Brigitte Grau

Anne-Laure Ligozat

Isabelle Robba

Anne Vilnat

Laura Monceaux
email: laura.monceaux@lina.univ-nantes.fr

FRASQUES: A Question Answering system in the EQueR evaluation campaign

Question-answering (QA) systems aim at providing either a small passage or just the answer to a question in natural language. We have developed several QA systems that work on both English and French. This way, we are able to provide answers to questions given in both languages by searching documents in both languages also. In this article, we present our French monolingual system FRASQUES which participated in the EQueR evaluation campaign of QA systems for French in 2004. First, the QA architecture common to our systems is shown. Then, for every step of the QA process, we consider which steps are language-independent, and for those that are language-dependent, the tools or processes that need to be adapted to switch for one language to another. Finally, our results at EQueR are given and commented; an error analysis is conducted, and the kind of knowledge needed to answer a question is studied.

Introduction

The growing interest for searching precise information on the Web or in collections of documents leads many researchers to develop question-answering (QA) systems. Such systems aim at providing either a small passage or just the answer to a question in natural language that pertains to factual information. Typical examples are "When was Franc ¸ois Mitterrand elected as president of France for the first time?", "Which animal becomes white in Winter?", "What is NATO?". In order to enlarge the search space, we work on two languages: English and French. This way, we are able to provide answers to questions given in both languages by searching documents in both languages also. At this time, we have developed three systems: QALC only processes English language, FRASQUES only processes French language, and the last one, MUSQAT, answers French questions in English. The three systems have been evaluated in QA evaluation campaigns. QALC participated to TREC 1 evaluation campaigns (from Trec8 to Trec11), MUSQAT participated to QA@CLEF 2 (in 2004 and 2005). We will present here FRASQUES and its results at the EQueR campaign [START_REF] Ayache | Campagne d'évaluation equer-evalda : évaluation en question-réponse[END_REF], the first campaign for Question Answering systems for French. EQueR is part of a larger evaluation campaign for natural language processing, EVALDA, which itself is part of a Technolangue program supported by the French Research Ministry. As we first developed QALC, we built FRASQUES by adapting it to French. So, when presenting FRASQUES in this paper, we will present how we modified the different processes that compose it. For this purpose, we will first present FRASQUES architecture in section 2. Then, section 3 will detail the modules, precise which ones 1 www.trec.nist.gov 2 www.clef-qa.itc.it are language-independent, and for those that are languagedependent, the changes that have been made to adapt them to a new language. We will finish by presenting and analyzing our results in section 4 before concluding.

Architecture of FRASQUES

Answer retrieval can be seen as a process able to recognize affirmative form of questions in texts, and thus to match a question with a sentence or a larger passage of text. The matching is possible only if linguistic variations between the two expressions are taken into account. Answering sentences can be seen as paraphrases of the questions, and thus it is important to recognize every possible variation of the question: synonyms (for example to elect and to vote), morphologic variants (for example to elect and election) and syntactic combinations of them (elected as president and presidential election). Thus, our QA systems focused on the recognition of these variations in the retrieved documents. Fastr [START_REF] Jacquemin | A symbolic and surgical acquisition of terms through variation[END_REF], a transformational shallow parser for the recognition of term occurrences and variants, will deal with multi-terms variants and extraction patterns with answer paraphrases. The architecture of FRASQUES (see Figure 1) is classically composed of tree main modules, namely a question analyzer, a document processing module and an answer extraction module. They all communicate by a central XML file. In order to process different languages, we defined common tags for equivalent language-dependent processes: POS tags and Named Entity tags. Question parsing is done thanks to the XIP parser [START_REF] Aït-Mokthar | Robustness beyond shallowness: incremental deep parsing[END_REF], which builds chunks and syntactical dependencies. Then, a set of rules calculates the focus (the object of the question that should be present in the answer) and the expected answer type, which can be either a named entity type or a general type, like colour, metal or music

Sentence processing

Sentence Weighting Figure 1: Architecture of FRASQUES, our question answering system instrument. This latter type is a word of the language. The search engine we use to explore the corpus is Lucene 3 , a Boolean search engine. The request sent to Lucene is made with the not empty words of the question, and, if no document is returned, a relaxed request is sent. The retrieved documents are then given to Fastr and the documents are reordered according to the presence of the question terms and their variants. Finally a subset of fifty documents is selected, and these documents are annotated with named entities types. The last module first computes a weight for each sentence of the selected documents, depending on the presence of question terms or variants, and only the sentences with a certain weight are kept. Then, we use a different approach if the expected answer is a named entity or a phrase of a general type. In this second case, we select answers by applying extraction patterns on the candidate sentences. These patterns are based on a morpho-syntactic tagging of the sentences and a particular tagging of the question terms or their synonyms. Patterns are recognized in sentences thanks to the Cass parser [START_REF] References | Partial parsing via finite-state cascades[END_REF].

Building a multilingual system

Question analysis

The question analysis module relies on a part-of-speech tagging and a syntactic parsing. Then several elements of information are determined: expected answer type, focus, question category, proper names of the question... The results of the question analysis will be used by all the other 3 http://lucene.apache.org/ modules of the system. An example of question analysis is given in Figure 2. In order to be able to switch from English to French, our first step had to consist in adapting the tagger and parser to the new language. The tool we use for the part-of-speech tagging is the TreeTagger4 in English, and both the Tree-Tagger and the XIP part-of-speech tagging step in French (the results of each tagger are merged in order to improve the tagging quality). TreeTagger parameter files exist in both English and French, and the output is the same for all the existing languages; XIP's output is converted into the TreeTagger format. As for the syntactic parser, two different tools are used: XIP for French in EQueR, and Cass for English. It was thus decided to project the syntactic analysis of the question in a more neutral format, this of the syntactic parsers evaluation campaign EASY5 . The output of each parser is converted into this format so that the rest of the question analysis be independent of the used parser. Then, the morpho-syntactic and syntactic analyzes are used to infer the characteristics of the question. Specific lexicons and rules have been developed for this task, but the core of this module is independent from the language. Thus, both languages are processed in a parallel way and some of the information returned use the same terms in French and in English, like for example the question category or the expected named entity type. Adding another language is therefore made easier, since only the lexicons and the pattern files should change, as summed up in Figure 3. This module was evaluated on corpora of similar questions in French and in English, and its results on both languages are quite close: around 90% of recall and precision for the expected answer type for example (for more details, see [START_REF] Ligozat | L'extraction des réponses dans un système de question-réponse[END_REF]).

Document retrieval

The search engine for the French collection is Lucene, a Boolean engine. The English collection is searched by MG 6 . As MG can operate Boolean or ranked retrievals, we exploited this characteristic to first conceive Boolean queries, and if they brought out too few or too many documents, we complement them by a ranked retrieval based on the cosine measure. The collection was indexed using the stemming option of MG. Queries are based on POS categories of words and a set of stop words. Proper Nouns and numeric data in the question are favoured. For the French collection, we switched to Lucene as MG had problems with accented words. As Lucene does not provide a stemmer, and as all our processes work on lemmatized texts, we decided to tag the whole collection using the XIP lemmatizer, combined with the TreeTagger for some specific cases, before indexing it. At the moment, in French, we only make use of basic Boolean queries, based on the question words and not their synonyms, thus the search engine returned documents containing the exact answer for only 73% to 76% of the questions compared to about 80% in English. Fortunately, the further election of fifty of these documents after re-indexation by Fastr did not entail any further loss.

