alert and flight initiation distance in king penguins: effects of colony, approach speed and weather

Keywords: Aptenodytes patagonicus, personality, human disturbance, optimal escape decisions, predation risk

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Understanding how wild animals react to threats -especially predators -and the economics underlying (optimal) escape decisions, is a central topic in behavioral ecology that has been widely studied by evaluating Alert (AD) and Flight Initiation (FID) Distances [START_REF] Tätte | Towards an integrated view of escape decisions in birds: relation between flight initiation distance and distance fled[END_REF][START_REF] Blumstein | What chasing birds can teach us about predation risk effects: past insights and future directions[END_REF]reviewed in Frid & Dill, 2002). AD and FID can be defined as the distances at which a focal animal interrupts its normal behaviour to become alert (AD) or begin to flee (FID) from an approaching predator. AD provides us with a surrogate of the amount of time, and possibly energy, invested by the focal individual into surveying its surrounding; i.e., the degree of vigilance [START_REF] Fernández-Juricic | Do variations in scanning behavior affect tolerance to human disturbance[END_REF][START_REF] Beauchamp | Vigilance, alarm calling, pursuit deterrence, and predator inspection[END_REF][START_REF] Uchida | Decreased vigilance or habituation to humans? Mechanisms on increased boldness in urban animals[END_REF]; but see [START_REF] Tätte | Antipredator function of vigilance re-examined: vigilant birds delay escape[END_REF]. Meanwhile, variation in FID informs us on the perceived predation-risk of the focal individual [START_REF] Blumstein | Developing an evolutionary ecology of fear: How life history and natural history traits affect disturbance tolerance in birds[END_REF][START_REF] Blumstein | What chasing birds can teach us about predation risk effects: past insights and future directions[END_REF][START_REF] Møller | Risk taking by singing males[END_REF].

In practice, the decisions that prey undertake when approached by a predator (AD and FID) can be simulated by performing non-lethal approaches by human experimenters [START_REF] Frid | Human-caused disturbance stimuli as a form of predation risk[END_REF]Beale and Monaghan, 2004a). Animals are expected to respond in much the same way to human approach stimuli as they would to actual predators since (1) both divert time and energy that could be otherwise invested in fitness enhancing activities; and (2) animals should be selected to overestimate rather than underestimate risk due to the cost of miscalculation, i.e., injury or death [START_REF] Frid | Human-caused disturbance stimuli as a form of predation risk[END_REF]. While AD can be hard to observe in some species or contexts, FID has the advantage of being easily measured and quantified [START_REF] Tarlow | Evaluating methods to quantify anthropogenic stressors on wild animals[END_REF]. Both can be standardized within and across studies [START_REF] Blumstein | Developing an evolutionary ecology of fear: How life history and natural history traits affect disturbance tolerance in birds[END_REF][START_REF] Møller | Risk taking by singing males[END_REF], and are species-specific [START_REF] Blumstein | Testing a key assumption of wildlife buffer zones: Is flight initiation distance a species-specific trait?[END_REF][START_REF] Møller | Flight distance of urban birds, predation, and selection for urban life[END_REF]Carette and Tella, 2011;[START_REF] Piratelli | Factors affecting escape distance in birds[END_REF]. As a consequence, FID in particular and AD when available, have become popular measures in conservation biology used in establishing set-back distances and buffer zones to minimize stress-related disturbances on wildlife [START_REF] Rodgers | Buffer-Zone Distances to Protect Foraging and Loafing Waterbirds from Disturbance by Personal Watercraft and Outboard-Powered Boats[END_REF][START_REF] Fernández-Juricic | Sensitivity of wildlife to spatial patterns of recreationist behavior: a critical assessment of minimum approaching distances and buffer areas for grassland birds[END_REF].

Although AD and FID are species-specific, there is fast accumulating evidence that FID (and to a lesser extent AD) can vary among populations of the same species and between individuals within the same populations [START_REF] Edwards | Individual traits influence vigilance in wild female eastern grey kangaroos[END_REF]. For instance, FID is often shorter in urban versus rural populations [START_REF] Piratelli | Factors affecting escape distance in birds[END_REF]Carette and Tella, 2017), suggesting either that these animals have habituated (or developed tolerance) to human disturbance (Burger andGochfeld, 1981, 1990;[START_REF] Walker | Habituation of adult Magellanic Penguins to human visitation as expressed through behavior and corticosterone secretion[END_REF], or that less tolerant individuals have migrated away from human presence [START_REF] Ellenberg | Habituation potential of yellow-eyed penguins depends on sex, character and previous experience with humans[END_REF]Carette andTella, 2010, 2011). Further, upon repeated approaches, FID has been shown either to decrease (habituation: [START_REF] Carter | Boldness, trappability and sampling bias in wild lizards[END_REF][START_REF] Petelle | Development of boldness and docility in yellow-bellied marmots[END_REF][START_REF] Arroyo | Individual variation in behavioural responsiveness to humans leads to differences in breeding success and long-term population phenotypic changes[END_REF], or increase (sensitization: [START_REF] Dill | The escape response of the zebra danio (Brachydanio rerio) II. The effect of experience[END_REF][START_REF] Wheeler | The effect of frequency and nature of pedestrian approaches on the behaviour of wandering albatrosses at sub-Antarctic Marion Island[END_REF], demonstrating within-individual plasticity. FID can display consistent inter-individual (repeatable) variation over time (Carette and Tella, 2010;[START_REF] Carter | Boldness, trappability and sampling bias in wild lizards[END_REF][START_REF] Van Dongen | Variation at the DRD4 locus is associated with wariness and local site selection in urban black swans[END_REF]. The same cannot be said of AD, which remains to be explored; however, vigilance behavior has often been found to be mildly repeatable [START_REF] Couchoux | Personality constraints versus flexible antipredation behaviors: how important is boldness in risk management of redshanks (Tringa totanus) foraging in a natural system[END_REF][START_REF] Roche | Among-individual variation in vigilance at the nest in colonial Cliff Swallows[END_REF]. Repeatable behavioral traits measured over time are a prerequisite for the characterization of individual personality or temperament traits [START_REF] Dingemanse | Criteria for acceptable studies of animal personality and behavioural syndromes[END_REF], and might suggest genetic or early environmental constraints shaping individual risk-taking behavior. In fact, due to its repeatability, FID is frequently used as a metric to explore boldness [START_REF] Atwell | Boldness behavior and stress physiology in a novel urban environment suggest rapid correlated evolutionary adaptation[END_REF][START_REF] Petelle | Development of boldness and docility in yellow-bellied marmots[END_REF][START_REF] Highcock | Intraindividual variability of boldness is repeatable across contexts in a wild lizard[END_REF][START_REF] Young | Evaluating behavioral syndromes in coyotes (Canis latrans)[END_REF], one of the five main personality traits defined by [START_REF] Réale | Integrating animal temperament within ecology and evolution[END_REF], which is associated with riskassessment and risk-taking, particularly in the context of predation and disturbance.

