Laurent Godet
email: laurent.godet@univ-nantes.fr

Abel Prampart

Vincent Lostanlen

Jean Nabucet

Pierre Aumond

Temporal structure of avian dawn chorus along an urbanization gradient

Keywords: Bird song, ALAN, tra c noise, anthropization, community, Europe

come

Introduction

The in uence of human activities on birdsong has been widely studied and bene t from detailed reviews (Marín-Gómez and MacGregor-Fors, 2021; Patricelli and Blickley 2006; Slabbekoorn 2013; Slabbekoorn and Ripmeester 2008). However, there are still research avenues to be explored to better understand the in uence of humans on the timing of bird vocal activity.

Regarding the anthropogenic pressures, many studies have sought to understand how birdsongs may differ between highly contrasted environments, mainly by comparing discrete habitats, such as cities versus countryside [START_REF] Cyr | Variation in song structure of house wrens living in urban and rural areas in a Caribbean small island developing state[END_REF][START_REF] Fuller | Daytime noise predicts nocturnal singing in urban noise[END_REF]; [START_REF] Lowry | Do the calls of a bird, the noisy miner (Manorina melanocephala), need adjustment for e cient communication in urban anthropogenic noise?[END_REF][START_REF] Redondo | Urban noise in uences vocalization structure in the House Wren Troglodytes aedon[END_REF]; Sánchez-Gonzáles et al. 2020); cities versus forests (e.g., [START_REF] Ripmeester | Habitat-related birdsong divergence: a multi-level study on the in uence of territory density and ambient noise in European blackbirds[END_REF]; or intra-urban versus peri-urban forests (Marín-Gómez and MacGregor-Fors 2019). These studies revealed important differences in birdsong between habitats such as difference of amplitude, frequency, song structure, nocturnal singing rate, or singing onset in different species. However, they did not identify the respective roles of different human pressures, while differences in a birdsong between two different habitats may be due to several different anthropogenic factors. The few attempts to investigate birdsong response along anthropization gradients (rather than comparing discrete habitats) mostly focused on a single or two factors (e.g., Nordt and Klenke 2013). In addition to experimental ex situ studies that led to major advances (e.g., [START_REF] Brumm | Noise-dependent song amplitude regulation in a territorial songbird[END_REF] showed in a pioneer way that common nightingales (Luscinia megarhynchos) sang louder in the presence of anthropogenic noise), most of the in situ studies focusing on a single human pressure deal with the impacts of noise (73 references listed in the Web of Knowledge on 09/01/2023 with the following search terms: "bird", "chorus", "noise"), followed by ALAN (23 references listed in the Web of Knowledge at the same date with the following search terms: "bird", "chorus", "ALAN" or "Arti cial light*") on birdsong. Few studies investigated two factors such as noise and ALAN simultaneously (but see for example Da [START_REF] Stuart | Social factors, not anthropogenic noise or arti cial light, in uence onset of dawn singing in a common songbird[END_REF], and the relative importance of each factor is subject to debate (e.g., noise better explains song timing in the European Robin (Erithacus rubecula) than ALAN according to [START_REF] Fuller | Daytime noise predicts nocturnal singing in urban noise[END_REF], but Da [START_REF] Silva | Arti cial night lighting rather than tra c noise affects the daily timing of dawn and dusk singing in common European songbirds[END_REF] found the opposite for ve of the six species they studied). Therefore, to our knowledge, hierarchizing the respective in uence of a set of different anthropogenic pressures on birdsong under natural conditions with in situ empirical studies remains challenging.

Looking at the model species, the majority of the studies focused on a single species or a small number of species, although an increasing number of studies worked on more than 10 species (Alquezar et From the perspective of the song variables studied, researchers proposed two families of approaches. A batch of studies developed (e.g., [START_REF] Sueur | Seewave, a free modular tool for sound analysis and synthesis[END_REF] or used (e.g., [START_REF] Farina | Spatial and temporal variation of bird dawn chorus and successive acoustic morning activity in a Mediterranean landscape[END_REF]) acoustic indices at the level of the bird community such as acoustic richness, diversity or complexity, promoting the concept of "soundscape" [START_REF] Grinfeder | What do we mean by "Soundscape"? A functional description[END_REF]). As it was not their primary purpose, such studies did not individualize the song response of the different species to human pressures. Another and much larger batch of studies focused on particular song variables at the species level, among which song frequency is by far the most studied. The pioneer study of [START_REF] Slabbekoorn | Birds sing at a higher pitch in urban noise[END_REF], demonstrating a change in song frequency in the Great Tit (Parus major) related to anthropogenic noise, opened avenues on many studies on the same species (e.g, Huffeldt et [START_REF] Fuller | Daytime noise predicts nocturnal singing in urban noise[END_REF]). If we consider that the chorus is a time wave that increases rapidly before sunrise and then gradually decreases, then such indices of chorus start and end time or day/night rhythm of singing can be considered quite partial to study it accurately. For example, two species may start or stop singing at the same time but not have the same singing rhythm during the whole chorus.

Regarding these gaps, through an empirical approach, the objective of our study is to hierarchize the respective in uences of different landscape, biotic and anthropogenic factors on the timing of bird chorus of different bird species along an urbanization gradient. The timing of the chorus will be studied for several species individually and at the scale of the whole community as well as according to different timing parameters.

Methods

Study site and sampling design

We recorded birdsongs in 36 stations following a regular sampling of three lines of 12 stations ranging from the city of Saint-Nazaire (SE of the study site) to the countryside (NW of the study area -Fig. 1). The exact location of each station was determined by several criteria: (i) a minimum spacing of 400 meters between two stations (as 300 m is a distance avoiding dependence between sampling site in ornithological eld surveys - [START_REF] Ralph | Handbook of eld methods for monitoring landbirds[END_REF]); (ii) the presence of a wooded area (to sample a homogeneous bird community); (iii) the access possibility to the sites.

Song sampling and treatment

In each station, we placed and programmed an AudioMoth (Open Acoustic Devices) to record sounds continuously from midnight to noon every day from May 5 to May 13, 2022. The selected sample rate was 24 kHz. Each AudioMoth was powered by three AA batteries and their maximum memory is 32 GB. We recorded all tracks in WAV format. To protect them from the weather, we placed them in Ziploc bags, a cost-effective solution with an acceptable impact on sound measurement regarding our study objectives (see for example Law et al. 2021). The sound levels measured by the Audiomoth eet were evaluated in a controlled laboratory environment. The tests were conducted at a distance of 5 meters from a white noise source (loudspeaker) emitting a sound level measured at 68 dB(A) with a class 1 sound level meter very close to the Audiomoth microphones. The standard deviation between the sound levels recorded by the sensors was found to be 1.53 dB(A), a low value compared to the variances observed across a range of measurement locations encompassing diverse environments, ranging from rural to urban areas.

We selected only one day to have recordings made at the same time and under identical weather conditions. May 9, 2022 was chosen because: (i) it was a weekday (a Monday) with normal human activity; (ii) and weather conditions were mild enough to make bird recordings possible (no wind, no rain).

In addition, by this date, all migratory birds, including the latest, had already arrived in the study area.

