Camille Vitet
email: camille.vitet@gmail.com

Patrick Duncan

Andre Ganswindt

Cheryl Mabika

Simon Chamaillé-Jammes

Do infanticides occur in harem-forming equids? A test with long-term sociodemographic data in wild plains zebras

Keywords: equids, group size, infant mortality, male turnover, sociality

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INTRODUCTION

Social dynamics can play a major role in shaping the population ecology and evolutionary trajectory of a species [START_REF] Clutton-Brock | Mammal Societies[END_REF]. Interactions between conspecifics can directly affect their fitness: to the extreme, some individuals can kill or be killed, as for instance in several mammalian carnivores during territorial conflicts [START_REF] Mech | Buffer zones of territories of gray wolves as regions of intraspecific strife[END_REF][START_REF] Mosser | Group territoriality and the benefits of sociality in the African lion, Panthera leo[END_REF][START_REF] Thompson | Causes and consequences of intergroup conflict in cooperative banded mongooses[END_REF]. More commonly, individuals can affect the reproductive output of others via various social behaviours, for instance, by limiting access to resources (e.g. interference competition) or mates (e.g. intra-sexual competition), or, in contrast, by taking care of one's offspring (e.g. communal breeding) [START_REF] Silk | The adaptive value of sociality in mammalian groups[END_REF].

A classic example of such link between social dynamics and individuals' fitness is infanticide by malesthe killing of dependent offspring by an unrelated conspecific adult male -which is widespread, occurring in taxa as varied as fish, amphibians, birds, and mammals [START_REF] Hausfater | Infanticide : comparative and evolutionary perspectives[END_REF][START_REF] Lukas | The evolution of infanticide by males in mammalian societies[END_REF].

Obviously, an infanticide decreases the reproductive output of the female whose offspring is killed. Conversely, the reproductive output of the infanticidal male is likely increased: the most commonly accepted hypothesis for the evolution of this behaviour, the 'sexual selection hypothesis', posits that an infanticidal male increases its mating opportunities by shortening the latency during which a female is unavailable to reproduce, either because of temporal infertility or behavioural rejection of mating attempts [START_REF] Dixson | Primate sexuality[END_REF][START_REF] Hrdy | Infanticide among animals: A review, classification, and examination of the implications for the reproductive strategies of females[END_REF][START_REF] Mcneilly | Lactation and fertility[END_REF].

The importance of infanticide by males, as a factor shaping population dynamics, remains controversial however. Previous works on rodents have shown that population growth rates can be dramatically reduced when the rate of male replacement is experimentally increased, probably because of an increased rate of infanticide, but infanticides were not directly observed [START_REF] Andreassen | Male turnover reduces population growth: an enclosure experiment on voles[END_REF][START_REF] Opperbeck | Infanticide and population growth in the bank vole (Myodes glareolus): the effect of male turnover and density[END_REF]. Studies on bears and lions have suggested that the selective killing of reproductive males by human hunters could affect the dynamics of whole populations due to the increased rate of male turnovers and thereby infanticides [START_REF] Loveridge | African lions on the edge: Reserve boundaries as "attractive sinks[END_REF][START_REF] Swenson | Infanticide caused by hunting of male bears[END_REF][START_REF] Whitman | Sustainable trophy hunting of African lions[END_REF]. However, there is still only scarce evidence from unmanipulated populations that infanticide matters at the population-level, and further studies are required to consolidate our understanding of the contribution of infanticide to population dynamics.

Infanticides occur mainly in species which can breed year-round and where reproduction is monopolized by a few males [START_REF] Lukas | The evolution of infanticide by males in mammalian societies[END_REF], and a number of equids such as feral horses (Equus ferus), Przewalski's horses (Equus ferus przewalskii), mountain zebras (Equus zebra), and plains zebras (Equus quagga), display such characteristics. These species form harems where a stallion (i.e. harem-male) is associated with several females and their dependent young, and can breed year round, traits that should have facilitated the evolution of infanticide. Males that do not hold a harem form loose bachelor groups and will eventually attempt to start a harem by 'abducting' young females, monopolizing dispersing young females or taking over a harem by replacing the stallion. In these harem-forming equids, infanticide by males is expected for several reasons (see references in [START_REF] Bartoš | Behavioral factors affecting reproduction in domestic horsessociobiological approach[END_REF][START_REF] Ebensperger | Strategies and counterstrategies to infanticide in mammals[END_REF][START_REF] Palombit | Infanticide as sexual conflict: Coevolution of male strategies and female counterstrategies[END_REF].

First, infanticide can reduce the latency for the next breeding attempt of the female. For instance, in plains zebras, the latency after a birth for the next breeding attempt can be as short as a few weeks and as long as 15 months [START_REF] Barnier | Inter-birth interval in zebras is longer following the birth of male foals than after female foals[END_REF]. If the costs of raising a foal influence the latency, then infanticide could potentially increase the stallion's reproductive success. Secondly, with the disappearance of her young, the female will not bear the costs of lactation anymore. This can lead her to have a better body condition and increases the chances that the next reproduction -with the infanticidal male -is successful. Finally, foals can be accidentally involved in fights and injured or killed, since newly established stallions usually exhibit high testosterone levels which, combined with the fact that mares may reject their mating attempts, can make for situations where the survival of foals is at risk. Male infanticide following a stallion turnover (i.e. replacement of a stallion by a different male) has often been reported in equids, but mostly in small and domestic, captive or reintroduced populations (Camargue horses: [START_REF] Duncan | Foal killing by stallions[END_REF]Przewalski's horses: Chen, Weng, Chao, Hu, & Taya, 2008;[START_REF] Dorj | Reproduction and mortality of re-introduced Przewalski's horse Equus przewalskii in Hustai National Park, Mongolia[END_REF][START_REF] Feh | Male infanticide and paternity analyses in a socially natural herd of Przewalski's horses: Sexual selection[END_REF][START_REF] Kolter | Social behaviour of Przewalski horses (Equus p. przewalskii) in the Cologne Zoo and its consequences for management and housing[END_REF][START_REF] Ryder | A case of male infanticide in Equus przewalskii[END_REF]. In captive plains zebras, 10 records of infanticidal attacks by males have been reported over 27 years of monitoring [START_REF] Pluháček | Male infanticide in captive plains zebra, Equus burchelli[END_REF][START_REF] Pluháček | Further evidence for male infanticide and feticide in captive plains zebra, Equus burchelli[END_REF][START_REF] Pluháček | Variation in Incidence of Male Infanticide within Subspecies of Plains Zebra (Equus burchelli)[END_REF]. These are all populations where natural sociality had been disrupted. Infanticide could also be common in captive and recently reintroduced equids not because it is adaptive, but because the behaviour results from increased aggressiveness due to social stress (C. Feh, pers.comm.). [START_REF] Penzhorn | Reproductive characteristics of a free-ranging population of Cape Mountain zebras (Equus zebra zebra)[END_REF] reported indirect evidence for infanticide in wild mountain zebras, but observations of infanticide in wild equids are scarce: [START_REF] Gray | An infanticide attempt by a free-roaming feral stallion (Equus caballus)[END_REF] observed an attempt of infanticide by a mustang, but argued that it was exceptional. Infanticide has been seen only once in wild plains zebras [START_REF] Ransom | Wild Equids: Ecology, Management, and Conservation[END_REF] but the relationships of the foal to the harem in which it occurred are unknown. Forced copulations following stallion turnovers occurred regularly in the mustangs studied by [START_REF] Berger | Induced abortion and social factors in wild horses[END_REF], leading him to suggest that feticide -the abortion of a fetus due to forced mating or sexual harassment by a conspecific adult male -might be adaptive in horses and other equids. The importance of such behaviour in equids remains controversial however [START_REF] Kirkpatrick | Changes in herd stallions among feral horse bands and the absence of forced copulation and induced abortion[END_REF]. Overall, the current state of knowledge is unclear about whether infanticide is common or rare in equids, and whether it matters or not for the dynamics of their populations (as implicitly suggested in [START_REF] Grange | What limits the Serengeti zebra population?[END_REF].

Here we use a long term study of the behaviour and demography of a large wild population of plains zebras conducted since 2004 in Hwange National Park (HNP, Zimbabwe) where stallion turnovers were recorded and accurate data on pregnancy were obtained by hormone assays. This study offers a rare occasion to test for the occurrence of infanticide after stallion turnovers and assess the potential influence of these turnovers on foal survival in a wild equid. Specifically, we test here the predictions that (1) the rate of stallion turnover increases with the number of reproductive females (i.e. subadult and adult females) in a harem, and (2) that foals in harems that experience, either as fetuses or soon after their birth, a stallion turnover have a lower survival probability than foals in harems where such event did not occur.

MATERIAL AND METHODS

Study species and site

The study was conducted in the eastern section of HNP in Western Zimbabwe over an area covering ca. 2000 km² (19°00'S, 26°30'E). The vegetation is dominantly bushy, characteristic of semiarid dystrophic savannas, but interspersed with patches of open grasslands [START_REF] Chamaille-Jammes | Spatial patterns of the NDVI-rainfall relationship at the seasonal and interannual time scales in an African savanna[END_REF]. The annual rainfall averages 600 mm, with most rains falling between November and April, the rainy season [START_REF] Chamaille-Jammes | Spatial patterns of the NDVI-rainfall relationship at the seasonal and interannual time scales in an African savanna[END_REF]. Predation pressure is high as lions (Panthera leo) are abundant (i.e. around 3.5 individuals 100 km -²) [START_REF] Loveridge | Conservation of large predator populations: Demographic and spatial responses of African lions to the intensity of trophy hunting[END_REF], and leopards (P. pardus), cheetahs (Acinonyx jubatus), and spotted hyenas (Crocuta crocuta) are also present, all known to attack zebra foals. In the study area, plains zebra density fluctuated slightly around 1 individual km -² (Chamaillé-Jammes, [START_REF] Chamaillé-Jammes | Seasonal density estimates of common large herbivores in Hwange National Park, Zimbabwe[END_REF][START_REF] Grange | Demography of plains zebras (Equus quagga) under heavy predation[END_REF] between 2004 and 2017, when we monitored the behaviour and fate of individual zebras.