AD and FID should be strongly selected in prey species, in a way that balances the survival benefits of escaping approaching predators with the costs of abandonning other fitness-enhancing activities such as reproduction [START_REF] Ydenberg | The Economics of Fleeing from Predators[END_REF]. Consequently FID is known to vary with the perceived risk of predator approaches [START_REF] Frid | Human-caused disturbance stimuli as a form of predation risk[END_REF]reviewed in Stankowich and Blumstein, 2005) including the size or number of predators (Beale and Monaghan, 2004a;[START_REF] Geist | Refeeding signal in fasting-incubating king penguins: changes in behavior and egg temperature[END_REF], directness of approach [START_REF] Smith-Castro | Behavioral responses of nesting birds to human disturbance along recreational trails[END_REF][START_REF] Sreekar | Influence of gaze and directness of approach on the escape responses of the Indian rock lizard, Psammophilus dorsalis (Gray, 1831)[END_REF]but see Fernández-Juricic et al., 2005), speed of approach [START_REF] Bateman | Who are you looking at? Hadeda ibises use direction of gaze, head orientation and approach speed in their risk assessment of a potential predator[END_REF][START_REF] Samia | Fifty years of chasing lizards: new insights advance optimal escape theory[END_REF]; but see [START_REF] Lafferty | Disturbance to wintering western snowy plovers[END_REF], and predator intent (i.e., predator suddenly turning towards the prey or maintaining a purposeful gaze; [START_REF] Cooper | Risk factors affecting escape behavior by the desert iguana, Dipsosaurus dorsalis: speed and directness of predator approach, degree of cover, direction of turning by a predator, and temperature[END_REF][START_REF] Bateman | Who are you looking at? Hadeda ibises use direction of gaze, head orientation and approach speed in their risk assessment of a potential predator[END_REF][START_REF] Sreekar | Influence of gaze and directness of approach on the escape responses of the Indian rock lizard, Psammophilus dorsalis (Gray, 1831)[END_REF]. FID has also been shown to vary with the time of day (Patelle et al., 2013;[START_REF] Piratelli | Factors affecting escape distance in birds[END_REF][START_REF] Ferguson | Look at the time: diel variation in the flight initiation distance of a nectarivorous bird[END_REF], can be reduced when prey have low energy reserves [START_REF] Beale | Behavioural responses to human disturbance: A matter of choice?[END_REF][START_REF] Piratelli | Factors affecting escape distance in birds[END_REF], are in a large group (dilution effect; [START_REF] Ydenberg | The Economics of Fleeing from Predators[END_REF]Burger andGochfeld, 1991, Santoyo-Brito et al., 2020), or are in close proximity to refuge [START_REF] Cooper | Universal optimization of flight initiation distance and habitat-driven variation in escape tactics in a Namibian lizard assemblage[END_REF]. AD has not been explored to the same extent as FID, but evidence suggests that vigilance behaviour is also modified by time of day [START_REF] Edwards | Individual traits influence vigilance in wild female eastern grey kangaroos[END_REF], weather conditions [START_REF] Couchoux | Personality constraints versus flexible antipredation behaviors: how important is boldness in risk management of redshanks (Tringa totanus) foraging in a natural system[END_REF], conspecific interactions [START_REF] Hess | Territorial aggression reduces vigilance but increases aggression towards predators in a cooperatively breeding fish[END_REF], sex and reproductive status [START_REF] Burger | Vigilance in African mammals: differences among mothers, other females, and males[END_REF], and group size [START_REF] Díaz | Effects of group size and distance to protective cover on the vigilance behaviour of black-billed magpies Pica pica[END_REF][START_REF] Carter | Individual variation in the relationship between vigilance and group size in eastern grey kangaroos[END_REF][START_REF] Boujja-Miljour | Individual vigilance profiles in flocks of House Sparrows (Passer domesticus)[END_REF].

The cost-benefit fitness trade-off of fleeing a tentative predator should be particularly strong for ground-laying birds tied to vulnerable nesting sites, such as penguins. Penguins commit a high amount of time and energy to reproduction (obligate bi-parental care, long-term fasting, prolonged breeding cycle and chick development; [START_REF] Williams | The penguins[END_REF], and face a strong fitness trade-off between the survival costs of defending their brood against predators (i.e., injuries and potential death for the adult) and the reproductive costs of abandoning their current reproduction but surviving to breed another year [START_REF] Montgomerie | Risks and rewards of nest defence by parent birds[END_REF][START_REF] Frid | Human-caused disturbance stimuli as a form of predation risk[END_REF][START_REF] Dowling | Should I stay, or should I go: modeling optimal flight initiation distance in nesting birds[END_REF]. Accordingly, penguins are usually highly territorial and defensive of their brood [START_REF] Viñuela | Nest defence of nesting chinstrap penguins (Pygoscelis antarctica) against intruders[END_REF][START_REF] Amat | Nest defence by chinstrap penguins Pygoscelis antarctica in relation to offspring number and age[END_REF][START_REF] Côté | Aggressiveness in king penguins in relation to reproductive status and territory location[END_REF], though within species there is clear variation on the degree of territoriality and aggression depending on brood value [START_REF] Amat | Nest defence by chinstrap penguins Pygoscelis antarctica in relation to offspring number and age[END_REF][START_REF] Côté | Aggressiveness in king penguins in relation to reproductive status and territory location[END_REF], the type of threat considered [START_REF] Lee | Behavioral responses of chinstrap and gentoo penguins to a stuffed skua and human nest intruders[END_REF], and bird personality [START_REF] Traisnel | Does it always pay to defend one's nest? A case study in African penguin[END_REF]. Surprisingly, few studies have investigated how variable AD and FID to approaching predators are in penguins, nor the factors affecting those traits, despite their importance in shaping breeding decisions, and despite the fact that several studies have documented marked effects of disturbance (e.g. ecotourism) on penguin behavior (vigilance and locomotory behavior, time budgets; [START_REF] Holmes | Testing the minimum approach distance guidelines for incubating royal penguins Eudyptes schlegeli[END_REF][START_REF] Holmes | Behaviour and breeding success of gentoo penguins Pygoscelis papua in areas of low and high human activity[END_REF][START_REF] Burger | Responses of Emperor Penguins (Aptenodytes forsteri) to encounters with ecotourists while commuting to and from their breeding colony[END_REF], physiological stress [START_REF] Ellenberg | Physiological and reproductive consequences of human disturbance in Humboldt penguins: the need for species-specific visitor management[END_REF][START_REF] Ellenberg | Previous experiences with humans affect responses of Snares Penguins to experimental disturbance[END_REF][START_REF] Ellenberg | Heart rate responses provide an objective evaluation of human disturbance stimuli in breeding birds[END_REF][START_REF] Viblanc | Coping with continuous human disturbance in the wild: Insights from penguin heart rate response to various stressors[END_REF][START_REF] Carroll | Prior exposure to capture heightens the corticosterone and behavioural responses of little penguins (Eudyptula minor) to acute stress[END_REF], or reproduction [START_REF] Giese | Effects of human activity on Adelie penguin Pygoscelis adeliae breeding success[END_REF][START_REF] Mcclung | Nature-based tourism impacts on yellow-eyed penguins Megadyptes antipodes: does unregulated visitor access affect fledging weight and juvenile survival[END_REF][START_REF] Ellenberg | Physiological and reproductive consequences of human disturbance in Humboldt penguins: the need for species-specific visitor management[END_REF]reviewed in Bateman and Fleming, 2017).