For each station, we listened to the recordings in the laboratory with an EPOS Sennheiser Adapt 360 headset. The number of individuals of each species heard singing was noted on time steps of one minute every 10 minutes from midnight to noon (i.e. 73 one-minute segments for each station, for a total listening time of 2,628 minutes). Only passeriformes, cuculiformes and columbiformes were retained, thus excluding the rare other species (e.g., waders, ducks, gulls, owls). We excluded bird calls and considered only bird songs. We only included calls for 4 species: 3 species for which songs are absent or rare (Eurasian magpie (Pica pica), carrion crow (Corvus corone), western jackdaw (Coloeus monedula) and 1 species for which songs are di cult to distinguish from calls when a group is vocalizing (house sparrow (Passer domesticus)). All species names were actualized following [START_REF] Gill | IOC World Bird List[END_REF].

Song variables

We calculated six song variables (Table 1). These six indices were calculated at three different scales. ( 1) At the station-species scale (e.g., the rst song hour of the European Robin at station #28). ( 2) At the species scale, to be able to rank the species in relation to each other. In this case, each of the 6 indices was averaged by species for all stations combined (e.g., the average of the rst song hour of the European Robin on all the stations where the species was recorded). ( 3) At the community level (we consider a community as the pool of species on a given station), we calculated community weighted mean (CWM) indices (Table 1, second column). A CWM index corresponds to one of the 6 species indices (Table 1, rst column) within the community weighted by the respective species abundance. For example, in a community composed of one individual of the species "x" with a song index of 10, and two individuals of the species "y" with a song index of 20, the CWM will be (1 x 10 + 2 x 20) / (1 + 2) = 16.67. CWMs have been largely used in the literature to characterize temporal or spatial change in bird communities (see for example [START_REF] Devictor | Birds are tracking climate warming, but not fast enough[END_REF][START_REF] Godet | Waders in winter: long-term changes of bird assemblages facing climate change[END_REF]). Here, it provides a simple metric to characterize each bird community based on one of six song indices. For example, a community with a high CMI (see Table 1) is dominated by species that sing late, and a community with a high CNI (see Table 1) is dominated by species that sing at night.

Biological factors

For each station, we calculated the bird abundance (total number of individuals of all the species detected), bird species richness (total number of species of all the species detected), bird species diversity (Shannon Index of all the individuals of all the species detected -Shannon, 1948), the TFSD (which captures the amplitude and tonal temporal changes, at a frequency around 4kHz, and is associated with the density of bird song phrases [START_REF] Aumond | Modeling soundscape pleasantness using perceptual assessments and acoustic measurements along paths in urban context[END_REF])). For the analyses at the species level, we also calculated the number of individuals of conspeci cs (i.e. the number of individuals of the same species).

Statistical analysis

We performed a Principal Component Analysis (PCA) on the values of the six song indices of all the recorded species (37 species) to sort the species according to their song characteristics.

At the species level, we selected the 20 species that have been recorded in at least 10 of the 36 stations to hierarchize the in uence of the 11 factors on their 6 song indices. For each of these 20 species, and for each song index, we considered the song index as a dependent variable and the 11 factors as independent variables. Hierarchical partitioning of variance (based on R²) was used to determine the proportion of variance of each song index explained by each factor [START_REF] Chevan | Hierarchical partitioning[END_REF][START_REF] Nally | Regression and model building in conservation biology, biogeography and ecology: the distinction between and reconciliation of 'predictive' and 'explanatory' models[END_REF]. This method enables the identi cation of variables whose independent correlation with the dependent variable is large, in contrast to variables that have little independent effect but a high correlation with the dependent variable resulting from joint correlation with other independent variables. Factors were then identi ed that independently explained a larger proportion of variance than could be explained by chance, by comparing the observed value of the independent contribution to the explained variance I to a population of Is from 1000 randomizations of the data matrix. Signi cance was accepted at the upper 95% con dence limit (Z-score of 1.65; Mac Nally, 2000; [START_REF] Walsh | Stormwater drainage pipes as a threat to a stream-dwelling amphipod of conservation signi cance, Strogammarus australis, in southeastern Australia[END_REF]). Note that because the partitioning of variance does not require non-correlated factors, we include all the factors (See Appendix S1.1 for a correlation plot of all the factors).

Hierarchical partitionings of variances were also used to test the in uence of the factors on (1) the total species abundance, species richness and species diversity; (2) the different community weighted mean indices (CFI, CPI, CMI, CmI, CNI, CDI); (3) β temporal song turnover and β temporal song nestedness. To avoid any circularity, because the values of abundance, species richness, species diversity but also β turnover and β nestedness are directly linked to the abundances and numbers of the species present, we exclude the 4 biological factors for these dependent variables.

Results

Species-speci c approach Among the 37 species recorded (Appendix S1.2). Each species was recorded on average in 13 stations (Appendix S1.3) with mean abundances per species and per station ranging from 0 to 5 individuals (Appendix S1.4.).

From midnight to noon, the number of singing individuals sharply increases from 5 a.m., reaches a peak at 6:31 a.m. (i.e. 10 minutes before sunrise), then slowly decreases until noon (Fig. 2-A).

Species can be sorted from early singers (e.g., common nightingale (L. megarhynchos), song thrush (Turdus philomelos) and common blackbird (T. merula)) to late singers (e.g., Eurasian nuthatch (Sitta europaea), garden warbler (Sylvia borin) or common cuckoo (Cuculus canorus)) according to the rst hour of their song (FIRST), the peak hour of their song (PEAK), the mean hour of their song (MEAN), the median hour of their song (MED), as well as their night song rate (NIGHT) (Fig. 2-B). Species can also be sorted from short-time to long-time singers according to their song duration (DUR) (Fig. 2-B). For detailed values of every indices for every species, see Appendix S1.5 to S1.9.

Note

Intra-speci c approach

In this section, we only used the 20 species that have been recorded in at least 10 stations (see Appendix

S1.3.).

The song indices of 17 species are linked to at least one of the landscape metrics (Fig. 3). As built area increases, six species tend to sing earlier, four sing more at night, ve sing during shorter period (only two sing during longer periods). As landscape diversity increases, species react in contrasting ways: three sing earlier, two later, one sing less during night, four song during longer period and two during shorter periods. As wooded area increases, two species sing later, one earlier, one less at night, one more at night and three sing during longer period.

Birds tend to sing earlier, more at night, and during shorter period in areas submitted to high arti cial lights (ALAN or number of street lights) and tra c noise (Fig. 3). With increasing levels of anthropogenic lights, nine species sing earlier, ve species sing for shorter periods (only 1 species sings during longer period).

With increasing levels of tra c noise, six species sing earlier, four species sing for shorter periods (only one species sings during longer period).

With increasing abundances, species richness, species diversity, and TFSD in the community, more species tend to sing later, less at night, and during longer periods, but few species have opposite relationships (Fig. 3). Almost all the species (16) sing during longer periods when the abundance of conspeci cs are high. With increasing abundances of all the species pooled together, six species sing later and three sing earlier, one single species sings more at night, and ve species sing during longer periods. Eurasian wren (Troglodytes troglodytes) is the only species with contrasting relations (Fig. 3). With increasing levels of species richness, four species sing earlier and four sing later, one species sings more at night, two sing less at night, one sing during shorter periods and only one during longer periods. With increasing levels of species diversity, six species sing later, two sing earlier, three sing less at night, two sing during shorter periods and one during longer periods. With increasing levels of TFSD, three species sing later, one earlier, two sing less at night, ve during longer periods, only one species sings during shorter periods.