Plains zebra populations are made of two basic social units: harem and bachelor groups [START_REF] Estes | The behavior guide to African mammals : including hoofed mammals, carnivores, primates[END_REF][START_REF] Klingel | The Social Organisation and Population Ecology of the Plains Zebra (Equus Quagga)[END_REF]. Non-territorial harems are composed of a stallion and most often several adult females, subadults of both sexes, and dependent offspring. Subadult and adult females are hereafter referred to as 'reproductive females'. In the study area, harem sizes range between 2 and 10 individuals (median: 5 individuals), and are positively correlated to the number of reproductive females in harems (Spearman rank correlation: r s = 0.89, N = 51, P < 0.001). Males that are not stallions form all-male bachelor groups, which range between 1 and 19 individuals (median: 3 individuals), and sometimes attempt to take over a stallion's position. In harems, young males and females disperse when they are around 2 years old (y.o.): dispersing females join already existing harems or form a new group with a bachelor, and males join bachelor groups.

Reproductive females may also change group, but this is rare: in this study, 92% of mares (N = 453) were still in the same harem after one year and 86% (N = 342) after two years. Therefore, although we give harems the same ID code from one session to the next when at least 25% of the females are the same than at the previous session, usually over 90% of the females are seen together at the next session.

Data collection

Observations were made twice a year, approximately one month in the wet season (between February and April) and three weeks in the dry season (between July and September). These monitoring periods are hereafter referred to as 'sessions'. We focused on harems, and determined group composition and identified new individuals. Field experience and the data presented here (see Results) suggest that stallion turnovers are not frequent enough to make the discontinuous sampling problematic, as the likelihood of several turnovers occurring between two sessions is very low. The zebras were identified by their unique stripe patterns [START_REF] Grange | Demography of plains zebras (Equus quagga) under heavy predation[END_REF] and were categorized into four age-classes: foal, from birth to 1 y.o.; yearling, between 1 and 2 y.o.;

subadult, between 2 and 4 y.o.; and adults, 4 y.o. and older. The age of previously unobserved young individuals was estimated using Penzhorn's criteria [START_REF] Penzhorn | Age determination in Cape Mountain Zebras Equus Zebra Zebra in the Mountain Zebra National Park[END_REF] combined with photos of foals of known age in the Hwange population. We used suckling behaviour as criteria to determine motherhood (as in [START_REF] Barnier | Inter-birth interval in zebras is longer following the birth of male foals than after female foals[END_REF]. Indeed, although the possibility for adoption and allosuckling cannot be fully discarded, these events are very rare in equids [START_REF] Olléová | Effect of social system on allosuckling and adoption in zebras[END_REF][START_REF] Pluháček | Suckling behavior in captive plains zebra (Equus burchellii): Sex differences in foal behavior[END_REF][START_REF] Topczewska | The Case of Communal Rearing of a Foal by Two Mares (Equus caballus)[END_REF]. In addition, we opportunistically collected dung samples from females (N = 357 from 90 mares); these were air-dried within 48h after collection and stored at room temperature until analysis for immunoreactive 20-oxopregnane and estrogen metabolite concentrations [START_REF] Barnier | Inter-birth interval in zebras is longer following the birth of male foals than after female foals[END_REF][START_REF] Ncube | Pattern of faecal 20oxopregnane and oestrogen concentrations during pregnancy in wild plains zebra mares[END_REF]. Hormone concentrations allowed females to be allocated to nonpregnant, mid-pregnancy (9 to 3 months to foaling) or late pregnancy (3 to 0 months to foaling) stages [START_REF] Ncube | Pattern of faecal 20oxopregnane and oestrogen concentrations during pregnancy in wild plains zebra mares[END_REF]. Thanks to this information, we knew that a foal had been born even when it died before we resighted the harem, or had been lost by abortion. We could therefore compare the survival probability of foals in their first year in harems with or without a stallion turnover, assuming that if the mother is observed, the detection probability of the foal if it is alive is 1. Under this realistic assumption, the observation of a mare, previously detected pregnant, without her foal is reliable evidence that the foal had not survived, as foals are dependent on their mother until the age of about 1 year. More details about the demographic monitoring of this population can be found in [START_REF] Grange | Demography of plains zebras (Equus quagga) under heavy predation[END_REF]. Demographic data and data on hormone levels collected between 2008 and 2017 are used here, corresponding to 19 sessions (10 in the wet season and 9 in the dry season) over 10 years.

During these sessions, ad hoc observations of behaviour were made, including attacks, mating and foaling. Although we did not specifically keep track of observation time, we estimated that a minimum of 5400 hours were spent directly observing zebras between July 2004 when the study started, and the last session in October 2019.

Data analysis

We first tested whether the probability of stallion turnover increases with the number of reproductive females in a harem (analysis 1). Stallion turnover was considered to have occurred if a harem was seen during two consecutive sessions with a different stallion at each session. For this analysis, we did not use information when the resighting of a harem occurs more than a year later (i.e. when the harem was not seen in two consecutive sessions), as there was too much uncertainty about how the number of reproductive females had changed during this period. In total, we observed 30 turnovers, out of 232 possible occasions where it could have occurred (i.e. when a harem is seen during a session and reobserved within a year, regardless of the stallion identity). We fitted generalized linear mixed models with logit links and a binomial distribution for errors to test the relationship between the likelihood of having observed a stallion turnover (response variable, binary coded with 1 for turnover and 0 for no turnover) and the number of reproductive females in the harem at the first session. To account for the fact that turnovers are more likely to occur as time passes, we included an additive effect of the log-transformed number of days between the two sessions. We also included the identity of the stallion and the identity of the harem as random effects on the intercept to account for the fact that stallions and harem females could differ in their ability to repel (for stallions) or willingness to accept (for females) an external male.

We also investigated whether stallion turnover affected the survival probability of foals (analysis 2), using the data obtained from the hormone analyses conducted on the dung samples. We focused on mares detected pregnant through hormone analyses (N = 29 in late pregnancy and N = 71 in mid-pregnancy) and compared the probability of reobserving them with a foal at the next session when the stallion was replaced between the date of dung sampling and the date of the first resighting of the mare at the next session, and when a stallion turnover did not occur. Females detected in mid-pregnancy are between 9 and 3 months to the foaling date, so observing them without a foal at the next session could indicate that the foal had been aborted

or died, but it is also possible that the foal was not yet born. However, this possible bias is independent of whether or not a stallion turnover occurred and will therefore not affect our results. Focusing only on females detected in mid-pregnancy (N = 89), we also tested the effect of stallion turnover on the probability of seeing a foal two sessions later (rather than at the next session). As the duration over which survival was estimated was greater, this analysis was more likely to be affected by other sources of mortality, and we consider it less robust, but note that it provided qualitatively similar results (Appendix Tables A1-A2, Fig. A1). We sometimes obtained two dung samples in the same pregnancy (N = 25), and if we did and the female was in late pregnancy it has been included in the analysis of late-pregnant females. In all cases the second sample also identified the female as pregnant (i.e. no abortion was observed). We tested the effect of stallion turnover on the probability of observing a foal at the next session (coded 1 = mare re-observed with a foal, 0 = mare re-observed without a foal) by fitting generalized linear mixed models with logit links and binomial distributions for errors.

Explanatory variables included: a binary variable coding for whether stallion turnover had occurred; the logtransformed number of days between the date of dung sampling and the date of first resighting of the mare, to control for the expected negative effect of the time between the date of dung sampling and the date of first resighting of the mare on foal survival (i.e. survival probability decreases as time passes); age of the mare, to account for its many potential positive effects on pregnancy success (e.g. [START_REF] Bartoš | Pregnancy disruption in artificially inseminated domestic horse mares as a counterstrategy against potential infanticide[END_REF][START_REF] Bartoš | Promiscuous behaviour disrupts pregnancy block in domestic horse mares[END_REF] and foal survival (e.g. [START_REF] Cameron | Aging and improving reproductive success in horses: Declining residual reproductive value or just older and wiser?[END_REF]; and season, to account for the potential influence of seasonal changes in forage quality and possibly predation risk, with the hypothesis that foal survival should be lower in the dry season: forage quality is lower, zebras remain near the few remaining waterholes that are also focus areas for hunting lions, and zebras' strategy to reduce this risk might be costly (see [START_REF] Courbin | Zebra diel migrations reduce encounter risk with lions at night[END_REF]. We also included the identity of the mare as a random effect nested within a harem identity random effect, as we had repeated measures on the same individuals. More complex model structures including random effects for sessions or years to account for temporal autocorrelations led to overfitting.

