Alexandre Barnini
email: alexandre.barnini@alumni.chimie-paristech.fr

Thierry Robin

Daniel Caurant

Thierry Gotter

Gérard Aka

Cedric Guyon

Pascal Guitton

Ronan Montron

Arnaud Laurent

Cédric Guyon

Towards Large-Mode-Area fibers fabricated by the full vapor-phase SPCVD process

Keywords: Rare earth-doped fiber, ytterbium, optical amplifier, laser, aluminosilicate fibers, large-mode-area fibers and photodarkening

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

INTRODUCTION

Since the first demonstration of a laser emission in 1960 by T. Maiman [START_REF] Maiman | Stimulated optical radiation in ruby[END_REF] , lasers represent a major lever of the scientific progress in the photonic world. They enabled the rise of new technolo447 2802gical applications in various fields: materials cutting [START_REF] Carter | Towards industrial ultrafast laser microwelding: SiO 2 and BK7 to aluminum alloy[END_REF] and welding, medicine [START_REF] Lefort | A review of biomedical multiphoton microscopy and its laser sources[END_REF] and defense [START_REF] Qu | Application and the key technology on high power fiberoptic laser in laser weapon[END_REF] . Fiber laser technologies have been first put aside by intense activities on crystal or gas lasers. After the fabrication of a first low-attenuation neodymium-doped-silica optical fiber core and its use as a laser cavity in the nineties [START_REF] Poole | Fabrication of low-loss optical fibers containing rare earth ions[END_REF] , research and development on fiber lasers have intensively grown. The large ratio of surface-to-active volume of optical fibers led to excellent heat dissipation [START_REF] Tünnermann | The renaissance and bright future of fibre lasers[END_REF] and a good spatial distribution of the signal, resulting in nearly Gaussian beams and higher stability [START_REF] Zervas | High power fiber lasers: A review[END_REF] . Ytterbium-doped silica with double-clad design are currently widely used for high power applications. Silica is of great interest as a host for ytterbium ions (and more generally for rare earth (RE) ions), because it leads to a broadening of the RE ion emission and absorption spectra compared to the similar crystal host, and consequently enables a more efficient optical pumping [START_REF] Jackson | Towards high-power mid-infrared emission from a fibre laser[END_REF] (at around 915 or 976nm in the case of ytterbium-doped optical fiber cores). Nowadays, tendency is to continuously increase output powers. When the power extracted from the fiber increases, deleterious non-linear effects are observed. In order to push their appearance threshold back, smaller lengths of fibers are used, and therefore core diameters are increased to lower the optical density. Finally, the refractive index (RI) of the core is decreased close to the clad RI in order to keep an almost single mode signal. These high power-tailored optical fibers are commonly named as large-mode-area (LMA) fibers.

In a previous paper [START_REF] Barnini | Rare earth-doped optical fiber core deposition using full vapor-phase SPCVD process[END_REF] , we have presented an innovative process named Surface Plasma Chemical Vapor Deposition (SPCVD) and we have suited it to the fabrication of fibers with 10µm core diameters and compositions (SiO 2 -Al 2 O 3 -Yb 2 O 3 -F) that were not accessible with the standard MCVD process, while precisely controlling the dopant incorporation both radially and between consecutive preforms. In this paper, we present our latest results on 11µm core diameter fibers and on 20µm LMA fibers synthesized using our custom-made SPCVD process. Fibers of various core compositions (SiO 2 -Al 2 O 3 -Yb 2 O 3 -F and SiO 2 -Al 2 O 3 -P 2 O 5 -Yb 2 O 3 ) are studied regarding their attenuation, their power conversion efficiency and their resistance to photodarkening.

PREFORM FABRICATION

Presentation of the SPCVD process

First described by Pavy et al. in 1986 10 , the SPCVD process was used for the production of telecommunication single mode fibers. The technology is based on a low-pressure microwave (2.45GHz) plasma used to dissociate a mixture of chloride, Freon gases and oxygen, in order to generate oxidation reactions at the inner surface of a synthetic silica tube. The tube is placed at the center of a tubular furnace heated at about 1100°C in order to get a vitrified deposit. By positioning the silica substrate tube under vacuum conditions, the ignition of a microwave discharge is possible. The microwaves propagate along the inner surface of the dielectric substrate tube thus supporting the plasma column: the plasma is self-sustained. But the amplitude of the electromagnetic field decreases from the point of application of the plasma to the end of the column, and so does the concentration of electrons. The plasma column subsists only above a critical concentration of 4.31x10 11 electrons.cm -3 , [START_REF] Golant | Bulk silicas prepared by low pressure plasma CVD: formation of structure and point defects[END_REF] . The reagents used in this paper for the deposits are: SiCl 4 , AlCl 3 , YbCl 3 , P 2 O 5 , CeCl 3 and C 2 F 6 . The deposit takes place on the first centimeters of the plasma column (Fig. 1). Since the microwave power applied dictates the length of the plasma column, by modulating this power, the deposit area can be shifted forward and backward in order to get a total length of deposit of several hundred millimeters. The plasma scanning frequency used in our experiments is 0.5Hz and we successfully synthesized a vitrified deposition of 400mm length in a 16x20mm (IDxOD) tube, where each glassy layer deposited has a thickness of several tenths of nanometers.

Evaporation of aluminum and rare earth chlorides

We use 5N purity anhydrous aluminum chloride (AlCl 3 ) as a precursor for aluminum, and the reagent is placed into a silica reactor. By heating the precursor in an oven at 100°C at around 1mbar, the vapors are generated and carried out to the plasma reaction area by way of an inert gas. A high temperature mass flow controller is located in the oven in order to properly control the amount of aluminum delivered to the reaction zone to ensure repeatable layer composition. We use 4N purity anhydrous ytterbium and anhydrous cerium chlorides as precursors for ytterbium and cerium respectively. The reagents are placed into two quartz reactors located close to the reaction zone (Fig. 2). The temperature of each reactor is controlled independently. By heating the precursors at around 800°C and 1mbar, the vapors are generated and carried out to the plasma reaction area by way of an inert gas. A great care has been taken to design the reactor such as to prevent any gas (and especially oxygen) to come into contact with the rare earth chloride powders during the deposition time. A simplified set-up (with only the evaporation of ytterbium chloride) is presented in Fig. 2.

PREFORM AND FIBER CHARACTERIZATIONS

Refractive index and chemical composition

The refractive index profiles (RIP) of the cores have been obtained using a PK2600 (Photon Kinetics) preform analyzer, scanning the preform both radially and longitudinally with a He-Ne light beam at 633nm. The chemical composition of the cores has been analyzed using an electron microprobe Cameca SX100 (15kV, 50nA), at the CAMPARIS department of the Pierre et Marie Curie University. The analysis has been made on slices of the preform, previously polished and metallized.

Attenuation

The attenuations of the cores presented in this work have been measured at 1310nm using the well-known Optical Time Domain Reflectometry method.

Power conversion efficiency and M² coefficient

In order to test our Yb-doped active cores synthesized by the SPCVD process, we used the laser cavity set-up presented in Fig. 3. Up to six 30W multimode pump diodes were used to inject power at 915nm in the double-clad Yb-doped fiber under test. The power of each multimode pump diode is first combined in a passive double-clad fiber through a pump combiner (LasFiberio). The Yb-doped fiber under test is spliced between two fiber Bragg gratings, R max and R min (made at iXblue photonics). R max reflects more than 99% of the laser signal at 1064nm (and delivers 98.5% of the pump signal at 915nm) whereas R min reflects around 9% of this signal, which enables to create a continuously-pumped laser cavity. The power conversion efficiency (PCE) is defined as the ratio between the output power at 1064nm and the absorbed pump power at 915nm.

For the evaluation of the laser beam quality, the M² parameter is measured and enables to quantify the deviation of the emitted beam from a perfect Gaussian beam (M²=1.0). The emitted beam at the output of the laser cavity is then focused on a beam analyzer (Ophir).

Evaluation of photodarkening phenomenon

Photodarkening (PD) is a well-known detrimental effect in aluminosilicate ytterbium-doped optical fiber [START_REF] Koponen | Photodarkening measurements in large mode area fibers[END_REF] impeding fiber laser lifetime. It can be appreciatively reduced by co-doping with cerium [START_REF] Engholm | Improved photodarkening resistivity in ytterbium-doped fiber lasers by cerium co-doping[END_REF] in aluminosilicate fibers or using a phosphosilicate [START_REF] Guerroue | Photodarkening in Ybdoped fibers for fiber lasers[END_REF] or an aluminophosphosilicate [START_REF] Jetschke | Efficient Yb laser fibers with low photodarkening by optimization of the core composition[END_REF] core composition with an equimolar Al/P atomic ratio.

We measured PD using a classic setup by core-pumping a short length of fiber at 976nm and measuring the fiber transmission at 635nm (Fig. 4). Indeed, it is known that colored-centers appear due to the pump signal and lead to strong absorption bands below 700nm [START_REF] Manek-Hönninger | Photodarkening and photobleaching of an ytterbium-doped silica double-clad LMA fiber[END_REF] .

RESULTS

The characterizations and results on our SPCVD-made fibers are presented in two parts. The first one focuses on fibers with 11µm core diameter and 130µm clad diameter, and the second one on larger core diameter fibers (20µm). , not studied previously, is called AlPYb. In order to successfully incorporate both aluminum and phosphorus with a vapor phase process, one has to be careful not to mix gaseous AlCl 3 and POCl 3 , because they react together to create an unwanted complex [START_REF] Birkeneder | Raman and NMR studies in the system phosphoryl chloridealuminum chloride[END_REF] , which condensates before the reaction zone.