Community approach

The total abundance and species richness are not signi cantly linked with any landscape nor anthropogenic indices but species diversity is signi cantly lower, rst with increasing arti cial lights, then with increasing built areas, and nally with the number of street lights (Table 2). First (CFI), peak (CPI), mean (CMI) and median song community (CmI) indices are signi cantly higher rst with increasing number of street lights, then with increasing levels of ALAN and built areas, whereas nocturnal song community index (CNI) and duration song community index (CDI) are signi cantly lower (Table 2). In other words, in areas dominated by high levels of built areas and high number of arti cial lights, bird communities tend to be more dominated by late singing species, by species singing less at night and species singing during shorter periods. The other factors have lower parts of explained variance (Table 2).

Temporal turnover signi cantly increases whereas temporal nestedness signi cantly decreases with increasing landscape diversity, street light numbers and tra c noise (Table 2).

For an illustrative purpose, a graphical representation of the temporal structure of all the stations are displayed in Appendix S3.

Discussion

An old story: each species has his own song timing and large-eyed species sing earlier

In this study, we used several metrics to measure the song timing of different species, going beyond measurements of the time of rst song of each species per station. Using this diversity of metrics, we were able to classify species by song time and duration. Our approach is above all a re nement to reveal that each species has its own song timing, as already shown several years ago (e.g., [START_REF] Allard | The rst morning song of some birds of Washington, DC: its relation to light[END_REF][START_REF] Allen | More notes on the morning awakening[END_REF]). However, the robustness of our classi cation is con rmed by comparing our results with other studies.

From unpublished data from Lluisia, Aubin and Sueur, Gil and Llusia (2020), found a similar sorting of the 11 species shared in their study and our study (Linear model based on the time ranks of the rst song of the species of the two datasets: F 1,9 =22.56, R²=0.71, p = 0.001 -Appendix S4).

In agreement with [START_REF] Thomas | Eye size in birds and the timing of song at dawn[END_REF], the second point is that large-eyed species tend to sing earlier than others. Eye-size is a good proxy of the visual capacity at low intensity [START_REF] Thomas | Eye size in birds and the timing of song at dawn[END_REF]. Largeeyed species can start singing early as soon as they can see enough to detect potential rivals or predators [START_REF] Thomas | Eye size in birds and the timing of song at dawn[END_REF]). Another explanation would be that birds sing until they can see enough to forage. Birds that have high visual capacity can start to forage early, and thus sing before this time, what has been demonstrated by an experimental approach on great tits (P. major) by Kalcenick (1979).

A broadening of knowledge: individuals of the same species adjust their song timing to their

Beyond the species-speci c approach, we found that for most bird species studied, individuals of the same species adjust their song timing to their environment. Most of the previous studies focuses on one or a small set of species. Our study demonstrate that different species may have similar responses to environmental conditions. In general, individuals sing earlier and for shorter periods of time in the most urbanized areas, especially in areas subject to arti cial lights and, to a lesser extent, tra c noise, and which are the most densely built-up. Conversely, birds sing longer where the abundances of their conspeci cs are high. These results reveal on a larger number of species what has been partly suggested or demonstrated in the literature.

Beyond the song timing onset, one of the novelties of our approach is to investigate several song timing indices, including song duration. For comparison purposes with other studies, if the "song duration" factor is set aside, we found that 9 species among 20 sang earlier in the more arti cially lit areas. Although the importance of arti cial lights seems not important in birdsong timing on tropical areas (e.g. The abundance of conspeci c is, by far, the factor that best explain the song duration: 16 species among 20 sing during longer period with increasing abundance of conspeci cs. Although it is impossible to distinguish the different individuals along the recordings, we can only hypothesize that either each individual tends to sing during a longer period or that individuals take turns to song. In dusky ycatchers (Empidonax oberholseri), Stehelin and Lein (2014) found that singing rates were higher on the day of playback than on the day before playback, suggesting that bird sing more when stimulated by conspeci c songs. In eastern kingbirds (Tyrannus tyrannus), In other words, with the increase of conspeci c abundances, most of the species sing during longer period, two species start to sing earlier, and the others have later mean and median song hours as well as lower night song rate, what is probably driven by the fact that their songs are spread over the whole morning (i.e. increase in song duration).

A new step in knowledge: urbanization changes song timing of bird communities At the community level, we found that built areas and arti cial lights tend to decrease species diversity.

Understanding which species and according to what life history traits is ltered by anthropogenic factors was not our purpose, and has been already well studied (see for example [START_REF] Croci | Does urbanization lter birds on the basis of their biological traits?[END_REF]). However, to our knowledge, the inclusion of song timing parameters among these traits remains understudied. We found that urbanized areas, and mostly lit and built area promote communities dominated by late singing species and species singing during short periods.

To our knowledge, the only study that has attempted to understand how the temporal structure of birdsong varies at the scale of a community, by taking into account the temporal place occupied by each species, is that proposed by Marín-Gómez et al. (2020). In their pioneer study, they proposed, rst theoretically, that the temporal patterns of the dawn chorus of a community can follow a random structure (i.e., the different bird species sing randomly in time), modular (i.e., each species sing one after the one -what we called "beta temporal turnover" in our study) or nested structure (i.e., the song of each species is added to the previous one over time -what we called "beta nestedness turnover" in our study). Through an empirical study, they demonstrated that peri-urban and intra-urban bird communities followed a modular pattern but that only the peri-urban had a clear sequential temporal structure. By studying a very different bird community (there are almost no species in common between their study and ours) in a very different area (temperate versus tropical), different sampling methods, and different metrics used to quantify the temporal structure of the dawn chorus, we surprisingly come with comparable conclusions. The temporal structure of the dawn chorus in peri and intra-urban, that corresponds to high to moderate level of urbanization, follows a beta temporal turnover, whereas in rural areas (not studied in Marín-Gómez et al.

(2020)) the structure follows a nestedness turnover. We may interpret our result as an alteration of the temporal structure of the dawn chorus by urbanization. Beyond this evidence, the consequences of this change for the ecology and the communication of birds at the interspeci c level remain to be explored.

Conclusions

To conclude, to our knowledge, this study is one of the rst to document the impact of urbanization on the temporal structure of birdsong at the intraspeci c, the inter-speci c and the community levels in a temperate area. The different facets of urbanization in uence bird chorus in a similar way: arti cial lights and built areas decrease bird species diversity and promote late-singing and short-singing species. For a given species the individuals living in lit, noisy, and built areas tend to sing earlier and during shorter periods. We also found that the abundance of conspeci c, that could also be driven by the level of urbanization, has a strong effect on the song timing and particularly song duration of almost all the species: bird sing during shorter period where conspeci c abundances are low. Finally, lit and noisier areas have a more important temporal song turnover with species singing one after the other rather than adding up over time (Fig. 4).

