Bruno Moriset
email: bruno.moriset@univ-lyon3.fr

Edward Elgar

The Geography of E-Commerce

Keywords: E-commerce, retail, marketplace, logistics

E-commerce has grown to enormous proportion, disrupting entire industries. Far from being virtual, e-commerce has a huge physical imprint and features a "mountainous" geography. Its uneven diffusion is driven by political, social and economic factors. All other things being equal, people buy more online in wealthy, well-connected countries, regions and communities. The case of China, by far the leading country for e-commerce and M-commerce, is unique: large parts of the country have "leapfrogged" from poverty straight into the digital economy. The geographic versatility of e-commerce is challenging public regulations: online retailers seek to avoid taxes on sales and income, and the growth of Web-based, customer-to-customer hospitality has got out of control in many cities, driving a backlash from local governments. Logistics is the cornerstone of e-commerce and the most visible part of its value chain. Major online retailers operate huge networks of warehouse and drive the growth of parcel express carriers such as FedEx, UPS, and DHL. Fast, reliable delivery is the critical part of the business, notably the final leg or 'last mile' to customers' homes. E-commerce is often made the scapegoat for the crisis of the retail industry which has materialized in store and shopping mall closures, and the bankruptcy of famous retail chains, notably in the U.S. However, experts and scholars consider that "physical" and virtual commerce are convergingrather than colliding -toward "omnichannel" models. In rural areas, e-commerce may drive the decline of small stores, but also play an inclusive role, connecting consumers and local producers to the global economy.

Introduction

Electronic commerce has grown today to enormous proportions, "disrupting" entire industries such as book and music publishing and retail, travel agencies, taxis, and hospitality. On September 4, 2018, Amazon.com, Inc. became the second company in history after Apple, Inc. to hit one trillion dollars of market capitalization. 1 In China, e-commerce may have captured about 28 percent of the global retail market. 2From its beginning, e-commerce has attracted the attention of geographers [START_REF] Leinbach | Worlds of electronic commerce: economic, geographical and social dimensions[END_REF][START_REF] Wilson | The fall of the mall? The impact of online travel sales on travel agencies[END_REF][START_REF] Couclelis | Pizza over the Internet: e-commerce, the fragmentation of activity and the tyranny of the region[END_REF][START_REF] Murphy | Grounding the virtual: the material effects of electronic grocery shopping[END_REF], although its geographic dimension is uneasy to capture. For centuries, stores, street markets, shopping malls, and "big box" supermarkets, have been instrumental in the design, growth, and social life of cities. However, since goods and services can be purchased on computers and smartphones without regard on time and location, and delivered at home a few days or even a few hours later, the value chain of e-commerce has lost most of its geographic significance in the eyes of the public. To some extent, ecommerce is subjected to the "death of distance" or "end of geography" fallacies which have, from the beginning, biased the comprehension of the digital economy [START_REF] Malecki | The digital economy: business organization, production processes and regional developments[END_REF]. Therefore, the primary purpose of this chapter is to shows that e-commerce does have a geography, and to explore this geography.

To understand the geographic features of e-commerce, one needs to comprehend the fundamentals of its business models, presented in section one. The second section explores the regional idiosyncrasies of e-commerce. The world map of e-commerce diffusion is uneven. It is dictated by purely geographic features such as distance to market and population density, and by economic, social and political factors, such as age structure, purchasing power, tax regimes and regulation of commerce, and the degree of information technology diffusion (IT-readiness). Section three is dedicated to the critical link between e-commerce and logistics. The delivery of goods to customers represents most of the physical presence of e-commerce, and the major part of its environmental footprint. Therefore, it is the overarching geographic issue of e-commerce. Section four investigates the local implication of e-commerce growth, in urban and rural environments.

Definitions and business models of e-commerce

E-commerce describes "sales of goods and services where the buyer places an order, or the price and terms of the sale are negotiated over an Internet, mobile device (Mcommerce), extranet, Electronic Data Interchange (EDI) network, electronic mail, or other comparable online system. Payment may or may not be made online" (U.S.Census Bureau 2018). In the largest meaning, e-commerce may span a wide spectrum of IT-intensive activities such as finance, telecommunications, software and computer services [START_REF] Leinbach | Worlds of electronic commerce: economic, geographical and social dimensions[END_REF]. The present paper focuses on activities which are close to "commerce" in the common sense, in particular wholesale and retail trade.

The main categorization of e-commerce used in the literature is based on the legal statuses of vendors and buyers (Figure 1). Trade between professionals or firms, notably wholesale operations, is said "business-to-business" (B2B). Sales by professional vendors or commercial enterprises to individual, end-customers fall in the category of "business to customer" ( B2C), or e-retail. The intermediation power of Web platforms has allowed millions of individual demands and offers to meet together, giving birth to the concept of "consumer-to-consumer" (C2C) e-commerce. "Consumer-to-business" (C2B) is a less common occurrence which is considered when individuals sell goods and services to a firm, by posting them on blogs, social networks or dedicated portals. For example, people can post photos on Adobe Stock, where they can be purchased by professional users such as advertisement agencies and magazines.

Other classifications are sometimes used. "Business-to-government" (B2G) describes transactions between private firms and public agencies or departments. The Internet is now widely used by governments throughout the procurement cycle at both national and local levels and requests for proposal are commonly posted on public agencies' websites. "M-commerce" describes online transactions made through smartphones and other mobile devices.

Figure 1. E-commerce categorization and examples of firms (in italics)

Buyer

Vendor

Business

(company, professional)

Customer (individual) Business (company, professional) B2B Amazon, Alibaba.com Made-in-China Tradeindia B2C Amazon AliExpress T-Mall JD.com Customer (individual)

C2B

Google AdSense Adobe Stock Jobster

C2C

Taobao eBay Airbnb

Logically, the attention of the public and scholars has been caught by B2C ecommerce, or e-retail, which has entered our everyday lives.Meanwhile, B2B has remained in the shadow [START_REF] Lilien | The B2B Knowledge Gap[END_REF], because people usually ignore value chain operations which occur between the factory and the store. The procurement chain that is necessary to the production of final goods and services is an increasingly globalized flow of intermediary goods, parts, and business services, which requires an endless series of commercial contracts, mostly hidden to consumers. Because the total of sales in a given value chain exceeds by far the final value-added and the price charged to end-customers, it is unsurprising that global B2B sales are much bigger than B2C. Statista (2017) estimates that the worldwide B2B e-commerce market in 2017 was worth 7.7 trillion dollars, to compare with B2C (e-retail) global sales of US$ 2.3 trillion. It is often uneasy to disentangle B2B and B2C e-commerce. For example, major online retailers such as Amazon and Alibaba also operate as neutral platforms for inter-firms transactions.

Electronic platforms and business models of e-commerce

The critical role of Web-based platforms derives from their limitless capacity of switching and disintermediation. The "miracle" of Airbnb, eBay and the likes, is that billions of people in the world can get the information that your apartment in Paris will be available for rent during the next holidays, that your lawn mower is for sale, or that you offer some seats in your car for a given trip against a modest fee3 . Disintermediation occurs when incumbent firms and institutions such as hotel chains, travel agencies, taxi companies, and music labels, are squeezed out or "uberized" by Web platforms through which individuals and small firms do business directly.

Similarly, traditional retailers may be passed over by commercial websites, which play the role of the sole intermediary between manufacturers and consumers.

In the early years of e-commerce, online stores were trading like traditional merchants, buying goods wholesale and reselling them to customers with a profit margin. Amazon and its followers such as Alibaba have later implemented a dramatic business innovation, the opening of their platforms to third-party merchants and sellers. In this "pure marketplace" model, the platform does not get ownership of the goods at any point of the trading process, but charges a fee on the transaction. This model is dominant within Alibaba's ecosystem (T-Mall, Taobao,AliExpress). The presence on leading marketplaces carries two main advantages for small and medium-sized enterprises: increased commercial visibility, and the access to global logistic systems (we elaborate on this topic below).

The difference between online merchants and mere marketplaces (Amazon is both) makes the interpretation of sales data a tricky exercise. There is a huge difference between the "revenue" (total of sales) of a given company and the "gross merchandise volume" (GMV) actually exchanged on its marketplaces. Alibaba Group revenue (about 40 billion dollars in 2017) is mostly made of fees charged on transactions made by third-party sellers. It pales in comparison to its global GMV, that surpasses those of Amazon by a wide margin (Table 1). The comparison with JD.com, China's second e-retailer is revealing: like a supermarket chain, JD.com buys wholesale and resells in retail. Said flatly, JD.com sells merchandise, while Alibaba sells trading services. To add to the complexity, some firms have a proportion of non-trade activities: Amazon's subsidiary Amazon Web Services is dedicated to cloud computing and data storage services.

Table 1. Amazon, Alibaba Group, and JD.com main data in 2017 (source: [START_REF] Amazon | E-commerce, transportation, and economic geography[END_REF], Alibaba Group Holding Ltd. 2018[START_REF] Jd | Annual report for the fiscal year ended December 31[END_REF]. Data for the fiscal year ended December 31, 2017 (Amazon, JD.com) and March 31, 2018 (Alibaba Group). Financial data in billion U.S. dollars.