For both analysis 1 and 2, we first fitted and reported full models, i.e. models integrating the explanatory variables presented above. The inclusion of the random effects led to convergence issues when models were fitted with a frequentist framework, and we therefore fitted models in a Bayesian framework using Stan [START_REF] Carpenter | Stan: A probabilistic programming language[END_REF] accessed using the package brms v. 2.13.5 [START_REF] Bürkner | brms: An R package for Bayesian multilevel models using Stan[END_REF] [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF]. Bayesian analysis is characterized by (i) the use of prior distribution for model parameters:

in R v. 3.6.2 (R
here, as commonly done, we used non-informative priors and checked that different priors led to the same conclusions; (ii) some stochasticity in the estimation process linked to the use of Monte-Carlo simulations: here, as often recommended, we ran four chains with 4000 iterations each. We confirmed convergence and quality of fit of the models using the criteria recommended for Bayesian analysis (Conn, We based our assessment of the strength of the relationship between explanatory variables and response variables on the model mean posterior estimates and their 90% and 95% credible intervals. We also compared the predictive accuracy of models with and without the explanatory variable of interest. We did so using the Widely Applicable Information Criterion (also known as Watanabe-Akaike Information Criterion, hereafter WAIC), which is a generalized version of the AIC that is commonly used in Bayesian modelling as it estimates the effective number of parameters from posterior distributions [START_REF] Mcelreath | Statistical rethinking: A Bayesian course with examples in R and Stan[END_REF][START_REF] Watanabe | Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory[END_REF]. This is usually important in models with random effects, as a priori determination of the number of parameters in this context is not clear. As with the AIC, the model with the lowest WAIC (hereafter 'top' model) has the best predictive accuracy. The standard error of the WAIC is obtained thanks to the use of the Monte-Carlo simulations, but more importantly, we can also obtain an estimation of the standard error of the difference in WAIC between a model of interest and the 'top' model. This allows understanding whether the WAIC of two models differ significantly. Additionally, we computed for each model its Akaike weight that, as for the AIC, can be interpreted as the probability that the model will make the best predictions, amongst the models tested.

However, as with the AIC, one should keep in mind that when nested models achieve similar predictive accuracy, the explanatory variables present in the more complex models should be considered non-informative and not considered to have an effect [START_REF] Arnold | Uninformative Parameters and Model Selection Using Akaike's Information Criterion[END_REF][START_REF] Leroux | On the prevalence of uninformative parameters in statistical models applying model selection in applied ecology[END_REF].

RESULTS

Based on the model parameters, the probability that a stallion turnover occurred between two sessions increased with the time separating the two sessions and the number of reproductive females in harems (Table 1), varying on average from 0.03 to 0.43 for harems having from 1 to 5 reproductive females (Fig. 1). Both variables were critical to predict the likelihood of observing a turnover (compare WAIC weights of models in Appendix Table A3). In particular, note that the model only accounting for time between sessions but not accounting for the number of females (model 3) had virtually no chance to make better predictions than the model accounting for it (model 1).

Over the >5400 hours of monitoring, we never witnessed an infanticide, or even a stallion attacking a foal. Such behaviour was also never reported to us by other researchers or tourist guides working in the area.

Based on the model parameters, the probability of observing a foal at the next session did not differ between situations when a stallion turnover occurred and those when it did not (Table 2, Fig. 2). This was also supported by the fact that accounting for turnovers into the models did not make these models more likely to predict whether a foal would be observed or not than models not accounting for turnovers (compare WAIC weights in Appendix Table A4).

The analysis of data from females observed mid-pregnant and resighted two sessions later also supported a lack of relationship between the probability of foal survival and whether or not the stallion was replaced between the two sessions (Appendix Tables A1-A2). We note however that the estimated difference between turnover and no-turnover situations was greater, with a tendency for the probability of observing a foal two sessions later to be lower when the stallion had changed (Appendix Fig. A1).

DISCUSSION

This study shows that the frequency of stallion turnover increases with increasing number of reproductive females in harems, therefore supporting our prediction. We did not however detect a significant reduction in foal survival after a takeover, and now discuss the various insights brought by our work.

Higher rate of stallion turnovers in larger female groups

As predicted, the frequency of stallion turnovers increases with the number of reproductive females in a harem. geladas [START_REF] Dunbar | Reproductive decisions: an economic analysis of gelada baboon social strategies[END_REF]. To our knowledge, this is the first demonstration that this effect of group size holds in equids. Larger groups may be more attractive for bachelor males, the presence of many females increasing their chance of siring their own offspring following harem takeover. However, females are not passive resources and their choice, although not well understood yet, may be important in accepting a new stallion and in shaping the benefits gained by the incoming male in terms of reproductive success [START_REF] Smuts | Male Aggression and Sexual Coercion of Females in Nonhuman Primates and Other Mammals: Evidence and Theoretical Implications[END_REF].

For instance, there are some observations of female wild horses that managed to prevent forced copulations by kicking and escaping from the newly established male [START_REF] Berger | Wild horses of the Great Basin : social competition and population size[END_REF]. Another possibility to explain the positive relationship between rate of male turnover and female group size is that larger harems with many females may be more difficult for the stallion to defend against intruding males, therefore increasing the likelihood of being taken over by a bachelor male. For instance, in wild horses, the energy invested by stallions in the defense of their harems increases with harem size, but the energy cost per female defended was reduced in larger harems, which could make them more attractive to bachelors [START_REF] Berger | Wild horses of the Great Basin : social competition and population size[END_REF]. Finally, harems composed of many reproductive females provide a more heterogeneous mating opportunity for the incoming male, the more numerous these females are, the greater the chance that some of them are not pregnant and available for reproduction.

In conclusion to this section, harem takeovers are frequent in this population, and larger females groups are more likely to experience stallion turnovers.

Lack of evidence for male infanticide following harem takeover in the wild

In captive plains zebras, Pluháček and colleagues have regularly observed forced copulations and attacks on foals [START_REF] Pluháček | Further evidence for male infanticide and feticide in captive plains zebra, Equus burchelli[END_REF][START_REF] Pluháček | Variation in Incidence of Male Infanticide within Subspecies of Plains Zebra (Equus burchelli)[END_REF]. In contrast, in our study population, no forced mating or infanticide event, nor even an attack of a stallion towards a foal, has been seen in more than 15 years of observations, with over 5400 hours spent watching the animals. We found no evidence to suggest that infanticide could specifically occur at times when no observations are conducted (e.g. night). We additionally showed here that stallion turnovers had no statistically apparent effect on foal survival -which should be case should infanticide occur. We however acknowledge that sample sizes in these analyses are small, and further studies will be welcomed to ascertain this conclusion. We also note that other processes, unrelated to infanticide, might lead to reduced foal survival after stallion turnovers: young foals can make inappropriate responses and get killed by accident in situations where stallions and other individuals are involved in attacks and chases as often happens during takeovers. This has been reported in horses for instance (C. Feh & P.

Duncan, pers. obs.; [START_REF] Duncan | Horses and Grasses: The Nutritional Ecology of Equids and Their Impact on the Camargue[END_REF]. The new male may be less attentive to protecting foals from predators.

Overall, our study suggests that, in this population, infanticide either does not occur or is rare. This is consistent with [START_REF] Pluháček | Further evidence for male infanticide and feticide in captive plains zebra, Equus burchelli[END_REF] report that they did not find any record of infanticide in the wild in plains zebras (but see [START_REF] Ransom | Wild Equids: Ecology, Management, and Conservation[END_REF] for one anecdotal observation).

Based on much more limited data, [START_REF] Klingel | Soziale Organisation und Verhalten freilebender Steppenzebras[END_REF] found a similar result in the Tanzania's Ngorongoro Crater population, where no infanticide was observed, although several takeovers of harems composed of pregnant females and young foals were recorded. [START_REF] Jaworska | Harem stallion changes are not associated with diminished reproductive performance of females in semi-feral Konik polski horses (Equus caballus)[END_REF] reported similar findings in a population of semi-feral Konik polski horses (E. caballus) where, over 31 years of monitoring, infanticide by males was never observed and stallion turnovers had no significant effects on female reproductive success.

These results contrast with studies of other harem-forming species where male infanticide following haremmale turnovers has been found (e.g. in lions: [START_REF] Bertram | Social factors influencing reproduction in wild lions[END_REF][START_REF] Packer | Reproductive success of lions[END_REF][START_REF] Packer | Adaptations of Female Lions to Infanticide by Incoming Males[END_REF]; blue monkeys: [START_REF] Butynski | Harem-male replacement and infanticide in the blue monkey (Cercopithecus mitus stuhlmanni) in the Kibale Forest, Uganda[END_REF][START_REF] Butynski | Comparative Ecology of Blue Monkeys (Cercopithecus Mitis) in High-and Low-Density Subpopulations[END_REF]. In wild horses, female reproductive success to the next parturition season was significantly lower in unstable groups that experienced a stallion turnover compared to stable groups [START_REF] Berger | Wild horses of the Great Basin : social competition and population size[END_REF], and, in reintroduced Przewalski's horses, 9% of all foal mortality reported was attributed to infanticide by a newly established stallion (53 of 580 foals between 1994 and 2019) [START_REF] Dorj | Reproduction and mortality of re-introduced Przewalski's horse Equus przewalskii in Hustai National Park, Mongolia[END_REF]U. Dorj, pers.comm.).