Declarations

Ethical Not applicable.

  al. 2020; Gil et al. 2015; Hu and Cardoso 2010a; Luther 2009; Marín-Gómez and MacGregor-Fors 2019; Polak et al. 2013; Rios-Chelen et al. 2012; Vincelette et al. 2020) and exceptionally more than 100 species in macroecology studies (e.g., Cardoso et al. 2018; Cardoso et al. 2020; Francis 2015; Hu and Cardoso 2010b). Therefore, investigating the impacts of human pressures on different species remain little explored.

  al. 2013), other tit species (Grace and Anderson 2015; LaZerte et al. 2016; Lee and Park 2019; Oden et al. 2015; Proppe et al. 2012) and several others on the White-Crowned Sparrow (Zonotrichia leucophrys) (Derryberry et al. 2016; Gentry et al. 2017; Luther and Derryberry 2012; Phillips et al. 2020). In addition to song frequency, other song parameters studied such as song structure (e.g., Hanna et al. 2011) or time spent singing (Díaz et al. 2011) are far less studied than song amplitude (e.g, Nemeth et al. 2013; Shiba et al. 2016; Templeton et al. 2016) and song timing (e.g., Arroyo-Solís et al. 2013; Da Silva et al. 2014, 2015, 2016, 2017; Da Silva and Kempenaers 2017; Dorado-Correa et al. 2016; Lee et al. 2017; Sánchez-Gonzáles et al. 2020). By and large, under noise pollution, birds tend to sing louder (Brumm 2004; Brumm and Todt 2002; Derryberry et al. 2017; Lowry et al. 2012; Nemeth et al. 2013; Sementili-Cardoso et al. 2021); at higher frequencies (Job et al. 2016; Proppe et al. 2012; Slabbekkorn and Peet, 2003); they may change their song structure (Hamao et al. 2011; Hanna et al. 2011); and tend to change their time of singing (Alquezar et al. 2020; Arroyo-Solís et al. 2013; Lee et al. 2017; Sierro et al. 2017). In the presence of ALAN, birds mainly tend to sing earlier (Da Silva et al. 2014, 2015, 2016, 2017; Miller 2006; although Lee et al. 2017 found the opposite). Few studies tested the in uence of human pressures on different song parameters together, what is a current challenge (see for example Sierro et al. (2017) testing the impact of aircraft noise on chorus timing, song frequency, song structure and time spent singing in European Blackbird (Turdus merula)). If we focus on the timing of birdsong, almost all the studies related to the impacts of ALAN on birdsong investigated the hour of the rst, or of the rst and last songs of a species (Da Silva et al. 2014, 2015, 2016, 2017; Da Silva and Kempenaers 2017; Dorado-Correa et al. 2016; Kempenaers et al. 2010; Marín-Gómez et al. 2020; Miller 2006; Nordt and Klenke 2013) or the part of nocturnal versus diurnal song activity

Figure 1 Study

 1 Figure 1

Figure 2 (

 2 Figure 2

Figure 3 Relationships

 3 Figure 3

Table 1

 1 Song variable used as dependent variables.Finally, we calculated two beta diversity indices, namely a temporal song turnover and a temporal song nestedness of birdsongs in each station. The temporal turnover of a given station indicates a replacement of the song of each species over time whereas temporal nestedness indicates a loss/gain of the song of each species over time. Following Baselga (2010), we used the Simpson dissimilarity index (βsim) to estimate the temporal turnover[START_REF] Lennon | The geographical structure of British bird distributions: diversity, spatial turnover and scale[END_REF][START_REF] Simpson | Mammals and the nature of continents[END_REF] and the index developed by Baselga (2010) (βnes), to estimate the temporal nestedness.Eye size of the speciesFor reasons detailed in discussion, bird species with larger eyes are known tend to sing earlier[START_REF] Thomas | Eye size in birds and the timing of song at dawn[END_REF]. To test if we also found this relation in our study, we tested the correlation between the eye size and the 6 song variables listed before with simple linear models. Eye sizes were taken from[START_REF] Thomas | Eye size in birds and the timing of song at dawn[END_REF] and we corrected this variable by the respective body masses of the species (also from[START_REF] Thomas | Eye size in birds and the timing of song at dawn[END_REF], taking the residuals of a linear model between eye size and body mass.Landscape factors. Within a radius of 300 meters around each AudioMoth, we calculated the landscape diversity (based on a Shannon index -Shannon (1948)); the area of wooded areas (in ha); and the area occupied by buildings (in square meters). The two rst indices were computed from a vector data based on the land-use available for all the administrative department in 2016 (BD-MOS 44 -

	Full name	Related	De nition	Units	Meaning
	(abbreviate	community
	name)	weighted mean
		index
		(abbreviate)
	First song	Community	Hour of the rst song.	Minutes	The value
	hour index	rst song hour		after	increases as
	(FIRST)	index (CFI)		midnight	the singing
					time gets
					later.
	Peak song	Community	Hour when the maximum number of	Minutes	The value
	hour index	peak song hour	individuals sing. If this maximum is	after	increases as
	(PEAK)	index (CPI)	reached several times, the earliest	midnight	the singing
			time is kept.		time gets
					later.
	Mean song	Community	Average singing hour.	Minutes	The value
	hour index	mean song		after	increases as
	(MEAN)	hour index		midnight	the singing
		(CMI)			time gets later
	Median	Community	Median singing hour.	Minutes	The value
	song hour	median song		after	increases as
	index	index (CmI)		midnight	the singing
	(MED)				time gets
					later.
	Rate of	Community	% of 1-minute time steps where the	Percentage The value
	nocturnal	rate of	species sings before sunrise (6:41		increases as
	singing	nocturnal	am on May 2022 in the study area)		the proportion
	index	singing index			of nighttime
	(NOC)	(CNI)			singing
					increases
	Duration	Community	Number of 1-minute time steps when	0 to 73	The value
	of the	duration of the	the species sings.		increases as
	song index	song index			the duration
	(DUR)	(CDI)			of the song
					increases

https://observatoire.loire-atlantique.fr/44/les-cartes/l-occupation-des-sols-en-loire-atlantique/r_8326) and the third one was extracted from a vector database produced by the IGN (BD-TOPO®) in 2018.

Tra c noise. In this study, we are employing the L50 indicator to translate the sound levels. This indicator is linked to the noise level surpassed for 50% of the measurement time, expressed in dB. This indicator holds the advantage of being resilient to sound events and providing a relatively accurate representation of the overall sound level

[START_REF] Can | Comparison of noise indicators in an urban context[END_REF]

). Given the spatial gradient sampling in this study, and with tra c noise being the primary sound source in urban and suburban environments, we can state that in our dataset this indicator exhibits a high correlation with tra c noise levels.

Arti cial lights. Two different indices were used to assess the level of arti cial lights at night. The rst index in the number of street lights in a 300 meters radius around each AudioMoth (extracted from a vector database of the energy syndicate "Territoire d'énergie Loire-Atlantique"). The second is the level of ALAN in a 300 meters radius around each AudioMoth extracted from the VIIRS Stray Light Corrected Nighttime Day/Night Band Composites for the month of April 2022.

  that the ve song timing indices (FIRST, PEAK, MEAN, MED, NIGHT) of the different species are correlated (R²>0.7 for all pairs, Appendix S1.11). Song duration (DUR) is the index the less correlated with the 5 other song timing indices.Species with larger eye sizes are species with the earliest song (linear models between PEAK and eye size: F 1,22 =5.36, p = 0.03, R²=0.20; between MEAN and eye size: F 1,22 =5.56, p = 0.03, R²=0.20; and between MED

	and eye size: F 1,22 =6.78, p = 0.02, R²=0.24) and species that sing more at night (linear model between
	NIGHT and eye size: F 1,22 =10.51, p = 0.004, R²=0.32 -see Appendix S2 for detailed results).