Preform characterizations

Figure 5 shows the RIP of the AlPYb and AlFYbCe cores made by the full vapor phase SPCVD. Both exhibit >3mm diameter cores with a slight inhomogeneity both on the sides and at the center (≈1mm) of the profiles. The mean refractive indexes of the AlFYbCe and AlPYb cores are respectively 2.30 and 2.20x10 -3 . The average measured composition of the dopants in both cores is given in table Two octagonal double-clad fibers with an 11/130 core-to-clad ratio and a core numerical aperture of 0.08 have been drawn from those preforms and are characterized in the following sections. The octagonal geometry was chosen so that the fibers could be easily tested with on the shelf components.

Fiber characterizations

In a first step, the fibers have been characterized in terms of core attenuation at 1310nm. The results are presented in table 2, where the drawing tension is noticed.

Numerical aperture

Drawing tension (g) Attenuation at 1310nm (dB/km) The drawing tension of our AlFYbCe fibers has been optimized in order to lower the attenuation at 1310nm down to 25.3dB/km, which is currently the lowest obtained for this core composition. The AlPYb core composition has been developed more recently, therefore the drawing tension is not optimized, but led to a 64.9dB/km attenuation at 1310nm which is compatible with the production of double clad fibers. The numerical aperture of both fibers is close to 0.08. RI measurement using our InterFiber Analysis IFA-100 optical fiber analyzer on these fibers did not show significant modification induced by the drawing phase indicating that no major diffusion mechanism takes place during the drawing process.

AlFYbCe and AlPYb fibers exhibit respectively a multimode pump absorption of 1.35 and 1.31dB/m at 915nm. The PCE, corresponding to the ratio of the cavity output power at 1064nm versus the absorbed pump power at 915nm, is given in Fig. 6. It was measured at 78% up to 44W of pump power for a 7.5m long piece of AlFYbCe fiber, and at 71.3% up to 28W for a 8m long piece of AlPYb fiber. These results are in line with the state of the art of similar core compositions made by other processes [START_REF] Unger | Influence of aluminumphosphorus codoping on optical properties of ytterbium-doped laser fibers[END_REF] . Moreover, the M² parameter has been measured at 1.06 for the AlFYbCe fiber and at 1.20 for the AlPYb fiber, at an output power around 3.8W.

The photodarkening phenomenon has been evaluated by core-pumping at 976nm around 10mm long of each fibers during 1000min, and the results are given in Fig. 7. We observe that the attenuation penalty at 635nm of each core remains low (only ≈26dB/m), compared to the SPCVD-made AlFYb fiber without cerium, whose attenuation keeps increasing. This result shows the major role of cerium to mitigate photodarkening in AlFYb cores compositions, but also the appreciated property of AlPYb cores compositions with an equimolar Al/P ratio to mitigate photodarkening without the need to incorporate cerium [START_REF] Jetschke | Efficient Yb laser fibers with low photodarkening by optimization of the core composition[END_REF] .

Finally, the 11/130 Yb-double clad fibers made by SPCVD exhibit good lasing properties with high PCE: 71.3 and 78.0% for AlPYb and AlFYbCe fibers respectively. The M² parameters are close to 1.0, especially for the AlFYbCe fiber (M²=1.06). Moreover, both fibers are photodarkening-resistant even though a small content of cerium is needed in the composition of AlFYb cores. We believe that the lasing properties can be improved by adding particularly a small content of germanium to the composition in order to reduce the attenuation of our rare earth-doped cores, as already demonstrated in the litterature [START_REF] Kirchhof | Dopant interactions in high power laser fibers[END_REF] .

The next section of this paper focus on fiber characterizations of AlFYbCe fibers with 20µm core diameters.

Characterizations of LMA fibers with 20µm core diameter

We present here the characterizations of two LMA fibers with 20µm core diameter. Both fibers have the same core composition: SiO

Preform characterizations

Figure 8 shows the RIP of the 20/130 and 20/400 preform cores made by the SPCVD process. As for previous RIP (Fig. 5), both exhibit >3mm diameter cores with a slight inhomogeneity on the sides but with a narrower raising of the refractive index at the center of the profiles (≈0.5mm). The average refractive indexes of the 20/130 and 20/400 cores are respectively 2.10 and 1.6x10

Fiber characterizations

The data given in table 4 present the characteristics of each fiber, where the drawing tension is pointed out. Because of the low NA of the 20/400 fiber, the attenuation at 1310nm couldn't be evaluated using the OTDR due to excessive bending losses. The maximum injected pump power for the 20/130 fiber is 136W, at which was obtained an output power at 1064nm of 100W and led to a PCE of 74.5%. The injected power is only limited by the number of available pump diodes, and it would be very interesting to test the fiber at higher powers. The M² parameter has been measured at 1.53 for this fiber at an output power of 10W. On the other hand, the injected pump power for the 20/400 fiber was limited to only 48W, and we obtained an output power of 24.5W. The measured PCE is around 53%, and the M² parameter has been measured at 1.03 for this fiber at an output power of 10W.

We believe that the PCE on this first version of an SPCVD-made 20/400 LMA fiber will be improved through splice process optimization. We did observe significant heating at the splice locations in our set-up and splice loss measurements were performed and confirmed unusually high signal losses. We are confident that the core quality is not the cause of the low PCE because equivalent composition cores yielded good lasing properties when used as 11/130 geometry type fibers. Furthermore, we measured some equivalent 20/400 fibers available on the market with our PCE test set-up and found similar values. Process improvement on splicing 400µm diameter fibers is ongoing, and updated results will be presented at the conference. Conversely, fibers with a 130µm clad diameter are regularly spliced and well handled, which can explain the high PCE obtained with the 20/130 fiber for such powers.

Furthermore, the photodarkening has not been evaluated yet on 20/130 and 20/400 fibers, but we do not expect any different behavior from the 11/130 AlFYbCe fiber, because the core composition is similar.

CONCLUSIONS

In this work, we have demonstrated the capability of the SPCVD process to produce various complex core compositions, that is to say SiO We have successfully drawn these preforms into fibers suited for moderate and high power lasers. The 11/130 AlFYbCe and AlPYb fibers have exhibited high PCE over 71% for output powers around 30W, with M² parameters close to 1. Photodarkening has been mitigated in both compositions, using a small content of cerium for the AlFYb core. The 20/130 fiber has also shown an excellent PCE of 74.5% for high powers up to 100W, unlike the 20/400 fiber whose measured PCE is rather low (53%), probably due to non-optimized splicing process for these large diameter fibers. Future work focuses on synthesizing new core compositions for 20/130 and 20/400 fibers and on improving the characterizations of these fibers, but also on studying other rare earth ions.

Figure 1 :

 1 Figure 1: Schematic principle of the SPCVD process

Figure 2 :

 2 Figure 2: Evaporation of anhydrous AlCl 3 and YbCl 3

Figure 4 :

 4 Figure 4: Set-up for the evaluation of the photodarkening

Figure 3 :

 3 Figure 3: Set-up for the evaluation of power conversion efficiency of Yb-doped fibers

Figure 5 :Table 2 :

 52 Figure 5: RIP of AlFYbCe (full line) and AlPYb (dashed line) preform cores

Figure 6 :

 6 Figure 6: PCE of 11/130 double clad AlFYbCe (circular dots) and AlPYb (rectangular dots) fibers

2 -

 2 Al 2 O 3 -Yb 2 O 3 -Ce 2 O 3 -F, but one has a 130µm clad diameter and is called 20/130, whereas the other one has a 400µm clad diameter and is called 20/400.

Figure 7 :Figure 8 :

 78 Figure 7: Photodarkening measurements on 11/130 AlFYb (dashed line), AlFYbCe (dots) and AlPYb (full line) fibers

Table 4 :

 4 Characteristics of the 20/130 and 20/400 cores As previously mentioned, RI measurement on these fibers did not show any significant modification induced by the drawing process from the preform-measured RI. 20/130 and 20/400 cores exhibit respectively a multimode absorption of 3.31 and 0.37dB/m at 915nm, therefore 3.9m long piece of 20/130 fiber and 27.0m long piece of 20/400 fiber have been used to evaluate the PCE, whose results are presented in Fig.9.

Figure 9 :

 9 Figure 9: PCE of AlFYbCe 20/130 (triangular dots) and 20/400 (circular dots) fibers

2 -

 2 Al 2 O 3 -Yb 2 O 3 -Ce 2 O 3 -F and SiO 2 -Al 2 O 3 -P 2 O 5 -Yb 2 O 3 .

Table 1 :

 1 1. Aluminum and ytterbium concentrations are almost the same in the two cores. Composition of the AlFYbCe and AlPYb cores

	% molar atomic	Al	Yb	F	P	Ce
	AlFYbCe	1.25	0.11	1.0	0	0.02
	AlPYb	1.33	0.11	0	1.28	0

Table 3 :

 3 -3 . The average content of the dopants in both cores is given in table3. Composition of the 20/130 and 20/400 cores Two octagonal double-clad fibers with a 20/130 and a 20/400 core-to-clad ratio and a core numerical aperture of 0.08 and 0.067 respectively have been drawn from those preforms and are characterized in the following sections.

	% molar atomic	Al	Yb	F	Ce
	20/130	1.17	0.10	0.98	0.030
	20/400	0.94	0.08	0.95	0.026


Verónica Muñoz Ramírez

Florence Forbes

Pierrick Coupé

Michel Dojat

No Structural Brain Differences in 'de novo' Parkinsonian Patients

come

Introduction:

In general, the diagnosis of Parkinson's disease (PD) is dependent on the identi cation of motor symptoms benchmarked by a loss of 50% of nigrostriatal neurons. This strongly motivates the de nition of biomarkers to detect PD at the earliest pre-clinical stages. Morphological brain differences between PD and healthy controls (HC) can potentially reveal key regions affected during the PD prodromal phase. Voxel-based morphometry (VBM) is a popular automatic technique allowing the detection of subtle morphometric group differences at a voxel level in structural MRI.

