Carmen Lía Murall
email: carmenlia.murall@outlook.com

Samuel Alizon

Modelling the evolution of viral oncogenesis

Most human oncogenic viruses share several characteristics, such as being DNA viruses, having long (co)evolutionary histories with their hosts and causing either latent or chronic infections. They can reach high prevalences while causing relatively low case mortality, which makes them quite fit according to virulence evolution theory. After analysing the life-histories of DNA oncoviruses, we use a mathematical modelling approach to investigate how the virus life cycle may generate selective pressures favouring or acting against oncogenesis at the within-host or at the between-host level. In particular, we focus on two oncoprotein activities, namely extending cell life expectancy and increasing cell proliferation rate. These have immediate benefits (increasing viral population size) but can be associated with fitness costs at the epidemiological level (increasing recovery rate or risk of cancer) thus creating evolutionary trade-offs. We interpret the results of our nested model in light of biological features and identify future perspectives for modelling oncovirus dynamics and evolution.

Introduction

Understanding viral oncogenicity is traditionally an endeavour of clinical microbiologists and relies on analysing molecular pathways (for a review, see e.g. [START_REF] Mesri | Human viral oncogenesis: A cancer hallmarks Analysis[END_REF]). Here, we adopt an ecological and evolutionary perspective, which has been extensively applied to study infection virulence over the years [START_REF] Alizon | Reconciling Pasteur and Darwin to control infectious diseases[END_REF] and has even re-emerged as a prism through which to analyse cancer dynamics [START_REF] Merlo | Cancer as an evolutionary and ecological process[END_REF].

Few viruses are known to directly cause cancer in humans: Epstein-Barr Virus (EBV), Hepatitis B Virus (HBV), Kaposi's sarcoma-associated herpesvirus (KSHV), Merkel cell polyomavirus (MCV), Human T-lymphotropic virus (HTLV-1), certain genotypes of Human papillomaviruses (HPVs) and three kinds of polyomaviruses, namely BK virus, JC virus and Simian Virus (SV40). Further details about the oncogenesis and epidemiology of these viruses can be found in other articles in this issue and in that of Chang et al. [START_REF] Chang | Human oncogenic viruses: nature and discovery[END_REF][START_REF] Gaglia | More than just oncogenes: mechanisms of tumorigenesis by human viruses[END_REF]. Also, the review by Mesri et al. [START_REF] Mesri | Human viral oncogenesis: A cancer hallmarks Analysis[END_REF] carefully compares the various pathways of viral oncogenes and their roles in triggering the hallmarks of cancer [START_REF] Hanahan | Hallmarks of cancer: the next generation[END_REF].

The evolutionary ecology perspective moves us away from proximate questions of how viruses cause cancer towards asking why do they cause cancer and, more practically, under what conditions? This approach requires stepping back and looking across human oncoviruses and squinting to look for patterns. Mathematics provides useful tools for this sort of abstraction, especially because stochastic processes [START_REF] Lenormand | Stochasticity in evolution[END_REF] or population dynamics feedbacks are difficult to anticipate [START_REF] Lion | Theoretical Approaches in Evolutionary Ecology: Environmental Feedback as a Unifying Perspective[END_REF].

In this article, we compare the life cycles of the above mentioned human oncoviruses using variations of classical viral dynamics models [START_REF] Nowak | Virus dynamics: Mathematical principles of immunology and virology[END_REF][START_REF] Perelson | Modelling viral and immune system dynamics[END_REF]. Since a virus that does not transmit from a host is bound to disappear, we develop a 'nested model' [START_REF] Mideo | Linking within-and between-host dynamics in the evolutionary epidemiology of infectious diseases[END_REF] to consider between-host effects. The model itself relies on a set of ordinary differential equations (ODEs), which we analyse using stochastic simulations that allow for the random evolution of cancer cell populations from infected cells, which we refer to as cancer initiation event [START_REF] Altrock | The mathematics of cancer: integrating quantitative models[END_REF]. By vary-ing few assumptions and parameters, we can study how oncogenic processes affect virus fitness at the within-host and between-host levels and how these effects depend on the virus life cycle.

Virulence and viral life cycles

In its most general definition, virulence is the decrease in host fitness due to the infection [START_REF] Read | The evolution of virulence[END_REF]. In the following, we assume that virus-induced cancer contributes to virulence, even though its effect on reproductive success can be limited (host mortality may occur late in life and effects on fertility may be unaffected). Figure 1 shows the global prevalence of 6 human oncoviruses as a function of their virulence (the number of yearly worldwide cancer cases divided by their global prevalence). We see that HR-HPVs and HBV are clearly the most clinically important of these viruses as they are responsible for higher numbers of cancer cases. Furthermore, these cancers can happen during host reproductive ages. Meanwhile, EBV and MCV are the human oncoviruses with the lowest virulence as they are nearly ubiquitous yet are responsible for less than half the number of cancer cases per year. We exclude from our analysis other polyomaviruses and non-HR HPVs given poor global estimates of viral prevalence. Note that the upper right corner of this graph is empty. In animal viruses, we know of at least one example, Marek's Disease Virus (MDV), a virus from the Herpesviridae family that was both prevalent and fairly virulent before vaccination [START_REF] Read | Imperfect vaccination can enhance the transmission of highly virulent pathogens[END_REF]. This shows that large DNA oncoviruses can reach high levels of virulence. The observation that no human oncovirus with high carcinogenicity reaches high prevalence reinforces our assumption that cancer contributes to virulence and is selected against in viral populations.