Table 2 .

 2 Relationships between (A) Basic community indices; (B) Song timing community indices; (C) βtemporal diversity and the 10 factors (the 11 th factors, related to the abundance of conspeci cs have been removed here, as it only relevant for species-speci c approach). Biological indices were removed for analysis related to basic community indices and β temporal diversity to avoid any circularity as their calculations are closely linked. Values indicate the percentage of explained variance in a song index for each of the 10 factors independently (i.e. the total is equal to 100% for a given dependent variable such as abundance, CFI or turnover) obtained through hierarchical partitionings of variance. White cells indicate non-signi cant relationships; light to dark-blue negative and signi cant relationships (light blue: 0 to 10%, medium blue 10 to 20%; dark blue: >20%); yellow to red positive and signi cant relationships (pale yellow: 0 to 10%; yellow: 10 to 20%; red: >20%). For rst (CFI), peak (CPI), mean (CMI) and median (CmI) community indices, a negative relation (in blue) means that the increase in the values of a factor is linked with a dominance of early singers in the community; a positive relation (from yellow to red) a dominance of late singers. For nocturnal song index (CNI), a negative relation (in blue) means that the increase in the values of a factor is linked with a dominance of species singing during day time in the community, a positive relation (in red) a dominance of species signing during nighttime. For duration song index (CDI), a negative relation (in blue) means that the increase in the values of a factor is linked with a dominance of short-term singing species in the community.

	Type of	Factors	A					B				C
	factors		Basic community indices		Song timing community indices	β temporal diversity
			Abundance Richness Diversity	CFI	CPI	CMI CmI	CNI	CDI	Turnover Nestedness
	Landscape Land.	2.63	4.97	7.92	1.29	1.37	1.74	1.59	1.43	1.11	21.81	22.18
		diversity
		Wooded	22.85	24.15	2.41	1.88	1.96	1.45	1.59	1.46	1.73	4.90	4.30
		area
		Built	9.74	13.21	29.71	18.34	19.50	19.30	19.35	18.28	14.94	14.68	15.88
		area
	Noise and	Lights	8.15	23.02	20.82	21.74	23.03	25.61	25.65	25.40	15.06	21.11	20.09
	light	numb.
		ALAN	16.24	12.44	33.35	19.73	19.74	18.48	18.61	17.54	19.98	14.70	14.90
		Traffic	40.38	22.20	5.78	5.03	5.58	3.55	3.58	3.77	9.59	22.80	22.65
		noise
	Biological	Bird ab.				9.96	8.95	7.81	7.51	4.10	12.75
		Sp.				10.05	7.18	5.08	6.37	3.00	15.95
		richness
		Sp.				6.50	6.23	3.81	3.82	13.67	6.67
		diversity
		TFSD				5.49	6.46	13.17	11.95	11.35	2.22

  Fringilla coelebs) as showed by[START_REF] Kempenaers | Arti cial night lighting affects dawn song, extra-pair siring success, and lay date in songbirds[END_REF] and Da[START_REF] Silva | Arti cial night lighting rather than tra c noise affects the daily timing of dawn and dusk singing in common European songbirds[END_REF]. Contrary to[START_REF] Kempenaers | Arti cial night lighting affects dawn song, extra-pair siring success, and lay date in songbirds[END_REF] and Da[START_REF] Silva | Arti cial night lighting rather than tra c noise affects the daily timing of dawn and dusk singing in common European songbirds[END_REF] we did not nd that Eurasian blue tit (Cyanistes caeruleus) and great tit (P. major) sing earlier with increasing light level. If we add song duration in the song indices, 5 species sing during shorter period, and only one sing during longer period in lit areas. Species that are the most responsive to lights are early singers (e.g., European robin (E. rubecula), common blackbird (T. merula), song thrush (T. philomelos), as already demonstrated by[START_REF] Kempenaers | Arti cial night lighting affects dawn song, extra-pair siring success, and lay date in songbirds[END_REF] but also Da Silva et al. (2014). The greater response of early singers has been explained by the fact that these species are more sensitive to light than late singers (McNeil et al. 2005; Thomas et al. 2002). We also found that 6 species sing earlier and 4 during shorter periods in noisy areas. Birds are thought to avoid rush hour of high tra c noise and thus sing earlier (Arroyo-Solís et al. 2013; Dorado-Correa et al. 2016; Nordt and Klenke 2013). The relative effects of lights compared to noise is still debated in the literature. Fuller et al. (2007) found that daytime noise better explains nocturnal singing of European robin (E. rubecula) than light pollution, and Nordt and Klenke (2013) had di cult to fully separate the effects of both factors. According to Dorado-Correa et al. (2016), in tropical area, noise but no light has effect on song timing. On the other hand, several studies demonstrated that arti cial light better explain song timing than noise (Da Silva et al. 2014; Lee et al. 2017; Marín-Gómez 2022). Our results suggest that light hasgreater impacts than noise on birdsong timing: for almost each song timing variable and each species, we found that light better explains song timing than noise, and 3 species react to light but not to noise.Among the landscape indices, built area is the factor that best explains song indices. With increasing level of built area 7 species sing earlier and 5 song during shorter periods. Only two species known to be highly synanthropic (Eurasian collared dove (Streptopelia decaocto) and house sparrow (P. domesticus) -see[START_REF] Guetté | Measuring the synanthropy of species and communities to monitor the effects of urbanization on biodiversity[END_REF]) sing during longer period in increasing level of built area. Similar results were obtained by[START_REF] Marini | Urban mountain chickadees (Poecile gambeli) begin vocalizing earlier, and have greater dawn chorus output than rural males[END_REF] who found that mountain chickadees (Poecile gambeli) sing earlier in cities than in rural areas and Sanchez-Gonzáles et al. (2020) who found that urbanization level (estimated by percentages of built structures and green area), but neither light nor noise, explain earlier start of song in the vermilion ycatcher (Pyrocephalus obscurus). The difference between urban and rural areas in the song timing may be explained in different ways. The most probable explanation is the effect of the urban heat island (temperatures are higher in built areas). Birds are known to sing earlier in warmer than in colder environments, the later requiring high energy costs[START_REF] Ward | Raised thermoregulatory costs at exposed song posts increase the energetic cost of singing for willow warblers Phylloscopus trochilus[END_REF]. Therefore, in colder areas (like in rural areas) birds will start to sing later than in urban areas. The lower song duration in highly built areas can also be explain by a lower quality of urban ecosystems due to a lower food resource: the longer birds spend foraging, the less time they have to sing. van Oort and Otter (2005) and van Oort et al. (2006) found for example that black-capped chickadees (Poecile atricapillus) tend to have lower song outputs in young forest than in old forest, due to food limitation in the former.

	, Dorado-Correa
	et al. 2016; Marín-Gómez et al. 2019, but see Marín-Gómez 2022), many studies documented results

similar to ours in temperate areas.