Methods:

We performed a VBM study of 144 de novo PD patients (age: 61.30y±9.06; sex: 53F) and 66 HC (age: 60.12y±11.39; sex: 23F) from the PPMI database [1] through two different state-of-the-art pipelines: 1) CAT12 [2] and 2) volBrain [3]. All 3D T1-weighted scans selected were obtained under the same acquisition conditions. Both CAT12 and volBrain follow similar pre-processing steps including intensity normalization, bias and noise correction. CAT12 registers the images to a reference brain using an af ne and non-linear method, whereas volBrain utilizes a linear af ne transformation. For tissue segmentation, CAT12 integrates a classical Markov Random Field and the Adaptive Maximum Posterior (AMAP) technique to reduce the dependency on tissue probability maps. In addition, partial volumes are estimated using two additional mixed classes: GM-WM and GM-CSF. volBrain robustly computes the mean values of the different tissues by excluding partial volume voxels and using an unbiased robust mean estimator [3]. Partial volume coef cients are computed as well. volBrain segments the brain into cerebrum, cerebellum, brainstem, hemispheres and seven subcortical structures (putamen, caudate, globus pallidus, thalamus, hippocampus, amygdala, and accumbens) with a multi-template method that considers a non-local label fusion scheme [4]. Additionally substantia nigra was manually delineated. The segmented images from both pipelines (Fig 1 ) were modulated and smoothed with an isotropic Gaussian kernel (8mm). The statistical analysis was performed with CAT12. We designed a general linear model (GLM) where age, sex, and total intracranial volumes (TIV) were used as covariates and compared GM and WM maps of PD vs HC with a twosample T-test. To equilibrate size populations [5], we repeated our analysis ve times with 66 controls versus 66 randomly selected patients using sampling with replacement technique. For the differential analysis, PD vs HC, no voxels survive (p<0.05 FWE corr.) for neither CAT12 or volBrain tissue images. We also analyzed independently the subcortical structures segmented by volBrain, previously deformed to CAT12 template space with DARTEL. No differences were found (p<0.05 FWE corr.). Exploratory analysis (p<0.001 uncorr.) revealed decreases in caudate nucleus, hippocampus, putamen and substantia nigra (manually segmented). No differences were found (p<0.05 FWE corr.) in the equilibrated populations.

Results:

Conclusions:

Using two recent approaches for accurate tissue classi cation (CAT12 and volBrain) we failed to detect robust structural differences between de novo PD patients and healthy controls. Findings of structural brain differences reported in the literature tend to be contradictory. This lack of consensus may be due to a variety of factors, notably the study of small cohorts, differences in segmentation techniques, and more importantly, the lack of correction for multiple comparison inevitably increasing false positive rates. We reinforce the message that VBM is a delicate technique involving many parameters that should be handled with care to avoid false positive impacting the nal results [5]. In sight of the lack of morphological differences, we suspect that early PD biomarkers may lie on the physiological properties of the Parkinsonian brain and could be investigated through quantitative MRI techniques (relaxometry, diffusion and perfusion imaging).

  ww5.aievolution.com/hbm1901/index.cfm?do=abs.viewAbs&subView=1&abs=1867 2/3

Disorders of the Nervous System:

Parkinson's Disease and Movement Disorders

Imaging Methods:

Anatomical MRI

Modeling and Analysis Methods:


Adèle Mennerat
email: adele.mennerat@uib.no

Anne Charmantier

Christian Jørgensen

Sigrunn Eliassen

Correlates of complete brood failure in blue tits: could extra-pair mating provide unexplored benefits to females?

Keywords: multiple mating, passerine bird, promiscuity multiple mating, passerine bird, promiscuity

Correlates of complete brood failure in blue tits: could extra-pair mating provide unexplored benefits to females?

Adèle Mennerat, Anne Charmantier, Christian Jorgensen, Sigrunn

Abstract

Behavioural ecologists have for decades investigated the adaptive value of extrapair copulation (EPC) for females of socially monogamous species. Despite extensive effort testing for genetic benefits, there now seems to be a consensus that the socalled 'good genes' effects are at most weak. In parallel the search for direct benefits has mostly focused on the period surrounding egg laying, thus neglecting potential correlates of EPC that might be expressed at later stages in the breeding cycle. Here we used Bayesian methods to analyse data collected over four years in a population of blue tits (Cyanistes caeruleus), where no support was previously found for 'good genes' effects. We found that broods with mixed paternity experienced less brood failure at the nestling stage than broods with single paternity, and that females having experienced complete brood failure in their previous breeding attempt had higher rates of mixed paternity than either yearling or previously successful females. To better understand these observations we also explored relationships between extra-pair mating, male and female phenotype, and local breeding density.

We found that in almost all cases the sires of extra-pair offspring were close neighbours, and that within those close neighbourhoods extra-pair sires were older than other males not siring extra-pair offspring. Also, females did not display consistent EPC status across years. Taken together our results suggest that multiple mating might be a flexible female behaviour influenced by previous breeding experience, and motivate further experimental tests of causal links between extrapair copulation and predation.

Introduction

One way for a male of a socially monogamous species to increase his fitness is by fertilizing extra-pair females, thus letting other males raise his extra-pair offspring (Trivers 1972). Extra-pair copulation (EPC) and its outcome, extra-pair paternity (EPP), are known to be widespread amongst socially monogamous birds (Griffith et al. 2002). In such systems males are predicted to reduce their parental investment when paternity in the nest is low or uncertain, and hence EPC is expected to increase the reproductive burden for promiscuous females (Westneat and Sherman 1993, Kempenaers and Sheldon 1997, Arnqvist and Kirkpatrick 2005, Houston et al. 2005, Schroeder et al. 2016). However, since EPC is a widespread strategy across avian taxa, it has been suggested that benefits from EPC could be gained not only by cuckolding males, but also by their female partners.

The observation that in many species females actively solicit extra-pair copulations (Davies 1992, Kempenaers et al. 1992, Sheldon 1994a) further suggests that EPCs might be (also) beneficial for females. Two main types of benefits for females have been hypothesized, namely direct and indirect benefits. Tests of direct benefits of EPC have mostly focused on precopulatory benefits (e.g. nuptial gifts) or increased access to resources held by extra-pair males (e.g. Gray 1997), and have been considered anecdotal in birds (Jennions andPetrie 2000, Griffith et al. 2002).

One other potential direct benefit of EPC is fertility insurance, whereby females would maximise fertilisation success by obtaining extra-pair sperm to compensate for infertility or sperm depletion of their social mates (Sheldon 1994b, Wedell et Indirect (genetic) benefits, on the other hand, have received much attention.

A main prediction is that if females seek EPC to increase the genetic 'quality' of their offspring, then extra-pair offspring should have higher survival and/or reproductive output than their within-pair half-siblings from the same nest. Although support for such genetic benefits has been documented in some cases, the effect was found to be weak at most (Akçay and Roughgarden 2007; but see Arct et al. 2015;Bowers et al. 2015), and a number of other studies found evidence of fitness costs -rather than benefits -incurred by extra-pair offspring (Sardell et al. 2011, Hsu et al. 2014). All in all, despite persistent interest, genetic benefits have received limited empirical support. This has eventually led to an emerging consensus that although genetic benefits may contribute through several weak mechanisms, they do not suffice to explain the frequency and levels of EPP observed in natural populations (Arnqvist andKirkpatrick 2005, Charmantier andSheldon 2006). It has also been suggested that EPC in females may be better explained by non-adaptive mechanisms such as genetic correlations between male and female behaviours, leading to indirect selection on female promiscuity. However this is often not considered a satisfactory general explanation for a phenomenon that is widespread both taxonomically and across ecological settings (Arnold and Owens 2002;Griffith et al. 2002;reviewed in Forstmeier et al. 2014).

Few studies of EPCs so far have explicitly considered that within-pair offspring are not the only fitness component a male may influence through his If males could, via some behavioural traits, contribute to the reproductive success of their extra-pair females in addition to the parental investment they provide at their own nests, these traits could be selected for (Székely et al. 2013). One major cause of reproductive failure is brood failure, i.e. the death of all nestlings. Despite the fact that brood failure can represent a potentially strong selection pressure, it is underrepresented in behavioural studies of breeding birds, mainly because observing or capturing breeding adults requires the presence of live nestlings. This, combined with the strong focus on comparing within-pair to extra-pair young in the search for indirect benefits, might explain why brood failure has never been considered as a potential correlate of EPC.

There can be various causes for brood failure at the nestling stage, the simplest being chick predation (Lima 2009). Predation on one of the parents can also result in brood failure, because of the energetic challenge it represents for the remaining parent to raise the brood alone. It is therefore not surprising that birds display a wide range of antipredator strategies during breeding (Lima 2009). In addition to alarm calls that may be perceived by neighbouring pairs as indicative of the nearby presence of a predator, breeding adults can also join in collective mobbing actions occurring in the neighbourhood (Caro 2005). In a number of small passerine species, it was observed that the more individuals join the mob, the sooner the predator tends to leave, and/or the longer it stays away (Hoogland and Sherman 1976, Flasskamp 1994, Krams et al. 2010, Consla and Mumme 2012, Grabowska-Zhang et al. 2012). Increasing the intensity of individual (e.g. alarm calling) and collective (e.g. mobbing) antipredator behaviours might therefore be Here we hypothesise that in such a case, broods having extra-pair sires in the close neighbourhood would experience lower rates of post-hatching failure caused by predation on chicks or on breeding adults. We explored this possibility in a Mediterranean population of blue tits (Cyanistes caeruleus), where no clear evidence was previously found for indirect (genetic) benefits of EPC (Charmantier and Blondel 2003;Charmantier et al. 2004). In this population we identified events of complete post-hatching brood failure that were directly or indirectly caused by predation, and explored how their frequencies relate to mixed-paternity, as well as to the proportion of extra-pair young (EPY) in the brood. We also assessed whether individual females displayed repeatable EPP status across years, and whether females having experienced brood failure displayed different levels of EPP compared to previously successful females.