Human oncoviruses are not monophyletic which implies that oncogenic traits evolved separately in a case of convergent evolution. Even in the case of HPVs, the two types responsible for the majority of cancers globally, HPV16 and HPV18, belong to different HPV species and the other genotypes in their species are significantly less oncogenic [START_REF] Bravo | Papillomaviruses: Viral evolution, cancer and evolutionary medicine[END_REF][START_REF] Willemsen | Origin and evolution of papillomavirus (onco)genes and genomes[END_REF]. Oncoviruses can be classified based on their genetic make up and replication modes. For instance, HPVs and polyomaviruses belong to the small DNA viruses, whereas EBV and KSHV belong to the large DNA viruses. In Table 1 we summarise key features and traits of these human oncoviruses, in order to illustrate how we abstracted their life cycles into three distinct groups. As seen in the table under 'viral class', we chose to group HBV and HTLV-1 as 'retro-like' viruses because HBV is a DNA virus with retrovirus features, while HTLV-1 is a true RNA retrovirus.

Summarising the properties of human oncoviruses highlights some common features (although there are exceptions). On average, human oncoviruses are mostly DNA viruses (HTLV being the exception) with a tropism for epitheliumrelated cells and immune cells. Most of them cause, or at least can cause, chronic infections. Their genomes contain oncogenes that increase the proliferation and survival rate of their host cells (though they can have many more functions). The highest degree of variation between these viruses comes from their transmission routes (even though they all involve close contact and bodily fluids) and their life cycles (with or without a latent stage and lytic or non-lytic). This is why our model focuses on the importance of the latter.

All of these viruses can only persist in human populations over the long-term through betweenhost transmission. Therefore, unless there is vertical transmission, the fittest virus strains are the ones that maximise infection duration, while maintaining the production of enough infectious viral particles. This clearly leads to trade-offs. For instance, mechanisms such as immune escape or immunosuppression that can decrease host recovery rate are also associated with cancers [START_REF] Frank | Mechanisms of pathogenesis and the evolution of parasite virulence[END_REF]. Similarly, increased production of virus particles can simultaneously increase transmission rate and virulence, as observed in the case of HIV [START_REF] Fraser | Virulence and pathogenesis of HIV-1 infection: an evolutionary perspective[END_REF]. Finally, it has also been argued that increased viral replication could lead to more rapid host recovery, e.g. in the case of HPV [START_REF] Murall | Could the human papillomavirus vaccines drive virulence evolution?[END_REF]. Overall, the fittest virus at the within-host level (i.e. the one that infects the highest number of cells) is not necessarily the one causing the highest number of secondary infections. To investigate this conflict between levels of adaptation, we resort to mathematical modelling.

Capturing the dynamics of different oncoviruses requires different models. However, in order to identify the effect of life cycle properties such as latency or budding on the fitness of an infection, we need a basis for comparison. We, High-risk HPV and HBV are less prevalent globally but cause more cancer cases per infection. In contrast EBV and MCV are very prevalent but cause fewer cancer cases per infection. The x-axis is obtained by dividing the estimated number of cancer cases worldwide by the global prevalence. Data originates from [START_REF] Lunn | Tumour virus epidemiology[END_REF]. therefore, only vary the structure of the life cycle itself and homogenise parameter values for our three classes of viruses. This has a cost in terms of biological realism (e.g. our 'large DNA' virus is idealised and will not correspond exactly to EBV or KHSV) but it allows us to better understand the selective constraints acting on oncogene activity and to see whether life cycle properties are sufficient to recover known differences in infection phenotypes such as duration or cancer risk.

Models

To abstract the various life cycles of these oncoviruses, we start with a model that is generic enough to represent any target cell population. Figure 2A shows an uninfected cell population with cells at rest (in phase G 0 of their cycle), denoted G u , and those that are in the replication phases of the cell cycle (namely G 1 , S, G 2 and M), denoted R u . Each cell division event results in two daughter cells at rest at a rate 2δ. The cells at rest die naturally at a rate µ and enter replication at a rate σ.

Our infection models capture two main activities that viral oncoproteins share across human oncoviruses and that affect the hallmarks of cancer (Table 1 and [START_REF] Mesri | Human viral oncogenesis: A cancer hallmarks Analysis[END_REF]): extending cell life expectancy (e.g. resisting cell death by preventing cell apopto-sis) and increasing cell proliferation and sustaining a proliferative program (e.g. inactivating the G 1 /S checkpoint and other tumour suppressor checkpoints and targeting RB1 and p53). These correspond to parameters 1 and 2 respectively.