Here, we investigated the variability of both AD and FID in breeding king penguins (Aptenodytes patagonicus). King penguins are large, ground-laying, flightless birds that form extensive colonies on the subantarctic shorelines. Breeding pairs incubate their single egg or young chick on top of their feet [START_REF] Stonehouse | The king penguin Aptenodytes patagonica of South Georgia[END_REF], therefore limiting their mobility. They are subject to on-land predation mostly by giant petrels, Macronectes halli and Macronectes giganteus, and brown skuas, Catharacta lonnbergi [START_REF] Hunter | The impact of avian predator scavengers on king penguin Aptenodytes patagonicus chicks at Marion Island[END_REF][START_REF] Descamps | Impact of predation on king penguin Aptenodytes patagonicus in Crozet Archipelago[END_REF]. Giant petrels and skuas especially target eggs and chicks, but petrels are also known to prey on injured adults [START_REF] Hunter | The impact of avian predator scavengers on king penguin Aptenodytes patagonicus chicks at Marion Island[END_REF]. These predators will harass incubating and brooding adults sometimes causing them to flee and abandon their eggs. Breeding adults have three choices: first to stay and fight, risking potentially fatal injuries; second to flee slowly cumbersomely with the egg on top of their feet clustering closer to neighbouring breeders; or finally, to flee entirely, guaranteeing survival but abandoning their current reproduction.

We calculated individual repeatabilities for AD and FID which were measured several times on incubating adults, and assessed the potential influences of approach speed, weather conditions, and time of day on AD and FID as these may impact the levels of vigilance and responsiveness to a threat. Specifically, we expected AD and FID to vary in a quadratic function, increasing at dawn and dusk, and coinciding with highest predation risk for chicks (giant petrel activity is highest at early and late hours of the night; Le [START_REF] Bohec | Nocturnal predation of king penguins by giant petrels on the Crozet Islands[END_REF][START_REF] Descamps | Impact of predation on king penguin Aptenodytes patagonicus in Crozet Archipelago[END_REF]. We further tested whether individuals sensitized or habituated to repeated approaches by a human experimenter by examining bird responses in two different colonies; one close to human settlements and one relatively unexposed to human disturbance. King penguins have been shown

to express significantly lower heart rate stress responses to human approaches in disturbed areas vs. undisturbed colony areas [START_REF] Viblanc | Coping with continuous human disturbance in the wild: Insights from penguin heart rate response to various stressors[END_REF]. Thus, we expected individuals measured in the colony close to human settlements to show habituation to approaching experimenters (decreased AD and FID compared to the undisturbed colony).

METHODS

Study sites

This study was conducted in mid-to-late January during the Austral summer of 2010-2011. Birds were selected from two colonies of king penguins located on Possession Island in the Crozet Archipelago, namely the colonies "La Baie du Marin" (BDM, 46°25'S -51°52'E) and "Jardin Japonais" (JJ, 46°21'S -51°43'E). BDM is home to ca. 22 000 breeding pairs [START_REF] Barbraud | Population trends of penguins in the French Southern Territories[END_REF] and is located on the east side of Possession Island in close proximity to a permanently inhabited research station built in 1961. This colony has been exposed throughout the year for the past 50 years to the daily presence of scientists and non-scientists in or close to the colony [START_REF] Viblanc | Coping with continuous human disturbance in the wild: Insights from penguin heart rate response to various stressors[END_REF]. During this time, birds in BDM have been regularly exposed to humans including tourist visits, censuses, population counts, and systematic monitoring.

Meanwhile, JJ is home to ca. 39 000 breeding pairs [START_REF] Barbraud | Population trends of penguins in the French Southern Territories[END_REF] and is located on the north side of the island some 13 km from BDM. JJ is a relatively undisturbed colony, far from the research station and visited by scientists only a few times every year for population count and census information.

Approach protocol

We repeatedly approached a total of 47 incubating birds in the two colonies (23 birds from JJ and 24 birds in BDM). Each individual was approached once per day over three consecutive days between the hours of 8:00 and 19:00 (from Jan. 11 -13 in JJ, and from Jan. 30 -Feb. 1 in BDM). It was not possible to find all birds on the subsequent days and so two birds in BDM were only approached once, and one bird each in JJ and BDM were only approached twice.

Following egg-laying, king penguin partners alternate incubation duties, allowing their partner to forage at sea while they fast on land [START_REF] Stonehouse | The king penguin Aptenodytes patagonica of South Georgia[END_REF]. The male takes the first incubation shift, and the egg hatches some 53 days later, usually during shift four when the female has possession of the egg [START_REF] Weimerskirch | The breeding biology and population dynamics of King Penguins Aptenodytes patagonica on the Crozet Islands[END_REF].

Following the STRANGE guidelines [START_REF] Webster | How STRANGE are your study animals[END_REF], we provide hereafter details on how incubating birds were selected and highlight potential biases related to the selection of our study subjects. Birds were selected haphazardly while incubating their eggs, and therefore we had no individual information on their sex, age, incubation shift, or previous experience with humans. Chosen individuals visually appeared in good physical condition, based on their plumage (shiny) and morphological (fat) appearance, and thus had not been fasting for extended periods of time. Individuals were selected at distance, and not after being approached or captured. Therefore, we expected no strong initial sampling bias in relation to how individuals were responding to human approaches (but see discussion).