What we report here is an intriguing link between extra-pair mating and both current and past brood failure. Given the results found, and in order to better decipher what might explain them, we also tested for relationships between extrapair mating, male and female phenotype, and breeding density. More specifically, we first explored the spatial range at which EPP was expressed, to better characterize the pool of males that females may have chosen EP sires from. Within this spatial range, we then tested whether EP sires differed from other potential mates in body size, body weight, age, geographical distance or breeding synchrony, which may Third, we tested whether females having EP offspring in their broods differed from other females in body size, weight, age, laying date or clutch size. Finally, since promiscuity may be affected by male availability (e.g. Charmantier and Perret 2004), we explored the links between two proxies of local breeding density and EPP.

Materials and methods

Study site and monitoring

We used data collected from 2000 to 2003 in a nestbox population of blue tits located in the Rouvière oak woodland near Montpellier, Southern France (43˚ 40' N, 03˚ 40' E, see Charmantier and Blondel 2003;Charmantier et al. 2004;Charmantier and Perret 2004). Breeding events were monitored, and individuals were ringed and measured using protocols described in e.g. Blondel et al. (2006). Blood samples were collected from nestlings 5 to 9 days after hatching, and adults were captured 10 to 15 days after hatching. There was no socially polygynous male in our sample.

Mixed paternity, i.e. the presence of EPY in broods was assessed in a total of 146 broods by comparing the genotypes of chicks (based on a set of seven microsatellite markers, see Charmantier and Blondel 2003;Charmantier et al. 2004;Charmantier and Perret 2004 for details) to that of the mother's social mate (i.e. the male providing offspring care at her nest). There was no case of mismatch between offspring and mother's genotype.

F o r R e v i e w O n l y 9
Field notebooks and databases were thoroughly checked to identify cases of posthatching brood failure (15 / 146), defined as death of all nestlings. No female in our dataset experienced more than one such brood failure over the four years of the study. Eight nests were not included in our sample because post-hatching failure occurred either before the chicks were 5 days old (4 cases) or before the adults could be captured (4 cases). We compared the frequencies of failure in mixedpaternity vs single-paternity broods using a Bayesian generalized linear mixedeffects model with brood failure as a binomial response variable, EPP status (i.e. whether the brood had single or mixed paternity) and year as fixed effect factors, and female identity (ID) as a random effect factor (MCMCglmm). We further explored how the probability of brood failure related to the proportion of EPY in a brood using a Bayesian generalized linear mixed-effects model with brood failure as a binomial response variable, proportion of EPY and year as fixed effect factors, and female ID as a random effect factor (MCMCglmm, see details below).

Previous breeding experience and current EPP

Focusing on those females that bred in two consecutive years over the four years of the study (n=81), we gathered information on EPP status (n=42) and brood failure (n=81) in the previous breeding season. Paternity, and hence EPP status could not be assigned for all years and all broods because not all males could be captured in all years. To explore whether EPP status was consistent across years we tested whether those females that previously had mixed-paternity broods had higher rates of EPP than those having had single-paternity broods. We used a Bayesian variable, previous EPP status as a fixed effect factor, and year as a random effect factor (MCMCglmm, see details below).

We also compared the frequencies of mixed paternity in broods of females having previously experienced brood failure to those of previously successful females. We used a Bayesian generalized linear mixed-effects model (MCMCglmm) with EPP status as a response variable, previous breeding experience (failure or success) as a fixed effect factor, and year as a random effect factor. Similarly we compared EPP status between yearling females (i.e. reproductively naive) and previously successful females.

Mapping neighbourhoods

Based on the GPS coordinates of nestboxes, and using Dirichlet tessellation, we estimated territories as Thiessen polygons around each active nest box, as these were shown to appropriately represent territory size in paridae (e.g. Wilkin et al. 2006). For territories at the edge of the study area, the outer border was defined so that the nest was located at the centre of the territory. The edges of the study area did not correspond to the edges of the forest (as only a portion of the forest was equipped with nest boxes), and there was no obvious difference in EPP between edge (n = 63 nests, 46% EPP) and central (n = 90 nests, 48% EPP) territories.

Excluding data from all edge nests would have resulted in a significant reduction of our sample, and we therefore decided to include all territories in our sample. From the maps obtained for each study year, we then assigned the territories surrounding each nest to one of four groups representing first, second, third, and 4+ order neighbours. First order neighbours are those nests sharing one territory border with the focal brood; second (resp. third) order neighbours shared border with the first (resp. second) order neighbours, and 4+ order neighbours consisted of the remaining territories in the population. Broods with a hatching date posterior to the date when the earliest brood in the population had fledged were excluded from our analysis, so that our sample only consisted of nests with overlapping periods of activity.

Spatial range of EPP

Across 146 broods, 69 (i.e. 47%) were identified as mixed-paternity broods. Among the 47 broods where paternity could be assigned to a known breeding male, 33 had at least one EPY sired by first-order male neighbours. A remaining number of 10, 3, and 1 broods had at least one EPY sired by second-, third-, and 4+-order male neighbours, respectively (Figure 1). Consistent with earlier findings in this population (Charmantier and Perret 2004), this indicates that EP sires are mainly chosen from the close neighbourhood. For the rest of this study, we therefore focused on first-order neighbourhoods as representing the main pool of potential EP sires that females may have chosen from. We tested whether EP sires and other first-order male neighbours differed in terms of male body size, weight, age, breeding asynchrony, and breeding distance to the focal brood. The difference in egg-laying dates was used as a measure of breeding asynchrony. Geographical distances were calculated from the GPS coordinates of nest boxes. Tarsus length, measured to the nearest 0.1 mm with a calliper, was used as a proxy for male body size. Body weight was measured to the nearest 0.1 g with a Pesola spring scale. Male age (in years) was determined from plumage coloration at first capture and from previous ring-marking records. We used minimum age at capture for those birds that were first caught as adults. We randomly selected one record for those individuals that were recorded in more than one year. To compare EP sires with other first-order neighbours we used Bayesian estimation, as this method is more powerful than classical t-tests (Kruschke 2013), via the online version of "BEST" for two-sample comparisons (Bååth 2012, see details below).

EP sires vs other first-order male neighbours

Females with mixed-paternity broods vs. other females

We tested whether females with mixed-paternity broods differed from other females in body size, weight, age, laying date, or clutch size. Female body size, weight, and age were measured as described for males, and laying date was defined as the date when the first egg in a clutch was laid. We randomly selected one record for those individuals that were recorded in more than one year. Comparisons were carried out using Bayesian estimation (BEST, Bååth 2012, see details below). Two different proxies for density were used, namely the number of first-order neighbours (ranging from 2 to 9) and the mean distance to first-order neighbours (ranging from 57.1 m to 238 m). To explore whether density might be related to EPP, we compared these two proxies between mixed-paternity and single-paternity broods using Bayesian estimation as above (BEST, Bååth 2012, see details below).

EPP rate and local breeding density

For each study year we also tested for spatial autocorrelation in EPP occurrence, which might indicate clustering in EPP events, using Moran's I (ape library, R 3.2.3, R Core Team 2015). Since Moran's I was never significant (see results) further analyses were performed assuming no spatial autocorrelation.

For all two-sample comparisons using BEST the burn-in period was 20000 and the number of iterations 200000 (Bååth 2012). For all Bayesian estimation analyses using MCMCglmm (MCMCglmm library in R 3.2.3, R Core Team 2015), family was defined as "categorical" and residual variance at the limit was set to 1.

The random effect variance structure (G) used in the prior included a variance set to 1 and a degree of belief (nu) set to 0.002. The number of iterations and thinning interval were defined so that the effective sample size was 1000 or more, while keeping autocorrelation between successive samples below 0.1 (Hadfield 2017). For almost all models the thinning interval was 200 and the number of iterations 300000 (except for the model with proportion of EPY as dependent variable, for which the thinning interval was 200 and the number of iterations 600000).

Convergence of the models was assessed by visual inspection of traces.

Results

F

o r R e v i e w O n l y
14 EPP rate and brood failure Mixed-paternity broods experienced complete brood failures less frequently than single-paternity broods (mixed: 3/69; single: 12/77; MCMCglmm: P = 0.02; Table 1A). In addition, brood failure occurrence decreased with increasing proportions of EPY (MCMCglmm: P = 0.01; Table 1B).

Previous breeding experience and current EPP

The probability of mixed paternity in a current year did not differ between females that previously had mixed-paternity broods (10/22) and those that previously had single-paternity broods (12/19) (MCMCglmm: P = 0.17; Table 2), suggesting low repeatability of mixed paternity for females. However, females having previously experienced complete brood failures had mixed-paternity broods more often (9/11) than previously successful females (32/70) (MCMCglmm: P = 0.02; Table 2), while the latter did not differ in EPP status from inexperienced (yearling) females (29/63) (MCMCglmm: P = 0.97; Table 2; Figure 2).

EP sires vs. other first-order male neighbours

Within first-order neighbourhoods of mixed-paternity broods, there was no difference between EP sires (n = 24) and other males (n = 60) in body size, weight, breeding asynchrony, or geographical distance (all 95% highest-density intervals included zero, Table 3A). EP sires were, however, older than other first-order male neighbours (BEST; Table 3A). 3B).