Although our results do not provide evidence for infanticide in wild plains zebra, this behaviour has been observed for this species in captivity [START_REF] Pluháček | Variation in Incidence of Male Infanticide within Subspecies of Plains Zebra (Equus burchelli)[END_REF] and the social and mating system of plain zebras should favor the emergence of infanticide behaviour [START_REF] Lukas | The evolution of infanticide by males in mammalian societies[END_REF]. This raises the question of why the situation is so different in the wild: a possible explanation is that conditions in captivity and recent reintroduction may alter the behaviour of the animals and elevate the frequency of infanticide events, the 'social pathology hypothesis' (discussed by [START_REF] Feh | Male infanticide and paternity analyses in a socially natural herd of Przewalski's horses: Sexual selection[END_REF]Van Schaik & Janson, 2000). Leaving this hypothesis aside, we see several possible hypotheses for why infanticide would not occur or be rare in the wild in plains zebras, although the species presents traits that should favour this behaviour: (1) the killing of a dependent offspring benefits infanticidal males only if it improves their reproductive success by shortening the interbirth interval of the mother, and this may not be the case in plains zebras. In Przewalski's horses, [START_REF] Feh | Male infanticide and paternity analyses in a socially natural herd of Przewalski's horses: Sexual selection[END_REF] found that infanticide did not reduce interbirth intervals and that mares whose foals had been attacked avoided affiliating with the infanticidal male later on, therefore contesting the 'sexual selection hypothesis' and calling into question the necessity for the incoming male to kill a dependent young in such condition. However, infanticide may still improve the reproductive success of infanticidal males by stopping lactation and improving the mare's body condition and subsequent pregnancy success. Despite this potential benefit, males do not appear to commit infanticide. This is unexpected, especially at a site like Hwange where a male's reproductive period may be limited by both high intra-male competition and high predation risk, as we would expect any possibility increasing their chance to reproduce to be used by males. Therefore, either these purported benefits do not exist, or, we tentatively suggest, it could be that the high foal loses due to predation reduce the need for males to resort to infanticide; (2) female plains zebras may have developed counterstrategies such as female sociality and/or maternal aggression and protectiveness, allowing them to protect their progeny against intruders. For instance, in feral horses, higher maternal protection when several males are present in a group and higher protection towards foals that are not sired by the stallion have been reported [START_REF] Cameron | Social grouping and maternal behaviour in feral horses (Equus caballus): The influence of males on maternal protectiveness[END_REF][START_REF] Gray | An infanticide attempt by a free-roaming feral stallion (Equus caballus)[END_REF][START_REF] Watts | Maternal protectiveness in feral horses: responses to intraspecific and interspecific sources of risk[END_REF]. In captive mountain zebra, a female was observed to actively defend her foal against an infanticidal male [START_REF] Joubert | The social organization and associated behaviour in the Hartmann zebra Equus zebra hartmannae[END_REF], and similarly, in Przewalski's horses, all females whose foal was attacked by an infanticidal male strongly defended their foal, and in one case, the mare was helped by her half-sister [START_REF] Feh | Male infanticide and paternity analyses in a socially natural herd of Przewalski's horses: Sexual selection[END_REF]. In wild horses, females have been shown to cooperate and help each other at aggressively repelling newly established males that coerce females to mate following group takeover [START_REF] Berger | Wild horses of the Great Basin : social competition and population size[END_REF]. These strategies are likely to exist in plains zebra too, although it has never been documented in this species; (3) females could have evolved means to proactively terminate the pregnancy to avoid energy loss if the likelihood of losing the foal due to infanticide was high after a stallion turnover [START_REF] Bartoš | How to escape male infanticide: mechanisms for avoiding or terminating pregnancy in mammals[END_REF]). In such case, which is known to occur in plains zebras in captivity [START_REF] Pluháček | Male infanticide in captive plains zebra, Equus burchelli[END_REF][START_REF] Pluháček | Further evidence for male infanticide and feticide in captive plains zebra, Equus burchelli[END_REF], infanticide could be rarely observed, although it would exist as a behaviour that could be expressed by a new male in presence of a foal.

Demonstrations of these effects in the wild remain scarce [START_REF] Bartoš | How to escape male infanticide: mechanisms for avoiding or terminating pregnancy in mammals[END_REF]. If this applied to our case, stallion turnovers would however lead to reduced offspring survival when offspring survival is estimated from pregnancy stage, as in our study. We did not find evidence of this in our limited dataset, but note that the contrast in offspring survival between turnover and no-turnover situations was greater when survival was assessed from mid-pregnancy onward. Therefore, testing the existence of pregnancy termination in wild plains zebras could be an interesting avenue of research, as it complexifies the evolutionary perspective needed to understand how social events could have demographic consequences.

Demographic impact of stallion turnovers

One of our key objectives was to test whether accounting for stallion turnovers was important to understand and analyze zebra population dynamics. [START_REF] Grange | What limits the Serengeti zebra population?[END_REF][START_REF] Grange | Demography of plains zebras (Equus quagga) under heavy predation[END_REF] established, using demographic analysis of zebra populations, that foal survival was generally low. They however also stated [START_REF] Grange | What limits the Serengeti zebra population?[END_REF]) that the processes involved in foal mortality had not been fully elucidated, and questioned the relative contribution of predation and social factors such as infanticide. Our study brings some insights: irrespectively of whether stallion turnovers can sometimes lead to infanticide or not, their demographic effect at the population level is likely limited, and other factors are more likely to explain the overall low foal survival observed.

CONCLUSION

In conclusion, this study offers the first demonstration for an equid that male turnover rates are high in the wild, and increase with female group size. Based on work in captivity, plains zebra is commonly cited as an example of species in which male infanticide occurs. However, our results suggest that caution should be applied when hypothesizing that infanticide occurs in the wild -we found no evidence of this, although we cannot conclude that it never occurs. We can however conclude that, in the studied population, an effect of stallion turnovers on foal survival is not readily apparent. Additionally, we suggest that high predation risk, which strongly reduces foal survival, may reduce the relative fitness gains of males committing infanticide vs.

those who do not, therefore affecting its evolution in the wild. More generally, our study shows that demographic signals of a priori important social processes should be investigated closely rather than assumed. as random effects. The estimates and their 90% and 95% credible intervals (CrI) are shown.

  Johnson, Williams, Melin, & Hooten, 2018): visual inspection of trace plot, Rhat<1, effective sample size >0.5 * post-warmup samples, posterior predictive checks. See McElreath (2020) for accessible additional information on Bayesian modeling.

  Similar results have been found in other species, mainly in non-human primates (red howlers:[START_REF] Crockett | Infanticide in red howlers: female group size, male membership, and a possible link to folivory[END_REF] colobus monkeys: Teichroeb et al. 2012; Thomas's langurs: Steenbeek & Van Schaik, 2001;

Figure 1 .

 1 Figure 1. The probability of a stallion turnover between two consecutive sessions as a function of the number of reproductive females in the harems at the first session. The black dots show the predictions from the model, for all observations of the dataset, with the mean ± SE of these values shown in red. For each category of the number of reproductive females, we also report the number of turnover (1) or no turnover (0) situations, also expressed as the percentage of observations within each category.

Figure 2 .

 2 Figure 2. The probability of observing a foal at the next session, for females that were determined pregnant in one session based on hormone analysis, in relation to whether or not the stallion was replaced in the meantime. The black dots show the predictions from the model, for all observations of the dataset, with the mean ± SE of these values shown in red. For each category of stallion turnover, we report the number of foals observed (1) or not observed (0) at the next session, also expressed as the percentage of observations within each category.

Figure A1 .

 A1 Figure A1. The probability of observing a foal two sessions later, for females that were determined pregnant in one session based on hormone analysis, in relation to whether or not the stallion was replaced in the meantime. The black dots show the predictions from the model, for all observations of the dataset, with the mean ± SE of these values shown in red. For each category of stallion turnover, we report the number of foals observed (1) or not observed (0) two sessions later, also expressed as the percentage of observations within each category.

Table 1 .

 1 Coefficients of the mixed model investigating the effect of the number of reproductive females in a harem on the probability of stallion turnover between two sessions (Pr (turnover) ).Variables are: the number of reproductive females (N fem ) and the log-transformed number of days between the two sessions (log(Days)) as fixed effects, and identities of the stallion (ID(Stallion)) and of the harem (ID(Harem))

	Effect type	Coefficient	Estimate	90% CrI	95% CrI
	Group-level ('random') effects	ID(Stallion)	1.60	0.57 -2.86	0.39 -3.19
		ID(Harem)	0.55	0.04 -1.34	0.02 -1.57
	Population-level ('fixed') effects	Intercept	-15.15	-23.02 --8.42 -25.00 --7.21
		N fem	1.25	0.68 -1.91	0.60 -2.05
		log(Days)	1.79	0.65 -3.09	0.43 -3.38

Table 2 .

 2 Coefficients of the mixed model investigating the effect of stallion turnover on the probability of observing a foal at the next session (Pr (obs next session) ).

	Effect type	Coefficient	Estimate	90% CrI	95% CrI
	Group-level ('random') effects	ID(Harem)	0.88	0.09 -1.98	0.04 -2.24
		ID(Harem):ID(Mare)	0.95	0.08 -2.28	0.04 -2.62
	Population-level ('fixed') effects	Intercept	3.49	-7.85 -14.77	-10.00 -17.07
		Turnover_true	-0.41	-1.70 -0.86	-1.95 -1.12
		log(Days)	-1.26	-3.54 --0.94	-4.06 -1.39
		Age(mare)	0.02	0.00 -0.04	0.00 -0.04
		Season_wet	1.18	0.21 -2.22	0.03 -2.44

Variables are: stallion turnover (Turnover, binary: no turnover (false), turnover (true)), the log-transformed number of days between the date of dung sampling and the date of first resighting of the mare (log(Days)), age of the mare in months when first resighted (Age(mare)), and season (Season, dry, wet) as fixed effects; and identities of the mare (ID(Mare)) and the harem (ID(Harem)) as nested random effects. The estimates and their 90% and 95% credible intervals (CrI) are shown.

Table A2 .