In the models with infections, new cell classes appear such as cells infected with viral episomes (G), virion-productive cells (P ), or budding cells (G P ). The density of free virions is denoted V . The flow diagrams in Figure 2 illustrate the mathematical models for each oncovirus group and the equations can be found in the Supplementary Information along with the R scripts used for the simulations. In practice, we implemented stochastic simulations of these systems of ODEs using the τ -leap Gillespie algorithm [START_REF] Gillespie | A general method for numerically simulation the stochastic time evolution of coupled chemical reactions[END_REF]. The assumptions related to this implementation are further described in the Supplementary Information and in the Discussion. The simulations allow us to store the number of divisions a cell has been through. Therefore, G is the total size of all the populations of cells G D , where D ∈ N is the number of divisions the cell has gone through.

Although not shown in Figure 2, we introduce a population of cytotoxic T-cells (CTLs), T, in each of the models following many previous models [START_REF] Alizon | Acute or chronic? Within-host models with immune dynamics, infection outcome and parasite evolution[END_REF]. Without these, virus populations would grow exponentially. Instead, we observe a wider range of immunological scenarios. To avoid unrealistic population densities, we assume a carrying capacity c) retro-like (HBV, HTLV-1) In small DNA viruses, infected cells that contain virus in episomal form (G) divide and produce either two similar daughter cells or makes virus-producing cells (P ) which can be lytic, i.e. kills the cells during viral production (e.g. polyomaviruses, such as MCV) or non-lytic, i.e. cells die at natural death rate (e.g. HPVs) and then releases virions (V ). (c) For retro-like viruses, infected cells (G p ) produce new virus particles (V ) that bud out from the cell's membrane. (d) For large DNA viruses, infected cells mostly exist in latent phases with the virus in episomal form (G) and virus producing infected cells (P ) are only made sporadically when a lytic phase is activated, which happens at rate η. Oncogenes lengthen cell life ( 1 ) and increase cell divisions ( 2 ).

budding virions Gp R ҉ σε 2 δ V b) small DNA (polyomaviruses, HPV) μ(1-ε 1 ) G R ҉ σε 2 δ 2 μ(1-ε 1 ) ~~V δ 1 P contains viral episomes viral productive cell (lytic or non-lytic) a) uninfected cells G u R u ҉ μ σ δ d) la at rest (G 0 ) on: 0 oncogenes ac� ≤ε 1 ≤ 1 ε 2 ≥ 1 rge DNA (EBV, KSHV) G R ҉ ~~σ ε 2 P V η Latency Lytic phase contains viral episomes δ μ(1-ε 1 ) replicating (G 1 , S, G 2 , M)
for the total number of infected cells and the total number of CTLs.

We also include a stochastic 'catastrophic' event, which corresponds to a cancer initiation event. The rate at which this event occurs at time t is given by ν D G D D p , where ν is a normalising constant parameter, D is the number of divisions a cell from the population G D has been through, and p is a parameter capturing the increase in cancer risk with the number of cell divisions. The rationale behind this assumption is that the lifetime risk of cancer in a tissue correlates with the number of stem cell divisions in the lifetime of this tissue [START_REF] Tomasetti | Variation in cancer risk among tissues can be explained by the number of stem cell divisions[END_REF]. By default, we assume that p = 1 but explore non-linear relationships in Supplementary Results.

Finally, to model the between-host level, we assume that infected hosts regularly interact with other hosts. Upon contact, the virus is transmitted with a probability that depends on the number of free virions (V ) at that time. Based on epidemiological data from HPV [START_REF] Winer | Condom use and the risk of genital human papillomavirus infection in young women[END_REF], we assume the probability of transmission saturates rapidly with increasing virus load.

Within-host simulations are run until one of the three possible outcomes of the model is reached: the virus is cleared, a cancer initiation event occurs, or the maximum time (set to 50 years) is reached. All the parameter estimates and initial conditions that are similar across all three viral groups were kept constant to facilitate the comparisons between life cycles. These are shown in Supplementary Information and chosen to be biologically realistic (see [START_REF] Murall | Epithelial stratification shapes infection dynamics[END_REF] for more details). 3a, the oncogenes have no action on the death rate and on the replication rate of the infected cell ( 1 = 0 and 2 = 1). For two of the life cycles (large-DNA and retro-like), we observe persistent infections, whereas for the small-DNA life cycle the infection is cleared. This makes sense given that in the first two life cycles, the homoeostasis parameters of the uninfected cells are barely affected by the infection (there is some increased cell death due to the immune response but it is compensated by rare reinfections by free virions). Notice also that the stochasticity is strong in these dynamics.

Results

Infection kinetics

In Figure 3b, we set 1 = 0.5, while keeping the other parameters unchanged. This increase in oncogene activity perturbs homeostasis, with a more rapid increase in the immune response (in orange), such that all life cycles lead to clearance. Finally, in Figure 3c, oncogenes increase the infected cell's life-expectancy and replication rate ( 1 = 0.5 and 2 = 3.5). This allows populations of infected cells to avoid clearance and achieve long-term persistence at high densities. As we will see below, cancer initiation events are only observed in such persistent infections.