Document Processing

Terms (composed of either a single word or of several words) are extracted from the questions through partof-speech filtering according to patterns describing noun phrases. Then the occurrences or variants of these terms in the documents are detected by Fastr rules enabling morphological and semantic transformations. Morphological families and set of synonyms are data given to Fastr. Thus, dealing with several languages requires conceiving transformational rules in each language.

The following pattern extracts the occurrence making many automobiles as a variant of the term car maker:

VM('maker') RP? PREP? (ART (NN|NP)? PREP)? ART? (JJ| NN| NP |VBD|VBG)0-3 NS('car')

VM('maker') is any verb in the morphological family of the noun maker and NS('car') is any noun in the semantic family of car. In French the rule for retrieving the variant is the same, while the original term is described by fabricant de voiture (NN of NN). Named Entities types are classical and we developed two modules for recognizing them. A first one for noun phrases: person, organization, state, city and a second module for numeric entities: different kinds of date (with the year, a day of a month, etc.), time, duration, period, etc. The first system is based on manually developed sets of rules that rely upon lexical information, linguistic constraints of language and contextual information. It was develop for French and English [START_REF] Elkateb | Extraction d'entités nommées pour la recherche d'informations précises[END_REF]. Rules combine constraints on words based on word features that are: the original form of the word, its lemma, its POS category, its semantic type(s) if it belongs to lexicon(s) (for instance first name or city) and its typography. A high level language was conceived for these rules and allows the description of all kinds of entities with few rules. For English, there are 7 rules for person recognition, 9 for locations and 7 for organizations. In French, there were 11 rules for persons, 19 for locations and 13 for organizations.

Here an example of a complex rule that tags an enumeration of persons in the input text. An enumeration is a sequence of persons names separated with commas. We have to tag each person alone. This rule is the same in the two languages. PMAJ signifies that the first letter is capitalized, ROM that the word has to be in Roman characters. Only the resources firstname has to be adapt for each language. The second module is developed in Perl language and is based on rewriting rules, also manually developed, but they are more numerous than those of the first system. Thus, only rules and data were to be changed, the core system remaining the same. For numeric entities, we based our conception on the English rules, and adapted them to French. Thus, adapting each rule written for English was faster than re-conceiving the initial set of rules, as for those local grammars, English and French are very close languages.

Sentence Processing 3.4.1. Patterns

The answer extraction module aims at extracting short answers from the candidate sentences. Candidate sentences are themselves extracted from the selected documents and then reordered by Fastr. In Frasques two strategies are adopted depending on the type of the expected answer. If the expected answer is a named entity, Frasques returns the named entity which is the nearest of the barycenter of the question words or of their variants. In the other cases, the extraction is more difficult, because we cannot rely as strongly on the type of the answer, which can be as well a verb a noun or an adjective, and the answers cannot be tagged as for named entities. Hence, we apply different patterns according to the type of the question and taking into account information provided by the question analysis. In the EQueR evaluation, we chose to use Cass parser for this extraction and we wrote patterns using Cass grammar rule formalism. Here, Cass is not used as a sentence parser, but its rule formalism enables us to tag the possible answers in the candidate sentences. Cass parser takes two files as input: in the first file, the sentences to parse are tagged by a morpho-syntactic parser (the TreeTagger is used in our architecture); and in the second file, the main characteristics of the question (provided by the question analysis) are tagged with particular tags: the focus (FC), the main verb (MV), the expected answer general type (GT). When they are available, the synonyms of these characteristics are also tagged. Cass is a cascaded finite-state parser; its rules are organised in several different levels and written as regular expressions. Figure 4 shows how we use these levels to tag the possible answers. The first level enables us to tag the different nominal groups (NG): NGFoc for instance is a nominal group that contains the question focus, while NGNP is a nominal group containing a proper noun (NP). Then, at the second level, the pattern FocusLeftAnswer expresses that if the candidate sentence contains an NGFoc followed by a separator followed by an NG then the NG is tagged as a possible answer.

These patterns enable us to correctly answer to the question Quelle est la monnaie nationale en Hongrie ? (What is the national currency in Hungary?). In this question the focus is monnaie (currency) and the main verb is être (to be). The correct answer is in the following candidate sentence La Banque nationale de Hongrie a dévalué la monnaie nationale, le forint, de 1 %... (The Hungarian National Bank devaluated the national currency, the forint, of 1%...). The final extraction module returns the NG the forint tagged by b=:

[FocusLeftAnswer [NGFoc [DT the] [ADJ national] [FC currency]] [VIRG ,] b=[NG [DT the] [NN forint]] ]
Using Cass formalism to write the extraction patterns presents several advantages. First of all, the rules are easily and quickly written. Moreover Cass application is not time consuming: as described in [START_REF] References | Partial parsing via finite-state cascades[END_REF], the speed of Cass is quite sensitive to the number of levels in the grammar, and in our patterns the maximum number of level is 4. Lastly, the passage from French to English is not difficult, few patterns are added, most of them consist in a simple translation of the Tree Tagger tags.

Sentence weighting and answer extraction

Sentence weighting is based on the presence rate of the question terms, either in their question form or in a variant form. The words are weighted according to a general resources built on a large corpus that encodes the significativity rate of a word according to its total number of occurrences in the corpus and the number of documents that contain it. A reward is added if some of the following features are present: words in the candidate sentence exactly the same as in the question, proximity of the words, presence of a named entity of the expected type. In order to extract the answer string, sentences are analyzed with Cass for applying extraction patterns. Patterns are language-dependent; however the process that tags the words depending of their role in the question and extract the phrases that are potential answers are quite the same in the two languages.

Results analysis

EQueR results

The EQueR campaign aimed at offering a evaluation opportunity for QA systems for French. The document collection came from different sources such as the newspapers Le Monde, or Le Monde Diplomatique or Senate debates. The types of questions proposed were quite varied: factual questions, definition questions, list questions (such as Quelles sont les 4 religions pratiquées en Hongrie ?), yes/no questions, as well as reformulations of some of the factual questions. Some of the questions had no answer in the corpus; the expected answer was then NIL. The general task (there was also a medical task) contained 500 questions with 407 factual questions, 32 definition ones, 31 list ones, and 30 yes/no ones. For each question, the systems were expected to return either the short answer to the question or a passage containing it. Up to 5 answers were authorized.

For this campaign, we submitted two runs, in order to test different selection document strategies. For the first run, all proper names were used without considering the threshold of 200 documents; for the second run, we checked the number of documents after each query. In the runs given for the campaign, a error remained in our last module, which reduced the size of the long answers, so we indicated here what our results could have been without this error. It is interesting to notice that the results on short answers are not far from those obtained by our English system QALC in the Trec evaluations. EQueR results being for the first five ranks, while Trec ones being for the first rank only, they could have been expected to be higher. Yet, in Trec, the Web was used as an additional source of information, and the answers provided by the collection and the Web were merged in order to improve the performance of our system.