 A2 Statistics of models investigating the effect of stallion turnover on the probability of observing a foal two sessions later (Pr).Models could include the effects of stallion turnover (turnover), the log-transformed number of days between the date of dung sampling and the date of first resighting of the mare (log(Days)), age of the mare when first resighted (Age(mare)), and season (ss) as fixed effects; and identities of the mare (ID(Mare)) and the harem (ID(Harem)) as nested random effects (identified as # in the table). A null model with no explanatory variable was also fitted. The table reports the effective number of parameters (pWAIC), the Widely Applicable Information Criterion (WAIC), the standard error of the WAIC estimate (SE), the difference between the WAIC of each model and the WAIC of the 'top' model (i.e. the model with the lowest WAIC, in bold) (dWAIC), the

	Models	Model ID	pWAIC	WAIC	SE	dWAIC	dSE	W
	Pr ~ turnover + #	1	13.76	120.33	7.43	0.00		0.15
	Pr ~ Age(mare) + #	2	13.34	120.98	6.87	0.64	4.80	0.11
	Pr ~ turnover + Age(mare) + #	3	15.34	120.99	7.91	0.66	2.46	0.11
	Pr ~ 1 + #	4	11.49	121.32	6.19	0.98	4.10	0.09
	Pr ~ ss + #	5	12.75	121.36	7.12	1.04	4.62	0.09
	Pr ~ turnover + ss + #	6	15.47	121.48	8.37	1.14	2.74	0.08
	Pr ~ Age(mare) + ss + #	7	15.08	122.02	7.89	1.70	5.34	0.06
	Pr ~ turnover + Age(mare) + ss + #	8	17.03	122.07	8.93	1.74	3.84	0.06
	Pr ~ turnover + log(Days) + #	9	15.36	122.12	7.85	1.80	1.22	0.06
	Pr ~ turnover + log(Days) + Age(mare) + #	10	17.08	122.90	8.31	2.58	2.84	0.04
	Pr ~ turnover + log(Days) + ss + #	11	17.22	123.46	8.82	3.12	3.16	0.03
	Pr ~ log(Days) + #	12	13.05	123.48	6.60	3.14	4.32	0.03
	Pr ~ log(Days) + Age(mare) + #	13	15.31	123.63	7.25	3.30	4.98	0.03
	Pr ~ log(Days) + ss + #	14	14.83	123.83	7.65	3.50	4.90	0.03
	Pr ~ log(Days) + Age(mare) + ss + #	15	16.84	123.92	8.30	3.58	5.58	0.02
	Pr ~ turnover + log(Days) + Age(mare) + ss + #	16	18.98	124.49	9.53	4.16	4.40	0.02

Table A4 .

 A4 Statistics of models investigating the effect of stallion turnover on the probability of observing a foal at the next session (Pr).

	Models	Model ID	pWAIC	WAIC	SE	dWAIC	dSE	W
	Pr ~ Age(mare) + ss + #	1	17.18	136.80	7.31	0.00		0.20
	Pr ~ Age(mare) + #	2	15.75	137.13	6.26	0.34	3.96	0.17
	Pr ~ 1 + #	3	15.04	138.31	4.70	1.52	5.34	0.10
	Pr ~ log(Days) + Age(mare) + ss + #	4	18.64	138.39	7.73	1.58	2.18	0.09
	Pr ~ ss + #	5	15.64	138.51	5.94	1.72	4.30	0.09
	Pr ~ turnover + Age(mare) + ss + #	6	18.61	139.09	7.74	2.30	1.24	0.06

Pr ~ turnover + Age(mare) + #

standard error of this difference (dSE), and the Akaike weight based on WAIC (W).

ACKNOWLEDGMENTS

We thank the Director General of the Zimbabwe Parks and Wildlife Management Authority for providing the opportunity to carry out this research. We acknowledge the support of the 'Zone Atelier' program of the CNRS.

We also thank the many people -too numerous to be named here -involved in this project over the years. We are particularly grateful to Claudia Feh for discussions on the conceptual framework which were more than useful. This work was supported by the French 'Agence Nationale de la Recherche' (grants SAVARID ANR-11-CEPS-003 and LANDTHIRST ANR-16-CE02-0001-01) and a PhD fellowship from 'Université de Montpellier' to C.V.

APPENDIX

Focusing on females detected in mid-pregnancy (N = 89), we investigated the effect of stallion turnovers on the probability of re-observing these mares with a foal two sessions later (rather than at the next session) when the stallion was replaced between the date of dung sampling and the date of the first resighting of the mare two sessions later, and when a stallion turnover had not occurred. Based on the model parameters, the probability of observing a foal two sessions later did not differ between situations when a stallion turnover occurred and those when it did not (Table A1, Fig. A1). We do note however that the point estimate for the turnover variable is more negative than in the analysis presented in the main text, and that the credible intervals are quite asymmetric around 0. Also, the turnover variable was included in the 'top' model (model 1, Table A2). However, the null model (model 4), by definition a simpler model nested in model 1, had a WAIC similar to the one of model 1 (dWAIC = 0.98 ±4.10 SE). This was reflected in the Akaike weights that were not much different (model 1: 0.15, model 4: 0.09). Also, another model that did not include the turnover variable was almost as good as model 1 in predicting the probability of observing a foal two sessions later (see Akaike weight of model 2 in Table A2). We should therefore conclude that, in the context of the dataset analyzed, none of the variables tested here, including the turnover variable, is informative to predict whether or not a foal would be observed two sessions after having detected a pregnancy.


published or not. The documents may come

Maritime flows and networks in a multidisciplinary perspective

Maritime flows and networks in a multidisciplinary perspective

It is almost inevitable when introducing a book about maritime networks to recall that more than 90 percent of world trade volumes are still supported by maritime transport. Seas and oceans occupy about 70 percent of the Earth's surface and coastal areas concentrated 16 and 39 percent of the world's total and urban populations respectively in the 1990s [START_REF] Noin | La population des littoraux du monde[END_REF]. This overwhelming importance is reflected by the great quantity of cultural, social, political, and scientific research about the sea in all its aspects. Dedicated sub-disciplines such as maritime history, geography, engineering, biology, and economics as well as institutions organise large-scale meetings to discuss the organisation and evolution of the sea as an ecosystem, a natural resource, and a vector of exchanges.

But what remains striking is that maritime transport has been much less studied than any other transport mode, especially from a network perspective. Existing research remains rather fragmented and scattered across the academic spectrum, which makes it difficult to review it exhaustively and to define any possible common framework. Five main reasons contribute to explaining such a fact: the dominance of a continental culture favouring studies of populated rather than "empty" spaces (Steinberg, 1999;[START_REF] Lewis | A maritime response to the crisis in area studies[END_REF]; the vague geographic distribution and morphology of maritime flows due to the absence of a track infrastructure [START_REF] White | Transport Geography[END_REF][START_REF] Rodrigue | The Geography of Transport Systems[END_REF]; the capture of most passenger and information flows by air transport and telecommunications since the second half of the 20th century; the continuous decline of maritime transport costs compared with other logistics costs; and the reluctance of scholars and experts to access and compile costly and hard to obtain maritime traffic statistics.

The World Seastems project No. 313847, funded by the European Research Council (ERC) over the period 2013-2018, is aimed primarily at compiling and analysing untapped historical records of global vessel movements over the contemporary period. Its international workshop held in June 2014 at the Paris Institute for Complex Systems (ISC-PIF), gathered many researchers with a similar focus, namely to provide a quantitative analysis of maritime networks in space and time. In so doing, the 20 chapters of the present book, written by 40 scholars from 12 countries and 10 academic backgrounds, offer a multidisciplinary perspective about one of the most vital pillars of world society.

The maritime network: late emergence of a multifaceted concept

A simple online search via Science Direct provided about 100 results for "maritime network" (as of 16 September 2014) compared with more than 10,000 results for road, global, or transport network, taking into account all scientific disciplines. Airline network scored 261, while trade, logistics, street, river, and railway ranged between 1,000 and 4,000 results each. Among maritime-related terms, "maritime network" scored less than maritime transport, trade, and traffic, shipping, port, or route, whereas "maritime transport" scored far below "road network", thereby illustrating the paramount importance of roads for daily commuting and trucking. Such a situation echoes the work of [START_REF] Danisch | Complétion de communautés par l'apprentissage d'une mesure de proximité[END_REF] who in their analysis of word co-occurrences found that "global shipping network" occupied a peculiar, peripheral situation with regard to the graph theory community. As a matter of fact, many scholarly works using the term maritime (or shipping) network make no reference to graph theory per se, in contrast to road, railway, air, and even river transport where network analysis had become a very common approach since the 1960s in the social sciences [START_REF] Ducruet | Structure and dynamics of transportation networks: Models, concepts, and applications[END_REF].

As pointed out by Lemarchand (2000, pp. 1-2), "the literature on networks ignores maritime places [while] port and maritime actors do not refer much to the concept of network". If the network traditionally describes technical systems made of material infrastructure, maritime routes exist on the map only so that the maritime network remains rather abstract, invisible, and decentralised, especially at the national scale where only a fragment of the network is perceived. The maritime network may refer to various realities according to different disciplines, such as trading linkages by sea organised by merchants in maritime history [START_REF] Gipouloux | The Asian Mediterranean: Port Cities and Trading Networks in China, Japan and[END_REF][START_REF] Tartaron | Maritime Networks in the Mycenaean World[END_REF], tactical or wireless communication networks between vessels in engineering, inter-firm alliances in maritime economics [START_REF] Caschili | An analysis of shipping agreements: The cooperative container network[END_REF], distribution of ocean carriers' schedules, and physical flows of vessels between ports. With reference to the European Motorways of the Sea initiative, [START_REF] Baird | Redefining maritime transport infrastructure[END_REF] even proposed to treat the floating deck of vessels just like road and rail infrastructure to favour integrated policies. In geography for instance, the maritime network had long been termed «system» (Bird, 1984, p. 26): "the ultimate system of maritime transportation is a true freedom of the seas whereby every port node can theoretically be linked to every other port node" (see also [START_REF] Slack | Pawns in the game: Ports in a global transportation system[END_REF].