Economies of scale and network effects: a "winner-take-all" economy

The economy of digital platforms shows "winner-take-all" features (Kenney and Zysman 2016) to a degree unseen since Andrew Carnegie and John D. Rockefeller. 4It was first epitomized by Microsoft's and Intel's dominances. It is today illustrated by the meteoric rise to near monopoly status of Google and Facebook. The supremacy of Amazon and Alibaba, the successes of Uber and Airbnb, tell a similar story. This tendency stems from two intertwined features of Web-based economic models: economies of scale and network effects.

Economy of scale -a fundamental concept in microeconomics -predates the digital economy. It occurs when costs of operation within a company are constant or rise at a slower pace than the final output and the volume of sales, leading to increasing margin and bigger return on capital. That explains the race for size common in all industries. In the sphere of e-commerce, the rule of economies of scale leads to a Darwinian process of selection and concentration. For example, a commercial website at the startup stage should "burn" huge amount of money in advertisement campaigns, while its competitors do the same. Only a few will sustain the process, achieve commercial success, and capture the market share of those who have failed [START_REF] Noe | Winner take all: competition, strategy, and the structure of returns in the Internet economy[END_REF]. For surviving firms, the sales/cost of ads ratio will increase and profitability will be in sight. Other effects of scale are seen in fulfillment operations such as warehousing and delivery.

Network effects are a complement of economies of scale. The "Metcalfe Law" says that the value of a network is theoretically proportionate to the square of the number of its users [START_REF] Metcalfe | Metcalfe's Law: a network becomes more valuable as it reaches more users[END_REF]. Getting more visitors and shoppers on a commercial website makes it possible to offer a larger catalog and to attract more third-party vendors who offer new goods and services, and fuel the attractiveness of the platform, with self-reinforcing, systemic effects.

The intermediation power of the Internet has given birth to a "sharing economy", sometimes called a "wikinomics" [START_REF] Tapscott | Wikinomics: how mass collaboration changes everything[END_REF], which can be identified in all four categories of e-commerce. These concepts are linked with the idea of "open innovation" [START_REF] Chesbrough | Open Innovation: the new imperative for creating and profiting from technology[END_REF]. Rising complexity, and the shortening of product lifecycles and time-to-market delays, have become definitive features of the digital economy. In this context, large firms must look outside the silos of their internal creative resources (for example R&D and design labs). In diverse industries such as aircraft and automobile manufacturing, or software, major companies have open dedicated platforms to third-party firms, private and public labs, and even individuals. For example software applications ("apps") for Apple's iPhones are sourced to millions of firms and individuals worldwide. On June 1, 2017, Apple announced that App Store, the platform on which iPhone users connect and download applications, has generated a global revenue of 70 billion dollars since 2008.5

The uneven diffusion of e-commerce

A retrospective view is necessary to comprehend the magnitude of change driven in the recent years by the growth of e-commerce. E-commerce made timid debuts in the pre-Internet era with the French Minitel in 1982) and Thomson Holidays, a travel agency, which experimented electronic sales through the a TV screen and a minicomputer interface [START_REF] Palmer | Using IT for competitive advantage at Thomson Holidays[END_REF]. Modern e-commerce began in the early 1990s in parallel with the diffusion of the Internet. Amazon was founded in 1994. Much hype followed. The promise of the "death of geography" attracted thousands of entrepreneurs and inflated the "dot.com bubble", notably in the U.S. However, most of the web-based ventures had underestimated the requirement of fulfillmentcustomer support and logistics -and collapsed in the "dot.com bubble bust" of the earlier 2000s [START_REF] Day | Shakeouts in digital markets: lessons from B2B exchanges[END_REF][START_REF] Indergaard | Silicon Alley: the rise and fall of a new media district[END_REF][START_REF] Zook | The Geography of the Internet Industry: venture capital, dot-coms, and local knowledge[END_REF]. In 2005, B2C (retailing) e-commerce market share in the U.S. amounted to a mere 2.4 percent, up from 1.1 percent in 2001. 6Today, e-retailing can by no means be regarded as a marginal phenomenon, with market shares exceeding 10 percent in many countries, and reaching an astonishing 28 percent in China (Table 2). Worth noting is the dramatic growth of sales made through mobile devices, mainly smartphones, or M-commerce. According to eMarketer, it is projected to reach 40 percent of online sales in the U.S. in 2018, and 75 percent in China -worth one trillion dollars. 7 The recent growth of e-commerce has been driven by the coming to maturity of the digital society, or "IT-readiness": mass diffusion of the Internet, powerful connected devices, reliable online payment services and digitally-enhanced logistics solutions.

The uneven development of e-commerce is explained by other local idiosyncrasies such as geography (density, percentage of urban population, transportation infrastructures), age structure (the elderly usually trade less online), and, above all, purchasing power: in 2018, B2C e-commerce sales in India (1.3 billion people) were smaller than France's (67 million).

Local regulations and commerce history matter. For example, the UK has a wellestablished tradition of mail-order sales, with a high degree of customer protection. That explains, in part, the high market share of e-commerce over global retail sales, which is second only to China.

However, every country pales in comparison to China in terms of e-commerce volume, market share, and speed of growth. In the last decade, China online sales surged from near zero to worth 1.5 trillion dollars, about three times those of the U.S. This achievement has been driven by a bundle of factors: the meteoric economic growth of the 2000s and 2010s, the tech-oriented consumption appetite of a young and newly enriched, urban middle class, and the innovative effort of local IT companies such as Alibaba Group and Tencent which have developed versatile mobile payment solutions such as Alipay and WeChat Pay.

The rise of China's e-commerce ecosystem is a textbook example of "leapfrogging."

In Western countries, people have got a car, and used to live near a shopping mall well before having a PC and an Internet connection, not mentioning a smartphone. At the startup stage, Amazon and other e-merchants have had to compete with a dense physical retail infrastructure, and a tradition of going shopping to the mall strongly anchored in the society. For its part, China jumped straight from mass poverty into the Internet era. Chinese citizens shop massively online because so many of them do not own a car to load at the nearest supermarket. And they use M-commerce because they often do not have a PC or a fixed line Internet connection, although nearly everybody, urban or rural, does have a smartphone.

Tax regimes and the geography of e-commerce

With the growth and rising sophistication of e-commerce, sales and profit taxation has become a serious issue for governments, notably in decentralized systems such as the U.S. or the European Union. E-commerce and other digital industries do not have the monopoly of tax avoidance and tax sheltering practices. But the fuzziness of ecommerce's geography and its ability to ignore political borders compound the problem governments are facing with. Tax regimes and jurisdictions are slow to follow the fast pace of growth and innovation in technology and marketing. As wrote Tarantola (2015, p. 316) "this new electronic frontier has grown from its infancy to an economic heavyweight in such a relatively short period of time that the legal framework simply has not had time to catch up."

This evolution has resulted in huge tax losses for governments. Estimates of sales tax loss for the U.S. states in 2017 range from 8 to 33 billion dollars (SCOTUS 2018).

The impotency of governments to collect properly corporate taxes and sales taxes on e-commerce operations results in market distortion and penalizes traditional businesses.

In the European Union, Ireland and Luxemburg are notoriously acting as tax heavens for IT-companies. Apple and Facebook have headquartered in Ireland, where the corporate tax rate of 12.5 percent is half the average of the other European countries. Amazon has headquartered European operations in Luxemburg, where the standard tax rate on commercial activities is about 29 percent while the tax on intellectual property income and royalties amount to a mere 5.7 percent. Therefore, Amazon has created in Luxemburg a financial holding which charges its main operating business with more or less fictitious intellectual services. In the words of M. Vestager, the European Commissioner for Competition, Amazon's holding is "an empty shell." In the end, Amazon was ordered by the European Commission to repay Luxemburg 250 million euros in back taxes (European Commission 2017).

In the U.S., the decision of the Supreme Court in South Dakota v. Wayfair Inc. (June 21, 2018) should be regarded as a decisive turn in the history of e-commerce taxation [START_REF] Liptak | Supreme Court Clears Way to Collect Sales Tax From Web Retailers[END_REF]. Up to now, the U.S. jurisdiction of ecommerce taxes was stating that sales in a given State should not be submitted to taxes until the vendor shows locally some "significant" physical presence, such as stores, supermarkets, and warehouses. In the 2018 decision, the Court considered that under the current conditions of e-commerce operations, "the physical presence rule is artificial in its entirety" (SCOTUS 2018, 14). The majority in the Court said that the existing tax regime based upon the 1992 decision was creating "market distortions" (10), "a tax shelter", and "an incentive to avoid physical presence in multiple States" which would deprive local communities of "storefronts, distribution points, and employment centers that otherwise would be efficient or desirable" (13).

From the geographer point of view, the most interesting point in the 2018 decision is the smart and pragmatic analysis of today's e-commerce geographic reality. The Court stated that consumers' PC and smartphones that host data and cookies resulting from transactions with online merchants are today as much significant as warehouses for the definition of business presence in a given area.