Importance of synonyms

We conducted a first study that measures the rate of question words and synonyms in the answering sentences of our system as well as of the participants in EQueR [START_REF] Barbier | Semantic knowledge in question-answering systems[END_REF]. The goal of this study was to determine what type of variants from the question words was most useful when searching for the answer. First, we checked that synonyms could be found for EQueR questions. While the average number of words per question was of about 6, around 13 Fastr synonyms and 7 Eu-roWordNet synonyms could be found. Then we studied the corpus formed by the correct passages given by the participants and we calculated the presence rate of synonyms in these passages. Among these passages, 82% do not contain any Fastr synonym, and 88% do not contain any EuroWord-Net synonym. The question words are much more frequent (60%) in the passages than the Fastr (4%) or EuroWordNet synonyms (3%). Several reasons explain those rather low rates of synonyms in the corpus. First, the synonym bases are not the ones the other participants use, moreover few of them take into account such knowledge. Second, in EQueR, a lot of correct answers could be found with the words of the question. It seems (it is also true in TREC campaigns) that there is often at least one formulation close to the question, which is probably due to the large amount of documents (1.5 gigabytes). Yet, since very few synonyms of the question words are found in the answers, the issue of the type of knowledge to use in QA systems should be explored.

Error analysis

In order to be able to improve our system, we traced part of its errors: as our goal was to study the answer extraction, we particularly focused on the questions for which our system extracted incorrect answers from sentences containing good answers. The corpus was thus of 74 questions. Several causes of errors were observed: 25 incorrect answers came from the use of a wrong pattern.

In 7 questions, the question analysis module wrongly returned a named entity as the expected answer type.

In 11 questions, the question analysis module failed to recognize a named entity type: for the question, À quel endroit s'est terminée la 21e édition du Dakar ? (In what place did the 21st Dakar rally finish?), the question analysis did not return the expected type LO-CATION.

In 15 questions, the answer extraction module had to chose between several named entities of the expected type, and chose an incorrect answer: for the question Combien y a-t-il de membres non-permanents au Conseil de Sécurité de l'ONU ? (How many nonpermanent members are there at the UN Security Council?), the system returns the incorrect answer cinq present in the sentence Le Conseil de scurit compte actuellement quinze membres dont cinq permanents disposant du droit de veto (...) et dix nonpermanents.

In 11 questions, the correct answer was not tagged with the correct named entity type: for the question Où sont exposées "Les Noces de Cana" ? (Where are "The Wedding Feast at Cana" displayed?), the answer Louvre is tagged as a proper name and not a location.

The remaining 5 errors are diverse. This error analysis was useful since it helped us spot the weaknesses of our system, and we conducted more thorough studies for some of the above issues: the pattern sets have been revised, and the lexicons used by the question analysis module were extended.

Conclusion

In this article, we have presented our French Question Answering system FRASQUES. This system has been adapted from our English Question Answering system QALC, which has been evaluated in the TREC campaign. All along this paper, we detailed the processes which are language independant, and for those that are language-dependent, we present the changes that have been made to adapt them to a new language. Our system has been built to allow a rather simple shift from a language to another. We then develop a system which is able to provide answers to questions given in both languages by searching documents in both languages also, that is MUSQAT which participates to multilingual evaluations (CLEF campaign). With these three systems, we are able to compare the results we obtained during the different campaigns. We also try to obtain benefits of these different experiments, to enhance our global results.

FocusFigure 2 :

 2 Figure 2: Example of a question analysis: Citez une filiale de la Générale des eaux ?

Figure 3 :

 3 Figure 3: Question analysis module

  "firstname"} OR {typography == "PMAJ"}) [1,5] ({typography == "ROM"} [0,1] (PERSON_COMMA) [0, 10] --> {Type ="PERSON", Rule = "Enumeration"}

Level 1 :Figure 4 :

 14 Figure 4: Pattern example in Cass grammar rule formalism

Table 1 :

 1 Table 1 presents the results we obtained at EQueR, and compares them to those obtained at TREC11 (for English). EQueR and TREC results

		Long	MRR	Short	MRR
		answers		answers
	EQueR run1	42%	0.37	26%	0.22
	EQueR run1	60%	0.48
	(corrected)
	EQueR run2	37%	0.32	24%	0.20
	Trec9	56%	0.40
	Trec11			28%
	(1st rank)

http://www.ims.uni-stuttgart.de/projekte/corplex/TreeTagger/

http://www.limsi.fr/Recherche/CORVAL/easy/

MG for Managing Gigabytes http://www.cs.mu.oz.au/mg/


Nicolas Dubos

Olivier Dehorter

Pierre-Yves Henry

Thermal constraints on body size depend on the population position within the species' thermal range in temperate songbirds

Keywords: Bergmann's rule, birds, climate warming, France, temperature anomaly, thermal range, wing length

Temperature effect on size along thermal range

INTRODUCTION

Although an increasing attention is given to body size change as a response to climate warming [START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF], this phenomenon is still little documented and its underlying mechanisms are poorly understood. The effects of rising temperatures on animal structural size can be mediated through effects on juvenile growth and size-dependent mortality (Gardner et al., 2014). The original proposal was that body size would decline with warming as a result of the advantage of being smaller under warmer conditions. With a higher surfacevolume ratio, smaller individuals can dissipate body heat more efficiently than larger individuals, which is advantageous in warm climates, as stated in Bergmann's rule [START_REF] Bergmann | Uber die Verhaltnisse der Warmeokonomie der Thiere zu ihrer Grosse[END_REF]. With climate warming, larger individuals would increasingly suffer from hyperthermia, and a size reduction is a possible adaptive response enabling individuals to cope with increasingly warm conditions [START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF].

The application of Bergman's rule to climate warming has received controversial evidence so far [START_REF] Teplitsky | Climate warming and Bergmann's rule through time: is there any evidence?[END_REF]. Despite rising temperatures, many species have not exhibited any change in body size over time [START_REF] Meiri | Global change and carnivore body size: data are stasis[END_REF][START_REF] Kruuk | Contrasting effects of climate on juvenile body size in a Southern Hemisphere passerine bird[END_REF], or the trend was opposite to the prediction, i.e. size increase [START_REF] Björklund | Increase in body size is correlated to warmer winters in a passerine bird as inferred from time series data[END_REF][START_REF] Pérez | Nestling growth rates in relation to food abundance and weather in the Arctic[END_REF]. This may be related to the complexity of temperature and other climatic impacts on physiology and body size (Gardner et al., 2014). Temperature change can potentially have contradictory effects depending on which biological feature is affected (e.g., body growth versus survival), and which aspect of temperature change is regarded (e.g., mean temperature versus heat wave frequency). For instance, increasing mean temperatures may impact body growth positively (Gardner et al., 2014), which is contradictory with the proposal of an application of Bergmann's rule to climate warming (i.e., selection for smaller in warmer mean temperatures). Besides, heat waves may select for larger individuals as a result of a lower evaporative water loss, enabling them to better evade dehydration [START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF].