The concept of "port system", suggesting linkages between ports was found in many works, but "in their preoccupation with the development of land communications (…) the authors neglected the development of maritime space" (Rimmer, 2007, p. 76). In addition, the port system concept was used interchangeably to describe multiple realities such as port (or maritime) range, region, façade, or seaboard, and mostly at the national scale, leading to confusion. The phased model of port system evolution proposed by [START_REF] Rimmer | The search for spatial regularities in the development of Australian seaports 1861-1961/2[END_REF] initially incorporated maritime linkages contrary to earlier models (Figure 1.1), but without concrete empirical validation as subsequent works continued focusing on individual port traffics and port hinterlands. The classic distinction between a French school focusing on forelands and a Dutch school more interested in hinterlands [START_REF] Weigend | The problem of hinterland and foreland as illustrated by the port of Hamburg[END_REF] led to distinct research pathways. For instance, the "port network" concept was proposed by Van Klink (1998) to describe the inland shift of port activities [START_REF] Van Klink | The port network as a new stage in port development: the case of Rotterdam[END_REF], but the same concept used in another context could also refer to a set of ports belonging to the portfolio of a given ocean carrier or terminal operator. When it comes to forelands, the French geographer André [START_REF] Vigarié | Ports de Commerce et Vie Littorale[END_REF] proposed the concept of "port triptych" to think simultaneously the port itself, the hinterland (inland market area), and the foreland (overseas markets). Yet, out of 399 scientific articles published in major geography journals between 1950 and 2012, only seven mentioned foreland in their title, against 29 for hinterland; 12 mentioned "network" of which only five for maritime networks and seven for barge, hinterland, and other networks [START_REF] Ng | The changing tides of port geography (1950-2012)[END_REF].

Other concepts such as transport chain, logistics chain, commodity chain, and value chain became frequent to describe ports' place in networks with a qualitative approach (see [START_REF] Robinson | Ports as elements in value-driven chain systems: The new paradigm[END_REF].

[Figure 1.1 here]

The emergence of a dedicated network vocabulary for describing maritime patterns and traffic came long after using more imaginary semantics. The French geographers René [START_REF] Perpillou | Géographie de la Circulation[END_REF] and André [START_REF] Vigarié | Géographie de la Circulation[END_REF], for instance, mentioned the constellation of ports and compared sea lanes to urban streets delivering flows of life in a city like arteries in a biological organism, respectively. Other concepts taken from other fields were gradually applied to maritime transport, such as corridor, loop, cycle, and hub. Graph-related concepts such as centrality and intermediacy were used about ports [START_REF] Fleming | Spatial characteristics of transportation hubs: Centrality and intermediacy[END_REF] alongside studies of site and situation, carrier choice and selection factors, and port competition to explain the emergence of hubs at certain locations, but without yet applying network analysis to maritime flows, so that "a connectivity index is used for airports (…) but does not exist for seaports" (de Langen et al., 2007, p. 31). This deficit became a growing issue, especially given that "the structure of [maritime] networks evolves over time [and therefore] the position of ports as nodes in the network also changes over time (…) understanding these changes is crucial for analysing the competitive position and growth prospects of (…) ports" (de Langen et al., 2002, p. 1). The conceptualisation of maritime transport as a network gave birth to many discussions that did not necessarily lead to empirical analyses of actual maritime flows, such as about security issues [START_REF] Kristiansen | Maritime Transportation: Safety Management and Risk Analysis[END_REF][START_REF] Angeloudis | Security and reliability of the liner containershipping network: Analysis of robustness using a complex network framework[END_REF] or operations research on navigation safety, ship routing and scheduling, and optimisation [START_REF] Christiansen | Ship routing and scheduling in the new millennium[END_REF][START_REF] Windeck | A Liner Shipping Network Design[END_REF]. Maritime economics barely refers to either graphs or networks in its central focus on management, pricing, markets, and finance, which is also true of wider transport economics [START_REF] Zwier | Connectivity and isolation in transport networks: A policy scenario experiment for the Greek island economy[END_REF][START_REF] Brooks | Maritime Transport[END_REF][START_REF] Leggate | International Maritime Transport : Perspectives[END_REF][START_REF] Stopford | Maritime Economics[END_REF].

The diversity of maritime data analyses

Before analysing maritime transport as a network, graphical representations of maritime flows long remained broad estimates of amount and geographic distribution [START_REF] Scarborough | Carte du Monde[END_REF][START_REF]Les routes maritimes internationales[END_REF][START_REF] Alexandersson | World Shipping: An Economic Geography of Ports and Seaborne Trade[END_REF]Central Intelligence Agency, 1973). Still in 2014, a geophysics paper reported "a lack of knowledge in the actual global distribution of the ships, i.e. vessel density, and its evolution over time due to economics or other causes" [START_REF] Tournadre | Anthropogenic pressure on the open ocean: The growth of ship traffic revealed by altimeter data analysis[END_REF]. This situation was already deplored in the 1940s when early economic geographers such as Ullmann ( 1949) provided an innovative cartography of maritime routes connecting the United States, claiming that maritime flows were useful to "take the pulse of world trade and movement" (see also Figure 1.2). Such a call did not, however, have many followers. Foreign trade statistics served to analyse overseas connections or maritime forelands of single ports such as Toronto [START_REF] Kerr | Overseas trade at the port of Toronto[END_REF], Genoa [START_REF] Rodgers | The port of Genova: External and internal relations[END_REF], Victoria [START_REF] Britton | Coastwise external relations of the ports of Victoria[END_REF], Clyde (Desbarats, 1971), Halifax and Saint John [START_REF] Patton | Railroad rate structures, ocean trade routes and the hinterland relations of Halifax and Saint John[END_REF], Irish Sea ports [START_REF] Andrews | Eighteenth century port forelands in the Irish Sea[END_REF], and ports in the countries of Norway [START_REF] Sommers | Distribution and significance of the foreign trade ports of Norway[END_REF], England [START_REF] Bird | Traffic flows to and from British seaports[END_REF][START_REF] Schirach-Szmigiel | Trading areas of the United Kingdom ports[END_REF], and Sweden [START_REF] Schirach-Szmigiel | Competition for the general cargo transports of Sweden's foreign trade[END_REF]. Such studies grew scarce until a recent revival based on the Chinese case (Wand and Ng, 2011). Accurately calculating and representing ship traffic densities on a larger scale demanded enormous data collection and extraction from printed reports on vessel movements such as on a world square grid [START_REF] Mckenzie | Maritime Dynamic Traffic Generator. Volume III: Density Data on World Maps[END_REF]. Until the 2000s, analyses of global maritime flows were bound to diagrams and simplified maps using United Nations (van den Bremen and de [START_REF] Van Den Bremen | The aggregate spatial patterns of maritime transport at world scale: A macro-scale approach in transport geography[END_REF] or other data [START_REF] Fossey | World Deep-Sea Container Shipping: A Geographical Economic & Statistical Analysis[END_REF][START_REF] Rodrigue | Straits, passages and chokepoints: A maritime geostrategy of petroleum distribution[END_REF]. Nevertheless in the 1980s, a few works mapped the nodal hierarchy of ports based on small data samples [START_REF] Marti | Patterns of United States-Canadian maritime container flows[END_REF][START_REF] Marti | Trade route 11: Methods to assess port exchanges of maritime containerized cargo flows[END_REF] using trade data to/from United States ports (Figure 1.3).

[Figure 1.2 here] [Figure 1.3 here]

It is only recently that scholars from various backgrounds, through interdisciplinary collaboration, have produced more elaborate representations of maritime flows on a larger scale, often from unexpected research domains. One of them is climatology, which made particular use of log books that reported weather conditions during ship voyages, as in the Climatological Database for the World's Oceans (CLIWOC) project for the period 1750-1850 [START_REF] Herrera | Climatological Database for the World's Oceans 1750-1850[END_REF], affiliated with similar projects such as ICOADS, RECLAIM, and Old Weather (see Figure 1.4). The same data also was used by historians to analyse technological progress in terms of sailing speed [START_REF] Ronnback | The speed of ships and shipping productivity in the age of sail[END_REF]. The extraction of archival records provided unprecedented knowledge of transatlantic slave voyages over the period 1500-1900 (Transatlantic Slave Voyages project), and trade flows across the Oresund Strait for the period 1634-1857 (Sound Toll project) 1 . In other fields such as 1

Other sources are worth mentioning although they have not yet been studied, such as the archives of the Suez Canal Authority, where every ship reported the precise content and value of its cargoes as well as the origin and anthropology and archaeology, the lack of knowledge on precise maritime circulations could be overcome by looking at sailing distances to explain the spread of languages in Australasia [START_REF] Coupé | Les premières traversées maritimes : une fenêtre sur les cultures et les langues dans la préhistoire[END_REF], demographic migrations in the Caribbean [START_REF] Friedman | Using viewshed models in GIS to analyze island inter-connectivity and ancient maritime pathways of the Pre-Columbian people in the Caribbean[END_REF], the diffusion of techniques [START_REF] Leidwanger | Modeling distance with time in ancient Mediterranean seafaring: A GIS application for the interpretation of maritime connectivity[END_REF], and sea-land accessibility in the Roman Mediterranean [START_REF] Scheidel | The Shape of the Roman World[END_REF].