EPP rate and local breeding density

Neither the number of first-order neighbours, nor the mean distance to first-order neighbours, differed between mixed-paternity and single-paternity broods (BEST, Table 4). In addition, in none of the study years was there any statistically significant spatial autocorrelation in EPP occurrence (Moran's I; year 2000, P = 0.83; 2001, P = 0.49; 2002, P = 0.48; 2003, P = 0.87).

Discussion

In this study we found a combination of patterns that, taken together, cannot be fully explained by current hypotheses of the benefits of EPC for females. We indeed found reduced brood failure in mixed-paternity broods compared to broods sired by a single male, and a negative relation between brood failure and the proportion of EPY in broods. Furthermore, in the same population no difference in age, morphometrics, or condition was previously found between cuckolded and noncuckolded males, nor between cuckolded and cuckolding males, and no difference in survival or recruitment was revealed between WP and EP offspring (Charmantier et al. 2004). The 'good genes' hypothesis therefore does not seem supported in this population, and more importantly, 'good genes' effects could not explain why all

F o r R e v i e w O n l y
16 nestlings in a brood would survive better, regardless of the genes they may carry, when the brood is sired by more than one male. Finally, given the common expectation that cuckolded males should provide less care and protection for their brood due to low paternity (but see Schroeder et al. 2016), our observations require alternative explanations.

A first tentative explanation for the difference in brood failure between brood types is that areas differed in both resource availability and extra-pair mating, with extra-pair mating higher in areas of high food abundance or low predation risk. Yet, while spatial autocorrelation in habitat types (Szulkin et al. 2015) and in fitness (Marrot et al. 2015) are present in this population, our dataset revealed no spatial autocorrelation in EPP occurrence or brood failure, and no effect of breeding density on EPP status within first-order neighbourhoods, suggesting that extra-pair mating occurred independently of local habitat quality (but see Charmantier and Perret 2004 for effects at larger spatial scales). Second, we hypothesized that variation in behaviour or other characteristics of males or females could influence both EPP occurrence and failure rate. For example, if multiply mating females had higher body condition, longer breeding experience, or specific behavioural types, this could translate into higher brood success (van Oers et al. 2004, Patrick et al. 2012). While we did not find any difference in age, body size, body condition, or breeding phenology between mothers of mixed-paternity broods and those of single-paternity broods, we did however not directly measure their behaviour, and cannot rule out that they might have differed in some other traits. This might also apply to males, and in particular the link between male

F o r R e v i e w O n l y 17
propensity to loose paternity and the level of protection and care received by their brood (e.g. Patrick et al. 2012;Schroeder et al. 2016), is an aspect that would require further investigation. However, differences in behavioural traits alone would not suffice to explain why older male neighbours would sire more EP offspring, irrespective of other phenotypic traits. One potential explanation is that in case of selective disappearance (Bouwhuis et al. 2009), male age might reflect male genetic quality, with older males being those better able to survive, and hence that EPP would be driven by a combination of personality and good genes effects. In the absence of any differences in survival or recruitment rate between WP and EP offspring (Charmantier et al. 2004), however, this explanation appears unlikely.

Even though our results remain correlative, they tend to suggest that females, by engaging in EPC with their close neighbours, would gain some protective advantage to their brood. Older males are potentially also those with the longest local breeding experience, and hence may be better able to warn the neighbourhood against predators or interact with neighbours in other beneficial ways. We also found that previous experience of complete, post-hatching brood failure by females was associated with a higher frequency of EPP, as compared to either unexperienced or previously successful females. This suggests that EPC may be a flexible female behaviour. Taken together our results suggest that EPP may confer a direct benefit in terms of decreased brood failure, perhaps via increased vigilance, mobbing, or other behaviours through which neighbouring adults may contribute even though they do not participate in chick provisioning. When breeding pairs, and particularly yearling individuals, settle in a territory there might be insufficient environmental cues available to accurately assess risk of future failure. If this risk is perceived during the fertile period, it follows from our reasoning that one way for females to respond would be by seeking more EPC. If the risk of failure is perceived after the end of the fertile period, such an immediate response becomes impossible, and females could benefit not only from moving to a safer site (e.g. Danchin et al. 1998, Doligez et al. 2004), but also from altering their mating strategy in their next breeding attempt (Lima 2009).

Experimental tests would be needed to establish a causal link between perceived risk of failure and EPP rate, and we are currently exploring this further. If true, this hypothesis might help explain why EPP seems to have low repeatability for females, not only in our study population, but also in other species (I. Winney, pers. comm.; Reid et al. 2011).

In our study population, the main predators on blue tit chicks are mustelids like the weasel Mustela nivalis and the common genet Genetta genetta (that learned to open Schwegler nestboxes from the front), while the main predator on adults is the Eurasian sparrowhawk Accipiter nisus. Brood failures resulted either from brood predation, i.e. disappearance of all nestlings from a nest box prior to day 15 (five cases), or corresponded to cases when one breeding adult disappeared shortly after having been observed feeding a brood with nestlings in good condition, and was never recorded again (i.e. in the 12 years following the end of the present study). We could infer that an individual was missing when it was previously caught and ringed (between 11 and 14 days post-hatching), but not observed again when the chicks

F o r R e v i e w O n l y
19 were measured at day 15 post-hatching (the presence and number of adults alarming was systematically noted). Even though we cannot provide definitive evidence, for such cases we assume that death by predation is the most likely cause of disappearance (10 cases). This assumption seems supported by recent observations in another population of blue tits, where almost all cases of complete brood failure were related to sudden and permanent disappearance of one of the parents; in those cases the missing parent was recorded (via automated monitoring) active at the nest up to the point where it disappeared, which points to predation as the most likely cause of disappearance (Santema and Kempenaers, unpublished results). But even assuming that nest desertion might explain some of the failing broods, our observations contradict the common assumption that males should be more prone to desertion of those broods where paternity is shared (Trivers 1972, Houston andMcNamara 2002). Here we observe the opposite, i.e.

that broods with single paternity are more prone to failure. In addition, as far as we can observe in our sample, EPP rate was not linked to pair-bond stability, as the frequency of mixed paternity did not vary between pairs that divorced and both individuals bred again separately (19 cases, 42% EPP), and those that remained stable (18 cases, 44% EPP). Noticeably, and irrespective of brood failure, EPP rate was found higher in cases where the previous male partner was never found again (33 cases, 61% EPP). Finally, we did not find any relation between EPP and two measures of local breeding density, which tends to contradict the assumption that EPC might simply emerge from high local availability of mating partners. Our hypothesis, i.e. that broods sired by multiple males would gain overall better success Identification of individuals in traditionally monitored passerine populations usually requires the recapture of ring-marked birds, which may lead to sampling bias because some individuals (e.g. early-failing breeders) have very low detection probabilities (Kidd et al. 2015). Fortunately, an increasing number of bird populations are now equipped with devices allowing automated or remote detection of individuals (e.g. Aplin et al. 2012;Farine et al. 2015), and this will make it easier to study brood failure and extra-pair behaviour of males and females. For example, a recent study using passive integrative transponder (PIT) tags showed that both male and female blue tits made frequent forays in the territories of their first-order neigbhours throughout the breeding season, which suggests that close neighbours interact in a number of ways that yet remain to be investigated (Schlicht et al. 2015).

A fundamental limitation of our study is the correlative nature of the results.

We do not claim to be providing definitive support for a causal link between EPP and predation, yet the intriguing observations reported here are consistent with it when taken together, while they cannot be fully explained by current alternative hypotheses. Similar evidence from other populations as well as field experiments such as manipulations of predator risk assessment are now required. This study illustrates the idea that focusing on brood failure might yield overlooked insights,

Abstract

Behavioural ecologists have for decades investigated the adaptive value of extrapair copulation (EPC) for females of socially monogamous species. Despite extensive effort testing for genetic benefits, there now seems to be a consensus that the socalled 'good genes' effects are at most weak. In parallel the search for direct benefits has mostly focused on the period surrounding egg laying, thus neglecting potential correlates of EPC that might be expressed at later stages in the breeding cycle. Here we used Bayesian methods to analyse data collected over four years in a population of blue tits (Cyanistes caeruleus), where no support was previously found for 'good genes' effects. We found that broods with mixed paternity experienced less brood failure at the nestling stage than broods with single paternity, and that females having experienced complete brood failure in their previous breeding attempt had higher rates of mixed paternity than either yearling or previously successful females. To better understand these observations we also explored relationships between extra-pair mating, male and female phenotype, and local breeding density.

We

Introduction

One way for a male of a socially monogamous species to increase his fitness is by fertilizing extra-pair females, thus letting other males raise his extra-pair offspring (Trivers 1972). Extra-pair copulation (EPC) and its outcome, extra-pair paternity (EPP), are known to be widespread amongst socially monogamous birds (Griffith et al. 2002). In such systems males are predicted to reduce their parental investment when paternity in the nest is low or uncertain, and hence EPC is expected to increase the reproductive burden for promiscuous females (Westneat and Sherman 1993, Kempenaers and Sheldon 1997, Arnqvist and Kirkpatrick 2005, Houston et al. 2005, Schroeder et al. 2016). However, since EPC is a widespread strategy across avian taxa, it has been suggested that benefits from EPC could be gained not only by cuckolding males, but also by their female partners.

The observation that in many species females actively solicit extra-pair copulations (Davies 1992, Kempenaers et al. 1992, Sheldon 1994a) further suggests that EPCs might be (also) beneficial for females. Two main types of benefits for females have been hypothesized, namely direct and indirect benefits. Tests of direct benefits of EPC have mostly focused on precopulatory benefits (e.g. nuptial gifts) or increased access to resources held by extra-pair males (e.g. Gray 1997), and have been considered anecdotal in birds (Jennions andPetrie 2000, Griffith et al. 2002).

One other potential direct benefit of EPC is fertility insurance, whereby females Indirect (genetic) benefits, on the other hand, have received much attention.