More importantly, the effect of temperature fluctuations probably differs between climatic regions. For instance, the physiological and ecological consequences of annual weather deviation are likely to depend on the average local climatic regime: in cool or cold regions (e.g., Collins et al., 2016;[START_REF] Pérez | Nestling growth rates in relation to food abundance and weather in the Arctic[END_REF][START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF], or during cool periods of the year (e.g., Gardner et al., 2014b), hot temperatures indeed affect body growth positively. In addition, events of extreme heat are also scarcer in temperate climates than in arid systems [START_REF] Garcia | Multiple dimensions of climate change and their implications for biodiversity[END_REF]. Observed body size variations are therefore expected to represent the response to fluctuations in average temperatures in temperate climates [START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF], whereas the influence of extreme hot events is expected to be particularly strong in arid, semiarid and tropical climates [START_REF] Holmgren | Extreme Climatic Events Shape Arid and Semiarid Ecosystems[END_REF][START_REF] Gardner | Effects of extreme weather on two sympatric Australian passerine bird species[END_REF]. In arid or semi-arid climates, larger individuals are expected to survive heat waves better, presumably because the smallest individuals show higher rates of evaporative water loss, and would be more exposed to dehydration and mortality during heat waves [START_REF] Mckechnie | Climate change increases the likelihood of catastrophic avian mortality events during extreme heat waves[END_REF].

For the same species, temporal variation in body size can differ between sites (e.g., [START_REF] Meiri | Global change and carnivore body size: data are stasis[END_REF][START_REF] Collins | Heterogeneous changes in avian body size across and within species[END_REF][START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF]. Within a species distribution range, populations are likely to have adapted locally to average meteorological conditions (e.g., [START_REF] Both | Climate change and timing of avian breeding and migration throughout Europe[END_REF]. Their response to changes in environmental conditions may therefore differ between the hottest and the coldest parts of their distribution range [START_REF] Both | Climate change and timing of avian breeding and migration throughout Europe[END_REF][START_REF] Socolar | Phenological shifts conserve thermal niches in North American birds and reshape expectations for climatedriven range shifts[END_REF]. This is the case for population trends of European birds: abundances decline towards the hot edge of their species distribution range, while they increase towards the cold edge [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]. Differential responses to climate change were also observed in avian phenology, with advancements in egg laying near the cold edge but not near the warm one (depending on the species; [START_REF] Both | Climate change and timing of avian breeding and migration throughout Europe[END_REF]. A similar pattern was found in the nesting success of Californian birds, with a positive effect of temperature anomaly towards the cold edge of species distributions, and a negative effect towards the warm edge [START_REF] Socolar | Phenological shifts conserve thermal niches in North American birds and reshape expectations for climatedriven range shifts[END_REF]. Individuals living close to the hot edge of their species distribution range are the most threatened by climate warming, because they live close to their upper thermal limit already [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF][START_REF] Deutsch | Impacts of climate warming on terrestrial ectotherms across latitude[END_REF][START_REF] Tewksbury | Putting the Heat on Tropical Animals The Scale of Prediction[END_REF][START_REF] Socolar | Phenological shifts conserve thermal niches in North American birds and reshape expectations for climatedriven range shifts[END_REF]. Conversely, individuals living at the cold edge are more coldlimited and would even benefit from hot anomalies, as a result of a lower exposure to cold stress [START_REF] Jiguet | Thermal range predicts bird population resilience to extreme high temperatures[END_REF]. Hence, across thermal ranges, the impact of climate warming on populations is expected to change gradually, and ranges from positive at the cold edge towards negative at the hot edge [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]. The influence of thermal anomalies would therefore depend on the relative position of the population within the distribution range, even within the inner part of species thermal ranges. Although this variation of the effect of temperature anomalies across a species range is now well acknowledged for population trends [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF], to our knowledge, it has not yet been investigated on body size responses to temperature changes.

Contrasting effects of temperature increase on body size across the thermal range are expected to occur through two main mechanisms: (i) direct, thermoregulatory costs, and (ii) indirect, ecological effects through ecosystem productivity [START_REF] Yom-Tov | Recent spatial and temporal changes in body size of terrestrial vertebrates: probable causes and pitfalls[END_REF] and temporally mismatched predator-prey interactions [START_REF] Husby | Testing mechanisms of Bergmann's rule: phenotypic decline but no genetic change in body size in three passerine bird populations[END_REF]. Firstly, the ability to thermoregulate depends on morphology, and the thermal constraint affecting morphology is expected to depend on the local climate. For instance, in song sparrows (Melospiza melodia), selection for heat retention was found to prevail in a continental climate during winter [START_REF] Danner | A critical season approach to Allen's rule: bill size declines with winter temperature in a cold temperate environment[END_REF], while for the same species, it was driven by heat dissipation in a Mediterranean climate during summer [START_REF] Greenberg | Heat loss may explain bill size differences between birds occupying different habitats[END_REF]. In this case, the differential morphological change affecting thermoregulation was applied to bill size. However, this should also apply to structural size, as heat loss/conservation can depend on the size of body appendices (e.g., Allen's rule; [START_REF] Allen | The influence of physical conditions in the genesis of species[END_REF] as well as on structural size (e.g., Bergmann's rule). In cold or cool regions (e.g., temperate to polar), individuals may be larger in warmer years (Collins et al., 2016;[START_REF] Pérez | Nestling growth rates in relation to food abundance and weather in the Arctic[END_REF][START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF] when the cold constraint on growth is alleviated. Tissue growth increases with temperature in two ways: by accelerating biochemical reactions and metabolism [START_REF] Gillooly | Effects of Size and Temperature on Metabolic Rate[END_REF], and by reducing the allocation of energy used for body heat maintenance [START_REF] Kendeigh | Tolerance of Cold and Bergmann's Rule[END_REF], so this energy can be reallocated to growth [START_REF] Gillooly | Effects of Size and Temperature on Metabolic Rate[END_REF][START_REF] Dawson | The importance of microclimate variation in determining size , growth and survival of avian offspring : experimental evidence from a cavity nesting passerine[END_REF]. Nestling growth may also be indirectly facilitated by warmer temperatures through the reduced thermoregulary load for parents: parents can spend more time foraging to provision nestlings with food, and less time at the nest to maintain them warm (e.g., [START_REF] Socolar | Phenological shifts conserve thermal niches in North American birds and reshape expectations for climatedriven range shifts[END_REF]. In warmer regions (e.g., dry tropical and Mediterranean), the risk that a temperature increase reaches detrimental or sub-lethal levels is higher [START_REF] Khaliq | Global variation in thermal tolerances and vulnerability of endotherms to climate change[END_REF]. Larger individuals may suffer more from increasing temperature, as interpreted with the application of Bergmann's rule to warming [START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF]. Secondly, body size depends on food availability during ontogeny. For secondary consumers, food availability depends on temperature-driven primary production [START_REF] Yom-Tov | Recent spatial and temporal changes in body size of terrestrial vertebrates: probable causes and pitfalls[END_REF]. In temperate regions, precipitation is rarely limiting, and higher temperatures would increase invertebrate abundance, i.e. the main resource for nestling and fledgling songbirds [START_REF] Bale | Herbivory in global climate change research: Direct effects of rising temperature on insect herbivores[END_REF]but see Carroll et al. 2015 for an opposite response in hygrophilic peatlands). In semi-arid systems, such as Mediterranean regions, invertebrate abundance is more constrained by drought, resulting from limited rainfall combined with high temperatures (Gardner et al., 2014). An increase in spring temperature may therefore result in larger body size in cool climates, whereas it could result in smaller body size in Mediterranean or dry tropical climates, in the case of co-occurrence with limited precipitation. Hence, direct and indirect effects of temporal variation in mean temperature on body size are expected to differ between the hottest and the coldest parts of the species ranges (Fig. 1).