[START_REF] Miller | Apparent effects of light pollution on singing behavior of American Robins[END_REF]

already found that American robin (Turdus migratorius) sing earlier in lit areas. More precisely, like in our study, other authors found that the same species, namely European robin (E. rubecula), common blackbird (T. merula) (Da Silva et al. 2014; Kempenaers et al. 2010,) as well as song thrush (T. philomelos) (Kempenaers et al. 2010) sing earlier with increasing arti cial light levels. We also found no response of 11 species among 20, among which common cha nch (

  [START_REF] Sexton | Dawn song of eastern kingbirds: intrapopulation variability and sociobiological correlates[END_REF] also demonstrated that songs are longer with increasing number of neighbors.If we focus on the in uence of abundance of conspeci c on the 5 other song timing indices (i.e. song duration set apart), we found that 7 species tend to sing later, only one sing earlier, and two sing earlier or later according to the song index used. However, we hypothesize that the increase in mean song hour, median song hour, and decrease in nocturnal song rate are driven by the important increase in song duration. When focusing on the song onset itself, as revealed by the rst song hour (FIRST), two species sing earlier when abundance of the conspeci c increases (Eurasian blackcap (Sylvia atricapilla) and common cha nch (F. coelebs)). The increase in the number of neighbors is known to promote earlier songs in many species (e.g.,Stehelin and Lein 2014; Stuart et al. 2019), and is even identi ed as more important than lights and noise by Stuart et al. (2019).

Funding

This was supported by grants from the Fondation de France.

Availability data and materials

Although the data are not yet stored on a repository, they are all available on request to the authors. It should also be noted that most of the raw and complete data concerning the analyses are provided in the appendices attached to the manuscript.

signi cant relationships; yellow to red positive and signi cant relationships. For rst, peak, mean and median hours a negative relation (in blue) means that the increase in the values of a factor is linked with earlier hours; a positive relation (from yellow to red) with later hours. For song duration, a negative relation (in blue) means that the increase in the values of a factor is linked with a shorter song period; a positive relation (from yellow to red) with a longer song period. On the right part of the gure: number of species for each dependent variable and each factor (in blue: number of species with a negative and signi cant relation; in red: number of species with a positive and signi cant relation).

Supplementary Files

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Coraline Lapre

Fanchao Meng

Mathilde Hary

Christophe Finot

Goëry Genty

John Michael Dudley

Genetic algorithm optimization of broadband operation in a noise-like pulse fiber laser

I. INTRODUCTION

Ultrashort pulse propagation in optical fiber is well known to lead to a wide range of complex nonlinear dynamics and processes such as modulation instability, soliton and self-similar evolution, and supercontinuum generation [START_REF] Agrawal | Nonlinear Fiber Optics[END_REF]. A comparably wide range of dynamics can be seen in modelocked fiber lasers, where the concept of the dissipative soliton in particular has provided a powerful framework within which to interpret the many different classes of laser operation that are observed [START_REF]Dissipative Solitons[END_REF][START_REF] Grelu | Dissipative solitons for mode-locked lasers[END_REF][START_REF] Turitsyn | Dissipative solitons in fiber lasers[END_REF][START_REF] Ryczkowski | Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser[END_REF][START_REF] Peng | Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers[END_REF][START_REF] Liu | Revealing the behavior of soliton buildup in a mode-locked laser[END_REF]. From the point of view of applications, most studies of fiber lasers have focused on designs that produce highly regular pulse trains [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF][START_REF] Fu | Several new directions for ultrafast fiber lasers[END_REF], but there has also been extensive study from a fundamental perspective on laser instabilities. Indeed, the study of instabilities in fiber lasers have led to new insights into processes such as soliton molecule formation [START_REF] Krupa | Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules[END_REF][START_REF] Herink | Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules[END_REF][START_REF] Liu | Real-time observation of the buildup of soliton molecules[END_REF], complex temporal pattern formation in lasers [START_REF] Huang | Versatile patterns of multiple rectangular noise-like pulses in a fiber laser[END_REF][START_REF] Klein | Ultrafast rogue wave patterns in fiber lasers[END_REF][START_REF] Zhou | Versatile multi-soliton patterns of noise-like pulses in a passively mode-locked fiber laser[END_REF], soliton rogue wave emergence [START_REF] Klein | Ultrafast rogue wave patterns in fiber lasers[END_REF][START_REF] Runge | Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers[END_REF], as well as intermittence and aperiodic transitions between different regimes of stability and instability [START_REF] Churkin | Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers[END_REF][START_REF] Lapre | Real-time characterization of spectral instabilities in a mode-locked fibre laser exhibiting soliton-similariton dynamics[END_REF].

A particularly unstable mode of fiber laser operation is the "noise-like pulse" (NLP) regime, where a large number (100-1000) of ultrafast pulses evolve randomly underneath a much broader envelope [START_REF] Horowitz | Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser[END_REF]. The NLP regime has been the focus of many recent experiments [START_REF] North | Raman-induced noiselike pulses in a highly nonlinear and dispersive all-fiber ring laser[END_REF][START_REF] Lecaplain | Rogue waves among noiselike-pulse laser emission: An experimental investigation[END_REF][START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF][START_REF] Li | Unveiling femtosecond rogue-wave structures in noise-like pulses by a stable and synchronized time magnifier[END_REF][START_REF] Santiago-Hernandez | Generation and characterization of erbium-Raman noise-like pulses from a figure-eight fibre laser[END_REF][START_REF] Wang | Generation of noise-like pulses with 203 nm 3-db bandwidth[END_REF][START_REF] Wang | Buildup of incoherent dissipative solitons in ultrafast fiber lasers[END_REF][START_REF] Du | Alternation of the mode synchronization and desynchronization in ultrafast fiber laser[END_REF], as well as demonstrations in applications such as low coherence metrology [START_REF] Keren | Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses[END_REF] and material processing [START_REF] Özgören | W, 31 MHz, square-shaped, 1 ns-pulsed all-fiber-integrated laser for micromachining[END_REF].

One recent study has reported an NLP laser around 1550 nm where the presence of highly-nonlinear fiber in the cavity leads to intracavity supercontinuum broadening with output spectra spanning 100's of nm [START_REF] Meng | Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser[END_REF]. However, achieving these particular bandwidths was found to require highly precise trial and error optimization of the nonlinear polarization rotation based saturable absorber.

In this paper, we report further experimental study of a broadband NLP laser, where we scan the laser operation over 50,000 polarization settings, and quantify that the broadest bandwidths are generated in only ∼0.5% of cases relative to the full sampled parameter space of laser operation.

For systematic access to this broad bandwidth regime, we use a genetic algorithm that successfully replaces trial and error to automatically optimize the cavity alignment.

II. RESULTS

EXPERIMENTAL SETUP AND METHODS

Figure 1 shows the experimental setup, which is based on the system previously described in Ref. [START_REF] Meng | Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser[END_REF]. The laser is a unidirectional ring cavity and uses non-polarization-preserving fiber. Fiber The saturable absorber segment is between F and G. The figure also shows how feedback from the optical spectrum (OSA) and the computed power spectrum from the oscilloscope (bottom left panel) are used as inputs to the genetic algorithm for laser optimization. ISO: isolator; θ 1 and θ 4 quarter-wave plate; θ 2 and θ 3 half-wave plate; PBS: polarizing beamsplitter; EDF: Erbium-doped fiber; HNLF: highly nonlinear fiber; WDM: wavelength-division multiplexer.