Oncovirus fitness landscapes

We then explored 984 different combinations of ( 1 , 2 ) and performed 25 stochastic simulations per combination. Figure 4a shows the mean duration of the infection. For large-DNA and retrolike viruses, starting from the bottom left corner, increasing oncogene activity, either by decreasing the death rate of the infected cell ( 1 ) or increas-ing its proliferation rate ( 2 ), decreases the duration of the infection. Increasing further oncogene effect increases infection duration, with 2 having the largest effect. Finally infection duration decreases again for very large values of 1 and 2 . For small-DNA viruses, increasing oncogene action increases infection duration right away. As for the other life cycles, higher values of 2 decrease infection duration.

Figure 4b shows the average time until a cancer initiation event for parameter sets where such an event occurred. For a given parameter set, the fraction of the 25 simulations that lead to cancer is negatively correlated with the time until this event occurs (Figure not shown). That cancer occurs more rapidly for stronger activity of the oncogenes coincides with the decrease in infection duration reported above. We again see a difference between the large-DNA and retro-like life cycles, for which most of the parameter sets studied do not lead to cancer (the white areas), and the small-DNA viruses, where cancer occurs more often. 2 has the strongest effect on the occurrence of cancer initiation events and their timing, but 1 also matters, especially for large-DNA and retro-like life cycles, as indicated by the slope separating the white area from the coloured one. Note that here we assumed that the number of divisions an infected cell has been through increases cancer risk linearly. If this risk is independent of the number of divisions or, conversely, if it increases more than linearly, we observed a similar shape but the cancer initiation event occurs more rapidly (Supplementary Figure S2).

Finally, in Figure 4c we show the infection fitness, that is the number of potential secondary infections (see the Supplementary Information). This measure combines infection duration and virion production, which monotonically increases with oncogene activity (Figure not shown). The pattern strongly resembles that in Figure 4a, suggesting that infection duration is the most important component of the infection for virus transmission. Oncovirus fitness is maximised for intermediate values of 2 . The optimal value of 1 depends on the value of 2 , although to a lesser extent for the small-DNA life cycle. Large-DNA and retrolike viruses exhibit a local fitness peak in the area with very limited action of the oncogenes but its height is limited because few virions are produced (see Figure 3a).

Maximising fitness

Most of the 984 parameter sets we explored lead to infections that produce virions and last long enough to be transmitted to other hosts. However, variations in infection fitness are such that viruses bearing non-optimal traits are likely to be rarely detected. In Figure 5, we analyse the properties of the 'fittest' viruses, that is the parameter sets that lead to the highest between-host fitness values in Figure 4c. In practice, for each life cycle we selected the 25 parameters sets with the highest fitness values and without any cancer ini-tiation event. We then did the same for parameter sets with a cancer initiation event. Our goal was to compare oncovirus strategies that avoid cancer to those that do not.

In Figure 5a, we see that for the fittest parameter sets, infection fitness is higher when there is no cancer (in black) compared to when cancer occurs (in grey). However, these differences are small, especially for the large-DNA life cycle. Interestingly, at the within-host level, the sets with cancer occurrence yield higher total virion production over the course of the infection (Figure 5b). This illustrates the importance of selection as a multilevel process, where a strategy maximising fitness For each parameter set, the time to cancer is calculated as the average of the time until a cancer initiation event for all the simulations, where such an event occurred. In white, cancer is never observed. Infection fitness is the log 10 of the number of potential transmission events. We explored 984 combinations of ( 1 , 2 ) with 25 simulations per combination. Other parameter values are default (see Supplementary Information).

at the within-host level may not be the fittest at the between-host level.

Next, we focus on the oncogene activity associated with these fittest parameter sets. As expected, in Figure 5c we find that the increase in replication rate, 2 , is much lower for small-DNA viruses. We also find that sets with cancer exhibit on average higher values of 2 . For 1 , we find no consistent differences in runs with or without cancer (Figure not shown) but we find its value to be slightly larger in retro-like life cycle (Figure 5d). This could be due to its life cycle, where the G stage is the one producing the virions, thus, increasing the life-expectancy of the cell also increases the time spent in the virion-producing stage.

Intuitively, we might have expected a strong effect of 1 in the large-DNA virus life cycle because it can take years before a G cell becomes a virion-producing cell (P ). This absence of ef- fect is a consequence of the assumption of the τleap Gillespie algorithm, which is memory-less (the time spent by a single cell in a G state does not affect its probability to switch to a P state). In the Supplementary Information, we use a classical modelling technique [START_REF] Lloyd | Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics[END_REF][START_REF] Choisy | Mathematical modeling of infectious diseases dynamics[END_REF] to prevent P cells from being produced too quickly 'by chance' (Supplementary Figure S3). This leads to a decrease in infection fitness, a strong increase in 1 , and a limited increase in 2 in the fittest parameter sets for the large-DNA life cycle.

Finally, for the fittest parameter sets with cancer, we show the fraction of simulations where can-cer events occurred (Figure 5e) and the average time at which it occurred (Figure 5f). The small-DNA life cycle stands out with more cancers occurring more rapidly. That large DNA viruses tend to cause cancer later than the other two groups is consistent with the biology (Table 1).