Selected individuals were marked from a distance (roughly 1 m) at the end of the first approach using a dot of non-permanent pressurized spray animal dye (Porcimark®, Kruuse, Lageskov; Denmark) on the belly for identification during subsequent approaches. All approaches were performed by the same observer (BG) dressed in the same clothing. Individuals were only approached if they were resting upon arrival of the observer (i.e., not engaged in aggressive, preening, or sleeping behaviours). The approach started after having observed the bird resting for at least one full minute before approaching it. During this time, the experimenter hid out of line of sight. Each approach had a set starting distance of 18 m, as measured with a laser telemeter (Leica DISTO TM D5 Lasermeter, Leica Geosystems AG, Hexagon, Sweden), which we standardized due to the known influence of starting distance on FID [START_REF] Blumstein | Flight-initiation distance in birds is dependent on intruder starting distance[END_REF][START_REF] Blumstein | Flush early and avoid the rush: A general rule of antipredator behavior[END_REF][START_REF] Dumont | Flight initiation distance and starting distance: biological effect or mathematical artefact[END_REF]. We chose a starting distance of 18 m based on preliminary observations of 59 king penguins, including courting (paired) and incubating birds (a sample representative of the various life-history stages in the colony, excluding moulting and chick-brooding birds), that showed the maximal distance at which birds exhibited signs of vigilance towards an experimenter was 12.45 m and the minimal distance was 3.03 m (mean  SD = 6.85  1.87 m). We used a starting distance 1.5 times greater than the maximal detection distance recorded in the preliminary study to ensure starting distance far exceeded maximum alert distance (see also [START_REF] Fleming | Scavenging opportunities modulate escape responses over a small geographic scale[END_REF].

The approaching observer followed a direct trajectory toward the focal individual, in plain line of sight, always starting from outside the colony. The experimenter walked until the first sign of alert was detected (the bird tilting its head or stretching its neck in the direction of the experimenter). At this distance, termed the Alert Distance (AD), the experimenter took a standardized one-minute pause to record AD and time. The time from the start of the approach until the bird became vigilant was recorded with a stopwatch and the remaining distance to the selected bird measured with a laser telemeter (closest cm). The approach was then resumed until the bird showed the first signs of fleeing (slowly walking away with its egg resting on its feet)termed Flight Initiation Distance, FID. Some birds never showed signs of flight while being approached, right up until close (FID = 0 m) (see also [START_REF] Bateman | Who are you looking at? Hadeda ibises use direction of gaze, head orientation and approach speed in their risk assessment of a potential predator[END_REF], for similar results in ibises). FID had therefore a zero-inflated distribution (see supporting information S1), suggesting this measure reflected two different processes: i) the decision to flee or not (0/1); and ii) the distance at which flight (escape) should occur if birds decide to flee. Hereafter, we analysed these two processes separately. We calculated the speed of approach (m/s) prior to the occurrence of AD and FID as the distance walked (m) divided by the duration of approach (s).

The mean speed  SE of approach prior to AD was 0.61  0.09 m/s (range = 0.44 -0.86 m/sec) and the mean  SE speed of approach between AD and FID was 0.57  0.10 m/s (range = 0.35 -0.90 m/s). Walking speed varied slightly due to topography, entering the colony, and breeder density.

At the start of each approach, we recorded air temperature to the nearest 1°C, and we scored wind speed, solar levels, and rain on a scale from 0 to 2, with half levels (i.e., 0.5) being allowed. A value of 0 indicated no wind or rain, or full cloud cover (no sun). A value of 2 indicated heavy wind or rain or full sun. Mean temperature was 10 °C (range = 7 -13 °C). As air temperature, wind speed, rain, and solar levels were naturally correlated, we used a Principal Components Analysis (PCA) to summarize all weather variables (package "FactoMineR", [START_REF] Lê | FactoMineR: An R package for multivariate analysis[END_REF]. This approach had the advantage of capturing climatic variation on a continuous scale through two independent and orthogonal axes, and avoided strong collinearity (VIFs >30) issues if 'raw' meteorological variables are used in the analyses. We kept the first two principal component (PC1 and PC2) which together explained over 84% of the variation in climate data.

Increasing PC1 (64.86% of variation) values were mainly associated with higher sun scores (correlation = +0.939) and higher temperature (+0.918), and to a lesser extent higher wind scores (+0.639), and lower rain scores (-0.686). In contrast, increasing PC2 (19.77% of variation) values were mainly associated with higher wind scores (+0.702), higher rain scores (+0.543), but not with sun scores (-0.010) or temperature (-0.061). Thus, increasing PC1 values described sunnier, warmer days while increasing PC2 values described windier, rainier days. On average, the climate conditions varied during our three approaches in both colonies (see supporting information S2), highlighting the need to control for climatic variation in further analyses.

Statistical analyses

All statistical analyses were performed in R 3.6.1. (R Development Core Team, 2020).

Results are presented as means  SE. We investigated the sources of variation in AD (gaussian distribution), the decision to flee or not (FID: 0/1, binomial distribution), and the distance at which flight was taken for birds that did decide to flee (FID > 0; gaussian distribution) using linear mixed models (LMM) and generalized linear mixed models (GLMM) with the appropriate error distribution. In all the models, we entered individual ID as a random factor to control for repeated measures, and we included as fixed effects the time of day, weather (PC1 and PC2), approach speed, approach order (three levels: first, second, or third approach), and the colony (two levels: BDM vs JJ). To test whether birds differed in their behavior at different times of day, and whether habituation or sensitisation to human approaches occurred differently between colonies, we also included second order interaction colony x approach order and time of day x time of day (viz., time 2 ) in our starting models. Second order interactions were dropped from the final model if not significant. Models were run using the lmer and glmer functions in the package "lme4" [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF]. The significance of the fixed effects was tested with the anova function (type 3) from the package "lmerTest" [START_REF] Kuznetsova | lmerTest Package: Tests in Linear Mixed Effects Models[END_REF] using F tests with Satterthwaite estimation for the denominator degree of freedom for models with a gaussian distribution. Pseudo-R 2 for the models were calculated using methods developed in [START_REF] Nakagawa | A general and simple method for obtaining R2 from generalized linear mixed-effects models[END_REF]. Prior to analysis, time of approach was converted to decimal time, and non-zero FIDs were log-transformed (natural log) to normalize the distribution of the residuals. Independent variables were checked for collinearity using Variance Inflation Factors (VIF) [START_REF] Zuur | A protocol for data exploration to avoid common statistical problems[END_REF]. A few VIFs were above 3 (see results), but those were considered acceptable as they represented different categorical levels of the same factor (e.g. approach order). All variables were scaled and centered prior to inclusion in the models to compare effect sizes [START_REF] Schielzeth | Simple means to improve the interpretability of regression coefficients[END_REF]. Where appropriate, we insured model residuals were normally distributed by visual inspection of density distributions, Q-Q plots, cumulative distribution functions, and P-P plots using the "fitdistrplus" package in R [START_REF] Delignette-Muller | fitdistrplus: An R package for fitting distributions[END_REF].