A ∼40 cm bulk-optics free space segment FG includes a nonlinear polarization rotation based saturable absorber. As shown in the figure, the input to the saturable absorber encounters sequentially a quarter-wave plate (angle θ 1 ), a half-wave plate (angle θ 2 ), a polarizing beamsplitter (PBS), a supergaussian filter, a half-wave plate (angle θ 3 ), and a quarter-wave plate (angle θ 4 ). This configuration allows a polarization-dependent loss to discriminate between pulsed and continuous wave (CW) operation in a fiber laser [START_REF] Hofer | Mode locking with cross-phase and self-phase modulation[END_REF]. The waveplates were placed in motorized rotation stages (Thorlabs PRM128) controlled by programmable DC servo motors (Thorlabs KD101). The spectral filter after the PBS (Andover (155FSX10-25) had 10 nm bandwidth (FWHM) and 80% peak transmission, and is used to control the bandwidth of the pulses reinjected into the EDF [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF][START_REF] Chong | Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress[END_REF]. The EDF was co-directionally pumped at 976 nm, and noise-like pulsed behaviour was observed at all values of pump power above the 40 mW pump threshold where pulsed laser operation is first observed. The laser output was sampled at various points as shown in the figure for spectral and temporal characterisation as described below. The cavity repetition rate is 6.28 MHz (roundtrip time of ∼159 ns.)

STATISTICAL ANALYSIS OF NLP BANDWIDTH

At all pump powers, the spectral characteristics were found to be sensitively dependent on the precise settings of the waveplates in the saturable absorber, which is of course a well-known property of lasers modelocked through nonlinear polarization rotation [START_REF] Sanchez | Models for Passively Mode-Locked Fiber Lasers[END_REF]. To investigate this further, we set the pump power at 195 mW (well above the threshold of ∼40 mW) and then we varied the angular orientations of the waveplates to effectively characterize the different states of laser operation over their full ranges. This was performed used Latin hypercube sampling to generate 50,000 quadruples (θ 1 , θ 2 , θ 3 , θ 4 ) to randomly sample the angular settings of the quarterwave plates (θ 1 , θ 4 ) over the range [0, π], and the half-wave plates (θ 2 , θ 4 ) over the range [0, π/2].

For each setting of waveplate angles, we measured the average spectrum of the laser output after the HNLF using an integrating OSA (Anritsu MS9710B) over a span of 1,500-1,750 nm. We note that the spectral bandwidth of the laser can actually extend out to above 2,100 nm at the -30 dB level because of supercontinuum broadening in the HNLF [START_REF] Meng | Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser[END_REF], but measuring this full wavelength span actually requires concatenation of spectra from two detectors. However, as we will see below, we found that simply optimizing the spectral width as measured up to 1,750 nm using the Anritsu MS9710B was sufficient to identify the targeted broadband operating regime.

(Note that once optimized, we characterized the full operating bandwidth using an Ocean Optics NIRQuest512 spectrometer that allowed measurements over an extended spectral range.) We also used a fast photodiode (Thorlabs DET08CFC/M-5 GHz) and 4 GHz oscilloscope (Rohde & Schwarz RTO2044) from which an FFT based intensity power spectrum was computed (see Fig. 1). As we discuss below, we can extract a contrast metric from fundamental harmonic peak in this spectrum to provides a convenient measure of operation in the NLP regime.

To illustrate the different regimes of laser behaviour that are observed as a function of the multidimensional space of waveplate orientations, we plot in Fig. 2 The results in Fig. 2(a)reveal the essential features of the dynamics, and show that the noiselike pulse states of bandwidth exceeding ∼20 nm exists in relatively well-defined "islands" within a broader state space where the laser operation is associated with narrowband or quasi-continuous wave operation. The broadest bandwidths exceeding ∼100 nm occupy only a very small fraction of observed output states and are observed for very particular combinations of waveplate positions as shown in the expanded view in Fig. 2(b). The average laser output power (measured after point C in the cavity) was typically ∼3 mW for operating points within the broadband islands and typically ∼3.5 mW in the narrowband regimes. Note that the randomness of these locations in the polarization space is attributed to the random birefringence in the cavity due to the use of non polarization-preserving fiber.

The variation in spectral properties across the polarization space is also shown in Fig. 3 Specific examples of a narrowband spectrum (dashed black line) and a broadband spectrum (solid black line) are also shown. The inset plots a broadband spectrum measured using the NIRQuest spectrometer to show spectral extension above 1750 nm.

To discuss the statistical properties of the different regimes of laser operation seen in this scan, Fig. 4 plots a histogram of the -20 dB laser bandwidth computed from the full set of 50,000 spectral measurements. The main plot uses a logarithmic vertical axis, whereas the inset shows an exploded view on a linear scale. The distribution is strongly long-tailed and indeed, only around 1,000 measured spectra (2% of the total measured dataset) have a bandwidth exceeding 20 nm.

Indeed, operation at a bandwidth greater than 20 nm can be taken as a useful indicator of entry into the NLP regime, as this is where points begin to cluster into the localized regions shown in

GENETIC ALGORITHM

Locating the optimal polarization orientation of a NLP laser is usually performed by trial and error, but we now discuss how this process can be replaced by a genetic algorithm (GA). Our use of GA optimization rather than other gradient methods here is motivated for several reasons.

Firstly, we note that the comparison between GA and other gradient methods remains an active topic of research in machine learning, and both techniques are known to have advantages and disadvantages [START_REF] Zingg | A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization[END_REF]. This said, gradient-based methods are known to show particular difficulties with noisy objective function spaces and inaccurate gradient calculations, and for the particular regime that we seek to optimize (from chaotic non-modelocked to broadband modelocked operation) a GA method is more suitable. We also remark that GA techniques have been previously applied to other passively modelocked fiber lasers [START_REF] Andral | Toward an autosetting mode-locked fiber laser cavity[END_REF][START_REF] Pu | Genetic algorithm-based fast real-time automatic mode-locked fiber laser[END_REF], and a further specific motivation of our work was to test the performance of a GA for a noise-like pulse laser. By keeping the optimization method the same as previous studies, it was possible to confirm the specific utility of the GA approach for a laser with complex broadband intracavity dynamics.

Our GA is summarised as follows. Each particular set of 4 waveplate orientations (θ 1 , θ 2 , θ 3 , θ 4 ) describes an "individual," with the setting of each waveplate constituting a "gene." We consider a population of 50 individuals with initial genes (angles) that are randomly selected and, based on the laser output characteristics, we calculate (and minimize) an objective function defined in order to discriminate between broadband NLP operation and other modes of narrowband CW or quasi-CW emission in the cavity. In this context, we note that it is essential we scan over all four waveplates.

For example, if we only varied θ 3 and θ 4 without also varying θ 1 and θ 2 , there is no guarantee that we would reach the broadest bandwidth regime as this would depend critically on the particular fixed θ 1 and θ 2 settings. It is also necessary to scan the waveplates over their full angular ranges.

Specifically, although the localized islands seen in Fig. 2(a) might suggest that we could locate the optimal bandwidth by scanning a limited angular range, the particular polarization settings associated with broadband operation are highly sensitive to variations in random fiber birefringence due to environmental factors. As a result, a reduced angular search space would be valid only for a finite period of time. For the most general utility of the technique, searching over the full parameter space is required.