Discussion

Cancer is often presented as an evolutionary deadend. For the host, it clearly bears little adaptive value. For oncoviruses, the problem is less straightforward. One obvious cost is that the host may die. Another direct cost is that infected cancer cells frequently contain incomplete viral genomes and tend to produce less or no virions. However, oncogenes have pleiotropic effects (often long before cancer appears) and can be associated with increased virus fitness (e.g. if they increase cell replication rate, thereby increasing virus load, or cell life expectancy).

In the end, the optimal level of viral oncogenesis is likely to result from the balance between selection at the within-host level for increased virus load and at the between-host level for infection duration. This conflict is particularly clear when analysing the fittest virus strategies: the strategies that can lead to cancer have higher virus production than the ones where cancer never occurs, but the latter are associated with more between-host transmission. This is because infection duration largely governs epidemiological fitness, which, in our study, likely results from our assumption that the probability of virus transmission per contact is high (in the case of HPV it has been estimated to be close to 90% [START_REF] Winer | Condom use and the risk of genital human papillomavirus infection in young women[END_REF]). With high infectivity per contact, virus load matters less than the number and frequency of these contacts when it comes to between-host fitness. However, infection duration may not be independent from virus load. For instance, HR-HPV chronic infections that regress tend to exhibit decreasing virus loads, whereas those that persist have constant or increasing virus loads [START_REF] Depuydt | Serial type-specific human papillomavirus (HPV) load measurement allows differentiation between regressing cervical lesions and serial virion productive transient infections[END_REF].

In our modelling approach, we have voluntarily restricted the range of scenarios to explore by assuming that viruses from the three life cycles have the same parameter values. In spite of this constraint, we find differences between the life cycles that are consistent with the biology. Perhaps the most striking of these differences has to do with the fitness landscape. Indeed, for the large-DNA and retro-like life cycles, the virus can achieve long-term persistence even with very limited action of the oncogenes. For the small-DNA life cycle this is not possible and we always have strong selection for increased replication rate of infected cells. We also find cancers to be more frequent in small-DNA viruses but they appear later in large-DNA viruses. Another interesting insight of our model comes from the differential effect of extending cell life duration, in that it depends on the virus life cycle. Indeed, for retro-like viruses spending more time in the G stage can be adaptive because this is the virion-producing stage. For large-DNA viruses, the strong added value of decreasing the death rate of the infected cell is only apparent if we add memory into the Gillespie algorithm (Supplementary Figures S3 andS4).

Many evolutionary biology models nest withinhost dynamics into an epidemiological framework [START_REF] Mideo | Linking within-and between-host dynamics in the evolutionary epidemiology of infectious diseases[END_REF]. The most delicate step in these models is the linking between within-host variables (e.g. virus load, number of target cells, number of immune cells) and epidemiological parameters (such as virulence, transmission rate and recovery rate). Transmission rate can usually be safely assumed to be related to virus load, but predictions are more difficult when it comes to virulence. Indeed, in experiments this trait is measured using ad hoc proxies (e.g. anaemia, decrease in body mass, case fatality ratio, time to death) even though theory predicts qualitative differences in virulence evolution depending on the measure used [START_REF] Day | On the evolution of virulence and the relationship between various measures of mortality[END_REF]. If virulence corresponds to cancer and if this event is explicitly included into the within-host model, the nesting becomes more intuitive and has a stronger mechanistic basis than with other viruses.

There are several ways in which our model could be extended. For simplicity, we stopped our simulations after the cancer initiation event event. However, our model allows us to follow the fate of a single cell that has become carcinogenic and there is now a wealth of mathematical models to lean on [START_REF] Frank | Dynamics of Cancer: Incidence, Inheritance, and Evolution[END_REF][START_REF] Altrock | The mathematics of cancer: integrating quantitative models[END_REF]. A possibility for future work would be to include stochasticity in the within-host spread of cancer clones. As discussed elsewhere [START_REF] Hartfield | Within-host stochastic emergence dynamics of immune-escape mutants[END_REF], the within-host environment at the time of cancer emergence, especially the activation state of the immune response, is likely to govern the probability of fixation. Further, we have not included interference of oncoproteins with the immune response through immunosuppression or immune evasion. These would be particularly interesting because they would affect the age distribution of the population of infected cells (see Supplementary Figure S1). Since the number of divisions a cell has been through increases cancer risk [START_REF] Tomasetti | Variation in cancer risk among tissues can be explained by the number of stem cell divisions[END_REF], this oncogene action would add a mechanistic link to cancer occurrence. In general, our modelling of the immune response is obviously a great simplification of the reality. However, similar assumptions are commonly used when modelling virus dynam-ics [START_REF] Wodarz | The dynamics of HTLV-I and the CTL response[END_REF][START_REF] Ciupe | Dynamics of Hepatitis B Virus Infection: What Causes Viral Clearance?[END_REF][START_REF] Huynh | Modeling the dynamics of virus shedding into the saliva of Epstein-Barr virus positive individuals[END_REF] and here it was especially important to be able to compare the three virus life cycles. Finally, another aspect we simplified has to do with the structure of the host tissue. Indeed, for viruses infecting tissues with 3D structures, such as epithelia, this structure could directly impact infection duration [START_REF] Murall | Epithelial stratification shapes infection dynamics[END_REF]. However, this would require virus-specific models since oncoviruses infect different tissues.