A company with a website accessible in South Dakota may be said to have a physical presence in the State via the customers' computers. A website may leave cookies saved to the customers' hard drives, or customers may download the company's app onto their phones. Or a company may lease data storage that is permanently, or even occasionally, located in South Dakot (SCOTUS 2018, 15).

Actually, Amazon will not be hurt by the recent decision, given it already collects sales taxes in the 45 states that have such taxes in place. 9 The company has been quarrelling for decades with state governments over the sales tax issue, sometimes threatening to close fulfillment facilities in states which tried to levy taxes on Amazon sales. However, since Amazon has turned to a behemoth, with over a hundred of physical locations (office, contact centers, and warehouses) throughout the U.S., it has to comply with local taxing jurisdictions.

Dissenting voices among the Court say that the burden of new sale taxes will fall mainly on "mom and pop" businesses, which could not meet the requirements of the thousands of different taxing jurisdictions in the U.S. However, to relieve the tax pressure on small businesses, many states have implemented a no-tax floor.

Logistics reigns supreme

Scholars have early recognized that logistics is the critical link within the value chain of e-commerce, and the most visible part of its geographical dimension (Anderson et al. 2003[START_REF] Murphy | Re)solving space and time: fulfilment issues in online grocery retailing[END_REF][START_REF] Murphy | Grounding the virtual: the material effects of electronic grocery shopping[END_REF]. J. Bezos, founder and CEO of Amazon, had understood from the beginning that, in the absence of physical sale outlets, the key challenge was the management of "the flow" to customers -hence the name of the company [START_REF] Dodge | Finding the source of Amazon.com[END_REF].

The absence of physical stores has huge implications on the retailing process, notably on the creation of trust. Consumers cannot touch and try their purchases, and cannot immediately take and carry them back at home. That does explain why e-commerce, when in the infancy, turned to standardized goods such as books and CDs from which few bad surprises are expected. Once the payment is processed, the commercial chain is invisible and out of touch: wait for days, hope that the good will not be damaged, lost, or stolen, pray that it will work or fit your body, nobody and nowhere to complain face-to-face. Sophisticated web interfaces, efficient customer support centers, and trustworthy payment systems, have been instrumental in the growth of e-commerce. But fast and secure delivery is the linchpin of e-commerce. Said simply, it is a battle against time and space.

The importance of logistics can be read in data on shipping costs and warehousing capacity disclosed by major online retailers. In a tremendous effort to reduce time of delivery, Amazon has so far prioritized investment over profitability. In the recent years, warehousing, transportation and delivery costs have grown faster than sales.

Between 2015 and 2017, Amazon's fulfillment expenses grew from 12.5 to 14.2 percent of net sales. Shipping costs nearly doubled from $11.5 billion to $21.7 billion, while sales rose "only" by 62 percent, from 99 to $160 billion10 ( [START_REF] Amazon | E-commerce, transportation, and economic geography[END_REF]. By the end of 2017, Amazon was operating worldwide 19.4 million square meters of fulfillment facilities, a floor area equivalent to 800 Walmart superstores. JD.com, China's second largest e-retailer, covers the country with 486 warehouses in 78 cities, with an aggregated area of 10 million square meters [START_REF] Jd | Annual report for the fiscal year ended December 31[END_REF]. [START_REF] Wang | Co-evolution between etailing and parcel express industry and its geographical imprints: The case of China[END_REF] show the much differentiated geography of e-commerce logistics in China. Customers in coastal China and main cities in the interior benefit from free and fast delivery solutions, but in the other parts of the country, accessibility to market is much unequal, and customers have to choose between heavy delivery fees or longer delays.

The results of Amazon's logistics effort are impressive. [START_REF] Sisson | 9 facts about Amazon's unprecedented warehouse empire[END_REF] reports that half the U.S. population is now living within 20 miles of an Amazon warehouse. In a letter to shareholders (April 18, 2018), the company says it has exceeded 100 million "Prime" subscribers who are eligible to free two-day shipping on 100 million items.

The service Prime Now" offers same-day delivery on one millions items in 50 cities and nine countries worldwide.11

Last generation warehouses are huge and highly automated, hosting hundreds of robots and miles of conveyor belts. However, warehouses and sorting facilities do not solve the "last mile" issue, or the last leg of delivery to customers' home. In "physical" commerce, customers use to carry their shopping basket back at home by their own means. Therefore, shelf replenishment materializes in huge packages and full pallets of goods like soft drink bottles, nutella jars, or the last best-seller edition, which are delivered from central warehouses at the back of supermarkets by heavy trucks. And "big box" stores or suburban shopping malls are often located close to an expressway. On the contrary, online retailers must deliver small packages and parcels, directly to the consumer door, in the narrow -sometimes pedestrian -streets of downtown, or in the labyrinthic residential suburbs. Allen et al. (2018) explain that last mile delivery materializes in a growing flow of vans and light goods vehicles such as UPS' iconic "package cars", which adds to the existing urban road congestion and pollution. The issue is made worse by the frequent stops made at the curbside. This trend conflicts with urban planning policies seen today in city centers which favor public transportation, cycling and walking.

The use of individual mail boxes is possible for very small parcels only. During opening hours, couriers cannot expect the presence of customers and their relatives at home. To solve this problem, e-retailers and third-party parcel express carriers such as FedEx, UPS, and DHL resort to pick up solutions. For example, DPD has deployed in Europe a network of 37,000 pick up stations -often managed by small neighborhood stores -and 2,260 lockers, used by 5600 online merchants. 12 Amazon is implementing its own network of lockers located in easily accessible spots such as transportation stations or supermarket entries (photo n° 1). On 20 June, 2018, the French Railway Company announced it had contracted with Amazon the fitting of 1000 lockers in its stations.13

Photo 1. Amazon lockers at the door of a French supermarket. Photo by the author, October 19, 2018.

When e-commerce shapes local economic landscapes

The disruption of retail

The fate of Randall Park Mall in North Randall (near Cleveland, Ohio) epitomizes the cross destinies of physical and electronic retails. Once one of the largest shopping malls in the U.S. (opening August 11, 1976), it was demolished in 2015 after a long decline and the closure of tenants such as Sears and Macy's. In fall 2018, Amazon opened on the site one of its largest and most advanced fulfillment center. Despite being highly automatized with robots and 26 miles of conveyor belts, the 200,000 square meters facility is likely to employ near 2000 people. A recruitment that is much welcomed in a community severely hit by the industrial decline. 14 Amazon's location choice is not fortuitous. Thanks to its central location within the country's transportation system, Ohio hosts so many warehouses that it can said the U.S. "ecommerce capital" [START_REF] Reagan | This is why Ohio is becoming the ecommerce capital[END_REF].

In a paper on online travel sales, [START_REF] Wilson | The fall of the mall? The impact of online travel sales on travel agencies[END_REF] wrote about the "fall of the mall". As a matter of fact, travel agencies have almost entirely been "uberized" by e-commerce and have disappeared from the urban landscape. So, the impressive growth of e-commerce rises a critical issue: should we forecast the complete collapse of "main street" and shopping malls, with dramatic consequence on cities urbanity and liveliness, without mention of the loss or displacement of millions of jobs?

The traditional retail industry is actually in deep trouble, notably in the U.S. In the recent years, chains like Macy's, Office Depot, J.C. Penney, Hancock Fabrics, American Apparel, Kmart, and Sears, among others, have closed stores by the thousands. Toys "R" Us went bankrupt in September 2017 and ceased operations during the summer 2018. Sears, the country's most iconic department store, filed for bankruptcy on October 15, 2018, after having shuttered 2800 stores over the past 13 years. 15 The rout of these famous brands leads pundits to question the very survival of shopping malls [START_REF] Guedim | Will shopping malls survive the decade?[END_REF]. According to a report published in 2017 by Crédit Suisse (a major international bank), one out of four shopping malls in the U.S. could close by 2022.16 "Retail apocalypse" and "dead mall" are now entries in Wikipedia.

Toward multichannel and omnichannel commerce

E-commerce is often made the scapegoat for the crisis of the retail industry. But the glut of commercial property, and the competition with low-cost supermarket chains and warehouse clubs must be mentioned as majors factors. In the end, traditional retail will not disappear, but it is submitted to a high degree of disruption [START_REF] Grossman | The industries that are being disrupted the most by digital[END_REF] and must reinvent itself.

To compete with e-commerce, physical stores and shopping malls must capitalize on their main asset: the potential for providing customers with an enjoyable living and socializing experience. Small and medium-sized malls and main streets in small, remote communities are likely to get into trouble. Meanwhile, shopping malls in tierone cities are getting bigger and smarter, offering a wide range of integrated services, entertainment and sport facilities, free wifi and dedicated apps, and cultural events such as live music or dance performances, wine testing or culinary demonstrations.