Repeatabilities and their confidence intervals were calculated using the functions rpt for AD, and FID and rptBinary for the decision to flee or not, from the "rptR" package in R [START_REF] Stoffel | rptr: Repeatability estimation and variance decomposition by generalized linear mixed-effects models[END_REF]. Repeatability was calculated as the ratio of among-individual variance in AD or FID (σ 2 α ) over total phenotypic variance (equal to the sum of among-individual variance and withinindividual variance, σ 2 ε ), so r = σ 2 α / σ 2 α + σ 2 ε [START_REF] Nakagawa | Repeatability for Gaussian and non-Gaussian data: A practical guide for biologists[END_REF]. We first calculated agreement repeatability, also called uncorrected repeatability, r, which is simply based on the among-and within-individual variance in AD or FID. Afterwards, significant effects from the above models, which influenced the expression of AD and FID, were controlled for when calculating adjusted repeatability r adj , (also called corrected repeatability) [START_REF] Wilson | How should we interpret estimates of individual repeatability?[END_REF].

Ethics statement

No animal was caught or handled over the course of this study. The research was approved by the Ethical Committee of the Institut Polaire Français -Paul-Emile Victor.

Authorization to enter the colony and approach birds was obtained from Terres Australes et Antarctiques Françaises. The observations complied with the current laws of France. No eggs or chicks were abandoned during the course of this study.

RESULTS

Alert Distance (AD)

On average, focal individuals became alert when the experimenter came to a distance of 6.94  0.18 m; (range = 1.89 -13.14 m) (Fig. 1A and1B). The interaction between approach x colony and time of day 2 did not have a significant effect influencing AD (F 2,111.0 =0.22, P=0.802

and F 1,90.9 =0.02, P=0.896, respectively), were sequentially removed from the model in that order (least significant term removed first). The final model with time of day, weather PC1, weather PC2, speed of approach prior to AD, approach order and colony, as fixed effects explained 13% (marginal R 2 ) of the total variation, and including individual as a random effect explained 22% (conditional R 2 ) of the total variation in AD (LMM, n=133 observations, N=47 individuals, 1.63 < VIFs < 3.68, among-individual 2 = 0.37; residual 2 = 3.63). We found no evidence that AD was significantly affected by the time of day (F Although some individuals appeared to be repeatable, many others displayed large variability in their AD (Fig. 1A and1B). Post-hoc power analyses (see Online Supplementary Material OSM 3) revealed that significant repeatability (power 0.8) for AD may be achieved for a sample size of 6 approaches on 47 birdsor 3 approaches on 140 birds.

Flight Initiation

Out of the 47 selected individuals, 41 (87.2%) decided to flee (i.e., move away with their egg on their feet) during at least one of their approaches (20 birds in JJ, and 21 birds in BDM): 23 individuals always fled, 12 individuals fled twice in three approaches, 6 fled once in three approaches, and 6 did not flee at all. This corresponded to 42 approaches out of a total of 135 (31%) that resulted in no FID. The FID of the individuals that decided to flee at least once was 2.83  0.16 m (range = 0.68 -8.58 m) (Fig. 1C and1D).

Time of day 2 and the interaction between approach x colony did not significantly influence the odds of fleeing (1) or not (0) during the approach (GLMMs; binomial, 2 =2.35, P=0.125 and 2 =4.97, P=0.083), and were sequentially removed from the model in that order (least significant term removed first). The final model with time of day, speed of approach between AD and FID, weather PC1 and weather PC2 explained 23% (marginal R 2 ) of the total variation, and including individual as a random effect explained 73% (conditional R 2 ) of the total variation in the odds of fleeing (GLMM, n=133 observations, N=47 individuals, 1.18 < VIFs < 5.36, among-individual 2 = 3.29; residual 2 = 6.11). The odds of fleeing were not significantly influenced by weather PC1 ( 2 =0.24, P=0.626), time of day ( 2 =1.19, P=0.275), speed of approach ( 2 =1.86, P=0.172), approach order ( 2 =4.98, P=0.083) or colony ( 2 =3.09, P=0.079).

(Fig. 3A). However, the probability of birds to flee increased significantly with increasing weather PC2 ( 2 =4.51, P=0.034), birds being more likely to flee from the approaching experimenter in windy and rainy conditions (Fig. 3A and3B). The decision to flee was significantly repeatable before (original-scale: r=0.504; CI 95 = [0.084, 1.724]; P<0.001) adjusting for weather, and increased slightly (r=0.573; CI 95 = [0.110, 1.686]; P<0.001) after accounting for the significant effect of weather PC2.

For those birds that decided to flee, time of day 2 and the interaction between approach x colony did not significantly influence FID during the approach (LMMs; F 1,66.5 =0.15, P=0.704 and F 2,67.8 =0.48, P=0.619, respectively), and were sequentially removed from the model in that order (least significant term removed first). The final model with time of day, speed of approach between AD and FID, weather PC1 and weather PC2 explained 37% (marginal R 2 ) of the total variation, and including individual as a random effect explained 62% (conditional R 2 ) of the total variation in FID (LMM, n=91 observations, N=41 individuals, 1.19 < VIFs < 5.56, amongindividual 2 = 0.13; residual 2 = 0.09). We found no evidence that FID was significantly affected by the time of day (F 4A and4B)

and decreased significantly with increasing weather PC2 (F 1,60.6 =5.17, P=0.027, Fig. 4A and4C).

In other words, FID decreased in windy and rainy conditions. Agreement FID repeatability was low and not significant (r=0.102; CI 95 = [0.00, 0.339]; P=0.248), but increased significantly when approach speed and weather PC2 were adjusted for in the model (r adj =0.258; CI 95 =[0.010, 0.511];

P<0.022).

DISCUSSION

Our study showed that, in king penguins, both the decision to flee and FID were significantly and moderately repeatable, whereas AD was not. Climatic conditions had marked effects on AD, FID and the probability for birds to flee, affecting repeatability estimates, and highlighting the need to consider external sources of variation in refining such estimates in the wild (discussed below).