Here, we aimed to begin a theoretically grounded conversation about the evolution of viral oncogenesis. We, thus, end with various lines of inquiry. For instance, we considered that variations in oncogenicity can, in part, be explained by virus genetics. For DNA viruses, this could be challenged given the large variation observed between patients and the low viral evolutionary rates. However, recent evidence shows that even when considering only one genotype, HPV16, the E7 gene exhibits less variability in samples from pre-cancers/cancers compared to the controls [START_REF] Mirabello | HPV16 E7 genetic conservation is critical to carcinogenesis[END_REF]. Similarly, one could also question whether the viruses we see are the fittest. Indeed, there could be physical constraints preventing the virus from reaching parts of the parameter space. In addition, the coevolutionary dynamics between humans and DNA oncoviruses could also be non-equilibrium processes. In the case of HPV16, it has recently been argued that the most virulent lineage known currently (HPV16A) could originate from Neanderthals and therefore be less adapted to modern populations [START_REF] Pimenoff | Transmission between Archaic and Modern Human Ancestors during the Evolution of the Oncogenic Human Papillomavirus 16[END_REF]. Overall, understanding the evolutionary constrains and conditions that explain varying degrees of viral oncogenicity should be studied more widely. Not only for academic interest but also for gleaning new insights into how to design evolution-proof intervention strategies [START_REF] Kennedy | Why does drug resistance readily evolve but vaccine resistance does not?[END_REF].

Data accessibility

The scripts used to generate the data can be found in electronic supplementary material along with most of data used to generate the figures.

Figure 1 :

 1 Figure1: Global prevalence and virulence of oncovirus infections in humans. High-risk HPV and HBV are less prevalent globally but cause more cancer cases per infection. In contrast EBV and MCV are very prevalent but cause fewer cancer cases per infection. The x-axis is obtained by dividing the estimated number of cancer cases worldwide by the global prevalence. Data originates from[START_REF] Lunn | Tumour virus epidemiology[END_REF].

Figure 2 :

 2 Figure 2: Human oncovirus life cycles. (a) For uninfected cells, generic host cells (G u ) enter the replication phases of the cell cycle (R u ) and produce two daughter cells. (b)In small DNA viruses, infected cells that contain virus in episomal form (G) divide and produce either two similar daughter cells or makes virus-producing cells (P ) which can be lytic, i.e. kills the cells during viral production (e.g. polyomaviruses, such as MCV) or non-lytic, i.e. cells die at natural death rate (e.g. HPVs) and then releases virions (V ). (c) For retro-like viruses, infected cells (G p ) produce new virus particles (V ) that bud out from the cell's membrane. (d) For large DNA viruses, infected cells mostly exist in latent phases with the virus in episomal form (G) and virus producing infected cells (P ) are only made sporadically when a lytic phase is activated, which happens at rate η. Oncogenes lengthen cell life ( 1 ) and increase cell divisions ( 2 ).

Figure 3

 3 Figure 3 illustrates typical time series for each of the three infection models. Each plot shows three stochastic realisations of the same model with the same parameter values. The three panels show three combinations of oncogene activity. In Figure3a, the oncogenes have no action on the death rate and on the replication rate of the infected cell ( 1 = 0 and 2 = 1). For two of the life cycles (large-DNA and retro-like), we observe persistent infections, whereas for the small-DNA life cycle the infection is cleared. This makes sense given that in the first two life cycles, the homoeostasis parameters of the uninfected cells are barely affected by the infection (there is some increased cell death due to the immune response but it is compensated by rare reinfections by free virions). Notice also that the stochasticity is strong in these dynamics.In Figure3b, we set 1 = 0.5, while keeping the other parameters unchanged. This increase in oncogene activity perturbs homeostasis, with a more rapid increase in the immune response (in orange), such that all life cycles lead to clearance. Finally, in Figure3c, oncogenes increase the infected cell's life-expectancy and replication rate ( 1 = 0.5 and 2 = 3.5). This allows populations of infected cells to avoid clearance and achieve long-term persistence at high densities. As we will see below, cancer initiation events are only observed in such persistent infections.

Figure 3 :

 3 Figure 3: Example within-host population dynamics with (a) no, (b) limited and (c) strong action of the oncogenes. In a), 1 = 0 and 2 = 1, in b) 1 = 0.5 and 2 = 1 and in c) 1 = 0.5 and 2 = 3.5. Each line type corresponds to a stochastic run. Colours indicate infected cells at rest (G), infected cells dividing (R), infected cells producing virions (P ), virions (V ), and cytotoxic T-cells (T ). For clarity, time is shown in a log scale for persisting infections (in c). Other parameter values are default (see Supplementary Information).

  0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 10.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1

Figure 4 :

 4 Figure 4: Oncogene effects in the three virus classes on (a) infection duration, i.e. mean final time reached, (b) time to cancer and (c) infection fitness.For each parameter set, the time to cancer is calculated as the average of the time until a cancer initiation event for all the simulations, where such an event occurred. In white, cancer is never observed. Infection fitness is the log 10 of the number of potential transmission events. We explored 984 combinations of ( 1 , 2 ) with 25 simulations per combination. Other parameter values are default (see Supplementary Information).