We assessed whether the effect of interannual variation in mean spring temperature on juvenile body size varies along a thermal gradient (11.2°C between the coldest and the hottest study sites; Fig. 1) in a temperate region (France) for nine songbird species. We predicted that, during hot springs (relative to the local average temperature), juveniles should be larger at the coldest sites, and smaller at the hottest sites (Fig. 1). In temperate climates, the tippingpoint of the effect of local temperature on body size sensitivity to temperature anomalies should depend on the position of populations within the species thermal ranges: the colder the location of a population, the more its growth should increase with temperature anomaly.

METHODS

Bird survey

We used individual records of songbirds caught during sessions of the French Constant bird ringing Effort Sites (CES) scheme, from 2000 to 2014 (Robinson et al., 2009; more information at http://crbpo.mnhn.fr, see 'STOC Capture'). Biometric data used in the present study were collected at 204 sites by 132 volunteer bird ringers, each site being monitored during 4.1 ± 3.3 SD years (Dehorter & CRBPO 2015). Each site was visited at least three times during the breeding season (average 3.6 ± 1.6 SD), from 15 May until 19 July. For a given site, number and location of mist-nets were kept constant throughout the years. Each captured individual was individually marked, identified to species and aged (juvenile for birds born during the ongoing breeding season; [START_REF] Svensson | Identification guide to European passerines[END_REF]. Most sites are located in shrublands, woodlands with dense understorey, or reedbeds [START_REF] Eglington | Latitudinal gradients in the productivity of European migrant warblers have not shifted northwards during a period of climate change[END_REF]. Our survey encompassed three major types of climate based on the Köppen Geiger classification [START_REF] Peel | Updated world map of the Köppen-Geiger climate classification[END_REF]: subalpine (corresponding to the subarctic climate, Dfc), temperate oceanic (Cfb), and hot-summer Mediterranean climates (Csa), with a thermal range of 11.2°C between the coldest (8.4°C on average) and the hottest sites (19.6°C on average; Fig. S1) during spring.

Biometric data

Wing length measurements were used as a proxy for body size [START_REF] Gosler | The field determination of body size and condition in passerines: a report to the British Ringing Committee[END_REF]; data for supposedly better proxies of body size, such as tarsus or longuest feather lengths were not available, and body mass data conveyed an information on precipitation-dependancy of body condition rather than on temperature-dependancy of body size, see [START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF]. We worked on post-fledgling juveniles only, because individual body size is determined during a short period of growth in small songbirds, taking place mainly during the nestling stage (c. 2-3 weeks), and continuing for a few weeks after fledging [START_REF] Salewski | Global warming and Bergmann's rule: do central European passerines adjust their body size to rising temperatures?[END_REF]Yom-Tom & Geffen 2011). When recaptures occurred (representing 10% of the data), we randomly selected one measurement per individual. In May-July, when captures took place, juvenile songbirds are still within a few kilometres from their birth site, and captured individuals can be assumed to have grown under the documented local climatic conditions. Adults were not considered as their wing length depends on multiple, confounding effects of climate throughout the life cycle (ontogeny, yearly molt and size-dependent mortality; Yom-Tom & Geffen 2011; Gardner et al., 2014).

As small sample sizes and data sparseness can compromise the robustness of inferences [START_REF] Yom-Tov | Recent spatial and temporal changes in body size of terrestrial vertebrates: probable causes and pitfalls[END_REF], we decided to include data for only (i) species ≥ 1000 measured individuals, and (ii) species.site.year sampling units with ≥ 10 measured individuals (Table S1). Since the hypotheses to be tested required that population position within the species thermal ranges varied across sampling sites (i.e., gradient of 'northern' / core / 'southern' populations), we measured the proportion of each species' thermal range that was included in our study area. To do this, we relied on the population thermal coordinate [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF], an index of the relative position of a given site, for a given species, within its European thermal range (Table S1;Fig S1). A population thermal coordinate is computed as the difference between the species thermal maximum (mean spring temperature of the hottest 5% of European Atlas grid cell; [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF] and the average temperature of a given site, divided by the species thermal range (°C). This index varies between 0 and 1. Values close to 0 represent populations near the species thermal minimum; values closer to 1 are populations near the species thermal maximum. We discarded one species (Acrocephalus schoenobaenus), because the thermal gradient represented by the study sites was very narrow (2.2°C between the coldest and the hottest sites, representing less than 15% of the species thermal range). For the remaining species, a wider proportion of their thermal ranged was represented (minimum for Sylvia communis = 31%, representing a thermal gradient of 4.2°; respectively, mean = 58% ± 13 SD and 8.5°C ± 2.3 SD for all species in Table S1). For seven species, surveyed sites fell well within the species thermal range (and edges were not documented), whereas for two species (Long-tailed tit Aegithalos caudatus, Common chiffchaff Phylloscopus collybita), some sites corresponded the hot edge of their respective thermal ranges. According to habitat preference, one species is a reedbed specialist (Common reed-warbler Acrocephalus scirpaceus), whereas the eight others are shrubland / woodland generalists (Great tit Parus major, Eurasian Blue tit Cyanistes caeruleus, Eurasian blackcap Sylvia atricapilla, Common whitethroat Sylvia communis, Common chiffchaff, Long-tailed tit, Eurasian blackbird Turdus merula, and European robin Erithacus rubecula; cf. Table S1, Fig. S2). The final dataset included nine species, all living in relatively similar thermal niches, resulting in a total of 34 101 juveniles measured (see details per species in Table S1).

Climatic data

We used daily mean temperature data, obtained from E-Obs [START_REF] Haylock | A European daily high-resolution gridded data set of surface temperature and precipitation for 1950-2006[END_REF], and for each site we computed: (i) yearly 'spring temperatures' (noted TS.Y), i.e. the mean temperature of a given year, at the site, for spring (from 1 April to 31 July, documenting between-year fluctuations of local thermal conditions), and (ii) 'local average temperature' (noted Ts), as the mean of TS.Y over the 2000-2014 period (documenting average or 'normal' thermal conditions at the geographical location of the capture site for the 1 April -31 July period). Because species are expected to be adapted to local thermal conditions (c.f., Bergmann's rule; Ashton 2002), we analysed the interannual variation in body size in response to temperature variations using annual local temperature anomalies (instead of raw temperatures). Local temperature anomalies (noted TAst) were computed for each site as the difference between TS and TS.Y. Analysing the effects of temperature anomaly and local average temperature simultaneously, enables the respective effects of temporal (TS.Y) and spatial (TS) variations in thermal conditions on body size to be disentangled. Temperature anomaly and local average temperature were largely uncorrelated (Pearson's r = 0.007).

Statistical analysis

Using Linear Mixed Models (MCMCglmm; [START_REF] Hadfield | MCMC methods for multi-respoinse generalized linear mixed models: The MCMCglmm R package[END_REF], we assessed the effects of yearly temperature anomalies TAst on the juvenile body size of our study species, and its interaction with the local average temperature Ts (to assess whether the effect of TAst varied along the species thermal range). We used uniform priors, with a burn-in of 20 000 iterations, followed by an additional 100 000 iterations for which posteriors were sampled with an interval of 100.