There are several indications that e-commerce and physical retail, rather than colliding, become complements in a "brick and click", multichannel commerce [START_REF] Currah | Behind the web store: the organisational and spatial evolution of multichannel retailing in Toronto[END_REF][START_REF] Steinfield | Situated electronic commerce: toward a view as complement rather than substitute for offline commerce[END_REF]). Evidence of the convergence is given by the tendency of major online merchants to seek for physical stores. In November 2017, Alibaba Group invested $2.9 billion to purchase a stake in Sun Art Retail Group Ltd., a major hypermarkets chain in China under the brands Auchan and RT-Mart. In January 2018, Tencent, China's largest Internet-based company, and JD.com, participated in a $5.4 billion investment in Wanda Commercial, China's leading operator of shopping malls. 17 Amazon has shown a similar tendency to go physical with the acquisition in 2017 of Whole Foods Market Inc., a grocery store chain, and the development of Amazon Go, a concept of automated grocery stores. Competition with e-commerce pushes traditional supermarket chains to a symmetrical move: in 2016, Walmart (the world biggest retail company by revenue) acquired Jet.com, an online seller, in order to improve its e-commerce operations.

To put emphasis on complementarity and combination, rather than mere juxtaposition, Verhoef, Kannan, and Inman (2015) consider the existence of omnichannel forms of retailing, or versatile combinations in time and space of electronic and physical operations. As a matter of fact, "click and collect" commerce has become increasingly popular, creating a new marketing and planning challenge for retailers [START_REF] Kirby-Hawkins | An investigation into the geography of corporate e-commerce sales in the UK grocery market[END_REF]. Auchan, a French hypermarket chain pioneered the "drive" service in 2000; Walmart followed in 2014. Customers order on the web and later get their basket of goods loaded in their car at the nearest store. This recombination of shopping practices is much suitable to the life in large cities, where time may be more precious than money. [START_REF] Pouyleau | E-commerce. Destructeur ou disrupteur d'immobilier physique?[END_REF] reports the example of FNAC (France's leading chain store of cultural goods and consumer electronics) whose outlet in La Gare du Nord, a major railway station in Paris, makes about 40 percent of its sales through articles purchased on www.fnac.com. New combinations of commerce practices are also found in the blogshop phenomenon, which has become much popular in Singapore. Blogshops are "niche markets of fast fashion" (Yeung and Ang 2015, 93) led by young entrepreneurs who have started a commerce -often of apparel and accessories -on a blog, with minimal initial funding. Once they have achieved some commercial success on the Web, many blogshops have established a physical store. Blogshops are a much informal model of commerce, driven by a community of "millennial" shoppers and sellers, auto-regulated through social networks.

E-commerce and rural areas: from digital divide to economic inclusion

When the digital economy was in the infancy, many had thought that information technology would act as the great leveller of geographic inequities in terms of accessibility to goods and services. Said flatly, this utopian vision did not materialize. On the contrary, an enormous literature shows that the domination of large cities over the surrouding areas has increased over the past three decades. In particular, cities play a unique role in creative and innovative activities [START_REF] Florida | The city as innovation machine[END_REF]).

In the field of e-commerce, the domination of cities over rural areas is driven by several factors. The persistence of a "digital divide" (Warf 2010, [START_REF] Salemink | Rural development in the digital age: A systematic literature review on unequal ICT availability, adoption, and use in rural areas[END_REF]) is often mentioned: lack of an adequate Internet connection, lower diffusion of digital devices. However, it is difficult to say if rural dwellers, all other things being equal, shop online more or less than people living in large cities, because social and economic factors (income, education, age) are more important than geography per se [START_REF] Clarke | The emerging geography of e-commerce in British retailing[END_REF]. De [START_REF] Blasio | Urban-Rural Differences in Internet Usage, e-Commerce, and e-Banking: Evidence from Italy[END_REF] on Italy, and [START_REF] Farag | E-shopping in the Netherlands: does geography matter?[END_REF] on the Netherland come to the conclusion that rural dwellers are intensive online buyers of much standardized goods such as books and CDs, because of the remoteness of stores.

In China, the remoteness from urban shopping malls and supermarkets may be an incentive to shop online. [START_REF] Fan | The Alibaba Effect: spatial consumption inequality and the welfare gains from e-Commerce[END_REF] finds evidence that people in small cities spend online a share of their revenue which is slightly bigger than those living in tier-one and tier-two cities. The access to a larger variety of goods is an important factor of the growth of e-commerce in rural China, which lacks from a dense networks of retail outlets. Major online retailers such as Alibaba and JD.com have contracted with rural communities to develop the production of high value-added products -for example organic food -and to sell it online to urban customers through their marketplaces. Most of these new agricultural ecosystems are known as Taobao Villages, from the name of Alibaba's main retail platform [START_REF] Lin | Taobao practices, everyday life and emerging hybrid rurality in contemporary China[END_REF]. As of 2017, Alibaba had developed a network of 70,000 clusters of farmers and local online vendors throughout the country.

In rural areas, low density and the lack of adequate transportation infrastructure may inflate delivery costs. In rural China, where 600 million people are living, online merchants are facing a big challenge. In the mountainous countryside of Sichuan, Shaanxi and Jiangsu provinces, JD.com is now routinely operating a flotilla of drones that supply isolated settlements (The Economist 2018). According to the company, each drone can carry 15 kg of packages, over 50 kilometers. Aircraft land in a dedicated area close to the houses; "village promoters" pick-up the payload and distribute the packages to customers. As of May 2017, JD.com said it had about 300,000 village promoters nationwide, and was planning the implementation of oneton load heavy drones.18

Conclusion

This chapter provides evidence that electronic commerce, far from being purely virtual, does have an original physical imprint, and features a mountainous geographic and economic landscape. As write Wrigley and Currah (2006, 340) "place, space and embeddedness continue to matter in the 'new e-conomy' of multichannel distribution."

The rise of B2B e-commerce has been instrumental in the emergence of a more global economy, based on fast supply chains and global outsourcing [START_REF] Peck | Offshore, Exploring the Worlds of Global Outsourcing[END_REF]. Some e-commerce firms have become corporate behemoths, whose office buildings, warehouses, and van flotillas are the tangible manifesto of their contribution to local economies. In this regard, the obsession of media and local policymakers around Amazon's 2017 request for proposals for the location of a new headquarters (said HQ2) has been revealing. The decision issued in November 2018 to locate in New York and Arlington, VA , a suburb of Washington, D.C., shows that urban buzz and face-to-face contact remain critical to business operations, even in a world of ecommerce. 19One cannot neglect the dark face of e-commerce. The flow of goods and packages adds to urban congestion, pollution, and greenhouse gas emission. Warehouse workers and online food couriers are often described as the galley slaves of the digital economy. In major tourist cities, the dramatic growth of Airbnb lodging has become controversial. It is accused of accelerating the displacement of middle-class households from the center to the periphery. To tackle this problem, many municipalities like Paris or New York have implemented coercive regulations.

However, e-commerce potential for growth remains enormous, even in rich countries. In an interview given to Forbes (September 30, 2018), J. Bezos, Amazon's CEO, said that the market size of the company "is unconstrained." 20 He was arguing on the fact that Amazon has so far captured a mere five percent of the global U.S. retail market. Such a grand vision, as we write above, does not predict the "fall of the mall." Apple Stores are getting larger, smarter, and are regarded among the most profitable stores in the world's retail industry because they provide customers with discovery and learning experience through human interaction [START_REF] Gallo | Ten reasons why the Apple Store was never a store[END_REF]. From the geographer and planner point of view, the main problem could occur in small towns and rural regions, where Apple and its fellows will never locate stores. As a key component of the digital economy, e-commerce fuels the obsolescence process which is threatening some local business ecosystems and their communities. But ecommerce may also have some inclusive virtue, for example when its helps communities of Chinese farmers to connect to the global economy.

Amazon.com, Inc.* Alibaba Group JD.com, Inc.

	Gross merchandise	300 ? (estimation)	768.4**	199.0
	volume (GMV)
	Annual revenue	177.9	39.9	55.7
	Cost of sales	111.9	17.1	47.9
	Income (loss) from	4.1	11.0	(0.128)
	operations
	Net income (loss) 3.0	9.8	(0.02)
	Active consumers -	552 million	292 million
	Growth of revenue	30.8%**	58.1%	40.3%
	1997-1998
	Brands	Amazon, Amazon	Taobao, Tmall,	JD.com,
		Fresh Amazon Go,	AliExpress,	Yihaodian
		Prime Pantry, Prime	Alibaba.com
		Now, Whole Foods
	* Includes results of Whole Foods Market from the date of acquisition by Amazon, August
	28, 2017.
	** Chinese market only

Table 2 . Retail e-commerce figures in selected economies, estimations for 2018 8 Sales 2018 (billion dollars) Percentage of total retail sales Main local e-commerce brands

 2

	China	1530	28.6	Tmall, Taobao, JD.com
	USA	526	10.0	Amazon
	UK	126	21.5	Tesco, Asos, Argos
	Japan	122	9	Rakuten
	Germany	71		Otto, Zalando
	South Korea	50.5	11.3	Gmarket, 11Street
	France	44	7.0	Cdiscount, Vente privée,
	India	32.7	2.9	Flipkart, Snapdeal

https://money.cnn.com/2018/09/04/technology/amazon-1-trillion/index.html

https://www.statista.com/statistics/379087/e-commerce-share-of-retail-sales-in-china;

As a matter of fact, the "miracle" is about search engines, algorithms, and computing power.