Figure 5 :

 5 Figure 5: Characteristics of infections maximising virus between-host fitness. a) Infection fitness, b) total number of virions produced during the infection, c) 2 , d) 1 , e) for each parameter set, the fraction of the simulations that lead to cancer and f) the years until cancer initiation event. In a, b and c, the 25 fittest sets with cancer are in grey and the 25 without cancer are in black. Dashed line show mean values.

Table 1 :

 1 Human oncovirus properties. Adaptation and extension of Table1from[START_REF] Lunn | Tumour virus epidemiology[END_REF].

Acknowledgments

This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (EVOLPROOF, grant agreement No 648963). The authors acknowledge further support from the CNRS, the IRD and the itrop HPC (South Green Platform) at IRD montpellier, which provided HPC resources that contributed to the results reported here (https://bioinfo.ird.fr/). We thank three anonymous reviewers for numerous suggestions.

Supplementary Information

One PDF file containing Supplementary Methods and Supplementary Results and two files with R scripts and simulation data.


Clovis Sabau
email: c.sabau@vetagro-sup.fr

Hélène Blasquiet-Revol

Sabau Clovis

Blasquiet-Revol Hélène

THE ELDERLY IN RURAL AREAS: AN OPPORTUNITY FOR THE CREATION OF ACTIVITY AND EMPLOYMENT THE ELDERLY IN RURAL AREAS: AN OPPORTUNITY FOR THE CREATION OF ACTIVITY AND EMPLOYMENT

Keywords: Active retiring, Creation of activities, Rural development, Service economy, Accompanying, Territory. Classification : R1, O15, O17

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

THE ELDERLY IN RURAL AREAS: AN OPPORTUNITY FOR THE CREATION OF ACTIVITY AND EMPLOYMENT 1 INTRODUCTION

The demographic recovery of rural areas is confirmed. Between 1999 and 2006 the population in predominantly rural areas increased by 0.7% per year. However, job creation is mainly correlated to urban dynamics, cities continue to concentrate mainly new jobs. In rural areas, the massive loss of agricultural jobs are not sufficiently compensated by the creation of service jobs. The maintenance and creation of jobs and activities are now necessary for the economic development of these territories.

The process of creation of activities in rural areas involves three inter-related figures: the creator, (the) accompanying structure (s) and the territory. In this context, the PSDR CreActE1 program assumes the need for close co-creation between these three poles. This triptyque depends on a combination of factors (system of actors at different scales, territorialised social context). Then research approaches emphasize on collective and social according to a strict individual framework, which allows us to relate actions and projects to a human and broad territorial context.

We are particularly interested in factors that can promote the emergence of activities and jobs in rural areas. Thus, as the program CreActE states, activity creation is then considered as soon as it is accompanied by the creation of a job or part of a job for the creator himself or other persons directly linked (eg employee). In this context, the issue of aging and services creation in rural areas holds a special attention, given the specificities of many rural areas that face an unbalanced age structure and issues of maintaining services.

The aim of this paper is firstly to review the context of an aging population and the terms associated with it. Then, we will focus on rural services which will lead to our problematics.

We then propose a theoretical framework that we have set up for this study, based on the service economy. We will then outline the methodology and will end up with some first descriptive results from the field.

AGING OF POPULATION AND SERVICES

2.1 Aging : phenomena and definition 2.1.1 France and aging population "In 2050, the proportion of people aged 60 and over will reach 32% [in Europe] and the proportion of very elderly would increase from 3% currently to 10% in 2050 [BARNAY etSERMET, 2007]. This quote sums up pretty well the phenomenon of aging in Europe and France. The numerous forecasts on the issue agree: there will be an absolute increase in the number of elderly (gerontogrowth) and an increasing proportion of elderly (aging) in the population [START_REF]Les territoires face au vieillissement en France et en Europe[END_REF].

In rural areas, aging arises from the bottom with the migration of young people who start to train (especially for higher levels of education) and find a job consistent with their training, that they are more likely to find in urban areas, considering the size of the labor market there.

There is also aging from the top due to three combined factors of gerontogrowth:

-The natural gerontogrowth, reflecting the rise in life expectancy thanks to medical advances. ERSA 2010 -The migratory gerontogrowth, because of migration from urban to rural areas; people that move into, either returning after their professional careers, or escaping the urban environment at the end of their careers.

-The cultural gerontogrowth, explained by movements of the age pyramid up, caused by the rise in age of more or fewer generations (because of past fertility and survival rates).

A set of economic and social issues emerge from these trends, among others [BARNAY etSERMET, 2007]:

-The health of seniors who will require (home) care and support.

-Economy: to ensure pensions, financing of health care and support systems to dependency.

-The (re) organization of the society: the number of elderly increasing, it raises questions about their participation and their place in society, in the workplace and within families.

Semantic Approach of Aging and defining our object of study

Old age is a concept and a sociodemographic reality [START_REF] Rochefort R | Vive le papy-boom[END_REF][START_REF] Caradec | Vieillir après la retraite : approche sociologique du vieillissement[END_REF]etc.] that is found at every times and in all places, but what does being old means? This question arises for both anthropologists, sociologists and demographers.