We first built null models (Model 0 in Table 1) that included only adjustment variables, to verify that the inclusion of temperature variables enhanced the explanatory power. The null model, and all the following models (Table 1) accounted for the following sources of variation in wing length: (i) differences in mean size between species (fixed, factorial Species effect), (ii) species-specific post-fledgling growth throughout the season, using logtransformed Julian date (noted log(Date)) as a fixed, linear effect in interaction with species [START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF], (iii) temperature-driven spatial differences between sites (e.g.

Bergmann's rule) using a fixed, linear effect of local average temperature Ts, and (iv) speciesspecific dependence on local average temperature (fixed, factorial Species x Ts interaction). This interaction term is justified by the fact that species may intrinsically respond differently to temperature [START_REF] Ashton | Patterns of within-species body size variation of birds : strong evidence for Bergmann's rule[END_REF], or may respond differently because the thermal ranges of the study species differ (e.g., for some species, French populations are located at the core of the thermal range, whereas for other species, French populations are closer to the species hot limit; Jarema et al., 2009). Consistent (v) between-observer, (vi) between-site and (vii) residual between-year variations were accounted for by random terms. Finally, (viii) comparative tests across species accounted for phylogenetic relatedness using pairwise phylogenetic distances. We extracted a set of 100 generated phylogenetic trees from [START_REF] Jetz | Global Distribution and Conservation of Evolutionary Distinctness in Birds[END_REF] and integrated these using the 'pedigree' argument of the MCMCglmm function, that allows the portion of body size variation due to additive genetic variance to be disentangled from other sources of variance.

Then we built a set of models to assess the statistical support for our prediction. We first considered the dependence of wing length on temperature anomalies (linear, additive effect of TAst, Model 1). Then we accounted for the possibility that species respond differently [START_REF] Jiguet | Thermal range predicts bird population resilience to extreme high temperatures[END_REF] by adding the TAst × Species interaction term (Model 2). The dependence on temperature anomaly could differ along the observed thermal gradient; this was allowed for by adding the TAst × Ts interaction term to model 1 (Model 3). In addition, this hypothesis was assessed with a model that also accounted for the possibility that species response to TAst differed between species (i. e. adding the TAst × Ts interaction to Model 2, resulting in Model 4). Eventually, we allowed for species-specific relationships between temperature anomaly TAst and local average temperature Ts, by adding a 3 rd -order interaction term between the effects of TAst, Ts and species (Model 5). This model allows for a different direction and/or strength of both temperature effects between species. Model 5 results in the following formula:

Wing Lengthisot ~ αi + βi1 . log(Date) + βi2 . Ts + β3 . TAst + βi3 . TAst + β4 . (TAst × Ts) + βi4 . (TAst × Ts)

+ 𝜀s + 𝜀o + 𝜀t + εisot
where αi is the average size of species i (intercept), βi1 is the slope for the effect of logtransformed Date for species i, βi2 is the species-specific slope for the effect of local average temperature Ts, β3 is the slope for the additive effect of temperature anomaly TAst, βi3 is the species-specific deviation from β3 (species interaction term), β4 is the slope for the interaction between the effects of temperature anomaly TAst and local average temperature Ts, βi4 is the species-specific deviation from β4 (species interaction term), 𝜀s, 𝜀o and 𝜀t hold respectively for the random terms for site, observer and year effects, and εisot is the residual variation.

The stepwise examination of predictions relied on the comparison of the six aforementioned models (Table 1), ranked on the basis of the Deviance Information Criterion (DIC, a Bayesian version of Akaike Information Criterion; [START_REF] Spiegelhalter | Bayesian measures of model complexity and fit[END_REF]. The model with the lowest value of DIC is considered to represent the best trade-off between parsimony and fit of the model to the data. Each model was fitted using 100 different phylogenetic trees, so that the average of all posteriors accounted for between-species phylogenetic dependence. All statistical analyses were performed under R version 3.3.0 (R Core Team, 2016).

RESULTS

The body size response to temperature anomaly TAst differed between species. The model allowing for species-specific responses was better supported than the model assuming an additive response, common to all species (Model 2, Table 1). In accordance with our prediction, this response to TAst varied along thermal gradients (Model 4 and 5 received the highest statistical support; Table 1). The effect of temperature anomaly on body size depends on the local average temperature.

On average across species, at an intermediate site (i.e., for a mean local average temperature Ts = 15.05°C) the higher the temperature anomaly, the longer the wing length (+0.9 mm per °C anomaly; Model 3 in Table S2). But, the warmer the site (local average temperature, Ts), the lower the effect of temperature anomaly on wing length (for a +1°C increase in local average temperature, the effect deceases by 0.052 mm per °C anomaly; Model 4 in Table S2).

At the hottest sites, the effect of temperature anomaly was even reversed, with a potential decrease in wing length in the warmest years (Fig. 2). The nature of this 'temperature anomaly -by -local average temperature' interaction may differ between species, but these differences seem to be of minor importance in our dataset (since ΔDIC is only 2 between models 4 and 5; Tables 1,S2). When plotting estimates for the interactive effects of TAst and Ts per species (Fig. 3,S2), the response of body size is largely similar across species. Relying on model 5, the three species showing a significantly positive effect of temperature anomaly at the coolest sites showed a significant interactive effect with local average temperature (i.e., Eurasian blackcap, long-tailed tit and great tit; Table S2). At the coolest sites (between 8.37 and 13.9°C depending on the species), body size increased significantly in warmer years for these species (respectively, by 0.86, 1.71 and 0.54 mm per °C; Table 2). The temperature anomaly effect decreased when the local average temperature increased: for a +1°C increase in local average temperature, the wing length of Eurasian blackcaps decreased by -0.072 mm per °C of anomaly, -0.324 mm per °C for long-tailed tits, and -0.072 mm per °C for great tits (Table S2). This effect decreased enough to become negative for two species at the warmest sites (i.e., long-tailed tit: -1.06 mm per °C of anomaly; European blackcap: -0.29 mm per °C of anomaly at a site with an average temperature of 18.2°C; Table 2; Fig. S3,S4). For these two species, the 'tipping-point' of local temperature, i.e. at which the sign of the effect of temperature anomaly changes, was located between the core and the hot edge of their respective thermal range (respectively for thermal coordinates of 0.77 and 0.70). For the great tit, the effect of temperature anomaly became null towards the hot edge of its thermal range (Table 2).

DISCUSSION

As expected in Figure 1, the response of body size to temperature anomaly depended on the position of populations within the species' thermal range. At the coldest sites, juveniles were larger in warmer years, but the size of those born at the warmest sites did not depend on spring temperature anomalies (or even declined in hot springs for some species).

The positive effect of temperature anomalies in cold regions may be related to both direct effects, through changes in thermoregulatory mechanisms, and indirect effects, through changes in food availability [START_REF] Yom-Tov | Recent spatial and temporal changes in body size of terrestrial vertebrates: probable causes and pitfalls[END_REF]. Warmer years induce a reduction of the cost of body heat maintenance in cool areas, enabling a higher energetic allocation to body growth [START_REF] Gillooly | Effects of Size and Temperature on Metabolic Rate[END_REF]. An alternative, non-exclusive hypothesis is that warming may also increase net primary production, thus improving invertebrate abundance [START_REF] Yom-Tov | Recent spatial and temporal changes in body size of terrestrial vertebrates: probable causes and pitfalls[END_REF][START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF]. In the present study, all study species are insectivorous during spring. Higher invertebrate abundance in some years may have enhanced juvenile protein intake, allowing them to reach larger fledgling sizes at the coolest sites [START_REF] Lindström | Early development and fitness in birds and mammals[END_REF].