Founders, respectively, of U.S. Steel and Standard Oil, which held a virtual monopoly on the U.S. steel and oil industries at the beginning of the 20 th Century

https://www.businesswire.com/news/home/20170601005532/en/Developer-Earnings-App-Store-Top-70-Billion/ (accessed 04 October 2018)

Source: U.S. Census Bureau, https://www.census.gov/mrts/www/data/pdf/06Q1.pdf

Alaska, Delaware, Montana, New Hampshire, and Oregon, do not have sales taxes.

Excluding sales by Amazon Web Services (AWS), mostly cloud computing and storage services.

https://blog.aboutamazon.com/company-news/2017-letter-to-shareholders. Prime subscribers pay a $99 fee or the equivalent annually. Same-day delivery is possible for orders passed before noon.

Formerly Deutsche Parcel Dienst, now a subsidiary of Groupe La Poste (France), https://www.pickup.fr/qui-sommes-nous/chiffres-cles.sls

https://www.gares-sncf.com/sites/default/files/field_files/2018-06/cp_amazon_sncf_gares_connexions_amazon_lockers_20.06.2018.pdf

https://www.cleveland.com/expo/news/erry-2018/08/4a6d12c4917317/amazon-plansmidseptember-open.html

https://www.nytimes.com/2018/10/14/business/sears-bankruptcy-filing-chapter-11.html

https://money.cnn.com/2017/06/02/news/economy/doomed-malls/index.html

https://www.bloomberg.com/news/articles/2018-01-29/tencent-leads-5-4-billion-investment-inwanda-commercial

http://corporate.jd.com/whatIsNewDetail?contentCode=6IhXLeeSAFLjLLlyuZatDA==

https://www.nytimes.com/2018/11/16/technology/week-in-tech-amazon-hq2.html


Iñaki Fernández Pérez
email: inaki.fernandez-perez@irit.framine.boumaza@loria.fr

Amine Boumaza

François Charpillet
email: francois.charpillet@loria.fr

Maintaining Diversity in Robot Swarms with Distributed Embodied Evolution

Introduction

Diversity in an evolving population, as a measure of how different its individuals are, is crucial for effective evolutionary adaptation. In artificial evolution and evolutionary robotics, diversity has been investigated either to analyze the dynamics of the evolutionary process, or to explicitly promote the search for diverse or novel individuals [START_REF] Rasmus | Diversity-guided evolutionary algorithms[END_REF][START_REF] Lehman | Abandoning objectives: Evolution through the search for novelty alone[END_REF]. An adequate level of diversity through evolution allows to better search, balancing between exploration, to find promising areas, and exploitation, to refine good solutions. This is even more necessary when the search space is deceptive, i.e. it is rugged, with valleys and many local optima, which corresponds to difficult optimization problems. A very active research topic in Evolutionary Computation concerns the explicit promotion of diversity, where diversity measures are used as an auxiliary objective to be maximized: searching for diverse solutions to the problem [START_REF] Lehman | Abandoning objectives: Evolution through the search for novelty alone[END_REF][START_REF] Doncieux | Beyond black-box optimization: a review of selective pressures for evolutionary robotics[END_REF]. Diversity measures can also be used to monitor and analyze the evolutionary process, better understand its dynamics, and trigger specific events depending on the diversity in the population (e.g. restarting an evolutionary process to enhace exploration, or stop evolution when the diversity gets too low). Typically, work on diversity in evolutionary robotics is restricted to evolving single-robot behaviors with a centralized evolutionary algorithm. The work by Gomes [START_REF] Gomes | Evolution of swarm robotics systems with novelty search[END_REF] is an exception, where the authors evolve behaviors for multirobot and swarm robotic systems using a novelty-based centralized algorithm. On the other hand, in distributed Embodied Evolution (dEE), [START_REF] Watson | Embodied evolution: Distributing an evolutionary algorithm in a population of robots[END_REF][START_REF] Bredeche | Embodied evolution in collective robotics: A review[END_REF] robots in a swarm locally communicate with each other to build their respective local populations. This entails different evolutionary dynamics to the global process, compared to centralized algorithms, due to local interactions between robots. Here, we analyze the influence on the diversity of the evolved behaviors of the distributed nature of dEE algorithms and the intensity of local selection pressure. Our experiments aim at answering the following questions: a) does distributed Embodied Evolution for robot swarms intrinsically maintains more diversity than centralized evolution?, and b) does local selection pressure influence diversity in distributed EE as it does in centralized algorithms? We first describe related work on dEE, and approaches to measure diversity in single and multirobot systems. Then, we describe the distributed EE algorithm used in our experiments, and our proposed generic diversity metric, that we compute at two levels, i.e. global (over the swarm) and local (on each local population). Finally, we detail our experiments, discuss the results, conclude and provide further research questions.

Related Work

A particularity of dEE is that selection is decentralized, with each robot of the swarm selecting over its local population, which is progressively built over the evaluation of controllers: robots exchange their active controllers and their respective fitness value when meeting. As such, local populations on different robots are different, and selection pressure applied over such subpopulations has different dynamics as compared to more classical centralized EAs. In [START_REF] Bredèche | Environment-driven Embodied Evolution in a Population of Autonomous Agents[END_REF], the authors investigate the influence of the environment on the behaviors evolved by mEDEA, a dEE algorithm that does not use a fitness measure to perform selection: selection is performed at random inside the local population of each robot. As such, the algorithm does not apply any task-driven selection pressure: it is rather the environmental selection pressure to reproduce and spread their genes that pushes evolution toward behaviors adapted to the environment that maximize the opportunities to meet other robots and mate. In [START_REF] Fernández Pérez | Comparison of selection methods in on-line distributed evolutionary robotics[END_REF], the authors evaluate the impact on the performance of the swarm of the intensity of selection pressure of the local selection operator in a dEE algorithm. The authors evolve neurocontrollers in a swarm of robots using different intensities of selection pressure, and conclude that the higher the selection pressure, the higher the performance, as opposed to classical centralized evolutionary algorithms, in which a lower intensity of selection pressure is usually preferred to maintain diversity in the population. This could indicate that distributed EE algorithms maintain such a diversity, necessary for the search to escape local minima.

Measuring diversity has been a topic of interest in the literature, and typically aims at two nonexclusive goals: understanding the dynamics of an evolutionary algorithm (diversity analysis, e.g. [START_REF] Ronald | Measurement of population diversity[END_REF]), and reinjecting diversity measures into the EA, e.g. for diversity promotion (e.g. Novelty Search [START_REF] Lehman | Abandoning objectives: Evolution through the search for novelty alone[END_REF]), to evolve a diverse set of individuals (e.g. Quality-Diversity algorithms [START_REF] Pugh | Quality diversity: A new frontier for evolutionary computation[END_REF]), to restart the algorithm [START_REF] Ghannadian | Application of random restart to genetic algorithms[END_REF], or to maintain a population able to adapt to unforeseen changes [START_REF] Trung | Evolutionary dynamic optimization: A survey of the state of the art[END_REF]. Generally, when investigating diversity in Evolutionary Robotics it is measured based on behaviors, instead of genotypic or phenotypic diversity. A behavioral descriptor must be defined (task-specific or task-agnostic, i.e. generic, based on sensorimotor values) to capture adequate features of the behavior resulting from a controller. These are then used by distance functions to compute diversity metrics. In [START_REF] Doncieux | Behavioral diversity measures for Evolutionary Robotics[END_REF], the authors propose four different behavioral diversity measures as a auxiliary objectives to evolve single-robot behaviors, which help circumvent the deceptiveness of the chosen task. In [START_REF] Gomes | Generic behaviour similarity measures for evolutionary swarm robotics[END_REF], the authors propose two diversity measures specifically designed for swarms of robots by capturing features of the joint behavior of a swarm, instead of features of single-robot behaviors. In their paper, the authors use these measures as novelty objective, linearized with fitness values into a single objective, for a centralized novelty-based EA to evolve diverse behaviors for robot swarms. In this paper, we measure behavioral diversity as a postanalysis measure to provide insights on the internal dynamics of distributed evolution. Specifically, we propose a generic behavioral diversity metric for distributed Embodied Evolution, taken at two levels (global, over the swarm, and local diversity, on the local population of each robot). While the algorithm on each robot can only rely on local information, since the diversity measures are not used by the robots, but used to analyze how diverse the behaviors are, this does not contradict the decentralized nature of the approach. Since we focus on characterizing diversity between individual robot behaviors, either among local populations or in the swarm, and not joint swarm behaviors, we chose to use mono-robot behavioral diversity measures, closer to [START_REF] Doncieux | Behavioral diversity measures for Evolutionary Robotics[END_REF], instead of basing our study on the diversity measures for swarm robotics in [START_REF] Gomes | Generic behaviour similarity measures for evolutionary swarm robotics[END_REF].