Between-and within-individual variation in flight initiation

Incubating king penguins showed significant (adjusted) repeatability both in the decision to flee from an approaching observer (0.57), and in the distance at which they initiated flight (0.26). In both cases, it is important to note that repeatability values increased when accounting for weather effects on behavior, which is not surprising since birds experienced different local climate conditions when they were approached. Notwithstanding, this underlines the importance of considering heterogeneity in individual habitats and timing of measures when establishing repeatability estimates from behavioral measures in the wild. Our repeatability values are comparable, albeit slightly lower, to those reported on FID in other studies: black swans, Cygnus atratus (r=0. 61, van Dongen et al., 2015), juvenile yellow-bellied marmots, Marmota flaviventris (r=0. 40, Petelle et al., 2013), Namibian rock agama, Agama planiceps (r=0.71, [START_REF] Carter | Boldness, trappability and sampling bias in wild lizards[END_REF], and burrowing owl, Athene cunicularia (r=0.88, [START_REF] Carrete | Individual consistency in flight initiation distances in burrowing owls: a new hypothesis on disturbance-induced habitat selection[END_REF], and generally moderate as would be expected for behavioral traits [START_REF] Bell | The repeatability of behaviour: a metaanalysis[END_REF]. The repeatability of both the decision to flee, and the distance at which flight was initiated, suggest that these behavioural traits could constitute good candidates for personality traits in breeding king penguins. This remains to be further explored however, since our power to detect behavioral plasticity in AD and FID occurring over longer periods was limited by the fact that birds in our study were only measured over a short period of time (3 consecutive days), and were not previously known individuals. Separating the repeatable and plastic aspects of alert and flight behavior to approaching predators in king penguins would benefit from further studies on individually monitored population where simple measures such as AD and FID are incorporated into monitoring schemes allowing to test for repeatability and plasticity over the lifetime of individuals [START_REF] Dingemanse | Behavioural reaction norms: animal personality meets individual plasticity[END_REF][START_REF] Dingemanse | Criteria for acceptable studies of animal personality and behavioural syndromes[END_REF]. Logistically, this would require permanent marking of individuals in order to follow them through a longer period of time and through different contexts. In addition, FID (and AD, see below) are likely to vary according to factors such as individual age, sex, stress responsiveness, or body condition (e.g. Seltman et al., 2012;[START_REF] Kalb | Flight initiation distance and escape behavior in the black redstart (Phoenicurus ochruros)[END_REF]. Testing for such factors in future studies should allow refining repeatability estimates, with repeatability increasing as more residual variation is accounted.

Repeatability estimates of individual propensity to flee and FID increased as extrinsic factors were accounted for in the models. This is not surprising, but highlights contrasting climate effects acting both on the propensity to flee (1/0) and on the distance at which birds initiated flight. Interestingly, weather PC2 (wind and rain) had opposite effects on these behavioral traits.

As conditions were windier and rainier, birds were more likely to flee, but those that fled had lower FID. This suggests that birds that fled waited until the last moment before they did so, which could be explained by the fact that they were less likely to detect the incoming threat in windy and rainy conditions. Wind speed has been shown to have contrasting effects on animal vigilance and escape behavior, from no effect to marked effects depending on the species and taxa (e.g., no effect: birds; [START_REF] Clucas | Attitudes and actions toward birds in urban areas: Human cultural differences influence bird behavior[END_REF][START_REF] Nordell | Flight initiation by Ferruginous Hawks depends on disturbance type, experience, and the anthropogenic landscape[END_REF][START_REF] Petrelli | First to flush: The effects of ambient noise on songbird flight initiation distances and implications for human experiences with nature[END_REF]reptiles;[START_REF] Mcgowan | The effect of human presence and human activity on risk assessment and flight initiation distance in skinks[END_REF]wind effects: birds;[START_REF] Reynolds | Defining separation zones for coastal birds at a wetland of global importance[END_REF]mammals;[START_REF] Wolf | Minimizing disturbance to wildlife by tourists approaching on foot or in a car: A study of kangaroos in the Australian rangelands[END_REF]. Increased wind speed has been shown in 17 of 18 studies to decrease an animal's ability to detect an approaching predator by masking sounds, smells and visual cues [START_REF] Cherry | Effects of wind on predator-prey interactions[END_REF]. Wind may also be a source of distraction [START_REF] Chan | Anthropogenic noise affects risk assessment and attention: The distracted prey hypothesis[END_REF][START_REF] Tätte | Antipredator function of vigilance re-examined: vigilant birds delay escape[END_REF], leading to delayed detection of approaching predators. It has been suggested that the magnitude of FID responses should decrease under harsh weather conditions, as the energy cost of fleeing increases [START_REF] Collop | Variability in the area, energy and time costs of wintering waders responding to disturbance[END_REF]. For endotherms wind chill increases thermoregulatory costs, and a trade-off might exist between investing energy into flight and that into thermoregulation [START_REF] Collop | Variability in the area, energy and time costs of wintering waders responding to disturbance[END_REF], but see also [START_REF] Reynolds | Defining separation zones for coastal birds at a wetland of global importance[END_REF]. Because penguins rely essentially on fat stores during incubation on-land [START_REF] Groscolas | Long-term fasting and re-feeding in penguins[END_REF], and because energy-depleted birds will abandon reproduction (Groscolas et al., 2000[START_REF] Gauthier-Clerc | Statedependent decisions in long-term fasting king penguins, Aptenodytes patagonicus, during courtship and incubation[END_REF], any energy savingshowever smallis critical. Thus, energy savings in harsh climate conditions may contribute in explaining why birds waited for the last moment to flee. FID also increased with increasing approach speed of the experimenter. Faster approach speeds after alert may be interpreted as greater threat by the targeted prey, and thus generating longer FID [START_REF] Stankowich | Fear in animals: A meta-analysis and review of risk assessment[END_REF][START_REF] Cooper | Universal optimization of flight initiation distance and habitat-driven variation in escape tactics in a Namibian lizard assemblage[END_REF][START_REF] Smith-Castro | Behavioral responses of nesting birds to human disturbance along recreational trails[END_REF][START_REF] Bateman | Who are you looking at? Hadeda ibises use direction of gaze, head orientation and approach speed in their risk assessment of a potential predator[END_REF].

It is interesting to note that it was not uncommon for the incubating penguins to stay and defend their eggs aggressively instead of attempting to flee (there was an FID of 0 m in 42 approaches of 135). For these birds either the perceived risk of the approaching threat (a human)

was not high enough to elicit a flight response, or the motivation to breed and defend the territory was stronger than that of attempting to flee. FIDs of 0 m have been observed in other ground laying birds: yellow-eyed penguins Megadyptes antipodes [START_REF] Ellenberg | Elevated hormonal stress response and reduced reproductive output in Yellow-eyed penguins exposed to unregulated tourism[END_REF][START_REF] Ellenberg | Habituation potential of yellow-eyed penguins depends on sex, character and previous experience with humans[END_REF], humboldt penguin Spheniscus humboldti [START_REF] Ellenberg | Physiological and reproductive consequences of human disturbance in Humboldt penguins: the need for species-specific visitor management[END_REF], magellanic penguins Spheniscus magellanicus [START_REF] Fowler | Behavioral and hormonal-responses of Magellanic penguins (Spheniscus magellanicus) to tourism and nest site visitation[END_REF][START_REF] Villanueva | Seasonal variation in the physiological and behavioural responses to tourist visitation in Magellanic penguins[END_REF], and African penguins Spheniscus demersus [START_REF] Pichegru | African Penguin tolerance to humans depends on historical exposure at colony level[END_REF]. King penguins are special in that they incubate their egg on their feet in a specialized brood pouch. Thus, fleeing is at any rate limited, and essentially amounts to clustering close to neighbours in the hope to benefit from confusion, dilution or selfish herd effects. In addition, fleeing may risk damaging or losing the egg, losing the breeding territory, suffering from increased aggression by territorial neighbours [START_REF] Côté | Aggressiveness in king penguins in relation to reproductive status and territory location[END_REF], or disturbing the thermal incubation environment required for chick development and survival. For instance, exposed eggs during transitory breeding abandonment in king penguins have been found to lose heat at a rate of 0.19 °C per minute (Groscolas et al., 2000).