A main prediction is that if females seek EPC to increase the genetic 'quality' of their offspring, then extra-pair offspring should have higher survival and/or reproductive output than their within-pair half-siblings from the same nest. Although support for such genetic benefits has been documented in some cases, the effect was found to be weak at most (Akçay and Roughgarden 2007; but see Arct et al. 2015;Bowers et al. 2015), and a number of other studies found evidence of fitness costs -rather than benefits -incurred by extra-pair offspring (Sardell et al. 2011, Hsu et al. 2014). All in all, despite persistent interest, genetic benefits have received limited empirical support. This has eventually led to an emerging consensus that although genetic benefits may contribute through several weak mechanisms, they do not suffice to explain the frequency and levels of EPP observed in natural populations (Arnqvist andKirkpatrick 2005, Charmantier andSheldon 2006). It has also been suggested that EPC in females may be better explained by non-adaptive mechanisms such as genetic correlations between male and female behaviours, leading to indirect selection on female promiscuity. However this is often not considered a satisfactory general explanation for a phenomenon that is widespread both taxonomically and across ecological settings (Arnold and Owens 2002;Griffith et al. 2002;reviewed in Forstmeier et al. 2014).

Few studies of EPCs so far have explicitly considered that within-pair offspring are not the only fitness component a male may influence through his There can be various causes for brood failure at the nestling stage, the simplest being chick predation (Lima 2009). Predation on one of the parents can also result in brood failure, because of the energetic challenge it represents for the remaining parent to raise the brood alone. It is therefore not surprising that birds display a wide range of antipredator strategies during breeding (Lima 2009). In addition to alarm calls that may be perceived by neighbouring pairs as indicative of the nearby presence of a predator, breeding adults can also join in collective mobbing actions occurring in the neighbourhood (Caro 2005). In a number of small passerine species, it was observed that the more individuals join the mob, the sooner the predator tends to leave, and/or the longer it stays away (Hoogland and Sherman 1976, Flasskamp 1994, Krams et al. 2010, Consla and Mumme 2012, Grabowska-Zhang et al. 2012). Increasing the intensity of individual (e.g. alarm calling) and collective (e.g. mobbing) antipredator behaviours might therefore be Here we hypothesise that in such a case, broods having extra-pair sires in the close neighbourhood would experience lower rates of post-hatching failure caused by predation on chicks or on breeding adults. We explored this possibility in a

Mediterranean population of blue tits (Cyanistes caeruleus), where no clear evidence was previously found for indirect (genetic) benefits of EPC (Charmantier and Blondel 2003;Charmantier et al. 2004). In this population we identified events of complete post-hatching brood failure that were directly or indirectly caused by predation, and explored how their frequencies relate to mixed-paternity, as well as to the proportion of extra-pair young (EPY) in the brood. We also assessed whether individual females displayed repeatable EPP status across years, and whether females having experienced brood failure displayed different levels of EPP compared to previously successful females.

What we report here is an intriguing link between extra-pair mating and both current and past brood failure. Given the results found, and in order to better decipher what might explain them, we also tested for relationships between extrapair mating, male and female phenotype, and breeding density. More specifically, we first explored the spatial range at which EPP was expressed, to better characterize the pool of males that females may have chosen EP sires from. Within this spatial range, we then tested whether EP sires differed from other potential mates in body promiscuity may be affected by male availability (e.g. Charmantier and Perret 2004), we explored the links between two proxies of local breeding density and EPP.

Materials and methods

Study site and monitoring

We used data collected from 2000 to 2003 in a nestbox population of blue tits located in the Rouvière oak woodland near Montpellier, Southern France (43˚ 40' N, 03˚ 40' E, see Charmantier and Blondel 2003;Charmantier et al. 2004;Charmantier and Perret 2004). Breeding events were monitored, and individuals were ringed and measured using protocols described in e.g. Blondel et al. (2006). Blood samples were collected from nestlings 5 to 9 days after hatching, and adults were captured 10 to 15 days after hatching. There was no socially polygynous male in our sample.

Mixed paternity, i.e. the presence of EPY in broods was assessed in a total of 146 broods by comparing the genotypes of chicks (based on a set of seven microsatellite markers, see Charmantier and Blondel 2003;Charmantier et al. 2004;Charmantier and Perret 2004 for details) to that of the mother's social mate (i.e. the male providing offspring care at her nest). There was no case of mismatch between offspring and mother's genotype. occurred either before the chicks were 5 days old (4 cases) or before the adults could be captured (4 cases). We compared the frequencies of failure in mixedpaternity vs single-paternity broods using a Bayesian generalized linear mixedeffects model with brood failure as a binomial response variable, EPP status (i.e.

whether the brood had single or mixed paternity) and year as fixed effect factors, and female identity (ID) as a random effect factor (MCMCglmm). We further explored how the probability of brood failure related to the proportion of EPY in a brood using a Bayesian generalized linear mixed-effects model with brood failure as a binomial response variable, proportion of EPY and year as fixed effect factors, and female ID as a random effect factor (MCMCglmm, see details below).

Previous breeding experience and current EPP

Focusing on those females that bred in two consecutive years over the four years of the study (n=81), we gathered information on EPP status (n=42) and brood failure (n=81) in the previous breeding season. Paternity, and hence EPP status could not be assigned for all years and all broods because not all males could be captured in all years. To explore whether EPP status was consistent across years we tested whether those females that previously had mixed-paternity broods had higher rates of EPP than those having had single-paternity broods. We used a Bayesian variable, previous EPP status as a fixed effect factor, and year as a random effect factor (MCMCglmm, see details below).

We also compared the frequencies of mixed paternity in broods of females having previously experienced brood failure to those of previously successful females. We used a Bayesian generalized linear mixed-effects model (MCMCglmm)

with EPP status as a response variable, previous breeding experience (failure or success) as a fixed effect factor, and year as a random effect factor. Similarly we compared EPP status between yearling females (i.e. reproductively naive) and previously successful females.

Mapping neighbourhoods

Based on the GPS coordinates of nestboxes, and using Dirichlet tessellation, we estimated territories as Thiessen polygons around each active nest box, as these were shown to appropriately represent territory size in paridae (e.g. Wilkin et al. 2006). For territories at the edge of the study area, the outer border was defined so that the nest was located at the centre of the territory. The edges of the study area did not correspond to the edges of the forest (as only a portion of the forest was equipped with nest boxes), and there was no obvious difference in EPP between edge (n = 63 nests, 46% EPP) and central (n = 90 nests, 48% EPP) territories.

Excluding data from all edge nests would have resulted in a significant reduction of our sample, and we therefore decided to include all territories in our sample.

F o r R e v i e w O n l y 11
From the maps obtained for each study year, we then assigned the territories surrounding each nest to one of four groups representing first, second, third, and 4+ order neighbours. First order neighbours are those nests sharing one territory border with the focal brood; second (resp. third) order neighbours shared border with the first (resp. second) order neighbours, and 4+ order neighbours consisted of the remaining territories in the population. Broods with a hatching date posterior to the date when the earliest brood in the population had fledged were excluded from our analysis, so that our sample only consisted of nests with overlapping periods of activity.

Spatial range of EPP

Across 146 broods, 69 (i.e. 47%) were identified as mixed-paternity broods. Among the 47 broods where paternity could be assigned to a known breeding male, 33 had at least one EPY sired by first-order male neighbours. A remaining number of 10, 3, and 1 broods had at least one EPY sired by second-, third-, and 4+-order male neighbours, respectively (Figure 1). Consistent with earlier findings in this population (Charmantier and Perret 2004), this indicates that EP sires are mainly chosen from the close neighbourhood. For the rest of this study, we therefore focused on first-order neighbourhoods as representing the main pool of potential EP sires that females may have chosen from.

EP sires vs other first-order male neighbours

F o r R e v i e w O n l y 12
We tested whether EP sires and other first-order male neighbours differed in terms of male body size, weight, age, breeding asynchrony, and breeding distance to the focal brood. The difference in egg-laying dates was used as a measure of breeding asynchrony. Geographical distances were calculated from the GPS coordinates of nest boxes. Tarsus length, measured to the nearest 0.1 mm with a calliper, was used as a proxy for male body size. Body weight was measured to the nearest 0.1 g with a Pesola spring scale. Male age (in years) was determined from plumage coloration at first capture and from previous ring-marking records. We used minimum age at capture for those birds that were first caught as adults. We randomly selected one record for those individuals that were recorded in more than one year. To compare EP sires with other first-order neighbours we used Bayesian estimation, as this method is more powerful than classical t-tests (Kruschke 2013), via the online version of "BEST" for two-sample comparisons, with 20000 burn-in steps and 200000 iterations (Bååth 2012, see details below).

Females with mixed-paternity broods vs. other females

We tested whether females with mixed-paternity broods differed from other females in body size, weight, age, laying date, or clutch size. Female body size, weight, and age were measured as described for males, and laying date was defined as the date when the first egg in a clutch was laid. We randomly selected one record for those individuals that were recorded in more than one year. Comparisons were carried out using Bayesian estimation (BEST, Bååth 2012, see details below).

EPP rate and local breeding density

Two different proxies for density were used, namely the number of first-order neighbours (ranging from 2 to 9) and the mean distance to first-order neighbours (ranging from 57.1 m to 238 m). To explore whether density might be related to EPP, we compared these two proxies between mixed-paternity and single-paternity broods using Bayesian estimation as above (BEST, Bååth 2012, see details below).

For each study year we also tested for spatial autocorrelation in EPP occurrence, which might indicate clustering in EPP events, using Moran's I (ape library, R 3.2.3, R Core Team 2015). Since Moran's I was never significant (see results) further analyses were performed assuming no spatial autocorrelation.