Methods and Experiments

The algorithm used in our experiments corresponds mEDEA with task-driven selection pressure [START_REF] Bredèche | Environment-driven Embodied Evolution in a Population of Autonomous Agents[END_REF][START_REF] Fernández Pérez | Comparison of selection methods in on-line distributed evolutionary robotics[END_REF]. Each robot in the swarm runs an independent instance of the algorithm. At every moment, a robot carries an active genome corresponding to its current neurocontroller, which is randomly initialized at the beginning of each experiment. A robot executes its controller for some time T e , while estimating its fitness and continuously broadcasting the active genome and its current fitness estimate to other nearby robots (and vice versa). Once T e timesteps are elapsed, the robot stops and selects a parent genome using a given selection operator. The selected genome is mutated and replaces the active genome (no crossover is used), the local population l is emptied, and a new generation begins. We designed a parameterized tournament selection operator, that, given a parameter θ sp ∈ [0, 1] and a local population, selects the genome with the best fitness in a random θ sp fraction of the population. The parameter θsp influences selection pressure by determining the actual tournament size, and the higher the tournament size, the stronger the selection pressure. If θ sp = 0, the fitness is disregarded and selection is random, while if θ sp = 1, the best genome in the population is selected (maximal selection pressure). Each experiment consists in running this algorithm for a given task, with a given θ sp , and either with selection operating on local populations (distributed), or on the global one (centralized), i.e. the set of all active genomes in the swarm. At each generation], in addition to measuring the swarm's average fitness, we measure behavioral diversity using our proposed metric of dispersion among a set of behaviors b:

Div(b) = 2 |b| • (|b| -1) |b-1| i=0 |b| j=i+1 d(b i , b j ), (1)
where b is a set of behavioral descriptors b i , and d(•, •) is a distance function between two behavioral descriptors. We aim at defining a diversity measure as generic as possible while still capturing differences in functional features of the corresponding neurocontrollers. In our approach, a behavioral descriptor for a given robot controller is defined as the list of motor outputs corresponding to an input dataset I, sampled at the beginning of each run, I = [in 1 , in 2 , . . . , in N ]. Each in k is a random vector of the size of the inputs of the controllers, uniformly sampled in the corresponding value range. To compute the behavioral descriptor of a controller c i , the entries in the input dataset are fed to the controller, and the corresponding outputs (o k i = c i (in k ) are recorded, serving as the behavioral descriptor for c i , i.e.

b i = [o 1 i , o 2 i , . . . , o N i ].
The distance between two behaviors, b i and b j , is computed as the average Euclidian distance between all their paired elements from b i and b j . In other words, the distance measures how different are the motor outputs computed by two neurocontrollers when confronted with the same set of inputs, and the global diversity, Div(•), is then computed as the average functional distance between each pair of behaviors in b. We use our proposed diversity metric to evaluate at each generation how diverse are the behaviors at the global level of the swarm (Div(b g swarm ), where b g swarm is the set of behavioral descriptors of the active robot controllers in the swarm at generation g), and at the local level of the local populations (for each robot r, Div(b g r ), where b g r is the set of behavioral descriptors of the local population of r at generation g; we report the average over the swarm ).

We measure the fitness and behavioral diversity over time when a swarm of robots uses this algorithm to adapt to two classical benchmark tasks for swarm robotics: navigation and item collection. For each task, we perform 10 variants, with 5 levels of selection pressure, θ sp ∈ {0, 0.25, 0.5, 0.75, 1}, with either robots locally exchanging genomes (distributed), or selecting on the global population (centralized). The experiments with selection on the global population do not comply with the distributed nature of swarm systems, and are used as control experiments to test if dEE intrinsically maintain more diversity than when selection is performed on the global population. In each experiment, a swarm of robotic agents is deployed in a simulated environment (Figure 1), containing food items in the collection task. Our experiments are run using the RoboRobo simulator [START_REF] Bredèche | Roborobo! a fast robot simulator for swarm and collective robotics[END_REF], which is a fast simulator for collective robotics. For the navigation task, each robot has 8 proximity sensors evenly spaced around the robot, which detect walls and other robots, with 8 additional item proximity sensors in the collection task. Each robot is controlled by a fully-connected perceptron with a bias neuron and no hidden layers, and maps sensory inputs to motor outputs (left and right wheel speed). The genome corresponds to a real-valued vector containing the weights of the controller (18 for navigation, and 34 for collection), adapted by either the distributed algorithm, or the centralized version.

The fitness for navigation rewards moving fast, straight and avoiding obstacles [START_REF] Nolfi | Evolutionary Robotics[END_REF], while in item collection it is the number of items collected by a robot. To evaluate the impact of distributed evolution on swarm performance and diversity, at every generation of each experiment, we measure the swarm fitness (average fitness over all the robots), and the global and local diversity. We compare the results (swarm fitness and diversity) of distributed evolution to centralized evolution, and the impact of the intensity of selection pressure in both cases.

Results and Conclusion

To compare diversity (either global or local) between centralized and distributed evolution, we use 2D histograms represented as heatmaps, where the x-axis and the y-axis correspond to the diversity in the distributed variant and in the centralized variant, respectively. Each datapoint is then the pair of diversity values corresponding to the same generation g in a distributed and a centralized run (randomly paired), i.e. (Div g D , Div g C ) for each pair of runs. The density of each bin in the histogram corresponds to the number of generations across all the runs when the pair of diversity values from the distributed variant and the centralized falls into that bin. If a plot is denser under the diagonal, it means that, overall, distributed evolution maintains more diversity, and vice versa. When comparisons are made between swarm fitness values, difference is reported iff Mann-Whitney tests yield p < 0.05. Figure 2 (resp. Figure 3) show the fitness of the swarm over generations for the navigation and the collection task (resp. the global and local Table 1: T e and σ are the evaluation time and std. dev. of the Gaussian mutation. behavioral diversity heatmaps). In both tasks, robots adapt solve the task, reaching high fitness in all the experiments except for the centralized experiment with θ sp = 0.0, which corresponds to random search in the entire population. The distributed variants with θ sp = 0.0 reach slightly higher values with lower variance than the centralized variants, especially in the more challenging collection task. Regarding item collection, the intensity of selection pressure seems to have little impact on the fitness in the distributed case, while in the centralized case, the highest performance is obtained when θ sp = 0.25 or θ sp = 0.5. On the other hand, when θ sp = 0.75, and especially when θ sp = 1, the swarm fitness is lower. This could be due to a possible loss of diversity when selection pressure is strong in the centralized case. Search could stagnate in local minima, being unable to escape, and thus yielding lower fitness, especially since item collection is arguably more difficult to evolve than navigation: the search space is bigger, and information from sensors of different nature needs to be integrated. In the case of distributed evolution with θ sp = 0.0, which corresponds to mEDEA algorithm, there is also an improvement, although slower, even in the absence of task-driven selection pressure. This is due to environmental selection pressure pushing toward behaviors that maximize mating chances by navigating the environment, and collecting items by chance in the item collection task. Figure 3 show that, when there is selection pressure (θ sp = 0.0), distributed evolution maintains more diversity, both local and global (denser areas under the diagonal). In the case of θ sp = 0.0, centralized evolution yields higher diversity than distributed evolution: the centralized case corresponds to random search, and, even if a diversity of behaviors is maintained, those behaviors do not provide any fitness, as shown before.

In this paper, our main hypothesis is that such algorithms intrinsically maintain diversity, since the genomes on the local repositories of the robots are built through local exchanges between robots when meeting, and are therefore different. To test such a hypothesis, we perform a set of experiments where a swarm of robots adapts to given tasks using a distributed EE algorithm. We test 5 intensities of selection pressure, in the distributed algorithm and in a control experiment with selection on the global population. We measure both the performance on the tasks and a proposed diversity measure designed for distributed evolution in robot swarms, both from local and global perspectives, and we conclude that, when there is selection pressure in our experiments, this approach systematically maintains more diversity, compared to centralized evolution, allowing to reach slightly higher performances, especially in the item collection task. This work opens questions on how to exploit such diversity measures: they could help regulating evolutionary operators, including the mating operator that defines genome migration between robots in distributed evolution [START_REF] Bredeche | Embodied evolution in collective robotics: A review[END_REF]: mating could be restricted to robots with similar behaviors, a form of reproductive isolation, which might favor the evolution of specialized niches. On the other hand, diversity measures could be used as novelty objectives. Searching for novelty in distributed evolution has recently received attention [START_REF] Galassi | Evolutionary strategies for novelty-based online neuroevolution in swarm robotics[END_REF][START_REF] Hart | Evolution of a functionally diverse swarm via a novel decentralised quality-diversity algorithm[END_REF], and we believe that our proposed diversity measures could be used to guide search in robot swarms.

Figure 1 :

 1 Figure 1: Simulated environment: enclosed square arena containing a swarm of robots and items (black and blue circles).

Figure 2 :

 2 Figure 2: Swarm fitness over generations for navigation (left) and item collection (right). Blue curves represent centralized evolution (C), while orange curves represent distributed evolution (D). θ sp is the intensity of selection pressure.