Our GA aims to minimize the compound objective function defined as:

C = S peak /S ref -δλ/δλ ref
where the first term selects for the appearance of a strong fundamental harmonic peak in the intensity power spectrum (see Fig. 1), and the second term selects for the generation of a broadband optical spectrum. In particular concerning the first term, S peak is the mean value of the fundamental harmonic peak computed within ±200 kHz of the laser repetition frequency, and the reference value of S ref = -35 dBm. When the laser is poorly modelocked, the value of S peak approaches the spectral noise floor (around -80 dBm) such that the contribution of the first term to the objective function is large. In contrast, the presence of a strong harmonic peak associated with modelocking results in S peak increasing towards the reference value so the contribution of the first term to the objective function decreases. Concerning the second term, δλ is the root mean square bandwidth of the spectrum measured on the OSA, and δλ ref = 10 nm is a reference value. Since the second term is associated with a minus sign, increasing the bandwidth relative to the reference acts to minimise the objective function. Since the objective function is based on two components (the harmonic peak and the bandwidth), it is important that these are appropriately weighted. Such weighting is included through the reference parameters S ref and δλ ref , and the values given above were based on extensive testing to ensure that the GA did not display divergent behaviour. Indeed, we tested the GA over more than 100 generations and did not find any evidence of divergence. We also note that any potential bandwidth-related divergence will be limited by the transmission window of the various elements in the system (the SMF28 and HNLF fiber, couplers etc.) which will result in a finite minimum value of the objective function.

The algorithm iterates using standard GA techniques [START_REF] Mitchell | An Introduction to Genetic Algorithms[END_REF][START_REF] Simon | Evolutionary Optimization Algorithms[END_REF]. For each subsequent generation, 3 individuals are selected as elite and propagate deterministically through to the next generation without change of genes. A crossover fraction of 0.7 is then applied to the non-elite individuals to generate 33 individuals in the following generation that are constructed combining genes from individuals with the lowest fitness values. The remaining individuals are constructed from mutation.

We then iterate and monitor the evolution of the fitness values over a number of generations. All coding was performed in MATLAB using the Global Optimization toolbox. The elite and crossover fractions were based on typical algorithm parameterisations, but the GA was found to work over a wide range of values.

Typical results of the GA optimization procedure are shown in Fig. 5. Specifically, over 20 generations, Fig. 5(a) plots the mean objective function computed over the 50 individuals in the population (red stars), as well as the minimum objective function for the best individuals (black stars). For completeness, Fig. 5(b) shows the spectra of the best individuals for selected generations as indicated on the right hand axis. The GA evolution shown in the figure reveals that we rapidly enter into a regime of convergence. Indeed, for these particular results, the algorithm appears to identify the optimal regime after only 2 generations, although the precise evolution for any particular experiment does depend on the initial genes that are selected randomly. Nonetheless, additional testing revealed that between 2-4 generations to enter into the optimal regime was typical.

We also remark that there is some small variation in the best value of the objective function which is attributed to residual hysteresis in the laser operation, a well known effect in such lasers [START_REF] Girardot | Autosetting mode-locked laser using an evolutionary algorithm and time-stretch spectral characterization[END_REF]. Once the GA has converged, the spectral characteristics are visually identical to the solid black curve shown in Fig. 3, associated with -20 dB bandwidths of ∼170 nm. Note that we performed extensive tests with multiple runs of the GA starting from different initial conditions, and they all yielded similar results to those in Fig. 5 with comparable -20 dB bandwidths after optimization. We also tested the algorithm performance for populations in the range 20-100, and the population of 50 for which we show results here was found to reliably yield convergence to the broadband regime for any initial condition. No significant improvement in the results was obtained using more than 20 generations.

Generation

III. DISCUSSION AND CONCLUSIONS

As a general conclusion, these results provide further insight into the operation of NLP lasers, and provide an additional example of the utility of machine learning techniques in optimizing laser operation in complex regimes. Our experiments have clearly shown the strong dependence of NLP operation on the precise settings of the saturable absorber polarization settings, and directly revealed the very small fraction of the full parameter space that is associated with the broadest bandwidths. However, despite this complexity, automatic optimization using a genetic algorithm has been shown to effectively locate the broadest bandwidth operating regimes associated with -20 dB bandwidths of ∼170 nm within only a few generations (only a few minutes of alignment.)

These results represent a significant improvement compared to trial and error (human) optimization where the need to monitor multiple instruments whilst adjusting four waveplates results in typical alignment times of several hours. In this context, we anticipate that the search time for the genetic algorithm could be further reduced with improved instrumentation. Specifically, our setup suffered from two particular bottlenecks: (i) the use of a scanning OSA to measure the spectrum for each individual in the population and at each generation; (ii) the use of bulk motorcontrolled rotation stages to modify the waveplate orientations in the saturable absorber for each individual in the population and at each generation. Whilst this equipment choice was convenient for experimental flexibility in a laboratory setup, there are alternatives available that would result in significantly faster acquisition and adjustment. For example, it could be possible to use a long wavelength filter and a simple photodetector to optimize the extension of the output spectrum, and an integrated polarization controller could replace the bulk system that we employed. In an industrial setting, optimization times of less than a minute should be achievable.

IV. ADDITIONAL INFORMATION DATA AND CODE AVAILABILITY

Data are available from the corresponding author upon reasonable request. All code used in the manuscript was the standard GA suite within the MATLAB Global Optimization toolbox.

FIG. 1 .

 1 FIG.1. Schematic of the NLP laser and our experimental setup. Labels A-H refer to different fiber segments.

2 FIG. 2 .

 22 FIG. 2. (a) False-color plot mapping how the -20 dB spectral bandwidth of the laser output varies as a function of waveplate angles θ 3 and θ 4 with pump power at 195 mW. (b) An expanded view over the region indicated by the white square in (a) to illustrate the rarity of operating states of bandwidths exceeding ∼100 nm (corresponding to red regions in the plot).

FIG. 3 .

 3 FIG.3. 2000 spectra measured with the Anritsu OSA, selected randomly from the full scan (gray curves).

Fig. 2 .

 2 Fig.2. The broadest bandwidths constitute an even smaller fraction of the operating states, with only ∼0.5% of the measured bandwidths exceeding 100 nm at the -20 dB level.

FIG. 4 .

 4 FIG. 4.Histogram of the measured -20 dB bandwidths from the full cavity scan of 50,000 polarization settings of the saturable absorber. The main plot uses a logarithmic scale for the vertical axis whereas the inset shows an exploded view on a linear scale to illustrate the long-tailed nature of the distribution.

FIG. 5 .

 5 FIG. 5. (a) Evolution of the objective function over 20 generations of the genetic algorithm. At each generation, we show the mean of the population (red stars) and the particular individuals corresponding to the minimum fitness values (black stars). (b) For the data in (a) we show the spectrum of the best individual for the generations as indicated on the right hand axis.

ACKNOWLEDGEMENTS F.M, C.L, and J.M.D.acknowledge support from the French Investissements d'Avenir programme, project ISITE-BFC (contract ANR-15-IDEX-0003) and project EUR (ANR-17-EURE-0002). G.G. acknowledges support from the Academy of Finland (Grants 318082, 333949, Flagship PREIN 320165). J.M.D. and C. F. also acknowledge project ANR-20-CE30-0004.

AUTHOR CONTRIBUTIONS STATEMENT

C.L. and F.M. contributed equally to this work in the development and study of the experimental system. Data analysis and interpretation of the results was performed by all authors (C.L, F.M., C.F., M.H., G.G., J.M.D.), and J.M.D. also provided overall project supervision. All authors also contributed to writing of the manuscript.

COMPETING INTERESTS

The authors declare no competing interests.