The opposite effect, found for two species (long-tailed tits and Eurasian blackcaps) at the warmest sites, is consistent with the application of Bergmann's rule to climate warming [START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF]. The consequences of a local increase in temperature on individual fitness have been shown to differ between species of different latitudes in a previous study [START_REF] Deutsch | Impacts of climate warming on terrestrial ectotherms across latitude[END_REF]. At low latitudes, warming has more deleterious consequences on fitness than at higher latitudes. This is due to the fact that, at low latitudes (e.g., tropical), species live close to the upper boundary of their thermal tolerance, while high latitude species live farther from that lethal limit [START_REF] Deutsch | Impacts of climate warming on terrestrial ectotherms across latitude[END_REF][START_REF] Tewksbury | Putting the Heat on Tropical Animals The Scale of Prediction[END_REF]. This process seems to apply at the intraspecific level, within species range. The negative effect of temperature anomaly on juvenile body size may be explained by two mechanisms. This may be the result of (1) a plastic response to environmental change on growth rates [START_REF] Teplitsky | Climate warming and Bergmann's rule through time: is there any evidence?[END_REF]. Hotter years in warm areas would bring growing juveniles into suboptimal thermal conditions for juvenile growth [START_REF] Mertens | Thermal conditions for successful breeding in Great Tits (Parus major L.) -I. Relation of growth and development of temperature regulation in nestling great tits[END_REF][START_REF] Rodríguez | Nestling growth is impaired by heat stress: An experimental study in a mediterranean great tit population[END_REF], which would result in smaller individuals. Size declines in hotter years could also be the result of (2) sizedependent mortality: the largest individuals would suffer the most from hyperthermia, and be more likely to die in warm years. However, lethal temperatures are rarely reached in temperate regions (mean number of days > 35°C = 0.13 ± 0.28 SD days per spring at our study sites). Hence, from the present dataset, even at the hottest sites, a higher mortality in larger individuals in hot years would not be expected in France. Most studies attempting to find a selection for smaller size failed, or found the opposite pattern (Gardner et al., 2014;[START_REF] Dunn | Dynamics of phenotypic change : wing length declines in a resident farmland passerine despite survival advantage of longer wings[END_REF]. The hypothesis of a cold constraint release for juvenile growth in hotter years is therefore the most likely in temperate climates. Our results are consistent with Danner and Greenberg (2005), suggesting that in temperate species, morphology is constrained by cold towards the coldest edge of their distribution rangeand potentially across most of their temperate distribution range (i.e. not all individuals achieve optimal body size)whereas at the hottest edge, heat (or drought-driven food shortage) would be the predominating constraint. An additional hypothesis is that very high temperatures could reduce parental foraging efficiency, e.g. due to physiological stress (hyperthermia, water loss) enhanced by reduced invertebrate activity [START_REF] Geiser | Impact of weather variation on feeding behaviour, nestling growth and brood survival in Wrynecks Jynx torquilla[END_REF][START_REF] Cunningham | Temperatures in Excess of Critical Thresholds Threaten Nestling Growth and Survival in A Rapidly-Warming Arid Savanna: A Study of Common Fiscals[END_REF]. Lower parental feeding frequency could affect offspring growth rate, and result in smaller fledglings [START_REF] Searcy | Effects of early nutrition on growth rate and adult size in song sparrows Melospiza melodia[END_REF].

The indirect effects of temperature anomaly on ecosystem productionand therefore food availabilityat the hottest sites may also differ from the coldest sites. In semi-arid environments, net primary production depends on precipitation to a greater extent than temperature (e.g., Gardner et al., 2014;[START_REF] Holmgren | Extreme Climatic Events Shape Arid and Semiarid Ecosystems[END_REF]. This may apply to the French Mediterranean region, as both climates are similar (see www.worldclimate.com). Hence, it is unlikely that temperature response is driven by changes in net primary production at the warmest study sites, which may explain the decreasing effect of temperature anomaly towards the hottest sites. Another hypothesis is that, because temperature change can impact food web structures (e.g., [START_REF] Edeline | Ecological emergence of thermal clines in body size[END_REF], a differential effect can be the consequence of differing changes in the biotic environment. The effect of temperature change on body size, through changes in food availability in ecosystems, may therefore depend on the regional climate and ecosystems, regardless of the population position within the species thermal range. These antagonistic or synergistic effects of local temperature, precipitation and ecosystem structures on individual body size deserve to be investigated in future research.

Body size response to warming may depend on the average climate under which the local population evolved, as found for temporal trends in population size [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]. The consequences of climate warming on populations are often more deleterious at the hot edge of species distribution, while it can be favourable at the cold edge [START_REF] Parmesan | A globally coherent fingerprint of climate change impacts across natural systems[END_REF][START_REF] Hickling | The distributions of a wide range of taxonomic groups are expanding polewards[END_REF][START_REF] Leroy | Forecasted climate and land use changes, and protected areas: the contrasting case of spiders[END_REF], with a linear graded response in between [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]. Although the present analysis included a relatively wide range of thermal conditions (> 11°C), the number of sites represented in cold and hot regions was limited (Fig. S1). We used species for which the distribution edges are not (or rarely) included in our study area (Fig. S2). Despite species response to warming which may be stronger at the edges of their distribution range [START_REF] Jarema | Variation in abundance across a species ' range predicts climate change responses in the range interior will exceed those at the edge : a case study with North American beaver[END_REF], we still detected a differential response along a fragment of their range. Moreover, while responses to warming are expected to be greater in thermal specialists (i.e., species with a narrow thermal range compared to other Palearctic species; [START_REF] Jiguet | Thermal range predicts bird population resilience to extreme high temperatures[END_REF], our results were obtained from species that are mostly thermal generalists (i.e., with a wide thermal range; Table S1). This suggests that differential effects of temperature change on body size may apply to a wide range of species (including thermal generalists), which is consistent with results obtained for population trends [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]. In spite of geographic and taxonomic limits, the pattern revealed is the one expected theoretically (cf. abundance, phenology patterns), and we provide the first evidence for a structured effect of temperature on body size. Studies performed at large geographic scale, aiming at testing the effect of temperature variation on body sizewhile assuming a uniform effectmay therefore fail to detect an effect of temperature change because it may be blurred by opposing effects between sites.

The estimated effect sizes for the influence of temperature anomaly on body size are small, ranging from -0.8 to 1.0 % of species' mean wing length per Celsius degree of annual anomaly. Compared to spatial effects of temperature (i.e., local average temperature; cf.