Figure 3 :

 3 Figure 3: Heatmap for comparing global and local diversity between centralized and distributed experiments in navigation (top 2 rows) and collection (bottom 2 rows).


domain: math shs

text:
Máire Ní Ríordáin
email: maire.niriordain@ucc.ie

Eílis Flanagan
email: eilis.flanagan@nuigalway.ie

Claire Brilly
email: claire.brilly@nuigalway.ie

Ensuring methodological rigor for investigating the discourse development of bilingual mathematics learners

Keywords: Methodology, methods, bilingualism, discourse, framework

Given the nature of investigating bilingual mathematics learners and learning environments, a key concern is how we can ensure that the rigor of our research is matched by the rigor of methodological frameworks and approaches employed. Our goal is to develop a theoretical framework and associated methodology and methods, in practice, in order to ascertain their suitability for investigating bilingual mathematics learners in an educational context. Moschkovich (2016) identified four key recommendations for conducting research on language: utilising interdisciplinary approaches, defining central constructs, building on existing methodologies, and recognizing central distinctions. Utilising Moschkovich's framework, this paper provides an appraisal of the methodology and methods to be employed in a research project examining bilingual mathematics learners.

Introduction

Investigating mathematics and languages is a complex process. Therefore, the authors argue that there is a need to develop appropriate research methods in order to investigate language use and its impact on mathematics learning. In particular, we believe that the role of language(s) should be examined within mathematical activity and in situ [START_REF] Barwell | Mathematics education, language and superdiversity[END_REF]. This paper draws from the researchers' current study, which explores the potential for developing a coherent and integrated interpretive theoretical framework to examine whether differences in languages, and their use, by bilingual mathematical learners have a differential impact upon cognitive mathematical processing, while recognizing the social aspects of learning. The project, entitled 'M²EID: Mathematical Metalevel developments in English and Irish language Discourses', is a mixed-methods study, comprising video-recorded observations, questionnaires and cognitive interviews. The research project is being undertaken with first year, undergraduate students, who choose to study Mathematics through a bilingual approach (English and Irish) during their first year of undergraduate education at the National University of Ireland, Galway (NUI Galway). This option runs parallel to its English-medium counterpart, which typically receives a large intake (at least 150) of students. Four weekly lectures are provided in the Irish language with all terminology given bilingually. In addition, lecturers may opt to describe more complex concepts (such as limit of a function) bilingually. The lectures are supplemented by the provision of a weekly workshop in English in addition to an Irish-medium workshop.

Given the nature of investigating bilingual mathematics learners and learning environments, a key concern of this paper is to describe and discuss how we can ensure that the rigor of our research is matched by the rigor of methodological frameworks and approaches employed. It is imperative to review epistemology and associated underlying assumptions in order to make meaningful the methodology and methods of the research being undertaken in a bilingual mathematics education context. [START_REF] Grix | The foundations of research[END_REF] definitions of 'method' and 'methodology' are valuable for interpreting these constructs. A 'method' refers to the procedures or processes by which data is gathered; whereas, a 'methodology' refers to both the theory applied to inform the research and the data analysis strategies employed as appropriate to the data collected (via the specific methods). While Grix's definitions regulate our M 2 EID research study, this paper focuses on possible methodological constructs that can frame such practice-based and context-driven bilingual classroom research. Consequently, the purpose of our paper is to describe and discuss the M 2 EID research methodology and methods utilising Moschkovich's (2016, p.1) recommended constructs for conducting research on language use and learning in mathematics. These are: (1) using interdisciplinary approaches, (2) defining central constructs, (3) building on existing methodologies, and (4) recognising central distinctions while avoiding dichotomies. The paper is structured in accordance with these four recommendations and outlines their application to the main research study (M 2 EID).

Using interdisciplinary approaches

Research on language and mathematics needs to consider interdisciplinary approaches in the development of methodology and methods and should be grounded in classroom discourse as well as language and bilingualism [START_REF] Moschkovich | Recommendations for research on language and learning mathematics[END_REF]. Therefore, this necessitates the development of integrative frameworks for examining, in situ, both the cognitive and social constructs of mathematics learning through and with languages.

In terms of the mathematics as a composite register comprising content, languages (e.g. English and Irish) and shifts between everyday and subject-specific registers, the authors emphasise the social and interpersonal aspects of language use and bilingualism in mathematics. Such aspects include the use of modes and gestures for communicating understanding and in particular, engagement in the situated and sociocultural practices of mathematical Discourses [START_REF] Gee | Social linguistics and literacies: Ideology in discourses[END_REF][START_REF] Moschkovich | A situated and sociocultural perspective on bilingual mathematics learners[END_REF]. Further, the M 2 EID study is aligned with the perspective that learning mathematics is essentially a discursive activity in which learners form and actively participate in a community of practice [START_REF] Lave | Situated learning: Legitimate peripheral participation[END_REF][START_REF] Lemke | Talking science[END_REF]. Therefore, learners develop unique sets of mathematical practices and modes of communicating with each other using all of the social, cultural and cognitive resources available to them. Consequently, a democratic process of learning emerges through a continuous cycle of negotiations in relation to views, beliefs, knowledge and meaning making [START_REF] Moschkovich | A situated and sociocultural perspective on bilingual mathematics learners[END_REF]. So, by adopting this comprehensive sociocultural perspective of learning and language use in mathematics, this study requires an interdisciplinary approach to research within this educational field. Based on the sociocultural nature of mathematical concepts and how we understand and communicate this nature, it is vital to consider how various disciplines contribute to mathematics education. In order to address the aims of this study we will draw on the principles of Discursive Psychology, Cognitive Psychology, Semiotics, Pedagogy and Anthropology to progress a unified approach to researching learning and language use within mathematics. Due to the multiontological nature of this grounding framework for the M 2 EID research project, it is essential to develop a dynamic and multifaceted methodological approach to the research, data collection and analysis strategies, which this paper focuses upon. Drawing on the body of relevant literature in this regard, the authors designed a methodology for investigating bilingual mathematics learners that is underpinned by [START_REF] Sfard | Thinking as communicating: Human development, the growth of discourses, and mathematizing[END_REF] commognitive framework for examining learning. This framework, described later in this paper, is founded on the premise that thinking is a form of (interpersonal) communication, and that learning mathematics entails extending one's discourse. [START_REF] Moschkovich | Recommendations for research on language and learning mathematics[END_REF] emphasises that research studies need to be clear and explicit in relation to the key constructs utilised. Considering the centrality of discourse to the commognitive approach, it is important therefore, that our perspective of discourse is outlined first. Discourses encompass more than verbal and written language and the use of technical language; discourses also involve communities, points of view, beliefs, values, and pieces of work [START_REF] Gee | Social linguistics and literacies: Ideology in discourses[END_REF]. Accordingly, we perceive mathematics as a discourse and a complex form of communication [START_REF] Sfard | Introduction: Developing mathematical discourse -Some insights from communicational research[END_REF]). Gee's concept of Discourse will inform the examination of conceptual mathematical development of bilingual learners, linking both the cognitive and social aspects of language use.

Defining central constructs

Equally difficult and demanding is the task of defining bilingualism and in particular defining whether a person is bilingual or not. To illustrate these concepts further we employ [START_REF] Grosjean | Individual bilingualism[END_REF] model of a continuum of modes with monolingual and bilingual occupying opposite endpoints; this continuum reinforces an understanding of bilinguals using their languages independently and jointly depending on the context/purpose in which the language(s) is being employed. Appropriately then, we support a non-deficit view of bilingual learners, combining everyday and mathematical registers and view language(s) as a resource and a support for learning. Our research is particularly concerned with the role of bilingual students' languages in mathematics teaching and learning. We consider mathematical language as a distinct 'register' within a natural language and each language will have its own distinct mathematics register, encompassing ways in which mathematical meaning is expressed in that language. Specifically, we are concerned with conceptual mathematical activity. This encompasses a knowledge of what it means to understand a concept and an appreciation of how such an understanding can be constructed by a student, thus providing a model of cognition for the concept [START_REF] Asiala | A framework for research and curriculum development in undergraduate mathematics education[END_REF]. Given that language influences thought and thinking and that each language will have its unique manner of constructing the concept, it is critical to develop an insight into the role and effect of bilingualism/languages on conceptual mathematical learning. In addition, language(s) facilitate the development of a student's mathematics register and participation in discourse. Consequently, it is an essential instrument of thought and it is vital for understanding and combining experiences and for organising concepts [START_REF] Vygotsky | Thought and language[END_REF]. We propose that there are differences 'between linguistically distinct versions of "the same discourse"' (Kim, Ferrini-Mundy & Sfard, 2012, p. 2) which correspondingly impact on mathematical learning. Therefore, it is the use of language as an instrument of thinking that is of importance, as well as its effect on cognitive processing.

When examining bilingual mathematics learners, it is important to address the social use of language within the learning context, not just its role in cognition. As previously noted, [START_REF] Moschkovich | How equity concerns lead to attention to mathematical discourse[END_REF] emphasises the importance of learning being illustrated within the sociocultural practices of a certain setting. These practices involve a process of describing learners and communities and considering culture as a set of practices, which actively involve participants [START_REF] Gutiérrez | Cultural ways of learning: Individual traits or repertoires of practice?[END_REF]. Hence, bilingualism is described in terms of learners' participation in and use of language(s) for different purposes and particularly in the context of mathematical discourse. Similarly, [START_REF] Moschkovich | How equity concerns lead to attention to mathematical discourse[END_REF] emphasises the importance of discerning between the conditions of learning and the processes for learning, and the importance of describing the curriculum, courses/programmes and teaching and learning approaches utilised that yield successful outcomes for different groups of learners.