Between-and within-individual variation in AD

In contrast to FID, the repeatability of AD was low (0.10) and not significant, but improved slightly (0.15) and was close to significant (P = 0.062) when accounting for the effects of climate (Weather PC1). As far as we are aware, there is no report of the repeatability of AD in the literature. Rather, researchers have considered vigilance behaviour when aiming to understand how animals respond to threats. More vigilant individuals are expected to detect predators earlier and thus become alert at longer distances [START_REF] Fernández-Juricic | Do variations in scanning behavior affect tolerance to human disturbance[END_REF][START_REF] Beauchamp | Vigilance, alarm calling, pursuit deterrence, and predator inspection[END_REF][START_REF] Uchida | Decreased vigilance or habituation to humans? Mechanisms on increased boldness in urban animals[END_REF]; but see [START_REF] Tätte | Antipredator function of vigilance re-examined: vigilant birds delay escape[END_REF]. Studies that measured repeatability in vigilance behaviours also reported low, but significant, repeatability: eastern grey kangaroos, Macropus giganteus, (r=0.07-0.14, [START_REF] Edwards | Individual traits influence vigilance in wild female eastern grey kangaroos[END_REF]redshanks, Tringa totanus, (r=0.21, Couchoux and Cresswell, 2012); house sparrows, Passer domesticus, (r=0. 13-0.22, Boujja-Miljour et al., 2018); cliff swallows, Petrocheldion pyrrhonota, (r=0.089, [START_REF] Roche | Among-individual variation in vigilance at the nest in colonial Cliff Swallows[END_REF]. As mentioned above, repeatability estimates are likely to increase as some residual variation is accounted for by including potential factors such as age, sex, or condition, that were

unfortunately not available in this study as individuals were not followed or handled. Dingemanse and Dochtermannn (2013) determined that for lower repeatabilities, >4 samples per individual were required if the total number of individuals is <100. Similarly, [START_REF] Wolak | Guidelines for estimating repeatability[END_REF] found fewer samples per individual were required for higher r values (3 samples per individual for an r of 0.8), but for an r of 0.2, the precision of the estimate continues to increase until up to 10 samples per individual. Because of time and field constraints we were only able to repeatedly approach 45 individuals 3 times. Yet, post-hoc power analyses revealed that doubling our sample size to 6 repeated measures per bird would have been sufficient to detect significant repeatability.

At any rate, repeatability was low, indicating that individuals were more flexible in this behavioral trait than in their decision to flee. Similarly, vigilance levels (and presumably AD)

have been found to be highly flexible [START_REF] Couchoux | Personality constraints versus flexible antipredation behaviors: how important is boldness in risk management of redshanks (Tringa totanus) foraging in a natural system[END_REF][START_REF] Edwards | Individual traits influence vigilance in wild female eastern grey kangaroos[END_REF] and sensitive to numerous biological factors such as group position and group size, distance to cover, predation pressure, season, weather, and time of day (reviewed in [START_REF] Elgar | Predator vigilance and group size in mammals and birds: a critical review of the empirical evidence[END_REF]. In our study, AD was significantly lower in warm and sunny conditions, suggesting that birds were less vigilant in good weather conditions.

Colony disturbance, predation pressure and STRANGE animals

We expected AD and FID to vary depending on colony and with changes in predation pressure throughout the day. However, our analyses suggests that neither were major factors influencing escape decisions in the king penguin. First, on-land predation in king penguin colonies is highest at dawn and dusk (Le [START_REF] Bohec | Nocturnal predation of king penguins by giant petrels on the Crozet Islands[END_REF][START_REF] Descamps | Impact of predation on king penguin Aptenodytes patagonicus in Crozet Archipelago[END_REF], whereas most of our measures were done between 8 AM and 6 PM. Extending measurements to early morning and late evening when predators are most active may allow to better capture potential effects of predation pressure on penguin behavior. Second, given that the two colonies surveyed in this study differ markedly in their exposure to human presence throughout the year (BDM is located next to a research station and breeders have seen humans almost every day for the past 50 years, whereas birds in JJ are rarely exposed to human visitors), we had expected birds in the BDM (vs. JJ) colony to habituate to approaching humans. However, the lack of difference in behavioral responses between the colonies is perhaps not so surprising. Previous findings indicate that birds breeding in more disturbed areas of the BDM colony show lower heart rate stress responses to an experimenter approaching to 10 m distance than birds in less disturbed areassuggesting a potential for habituation to the presence of humans in chronically disturbed areas [START_REF] Viblanc | Coping with continuous human disturbance in the wild: Insights from penguin heart rate response to various stressors[END_REF]. Yet, heart rate responses were similar between the disturbed and undisturbed areas when birds were approached up to contact and captured [START_REF] Viblanc | Coping with continuous human disturbance in the wild: Insights from penguin heart rate response to various stressors[END_REF].

Although birds were not captured in the present study, they were approached up close (to a few cm), and the risk assessed was presumably more comparable to a capture than to an observer standing some 10 m distant.

Previous studies in similar seabirds have shown contrasted responses to human approaches. For instance, whereas Magellanic (Spheniscus magellanicus), African (S. demersus),

and Gentoo penguins (Pygoscelis papua) show reduced behavioural and/or physiological responses (heart rate or corticosterone concentrations) to human visitation in high disturbance areas [START_REF] Van Heezik | Effect of human disturbance on beach groups of jackass penguins[END_REF][START_REF] Fowler | Behavioral and hormonal-responses of Magellanic penguins (Spheniscus magellanicus) to tourism and nest site visitation[END_REF][START_REF] Walker | Physiological and behavioral differences in Magellanic Penguin chicks in undisturbed and tourist-visited locations of a colony[END_REF][START_REF] Walker | Habituation of adult Magellanic Penguins to human visitation as expressed through behavior and corticosterone secretion[END_REF][START_REF] Holmes | Behaviour and breeding success of gentoo penguins Pygoscelis papua in areas of low and high human activity[END_REF][START_REF] Villanueva | A matter of history: Effects of tourism on physiology, behaviour and breeding parameters in Magellanic Penguins (Spheniscus magellanicus) at two colonies in Argentina[END_REF][START_REF] Pichegru | African Penguin tolerance to humans depends on historical exposure at colony level[END_REF], yellow-eyed penguins (Megadyptes antipodes) appear to sensitize to human exposure through higher stress responses [START_REF] Ellenberg | Elevated hormonal stress response and reduced reproductive output in Yellow-eyed penguins exposed to unregulated tourism[END_REF]. Taken together, these results highlight two important points: (1) behavioural and physiological responses to approaching predators (or humans) may tell seemingly different stories. A proper understanding of prey responses to approaching predators requires the integrative assessment of both physiological stress responses and behavioural reactions.