For all two-sample comparisons using BEST the burn-in period was 20000 and the number of iterations 200000 (Bååth 2012). For all Bayesian estimation analyses using MCMCglmm (MCMCglmm library in R 3.2.3, R Core Team 2015), family was defined as "categorical" and residual variance at the limit was set to 1.

The random effect variance structure (G) used in the prior included a variance set to 1 and a degree of belief (nu) set to 0.002. The number of iterations and thinning interval were defined so that the effective sample size was 1000 or more, while keeping autocorrelation between successive samples below 0.1 (Hadfield 2017). For almost all models the thinning interval was 200 and the number of iterations 300000 (except for the model with proportion of EPY as dependent variable, for which the thinning interval was 200 and the number of iterations 600000).

Convergence of the models was assessed by visual inspection of traces.

Results

EPP rate and brood failure

Mixed-paternity broods experienced complete brood failures less frequently than single-paternity broods (mixed: 3/69; single: 12/77; MCMCglmm: P = 0.023; Table 1A). In addition, brood failure occurrence decreased with increasing proportions of EPY (MCMCglmm: P = 0.012; Table 1B).

Previous breeding experience and current EPP

The probability of mixed paternity in a current year did not differ between females that previously had mixed-paternity broods (10/22) and those that previously had single-paternity broods (12/19) (MCMCglmm: P = 0.17; Table 2), suggesting low repeatability of mixed paternity for females. However, females having previously experienced complete brood failures had mixed-paternity broods more often (9/11) than previously successful females (32/70) (MCMCglmm: P = 0.02; Table 2), while the latter did not differ in EPP status from inexperienced (yearling) females (29/63) (MCMCglmm: P = 0.979; Table 2; Figure 2).

EP sires vs. other first-order male neighbours

Within first-order neighbourhoods of mixed-paternity broods, there was no difference between EP sires (n = 24) and other males (n = 60) in body size, weight, breeding asynchrony, or geographical distance (all 95% highest-density intervals included zero, Table 3A). EP sires were, however, older than other first-order male neighbours (BEST; 3B).

EPP rate and local breeding density

Neither the number of first-order neighbours, nor the mean distance to first-order neighbours, differed between mixed-paternity and single-paternity broods (BEST, Table 4). In addition, in none of the study years was there any statistically

Discussion

In this study we found a combination of patterns that, taken together, cannot be fully explained by current hypotheses of the benefits of EPC for females. We indeed found reduced brood failure in mixed-paternity broods compared to broods sired by a single male, and a negative relation between brood failure and the proportion of EPY in broods. Furthermore, in the same population no difference in age, morphometrics, or condition was previously found between cuckolded and noncuckolded males, nor between cuckolded and cuckolding males, and no difference in survival or recruitment was revealed between WP and EP offspring (Charmantier et al. 2004). The 'good genes' hypothesis therefore does not seem supported in this

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16 population, and more importantly, 'good genes' effects could not explain why all nestlings in a brood would survive better, regardless of the genes they may carry, when the brood is sired by more than one male. Finally, given the common expectation that cuckolded males should provide less care and protection for their brood due to low paternity (but see Schroeder et al. 2016), our observations require alternative explanations.

A first tentative explanation for the difference in brood failure between brood types is that areas differed in both resource availability and extra-pair mating, with extra-pair mating higher in areas of high food abundance or low predation risk. Yet, while spatial autocorrelation in habitat types (Szulkin et al. 2015) and in fitness (Marrot et al. 2015) traits. This might also apply to males, and in particular the link between male propensity to loose paternity and the level of protection and care received by their brood (e.g. Patrick et al. 2012;Schroeder et al. 2016), is an aspect that would require further investigation.

However, differences in behavioural traits alone would not suffice to explain why older male neighbours would sire more EP offspring, irrespective of other phenotypic traits. One potential explanation is that in case of selective disappearance (Bouwhuis et al. 2009), male age might reflect male genetic quality, with older males being those better able to survive, and hence that EPP would be driven by a combination of personality and good genes effects. In the absence of any differences in survival or recruitment rate between WP and EP offspring (Charmantier et al. 2004), however, this explanation appears unlikely.

Even though our results remain correlative, they tend to suggest that females, by engaging in EPC with their close neighbours, would gain some protective advantage to their brood. Older males are potentially also those with the longest local breeding experience, and hence may be better able to warn the neighbourhood against predators or interact with neighbours in other beneficial ways. We also found that previous experience of complete, post-hatching brood failure by females was associated with a higher frequency of EPP, as compared to either unexperienced or previously successful females. This suggests that EPC may be a flexible female behaviour. When breeding pairs, and particularly yearling individuals, settle in a territory there might be insufficient environmental cues available to accurately assess risk of future failure. If this risk is perceived during the fertile period, it follows from our reasoning that one way for females to respond would be by seeking more EPC. If the risk of failure is perceived after the end of the fertile period, such an immediate response becomes impossible, and females could benefit not only from moving to a safer site (e.g. Danchin et al. 1998, Doligez et al. 2004), but also from altering their mating strategy in their next breeding attempt (Lima 2009).

Experimental tests would be needed to establish a causal link between perceived (between 11 and 14 days post-hatching), but not observed again when the chicks were measured at day 15 post-hatching (the presence and number of adults alarming was systematically noted). Even though we cannot provide definitive evidence, for such cases we assume that death by predation is the most likely cause of disappearance (10 cases). This assumption seems supported by recent observations in another population of blue tits, where almost all cases of complete brood failure were related to sudden and permanent disappearance of one of the parents; in those cases the missing parent was recorded (via automated monitoring) active at the nest up to the point where it disappeared, which points to predation as the most likely cause of disappearance (Santema and Kempenaers, unpublished results). But even assuming that nest desertion might explain some of the failing broods, our observations contradict the common assumption that males should be more prone to desertion of those broods where paternity is shared (Trivers 1972, Houston andMcNamara 2002). Here we observe the opposite, i.e.

that broods with single paternity are more prone to failure. In addition, as far as we can observe in our sample, EPP rate was not linked to pair-bond stability, as the frequency of mixed paternity did not vary between pairs that divorced and both individuals bred again separately (19 cases, 42% EPP), and those that remained stable (18 cases, 44% EPP). Noticeably, and irrespective of brood failure, EPP rate was found higher in cases where the previous male partner was never found again (33 cases, 61% EPP). Finally, we did not find any relation between EPP and two measures of local breeding density, which tends to contradict the assumption that Identification of individuals in traditionally monitored passerine populations usually requires the recapture of ring-marked birds, which may lead to sampling bias because some individuals (e.g. early-failing breeders) have very low detection probabilities (Kidd et al. 2015). Fortunately, an increasing number of bird populations are now equipped with devices allowing automated or remote detection of individuals (e.g. Aplin et al. 2012;Farine et al. 2015), and this will make it easier to study brood failure and extra-pair behaviour of males and females. For example, a recent study using passive integrative transponder (PIT) tags showed that both male and female blue tits made frequent forays in the territories of their first-order neigbhours throughout the breeding season, which suggests that close neighbours interact in a number of ways that yet remain to be investigated (Schlicht et al. 2015).

A fundamental limitation of our study is the correlative nature of the results.

We do not claim to be providing definitive support for a causal link between EPP and predation, yet the intriguing observations reported here are consistent with it when taken together, while they cannot be fully explained by current alternative hypotheses. Similar evidence from other populations as well as field experiments such as manipulations of predator risk assessment are now required. This study

  Strikingly, direct benefits in terms of the contribution of extra-pair males to post-hatching brood success have scarcely been investigated.

  which males might enhance the post-hatching reproductive success of neighbouring extra-pair females, without directly contributing to chick provisioning(Eliassen and Jørgensen 2014, Sheldon and Mangel 2014).

  male phenotypes were more likely to sire EP offspring.

  -effects model with current EPP status as a response

  -paternity broods vs. other femalesFemales with mixed-paternity broods (n = 45) did not differ from other females (n = 57) in body size, weight, age, laying date or clutch size (all 95% highest density intervals included zero; BEST; Table

  copulatory mechanisms, therefore appears as the most parsimonious explanation given the set of patterns of EPP and complete brood failure (likely due to predation) in this population.

Figure 1 .

 1 Figure 1. Distribution of the spatial distances between EP offspring and the

Figure 2 .

 2 Figure 2. Mixed paternity in relation to the experience of females (success or failure

  Figure 1 598

  would maximise fertilisation success by obtaining extra-pair sperm to compensate for infertility or sperm depletion of their social mates(Sheldon 1994b, Wedell et al.

  Strikingly, direct benefits in terms of the contribution of extra-pair males to post-hatching brood success have scarcely been investigated.

  males could, via some behavioural traits, contribute to the reproductive success of their extra-pair females in addition to the parental investment they provide at their own nests, these traits could be selected for(Székely et al. 2013). One major cause of reproductive failure is brood failure, i.e. the death of all nestlings. Despite the fact that brood failure can represent a potentially strong selection pressure, it is underrepresented in behavioural studies of breeding birds, mainly because observing or capturing breeding adults requires the presence of live nestlings. This, combined with the strong focus on comparing within-pair to extra-pair young in the search for indirect benefits, might explain why brood failure has never been considered as a potential correlate of EPC.

  which males might enhance the post-hatching reproductive success of neighbouring extra-pair females, without directly contributing to chick provisioning(Eliassen and Jørgensen 2014, Sheldon and Mangel 2014).

  databases were thoroughly checked to identify cases of posthatching brood failure (15 / 146), defined as death of all nestlings. No female in our dataset experienced more than one such brood failure over the four years of the study. Eight nests were not included in our sample because post-hatching failure

  -effects model with current EPP status as a response

  significant spatial autocorrelation in EPP occurrence (Moran's I; year 2000, P = 0.83; 2001, P = 0.49; 2002, P = 0.48; 2003, P = 0.87).

  emerge from high local availability of mating partners. Our hypothesis, i.e. that broods sired by multiple males would gain overall better success through post-copulatory mechanisms, therefore appears as the most parsimonious explanation given the set of patterns of EPP and complete brood failure (likely due to predation) in this population.