[Figure 1.4 here] Other themes and issues included the effects of network centricity on maritime warfare based on the queuing theory [START_REF] Fewell | An approach to modelling the effects of network centricity in maritime warfare[END_REF], geospatial analysis of maritime piracy [START_REF] Leymarie | UNOSAT Global Report on Maritime Piracy[END_REF], modelling of optimal shipping routes to prevent collisions and oil spills [START_REF] Höglund | Environmentally safe areas and routes in the Baltic proper using Eulerian tracers[END_REF], simulation of attacks on the intermodal shipping network [START_REF] Earnest | Contagion in the transpacific shipping network: International networks and vulnerability interdependence[END_REF], calculation of a composite index of global urban accessibility based on raster data including maritime flows [START_REF] Nelson | Travel time to major cities: A global map of Accessibility[END_REF] (see Figure 1.5), and the mapping of traffic densities based on ship detection [START_REF] Tournadre | Anthropogenic pressure on the open ocean: The growth of ship traffic revealed by altimeter data analysis[END_REF], voluntary observing ships [START_REF] Vettor | Detection and analysis of the main routes of voluntary observing ships in the North Atlantic[END_REF], and Automated Identification Systems (AIS) (Le [START_REF] Guyader | Exploitation de données AIS pour la cartographie du transport maritime[END_REF]. Measuring the environmental impacts of shipping also provided among the most detailed and aesthetically advanced maps of global maritime flows, focusing on ship emissions [START_REF] Corbett | The Impacts of Globalisation on International Maritime Transport Activity[END_REF][START_REF] Halpern | A global map of human impact on marine ecosystems[END_REF][START_REF] Leonardi | A method for assessing the carbon footprint of maritime freight transport: European case study and results[END_REF]. Specific commodity flows in relation to United States ports using MARAD data were mapped also using Geographical Information Systems (GIS) methods combined with Google Earth 3D visualisations [START_REF] Shen | An exploratory analysis and visualisation of U.S. global trade patterns through maritime freight movement between U.S. ports and world ports[END_REF] (see Figure 1.6). In maritime geography, scholars proposed mapping the service networks of ocean carriers based on schedule data [START_REF] Robinson | Asian hub/feeder nets: The dynamics of restructuring[END_REF][START_REF] Comtois | Géopolitique et transport : Nouvelles perspectives stratégiques dans le détroit de Taïwan[END_REF][START_REF] Frémont | Les stratégies des armateurs de lignes régulières en matière de dessertes maritimes[END_REF][START_REF] Rimmer | China's extra and intra-Asian liner shipping connections, 1990-2000[END_REF][START_REF] Frémont | Global maritime networks: The case of Maersk[END_REF][START_REF] Frémont | Maritime networks: A source of competitiveness for shipping lines[END_REF] but still without direct engagement in network science, although some visualisations already underlined the centralisation of links around certain hubs (Figure 1.7). Another example is in maritime economics where disaggregated data of shipments served to measure the effect of maritime networks, services structure, and port infrastructure variables on maritime transport costs [START_REF] Martinez-Zarzoso | Maritime networks, services structure and maritime Trade[END_REF].

[Figure 1.5 here] [Figure 1.6 here] [Figure 1.7 here] A recent surge in maritime network analysis: towards a convergence?

Maritime networks for many years did not fit well into the traditionally "planar culture" of graph theoretical approaches of the academic literature [START_REF] Ducruet | Spatial science and network science: Review and outcomes of a complex relationship[END_REF]. In the 1960s, the vast majority of network analyses focused on planar graphs (no crossing between links, or edges, without creating a node, or vertex) such as power grids, road networks, etc. The only exception was the PhD dissertation of Ross [START_REF] Robinson | Spatial structuring of port-linked flows: the port of Vancouver, Canada[END_REF], deeply rooted in graph theory, geography and regional science, for its application to the analysis of the maritime network within Vancouver port and with other British Columbia ports (see Figure 1.8): "it is possible to define the spatial patterns of functional relationships between ports by examining the linkages which are sustained by the inter-port shipping movements of foreign trade vessels. Such an analysis provides not only an accurate measure of the linkages themselves but also clarifies the relationships between ports, the spatial organisation of port functions and the functional status of individual ports within the total group (…) The system of ports operating interdependently may now be regarded in abstract form as a set of points or nodes in a network, a transportation network in which the lines or links in the network are in fact 'imaginary routes'" (Robinson, 1968, pp. 95-97). A port network development model was also proposed to depict four phases that may apply to other regions of the world (Figure destination of its voyage (see: http://suezcanal.bibalex.org/Presentation/home/home.aspx).

1.8). Strangely enough, and even after its partial publication in a renowned journal a few years later [START_REF] Robinson | Modelling the port as an operational system: A perspective for research[END_REF], that pioneering work found no followers until the 1990s, mainly due to the wider shift from quantitative to behavioural approaches in the social sciences [START_REF] Ducruet | Spatial science and network science: Review and outcomes of a complex relationship[END_REF][START_REF] Ng | The changing tides of port geography (1950-2012)[END_REF]. It was only in the 1990s that scholars began to analyse maritime flows using a dedicated network methodology, just like airline or multinational firms networks; there was another unpublished PhD dissertation, this time on the North Atlantic region based on carrier schedule data [START_REF] Helmick | Concentration and Connectivity in the North Atlantic Liner Port Network[END_REF], but with no reference to Robinson's initial breakthrough.

[Figure 1.8 here] Starting with a simple count of vessel calls at world ports [START_REF] Brocard | Les réseaux de circulation maritime[END_REF], and a preliminary paper on the matter [START_REF] Joly | Structuration des lignes maritimes régulières de navires porte-conteneurs[END_REF], another pioneering work was the PhD dissertation of Olivier Joly (1999) who provided the first-ever network analysis of maritime container flows at the global scale, revealing the bipolar structure of the global maritime network centred upon Europe and Asia (Figure 1.9). The fast-growing field of complex networks recorded its first paper about maritime networks in 2007, which described the topological structure of container shipping networks in China [START_REF] Xu | Empirical analysis of the ship-transport network of China[END_REF] and later on, the world [START_REF] Deng | Worldwide marine transportation network: Efficiency and container throughput[END_REF][START_REF] Hu | Empirical analysis of the worldwide maritime transportation network[END_REF][START_REF] Doshi | Mining maritime schedules for 9nalyzing global shipping networks[END_REF]; these works were based on carriers' schedules and collaborations with physicists. Most of the time such works looked at the small-world and/or scale-free network structure of container flows (see also [START_REF] Hu | Topology analysis of China's port shipping network[END_REF], with reference to drastically different concepts and literatures than those of scholars interested in operations research and optimisation. The latter school recently provided many applications of the hub allocation model to container flows among Asian ports [START_REF] Low | Network effects in the East Asia container ports industry[END_REF][START_REF] Asgari | Network design approach for hub ports-shipping companies competition and cooperation[END_REF][START_REF] Jiang | Port connectivity study: An analysis framework from a global container liner shipping network perspective[END_REF]. Research on marine bioinvasions benefitted from globally available AIS data tracking the real-time position of vessels through growing collaboration between biology and physics [START_REF] Kaluza | The complex network of global cargo ship movements[END_REF][START_REF] Concepcion | Resolving natural ranges and marine invasions in a globally distributed octocoral (genus Carijoa)[END_REF][START_REF] Keller | Linking environmental conditions and ship movements to estimate invasive species transport across the global shipping network[END_REF][START_REF] Seebens | The risk of marine bioinvasion caused by global shipping[END_REF] (see Figure 1.10).

[Figure 1.9 here] [Figure 1.10 here] Geographers also provided various studies of hub-and-spokes systems in liner shipping networks at the regional level using elements of graph theory and spatial analysis, such as for the Caribbean basin [START_REF] Veenstra | Analysing container flows in the Caribbean[END_REF][START_REF] Mccalla | Hierarchical network structure as seen in container shipping liner services in the Caribbean basin[END_REF], Canary Islands [START_REF] Tovar | Container port competitiveness and connectivity: The Canary Islands main ports case[END_REF], Mediterranean basin [START_REF] Cisic | Network analysis applied to Mediterranean liner transport system[END_REF], northeast Asia (Ducruet et al., 2010a), and southern Africa [START_REF] Fraser | Peripherality in the global container shipping network: the case of the Southern African container port system[END_REF]. Global-level analyses also gradually became prominent about the container business to map nodal regions (Wang and Wang, 2011;[START_REF] Ducruet | The worldwide maritime network of container shipping: Spatial structure and regional dynamics[END_REF] and evaluate network vulnerability with reference to interoceanic canals [START_REF] Ducruet | The polarization of global container flows by interoceanic canals: Geographic coverage and network vulnerability[END_REF], also based on multiple fleet types and the concept of multigraph or multiplex graph [START_REF] Ducruet | Network diversity and maritime flows[END_REF]. Economists as well recently started to investigate the correlation between centrality and accessibility measures of port nodes and their broader traffic attributes [START_REF] Wang | Measuring container port accessibility: An application of the Principal Eigenvector Method (PEM)[END_REF][START_REF] Lam | Dynamics of liner shipping network and port connectivity in supply chain systems: Analysis on East Asia[END_REF][START_REF] Li | Centrality in global shipping network basing on worldwide shipping areas[END_REF][START_REF] Xu | Evolution of regional inequality in the global shipping network[END_REF], such as macro-scale analyses of country pairs based on their maritime connectivity [START_REF] Fugazza | Building a dataset for bilateral maritime connectivity[END_REF]. In the same vein, Ducruet et al. (2014a) used a multilevel analysis to show the influence of port centrality on average ship turnaround times globally. In particular, degree centrality and hub position of ports (as measured by the clustering coefficient) speed up their cargo handling operations while the volume of container throughput has the opposite effect, but this is even truer in richer countries.