Due to the multifaceted process of investigating bilingual learners' use of language in mathematics education, it is vital that an extensive research methodology is developed to facilitate examination of central constructs such as discourse, bilingualism, and language use.

Building on existing methodologies

Research examining the development of mathematical learning and its relation to language draws on multiple theoretical frameworks to support investigations and accordingly methodological approaches [START_REF] Moschkovich | Recommendations for research on language and learning mathematics[END_REF]. Adopting [START_REF] Sfard | Introduction: Developing mathematical discourse -Some insights from communicational research[END_REF] commognitive approach, data collection and analysis must adhere to its five methodological principles. These principles have been expounded upon to reflect our investigative framework and are 1) Operationality, 2) Completeness, 3) Contextuality, 4) Alternating Perspectives and 5) Directness. First, Operationality refers to the provision of a balanced account of the process through the sharing of practical, unambiguous stories that emerge from the study. Second, Completeness of the research emphasizes that the unit of analysis must comprise the entire discourse related to the topic. The researchers extended this principle for M²EID to include the documentation of such discourses (plausible developmental trajectories) in both the English and Irish languages. Third is Contextuality, which encompasses the premise that all interaction can be characterized as a learning event. We extend this, in the given context, to the need to examine when and how bilingual students/researchers use their language(s) in interactions. The fourth principle is that of Alternating Perspectives and explains the interchangeability of the researcher's insider/outsider methods of using words. This is intensified within a bilingual context because consideration must be given to both languages, their use within the given context as well as the possibility of significant differences between researcher and participant discourses. Fifth, the principle of Directness affirms that all descriptions of the study should commence with the specific raw data from the participants rather than the researcher's interpretation of that data. The application of these distinctive methodological standards will provide unique insights into the processes of bilingual mathematics learning and potentially contribute to the development of an empirical research base to ensure rigor in examining whether differences in languages, and their use, by bilingual mathematical learners have a differential impact upon cognitive mathematical processing.

Further to adopting Sfard's approach, it is vital to consider that epistemological assumptions inform methodology, which subsequently engender the methods employed to collect data. Therefore, aligned with the interdisciplinary foundations of the M²EID research project, the following are the proposed methods to be utilised in the study in order to ensure that a robust methodological framework and approaches support our inquiry.

1. Discourse models: This study will map the plausible developmental trajectories in both the English and Irish languages with respect to students' learning in various mathematical topics -e.g. functions-as consistent with the NUI Galway undergraduate module. The purpose of discourse models is to examine how language nuances and use affect learning [START_REF] Kim | How does language impact the learning of mathematics? Comparison of English and Korean speaking university students' discourses on infinity[END_REF]. 2. Videographic evidence: This study will identify and explore when and how bilingual learners at NUI Galway employ each language (English and Irish) when engaged in mathematical learning. Specifically, the research will examine the cognitive functions of code switching and language use within a natural educational context, while also providing for the social aspects of learning. Videography is an effective method of examining teaching and learning experiences in naturalistic contexts and the affordances of modern technologies provide opportunity to document, share and analyse cases of particular practice [START_REF] Derry | Conducting video research in the learning sciences: Guidance on selection, analysis, technology, and ethics[END_REF]. All lectures and tutorials relating to the bilingual mathematics module in NUI Galway will be recorded and analysed as appropriate. 3. Questionnaire: The purpose of the first part of the questionnaire is to gather participants' background data. The second part of the questionnaire will engage participants in discourses related to particular mathematical topics (linked to the developed discourse models) with the option of utilising English or Irish or both languages. The Cognitive Aspects of Survey Methodology (CASM) model will guide participants in an activity series involving thinkingaloud their thought processes as they recall prior knowledge and experiences of mathematical discourses while answering the questions [START_REF] Desimone | Are we asking the right questions? Using cognitive interviews to improve surveys in education research[END_REF]. The focus will rest on conceptual mathematical activity based upon a variety of constructs, both familiar (such as functions and their analysis) and new (such as logical form, equivalence relations and classes, and related number theoretic constructs). A primary mathematical objective of the first year module in NUI Galway is to facilitate and develop advanced mathematical thinking. 4. Video-recorded Cognitive Interviews: Cognitive interview methods will be employed to explore respondents' explanations of the answers in order to acquire comprehensive knowledge about how well respondents comprehend, appreciate or even misinterpret the specific mathematics concepts central to the study [START_REF] Desimone | Are we asking the right questions? Using cognitive interviews to improve surveys in education research[END_REF]). Participants will engage in paired discussion of mathematical tasks (the same as in the questionnaire) and justify their answers where appropriate.

It is proposed that the combination of the above methods facilitates a progressive and incorporative investigation into the cognitive aspects of bilingual mathematics learning and to evaluate the impact of languages on mathematics learning in practice.

Recognizing central distinctions while avoiding dichotomies

With [START_REF] Sfard | Thinking as communicating: Human development, the growth of discourses, and mathematizing[END_REF] commognitive framework undergirding the approach, the following are key aspects of the methodological framework under investigation [START_REF] Ní Ríordáin | Bilingual mathematics learners, conceptual mathematical activity and the role of their languages. How best to investigate[END_REF]:

 Discourse changes: If assuming the premise that mathematical learning involves initiation into the discourses of mathematics, then learning mathematics involves substantive discursive changes for learner. Sfard (2012, p. 3) distinguishes between two types of mathematical learning (change in discourse) as follows: object-level learning (expansion of what is known already and is mainly accumulative) and meta-level learning (change of meta-discursive rules and is a more radical and complex change). Within the proposed framework, development refers to a change in discourses. Accordingly, we refer to the development of students' mathematical discourses as opposed to the development of the students themselves.

 Sociocultural perspectives: Discourse is more than just language. We utilize Gee's (1996, p. 131) work which refers to Discourse as incorporating both talk and non-talk modes of participation such as gestures and artifacts, as well as participation in a social group. The employment of this definition synchronises with the concepts of discourses inherent within the sociocultural and Community of Practice perspectives.

 Community of practice: Within the framework, thinking can be defined as the activity of communicating with oneself. Accordingly, mathematical thinking can be viewed as a discourse, which in turn is a form of communication and involves being part of a mathematical community. Taking this view, the language or languages in which mathematics is being learned becomes an important issue for consideration.

 Conceptual learning: Given that language influences thought and thinking [START_REF] Vygotsky | Thought and language[END_REF] and that each language will have its own way of constructing the concept, insight into the role and effect of bilingualism/languages on conceptual mathematical learning is critical.

We consider languages and registers as vital resources and skills for learning and language use in mathematics. [START_REF] Grosjean | Individual bilingualism[END_REF] concept of a continuum of modes will be employed to trace bilinguals' use of languages in situ.

 Linguistic relativity hypothesis: It is the use of language as an instrument of thinking that is of importance, as well as its effect on cognitive processing. The linguistic relativity hypothesis proposes that the vocabulary and phraseology of a particular language influences the perceptions and thinking of speakers of that language [START_REF] Whorf | Language, thought and reality[END_REF]. Accordingly, each language (e.g. English or Irish) has a different cognitive system that influences concept formation and development. The study adopts the premise that a language influences, rather than determines, our mathematical thinking, and is cognisant of the impact of linguistic distinctions in a particular discourse on mathematics learning [START_REF] Kim | How does language impact the learning of mathematics? Comparison of English and Korean speaking university students' discourses on infinity[END_REF].

 Meta-discourses: The proposed framework is primarily concerned with meta-level developments in mathematical discourses. Since our focus is on bilingual mathematics learners, it is important that an analysis of the language(s) in which the discourse is taking place is conducted. In particular, the successive meta-discourses relating to mathematical topics of interest will be documented and compared between languages.

 In situ research: Since the development of discourses is essentially a product of collective human actions, the specific contexts must be acknowledged. Hence, learning and language use in mathematics will be analyzed within the social, cultural and cognitive practices of the particular learning context [START_REF] Moschkovich | How equity concerns lead to attention to mathematical discourse[END_REF].

Conclusion

Utilising Moschkovich's framework, this paper has provided an appraisal of the methodology and methods to be employed in the M²EID project, which is concerned with examining bilingual mathematics learners in situ. We assume that methodology is inclusive of both theory and methods. Accordingly, it is of importance to outline the underlying theoretical assumptions relating to the M²EID project, as well as how we plan on documenting, describing and explaining these phenomena. Hence, a core consideration for our project is what data to collect and how to collect such data. Therefore, a key aim of the M 2 EID research project is to evaluate the proposed methodology and methods in practice in order to ascertain their suitability for investigating bilingual mathematical learners in an educational context. In particular, the project will evaluate whether differences in languages, and their use, by bilingual mathematical learners have a differential impact upon cognitive mathematical processing, when engaged in conceptual mathematical activity.

Proceedings of CERME10

Acknowledgment

The M 2 EID research project is funded by the Irish Research Council -New Horizon's Research Grant (REPRO/2015/53).