Figure 1 .

 1 Figure 1. Distribution of the spatial distances between EP offspring and the

Figure 2 .

 2 Figure 2. Mixed paternity in relation to the experience of females (success or failure

  Figure 1 599

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  o r R e v i e w O n l y Distance class of EP sire territory (% EP sires in distance class)

Table 1 .

 1 Results of Bayesian generalized linear mixed-effects models (MCMCglmm )

		Posterior	Lower 95%	Upper 95%	Effective sample	P
		mean	CI	CI	size
	A. EPP status
	EPP status	-1.57	-3.08	-0.19	1334	0.018
	Year	-0.57	-1.13	-0.02	1368	0.051
	B. Proportion EPY
	of EPY Proportion	r o F -6.98 -13.85	-0.68	1150	0.012
	Year	-0.57	R -1.16	0.04	2985	0.054
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explaining the probability of complete post-hatching brood failure in relation to either (A) the EPP status of broods (mixed vs single paternity) or (B) the proportion of EPY in broods. See Methods.

Table 2 .

 2 Results of Bayesian generalized linear mixed-effects models (MCMCglmm,

			Mean ± SD	95% HDI
					Min	Max
	A. Males		EP sires	Other males
			(n=24)	(n=60)
	Tarsus length (mm)		16.86 ± 0.39	16.90 ± 0.41	-0.15	0.25
	Body weight (g) F o Age (y)	10.82 ± 0.43 2.21 ± 0.98	11.10 ± 0.53 1.93 ± 1.40	-0.01 -1.52	0.46 -0.73
	r Breeding synchrony (d)	0.38 ± 7.96	1.93 ± 8.20	-2.24	5.54
	Distance to brood (m)	R e 133.64 ± 74.19 107.67 ± 43.38 -58.1	9.99
			v i
	B. Females		e With EPY w (n=45)	Without EPY (n=57)
	Tarsus length (mm) Body weight (g)		16.43 ± 0.42 O 16.49 ± 0.55 n l 11.04 ± 0.48 10.92 ± 0.60	-0.26 -0.10	0.13 0.34
	Age (y)		1.76 ± 1.05	y 1.61 ± 0.82	-0.26	0.49
	Laying date (d)		35.51 ± 5.43	34.86 ± 5.76	-2.03	3.37
	Clutch size		9.71 ± 1.68	9.77 ± 1.50	-0.71	0.55
						30

see Methods) explaining the probability of mixed paternity in broods of a current year in relation to (A) the EPP status of the same female's brood the previous year, (B) brood outcome in the previous year (fledging vs complete post-hatching brood failure), or (C) breeding experience of the female (either yearling or having previously fledged a brood).

Table 3 .

 3 Comparison of EP sires with other first-order male neighbours of mixed-EP sires were older than other first order, male neighbours of mixed-paternity broods. There was no credible difference in any of the other male or female variables, since all other 95% HDIs included zero (BEST, see Methods).

	paternity broods (A), and of females with and without EPY (B). The 95% highest
	density interval (HDI) represents the credible interval of the difference in means

Table 4 .

 4 Breeding density (as represented by two different proxies) in first-order

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neighbourhoods of mixed-paternity (with EPP) and single-paternity broods (no EPP). The 95% highest density interval (HDI) represents the credible interval of the difference in means between the groups. Both 95% HDIs included zero, which means that there was no credible difference in breeding density (BEST, see Methods).

  male phenotypes were more likely to sire EP offspring.Third, we tested whether females having EP offspring in their broods differed from other females in body size, weight, age, laying date or clutch size. Finally, since

	indicate whether certain
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size, body weight, age, geographical distance or breeding synchrony, which may

  Table3A).

	Females with mixed-paternity broods vs. other females
	Females with mixed-paternity broods (n = 45) did not differ from other females
	(n = 57) in body size, weight, age, laying date or clutch size (all 95% highest density
	intervals included zero; BEST; Table
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  are present in this population, our dataset revealed no spatial autocorrelation in EPP occurrence or brood failure, and no effect

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	e of breeding density on EPP status within first-order neighbourhoods, suggesting w that extra-pair mating occurred independently of local habitat quality (but see Charmantier and Perret 2004 for effects at larger spatial scales). Second, we O n
	l hypothesized that variation in behaviour or other characteristics of males or y
	females could influence both EPP occurrence and failure rate. For example, if
	multiply mating females had higher body condition, longer breeding experience, or
	specific behavioural types, this could translate into higher brood success (van Oers
	et al. 2004, Patrick et al. 2012). While we did not find any difference in age, body
	size, body condition, or breeding phenology between mothers of mixed-paternity
	broods and those of single-paternity broods, we did however not directly measure
	their behaviour, and cannot rule out that they might have differed in some other
	17

  Taken together our results suggest that EPP may confer a direct benefit in terms of decreased brood failure, perhaps via increased vigilance,

	mobbing, or other behaviours through which neighbouring adults may contribute
	even though they do not participate in chick provisioning.
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Table 1 .

 1 Results of Bayesian generalized linear mixed-effects models (MCMCglmm ) explaining the probability of complete post-hatching brood failure in relation to either (A) the EPP status of broods (mixed vs single paternity) or (B) the proportion of EPY in broods. See Methods.

		Posterior	Lower 95%	Upper 95%	Effective sample	P
		mean	CI	CI	size
	A. EPP status
	EPP status	-1.5762	-3.0822	-0.190	1334174	0.0183
	Year	-0.576	-1.136	-0.021	1368485	0.051
	B. Proportion EPY
	of EPY Proportion	r o F -6.968 -13.8516	-0.6807	1150004	0.012
	Year	-0.57	R -1.167	0.0405	2985008	0.0546
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Table 2 .

 2 Results of Bayesian generalized linear mixed-effects models (MCMCglmm, see Methods) explaining the probability of mixed paternity in broods of a current year in relation to (A) the EPP status of the same female's brood the previous year, (B) brood outcome in the previous year (fledging vs complete post-hatching brood failure), or (C) breeding experience of the female (either yearling or having previously fledged a brood).

			Mean ± SD	95% HDI
					Min	Max
	A. Males		EP sires	Other males
			(n=24)	(n=60)
	Tarsus length (mm)		16.86 ± 0.39	16.90 ± 0.41	-0.15	0.25
	Body weight (g) F o Age (y)	10.82 ± 0.43 2.21 ± 0.98	11.10 ± 0.53 1.93 ± 1.40	-0.01 -1.52	0.46 -0.73
	r Breeding synchrony (d)	0.38 ± 7.96	1.93 ± 8.20	-2.24	5.54
	Distance to brood (m)	R e 133.64 ± 74.19 107.67 ± 43.38 -58.1	9.99
			v i
	B. Females		e With EPY w (n=45)	Without EPY (n=57)
	Tarsus length (mm) Body weight (g)		16.43 ± 0.42 O 16.49 ± 0.55 n l 11.04 ± 0.48 10.92 ± 0.60	-0.26 -0.10	0.13 0.34
	Age (y)		1.76 ± 1.05	y 1.61 ± 0.82	-0.26	0.49
	Laying date (d)		35.51 ± 5.43	34.86 ± 5.76	-2.03	3.37
	Clutch size		9.71 ± 1.68	9.77 ± 1.50	-0.71	0.55
						30

Table 3 .

 3 Comparison of EP sires with other first-order male neighbours of mixedpaternity broods (A), and of females with and without EPY (B). The 95% highest density interval (HDI) represents the credible interval of the difference in means 31 between the groups. EP sires were older than other first order, male neighbours of mixed-paternity broods. There was no credible difference in any of the other male or female variables, since all other 95% HDIs included zero (BEST, see Methods).

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Table 4 .

 4 Breeding density (as represented by two different proxies) in first-order neighbourhoods of mixed-paternity (with EPP) and single-paternity broods (no EPP). The 95% highest density interval (HDI) represents the credible interval of the difference in means between the groups. Both 95% HDIs included zero, which means that there was no credible difference in breeding density (BEST, see

	Methods).

Journal of Avian Biology

Acknowledgements

We thank Philippe Perret, Jacques Blondel and Marcel Lambrechts for assistance on the field, as well as all other students, postdocs and fieldworkers who collected data in the Rouvière study site in 2000-2003. Thanks to Göran Högstedt, Adriana Maldonado Chaparro, and Kristina Beck for providing feedback on earlier drafts of this manuscript. We are also grateful for constructive comments from two anonymous referees. AC was funded by the European Research Council (Starting grant ERC-2013-StG-337365-SHE to AC) and the OSU OREME. SE, CJ and AM were funded by the Research Council of Norway (grant 222021/F20). All applicable national guidelines for the care and use of animals were followed, and all procedures performed were in accordance with the ethical standards of the institution at which the studies were conducted.

Acknowledgements

We thank Philippe Perret, Jacques Blondel and Marcel Lambrechts for assistance on the field, as well as all other students, postdocs and fieldworkers who collected data in the Rouvière study site in 2000-2003. Thanks to Göran Högstedt, Adriana Maldonado Chaparro, and Kristina Beck for providing feedback on earlier drafts of this manuscript. We are also grateful for constructive comments from two anonymous referees. AC was funded by the European Research Council (Starting grant ERC-2013-StG-337365-SHE to AC) and the OSU OREME. SE, CJ and AM were funded by the Research Council of Norway (grant 222021/F20). All applicable national guidelines for the care and use of animals were followed, and all procedures performed were in accordance with the ethical standards of the institution at which the studies were conducted.