Another avenue of research has been to unravel the regionalism of maritime flows. A wide variety of network clustering methods has been used in various contexts, such as the Atlantic (Ducruet et al., 2010b) and the world [START_REF] Ducruet | Maritime constellations: A complex network approach to shipping and ports[END_REF]Ducruet et al., 2014b) to detect the influence of geographic proximity on the distribution of flows or the emergence of a cohesive region such as Europe. Complementary views were offered by the study of particular regions such as the Korean Peninsula [START_REF] Ducruet | Political and economic factors in the evolution of North Korea's maritime connections[END_REF], the East Asian maritime corridor (Ducruet et al., 2011a), the Le Havre-Hamburg range [START_REF] Plasschaert | Redefining the Hamburg -Le Havre range in maritime networks[END_REF], the East-West maritime corridor [START_REF] Tran | Empirical analysis of the container liner shipping network on the East-West corridor[END_REF], Greece [START_REF] Tsiotas | Analysing the maritime transportation system in Greece: A complex network approach[END_REF][START_REF] Tsiotas | Analysing the maritime transportation system in Greece: A complex network approach[END_REF]North Africa (Mohamed-Chérif and[START_REF] Ducruet | The polarization of global container flows by interoceanic canals: Geographic coverage and network vulnerability[END_REF]. Graph theoretical methods as well as social network analysis (SNA) revealed the backbone of maritime flows and emergent hub ports [START_REF] Cullinane | The hierarchical configuration of the container port industry: An application of multiple linkage analysis[END_REF][START_REF] Montes | General cargo and containership emergent routes: A complex networks description[END_REF][START_REF] Gonzalez-Laxe | Maritime degree, centrality and vulnerability: Port hierarchies and emerging areas in containerized transport (2008-2010)[END_REF][START_REF] Seoane | Foreland determination for containership and general cargo ports in Europe (2007-2011)[END_REF][START_REF] Wang | Traffic consolidation in East Asian container ports: A network flow analysis[END_REF]. The global maritime network was also analysed through its complementarity with the global airline network regarding their respective and mutual connectivities [START_REF] Parshani | Inter-similarity between coupled networks[END_REF]Ducruet et al., 2011b;[START_REF] Woolley-Meza | Complexity in human transportation networks: A comparative analysis of worldwide air transportation and global cargo-ship movements[END_REF] and the spread of infectious diseases [START_REF] Tatem | Global traffic and disease vector dispersal[END_REF], and with the global road network to estimate cost effects on port and route performance [START_REF] Tavasszy | A strategic network choice model for global container flows: Specification, estimation and application[END_REF]Wang et al., 2012).

Perspectives and structure of the book

Although the late application of network analytical methods to maritime transport flows has been somewhat counterbalanced by a growing number of empirical studies, this book addresses several unresolved issues. First, most studies remain static, so that the dynamic properties of change in maritime network organisation and spatial distribution remain unclear. Second, the majority of recent works have focused on flow patterns but without explicit reference to any theoretical model, be it spatial or statistical. Third, the maritime network is not an isolated entity floating in an abstract space or defined only by its costs or benefits. It is a component of the society we live in, and as such its analysis should consider its local and regional embedding. This first part of the book, Introduction to Maritime Network Analysis, addresses the aforementioned issues in both theoretical and practical ways. Chapter 2, by Anne Bretagnolle, particularly stresses the emergence of city-systems throughout history, defined as networks of cities linked by certain transport modes, including maritime transport, although it lost its ability to move information and people in the second half of the 20 th century. Chapter 3, by Antoine Frémont, complements the previous chapter in that it concerns maritime transport actors (shipping lines) and how the CMA-CGM has evolved alongside technological and managerial transformations in the container business. Chapter 4, by Marc Barthelemy, focuses on the concept of spatial network and how it is analysed in the current transdisciplinary literature. It implicitly raises a crucial question: how can maritime networks contribute to such a fast-growing, mainstream research arena?

The second part of the book, Modelling Past Maritime Networks, comprises five chapters all concerned with the specific difficulties of using old data sources to map and analyse maritime networks. The lack of knowledge on actual Bronze Age maritime routes created the opportunity for Ray Rivers, Carl Knappett, and Tim Evans to simulate the distribution of inter-island maritime links in the Aegean Sea based on archaeological records and spatial models (Chapter 5). When route data does exist, problems are all but eliminated as new ones emerge, as seen in the other contributions. This was particularly well discussed and overcome by Mélanie Fournier in her visualisation experiment of Venice's maritime trade during the Middle Ages (Chapter 6); by Silvia Marzagalli when creating a new database on 18th century shipping flows allowing her to map, among other things, the distribution of French seaborne trade in the world (Chapter 7); by Liehui Wang, Theo Notteboom, and Lei Yang, who show the convergence or divergence of British and Japanese maritime colonial networks in 1920s China based on local archives (Chapter 8); and by César Ducruet, Sébastien Haule, Kamel Ait-Mohand, Bruno Marnot, Zuzanna Kosowska-Stamirowska, Laura Didier, and Marie-Anne Coche, who have extracted and mapped thousands of vessel movements from the world's biggest source of shipping information, Lloyd's List, to represent major shifts of maritime activity since the late 19th century to the present (Chapter 9).

The third part, composed of five chapters, is entitled Topology and Spatial Distribution of Maritime Networks. These works all apply wider statistical and spatial models of networks and trajectories to massive maritime data. The analysis by Frédéric Guinand and Yoann Pigné (Chapter 10) of daily connectivity changes in the global container shipping network is a very innovative approach that sheds new light on seasonal and cyclical dynamics in liner shipping as well as on temporal graphs, a novel approach to maritime networks with huge potential to zoom on particular events and nodes. The following work by Laurent Etienne, Erwan Alincourt and Thomas Devogele (Chapter 11) provides a critical analysis of real time vessel positioning data based on radar information or AIS to identify peculiar ship behaviour within aggregated maritime trajectories, an approach which has direct implications for port and maritime security. The identification of clusters in the global maritime network by Charles Bouveyron, Pierre Latouche, Rawya Zreik, and César Ducruet (Chapter 12) allows us to better define the functional specialisation of port nodes within a system of interlocked components connected by various fleet types, with cores, peripheries, and brokers. Another way to link maritime networks with mainstream network analytical research is shown by Serge Lhomme (Chapter 13) who measures the vulnerability of liner shipping networks to random or targeted failures of port nodes. This work sheds new light on the geographic dimension of network dereliction under certain attack scenarios, taking into account the weight of links and nodes as well as possible traffic shifts due to rerouting. Lastly, Michael Gastner and César Ducruet (Chapter 14) question the statistical structure of global cargo ship traffic with reference to wellknown models such as scale-free and small-world networks. They also emphasise noticeable changes over time in the distribution of the port hierarchy that correspond to important technological breakthroughs in the industry.

The last part of the book, Maritime networks and regional development, provides a closer look at the local embedding of maritime flows. Ronald Halim, Jan Kwakkel, and Lorant Tavasszy (Chapter 15) use simulation and spatial econometric methods to show direct connections between port traffic, maritime network design, trade, and economic development by choosing different parameters and scenarios in their global network model. An exploratory analysis of Pacific Rim port regions is proposed by César Ducruet and Hidekazu Itoh (Chapter 16) to seek the local socio-economic determinants of maritime connectivity in a network composed of different fleet types. Territorial factors thus play an important role as seen with the tendency for richer, more urbanised regions specialised in the tertiary sector to be more dominant in the network and to centralise higher-valued flows. At the country level, David Guerrero, Claude Grasland, and César Ducruet (Chapter 17) revisit the gravity model by comparing trade flows to maritime container flows on country pairs. They particularly highlight the facilitation of trade by shipping frequency, especially for manufactured goods, and the geographic essence of this relationship notwithstanding a number of outliers among countries. By linking spatial economics with spatial statistics, network analysis, and GIS, Igor Lugo provides a novel approach to systems of cities (Chapter 18) based on the case of Mexico, where urban nodes as well as port locations are connected via road segments. Such a combined approach has important implications for further understanding multimodal urban centrality and accessibility. The analysis by Nora Mareï and César Ducruet (Chapter 19) of the network configuration of maritime container flows in three different regions of the world discuss the respective influences of regional integration processes and carrier/port selection and competition dynamics on port hierarchies. A new measure of intra-versus extra-regional vessel circulation allows us to detect noticeable differences in the way such basins are organised and have evolved in recent decades. The last contribution to this part and to the book by César Ducruet,Sylvain Cuyala,Ali El Hosni, re-explores the longstanding portcity issue by measuring the influence of urban demographic size on the spatial pattern of global maritime flows between 1950 and 1990. Larger cities maintained their overwhelming dominance in terms of centrality, but at the same time, port hierarchy and urban hierarchy gradually became less overlapped.

  César DUCRUET, CNRS & UMR 7235 EconomiX, Nanterre, France Pre-final version of the chapter published in Ducruet C. (Ed.) (2015) Maritime Networks. Spatial Structures and Time Dynamics. Routledge Studies in Transport Analysis, pp. 3-26.

Figure 1 . 1

 11 Figure 1.1 Spatial model of the evolution of a port system including maritime linkages Source: Rimmer (2007).

Figure 1

 1 Figure 1.2 A cartography of US maritime trade, 1938. Source: Ullman (1949).

Figure 1 . 3

 13 Figure 1.3 Nodal hierarchy of US-European ports in maritime container flows, 1974 and 1977. Source: Marti and Krausse (1983).

Figure 1 . 4

 14 Figure 1.4 Map of British vessel flows based on log books, 1750-1800. Source: James Cheshire (2012).

Figure 1

 1 Figure 1.5 A global map of urban accessibility. Source: Nelson (2008).

Figure 1 . 6

 16 Figure 1.6 World distribution of US maritime trade in 2D and 3D, 2002. Source: Shen et al. (2013).

Figure 1 . 7

 17 Figure 1.7 The port network of Evergreen based on schedule data, 2000. Source: Comtois and Wang (2003).

Figure 1 . 8

 18 Figure 1.8 The foreign trade shipping network of Vancouver (a), British Columbia ports (b) and related spatial model (c)

Figure 1 .

 1 Figure 1.10 Distribution and density of world maritime flows based on AIS data, 2007.

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. [313847] 'World Seastems'.