(2) both behavioural and physiological responses are fine-tuned mechanisms integrating risk assessment into optimal escape decisions.

Finally, we must consider how STRANGE were the animals in our study [START_REF] Webster | How STRANGE are your study animals[END_REF]. We selected birds in the colonies haphazardly, with no knowledge of their sex, age or past experience. Nonetheless we did not capture and measure bird morphometrics in our study, but visually targeted birds that appeared in overall good physical condition in order to minimize the risk of breeding abandonment for energy-depleted birds (Groscolas et al., 2000[START_REF] Gauthier-Clerc | Statedependent decisions in long-term fasting king penguins, Aptenodytes patagonicus, during courtship and incubation[END_REF] in this protected species. Our measures on individual birds were done over a few days during which changes in body condition were likely relatively minor. However, we might not have captured the full range of behavioral expression of AD and FID, particularly for birds of low body condition. This is important to consider since individuals in poor body condition may have enhanced stress and FID responses to approaching experimenters [START_REF] Seltmann | Stress responsiveness, age and body condition interactively affect flight initiation distance in breeding female eiders[END_REF], and emphasizes the importance of controlling for body conditionwhere feasiblein performing repeated measures on wild animals.

As this study only tested the response to repeated approaches in two colonies, which will have obvious differences in colony size, density, and topography, replicating this study over additional colonies would help in a better characterisation of the factors shaping escape decisions in penguins. In addition to landscape and social differences between colonies, there are also possible differences in predation pressure and genetic differentiation. Furthermore, the sampling in the two colonies took place 20 days apart, allowing for possible differences in the reproductive cycle to manifest. Lastly, sampling only occurred over a span of three days. Further studies should investigate these factors in more depth, as well as test repeated approaches over a longer time periodand over the lifetime of individual birds. In particular, these would help in capturing a greater range of weather conditions, and better understanding the extent of repeatability and plasticity of these behavioral traits [START_REF] Dingemanse | Criteria for acceptable studies of animal personality and behavioural syndromes[END_REF].

The response of a wild population to human disturbance creates special considerations in a world that is increasingly accessible to humans. Ecotourism and wildlife tourism, or travel to natural areas to engage in shared experiences with wildlife and whose aim is to conserve the environment through education and local spending, are increasingly common activities. As a charismatic anthropomorphic animal, penguins have garnered much attention. In many species, habituation occurs in response to disturbances caused by tourists [START_REF] Van Heezik | Effect of human disturbance on beach groups of jackass penguins[END_REF][START_REF] Fowler | Behavioral and hormonal-responses of Magellanic penguins (Spheniscus magellanicus) to tourism and nest site visitation[END_REF][START_REF] Holmes | Behaviour and breeding success of gentoo penguins Pygoscelis papua in areas of low and high human activity[END_REF][START_REF] Villanueva | Seasonal variation in the physiological and behavioural responses to tourist visitation in Magellanic penguins[END_REF]. However, even in species that have habituated to disturbance, human presence can impact natural behaviours, time budgets, heart rates and stress levels [START_REF] Holmes | Testing the minimum approach distance guidelines for incubating royal penguins Eudyptes schlegeli[END_REF][START_REF] Walker | Physiological and behavioral differences in Magellanic Penguin chicks in undisturbed and tourist-visited locations of a colony[END_REF][START_REF] Walker | Habituation of adult Magellanic Penguins to human visitation as expressed through behavior and corticosterone secretion[END_REF][START_REF] Burger | Responses of Emperor Penguins (Aptenodytes forsteri) to encounters with ecotourists while commuting to and from their breeding colony[END_REF][START_REF] Viblanc | Coping with continuous human disturbance in the wild: Insights from penguin heart rate response to various stressors[END_REF][START_REF] Villanueva | A matter of history: Effects of tourism on physiology, behaviour and breeding parameters in Magellanic Penguins (Spheniscus magellanicus) at two colonies in Argentina[END_REF][START_REF] Pichegru | African Penguin tolerance to humans depends on historical exposure at colony level[END_REF]. For species that cannot habituate or which have sensitized to disturbance, individuals may experience negative impacts on their reproductive success ultimately endangering the population as a whole [START_REF] Giese | Effects of human activity on Adelie penguin Pygoscelis adeliae breeding success[END_REF][START_REF] Mcclung | Nature-based tourism impacts on yellow-eyed penguins Megadyptes antipodes: does unregulated visitor access affect fledging weight and juvenile survival[END_REF][START_REF] Ellenberg | Physiological and reproductive consequences of human disturbance in Humboldt penguins: the need for species-specific visitor management[END_REF][START_REF] Ellenberg | Elevated hormonal stress response and reduced reproductive output in Yellow-eyed penguins exposed to unregulated tourism[END_REF][START_REF] Ellenberg | Previous experiences with humans affect responses of Snares Penguins to experimental disturbance[END_REF][START_REF] Ellenberg | Heart rate responses provide an objective evaluation of human disturbance stimuli in breeding birds[END_REF][START_REF] Carroll | Prior exposure to capture heightens the corticosterone and behavioural responses of little penguins (Eudyptula minor) to acute stress[END_REF]. Knowledge of AD and FID may help inform policy makers when deciding appropriate viewing guidelines for tourists [START_REF] Ellenberg | Physiological and reproductive consequences of human disturbance in Humboldt penguins: the need for species-specific visitor management[END_REF][START_REF] French | Behavioural consequences of human disturbance on subantarctic Yellow-eyed penguins Megadyptes antipodes[END_REF].

ACKNOWLEDGEMENTS

We thank Trish Fleming and an anonymous reviewer for their thorough and helpful comments on a previous version of the manuscript. This work was supported by the French Polar Institute (IPEV) through the IPEV 119 ECONERGY polar program, and by the French National Center for Scientific Research (CNRS). TLH was supported by a PhD scholarship from the Initiative d'excellence (IdEX), Investissements d'Avenir, Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation. We are grateful to the Terres Australes et Antarctiques Françaises (TAAF) for providing logistic support in the field, and to the field personnel and field assistants for providing help and support along the way.

Author contributions: Conception and design: RG, VAV; data acquisition: BG; data analysis: TLH, CS, PB, VAV; writing: TLH. Revision: TLH, VAV, PB. All authors read and commented on the final manuscript.

CONFLICT OF INTEREST STATEMENT

The authors declare that they have no conflict of interest.