Bergmann's rule), these effects sizes were of similar magnitude (-0.23 to 0.16 % per Celsius degree; Table S2). In other studies focussing on temporal variation in bird size, the effect of mean temperature of the breeding period was about 1 % of the juvenile wing length in Australia (Gardner et al. 2014), and the effect of summer temperature ranged between -0.63 and 0.15 % per Celsius degree in eastern North America [START_REF] Collins | Heterogeneous changes in avian body size across and within species[END_REF]. Formerly, [START_REF] Dubos | Disentangling the effects of spring anomalies in climate and net primary production on body size of temperate songbirds[END_REF] have even clarified that, when analysing additive effects of annual weather on wing length across sites and species, they could explain 5% of the total variance in juvenile wing length at best, i.e. the additive and specie-specific variation between years. All the remaining variance actually corresponds to site-specific annual variations (7%) or siteand species-specific annual variations (88%). Hence, we acknowledge that effect sizes are indeed small, and that this questions the biological relevance of the corresponding size changes. This concern about small size effects applies to most existing studies on short-term body size changes, and is a recurrent issue in ecology [START_REF] Møller | How much variance can be explained by ecologists and evolutionary biologists[END_REF]. Given the multiple determinants of body size, it even appears obvious that body size cannot drastically change between years and generations. Hence, whatever the influence of the environment on juvenile body size, it will always be restricted to a narrow range of change of average size, beyond which other compensatory mechanisms start to play (e.g. offspring mortality, early termination of growth). We are not aware of a statistical framework, applicable to existing data, which would allow to objectively qualifying the biological relevance of the observed, statistically robust effects of temperature on wing length.

In the present study, we focussed on spring temperatures because this corresponds to the period of body growth, as body size has been shown to be mainly driven by the conditions during this period (Yom-Tov Geffen, 2011), and because in songbirds, body growth ends soon after fledging (some weeks). However, high temperatures may drive size-dependent mortality in juveniles, as they are more exposed to hypo-or hypertheremia than their parents [START_REF] Mertens | Thermal conditions for successful breeding in Great Tits (Parus major L.) -I. Relation of growth and development of temperature regulation in nestling great tits[END_REF]. In addition, size-dependent mortality can also affect adults (Gardner et al., 2014), and mortality can occur at later stages of individuals' life (i.e., carry-over effects; van [START_REF] Van De Pol | Identifying the critical climatic time window that affects trait expression[END_REF]. Getting the full picture of body size responses to temperature will require to investigate its effects during other parts of the year (e.g., winter, when bird mortality is the highest in temperate climates; [START_REF] Van Balen | Population Fluctuations of the Great Tit and Feeding Conditions in Winter[END_REF], at different time-scales [START_REF] Kruuk | Contrasting effects of climate on juvenile body size in a Southern Hemisphere passerine bird[END_REF], and include assessments of size-dependent mortality (e.g., using markrecapture approaches).

To conclude, the differential effect of climate warming along species range already found in species distributions [START_REF] Hickling | The distributions of a wide range of taxonomic groups are expanding polewards[END_REF], phenological shifts [START_REF] Both | Climate change and timing of avian breeding and migration throughout Europe[END_REF] and population trends [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]) also applies to body size. We predict that climate warming would induce body size increases (up to optimal body size) more frequently at the cold edge of species distribution ranges, and body size declines would be more likely at the hot edge. In France, the impact of warming on avian population dynamics may impact body size negatively at the warmest sites, corresponding to the Mediterranean region, where species (including our study species) live closer to the upper boundary of their thermal tolerance [START_REF] Jiguet | Bird population trends are linearly affected by climate change along species thermal ranges[END_REF]. As individual fitness is often size-dependant, with the largest surviving and/or reproducing better [START_REF] Lindström | Early development and fitness in birds and mammals[END_REF][START_REF] Ronget | Causes and consequences of variation in offspring body mass: Meta-analyses in birds and mammals[END_REF], it is to be feared that size decline may impact populations negatively. To assess the robustness and generality of our conclusions, future studies should investigate the synergistic effects of local temperature anomalies (weather fluctuations) and local average temperatures (climate) on body size across a larger number of species (including a broader spectrum of life-history traits, and particularly more thermal specialists), and across a broader climatic range, to include the entire thermal ranges of the species studied. Another challenge for future studies on the link between body size and temperature fluctuations will be to sort out the proximate mechanisms at play (e.g. ontogeny versus mortality, and thermal versus trophic pressure). Predicted values were obtained from MCMCglmm (Model 3, see text and Table 1). Local average temperature is the mean spring temperature of a given site for the period 2000-2014.

Wing length was centred on the mean value per species. Species-specific predicted values are shown in supporting information (Fig. S3).

Fig. 1

 1 Fig. 1 Theoretical framework for a differential effect of climate warming on body size

Fig. 2

 2 Fig. 2 Residual response of average juvenile wing length to temperature anomaly along a

Fig. 3

 3 Fig. 3 Species-specific response of juvenile wing length to spring temperature anomaly,

Table 1

 1 Set of models used to assess the relationship between juvenile wing length, local temperature anomaly, local average temperature and species identity. The lowest Deviance Information Criterion (DIC) indicates the 'best' model (in bold), and ΔDIC is the DIC difference with the best model. TAst holds for the local temperature anomalies for a site s in year t, during the breeding season. Ts is the average temperature for a site s across the 2000-2014 breeding seasons. All models included the same adjustment variables (see text). Based on DIC, Models 4 and 5 received similar statistical support.

	Model Model description	DIC	ΔDIC
	M0	Species + Ts + Species × Ts	150879	28
		+ other adjustment var. (see text)
	M1	M0 + TAst	150878	27
	M2	M1 + TAst × Species	150860	9
	M3	M1 + TAst × Ts	150869	18
	M4	M2 + TAst × Ts	150851	2
	M5	M4 + TAst × Ts × Species	150849	0

Table 2

 2 Estimates of Temperature anomaly (TAst) at the observed coldest (Tsmin) and hottest (Tsmax) species-specific study sites, and the local average temperature (Ts) where the temperature anomaly effect is predicted to reverse (i.e., is null). Numbers in parentheses indicate the corresponding thermal coordinate (a value of 0 represents the coldest sites where the species can be present, and 1 represents the hottest sites; TableS1). Predicted values were obtained from MCMCglmm posterior estimates (Model 5 in Table1) and accounted for phylogenetic relatedness (species are sorted accordingly).

	Species	Ts min (°C)	TAst effect at Ts min Slope % of wing (mm.°C -1 ) length	Ts max (°C)	TAst effect at Ts max Slope % of wing (mm.°C -1 ) length	Ts (°C) at null TA effect
	Parus major	13.2	0.54	1.0	19.6	-0.02	-0.3	20.9 (1.00)
	Parus caeruleus	11.0	-0.25	-0.8	19.6	0.22	0.2	-
	Acrocephalus scirpaceus	8.4	-0.13	-0.7	18.8	0.39	0.1	-
	Sylvia atricapilla	8.5	0.86	0.5	18.2	-0.29	-0.3	15.1 (0.70)
	Sylvia communis	12.0	0.28	0.7	19.6	-0.15	-0.3	15.1 (0.79)
	Phylloscopus collybita	11.4	0.12	0.8	18.2	0.12	0.2	-
	Aegithalos caudatus	8.4	1.71	0.9	18.2	-1.06	-0.1	16.4 (0.77)
	Turdus merula	13.9	0.68	0.3	18.2	-0.39	-0.4	12.3 (0.60)
	Erithacus rubecula	8.4	0.16	0.6	18.0	0.13	0.2	-

DATA ACCESSIBILITY:

The dataset used in this analysis is available as an R object in supporting information.