Guerin [GUÉRIN] insists that age is a social construct that evolves according to standards that will give the society. According to him, age has "rejuvenated" because of the increased life expectancy and improved health and training of over 60.

Those working on « contemporary data » use categorizations defined by conventional thresholds, such as 60 or 65 years-old, which are provided by national statistical agencies and more or less internationally standardized (that everyone recognizes the value although acknowledging the descriptive limits). These thresholds have a history. They have emerged « in the wake of the political arithmetic of the late modern period, when occured the establishment of the first census » [START_REF] Gourdon | Vieillesse, vieillesses : un regard historique[END_REF]. They have then been sustained with the establishment of national statistics in the nineteenth century. They thus primarily reflect statistical logics. The World Health Organization defines an aged person from 60 years. It is also an age which has been retained in French law for certain benefits or measures for the elderly that are called "vulnerable".

In looking more closely, we found a multitude of terms that refer to the concept of aging without any precise and scientifically appropriate definition behind each2 . In connection with their employment situation, we have sought to deepen two: senior and retired.

The term "senior" was born of the creativity of marketers who have borrowed from the sports jargon [START_REF] Rochefort R | Vive le papy-boom[END_REF]. However, there exists no official definition. It is rather vague on the social situation (active, early-retired, retired) and age (45-50 years to 60-65 years). More politically correct, it has a positive connotations and refers for example to sports (junior, senior, veteran) [GUÉRIN, 2002]. The French Larousse Dictionary defines as "more than fifty years." Similarly, in the 2006-2010 National Concerted Plan employment for Seniors Employment, reference is made to more than 50 years. The French Government, taking the standard set by the EU, defines the elderly as "persons aged 55-64 years." Also seniors may still remain active and might therefore be included within the active population.

The term "retiree" is more explicit since it is defined by the Oxford Dictionary as a "person who has leave one's job and cease to work, typically on reaching the normal age for leaving service." Taken in a broader sense here, we consider the term retiree "including nonpensioners partners and people that benefit from the French minimum wage for olerly people" [ROCHEFORT, 2000, p.24]. For now, given the current French pension system, the concept of retirement is normalized, and can include a set of people to a point in their life course, once their career "complete" and retirement acknowledge. However, the existing measures dedicated to early retirement, unemployment, income and retirement pension cumulation (which will be explained below), etc. tend to "blur the boundaries between the various social risks and facilitates the amalgam among that every statutes" [START_REF] Perrin- | Etre vieux et être à la retraite : La fin d'une tautologie[END_REF]according to GUILLEMARD A-M, 2003].

The pathway to retirement is a time of transition for all so called « older people » [START_REF] Caradec | Vieillir après la retraite : approche sociologique du vieillissement[END_REF]. Moreover, as demonstrated by a study of INRA , 2009]. Furthermore, at the age of 60, it is possible for the employee to choose when he will retire. It is therefore usually a choice, but is rarely linked with an anticipation on the content of free time available once the deadline has arrived [START_REF] Caradec | Vieillir après la retraite : approche sociologique du vieillissement[END_REF]. In connection with the previous point, it should be noted that it is not possible to reverse, when someone decides to go on retirement. The change is important, and motivations are varied (health states, type and difficulty of work, pensions systems ...) [MAHIEU ET SEDILLOT, 2001 ; VOLKOFF ET [START_REF] Veltz | Départs en retraite, précoces ou tardifs : à quoi tiennent les projets des salariés quinquagénaires[END_REF] ; DEBRAND ET [START_REF] Debrand | What are the motivations of pathways to retirement in Europe: Individual, Familial, Professional Situation or Social Protection System? Working Paper[END_REF] . Moreover, because of their age, pensioners have certain professional and personal experience ("wisdom") [START_REF] Vimont | Le nouveau troisième âge, une société active en devenir[END_REF]. They will then seek to make it more or less a benefit for the society.

« The nebula of services »

We have seen that the proportion of pensioners in the population is growing. They express specific needs in terms of entertainment and services, and inject new dynamism into the territories. The aging population will interfere with the labour market, its mutations, its management and even its own aging. It therefore raises up « the question about the future supply and demand of traditional or new goods and services subject to effects of age, generation or period [START_REF] Parant | Vieillissement en Europe à l'horizon 2050 : apports et limites des projections[END_REF]. Service activities account for nearly 70% of GDP and employment in most developed countries [DJELLAL ET [START_REF] Dessaint M.-P. ; Flammarion | Une retraite heureuse, ça dépend de vous[END_REF]. There has been a gradual reorganization of the networks over the last 25 years. In some cases, the mesh was densified to meet specific needs (infants, elderly), but in most cases it was released and concentrated in clusters or poles while growing use of cars [ETD, 2008]. Today, new challenges appear: evolution of society and therefore demands in service, rising fuel prices which increases the number of "captive people" in rural areas, climate issues and preservation of the environment, etc. that change the location of services. Thus, some rural areas are gaining new residents that increase the demand for new services. And others are concerned about maintaining existing services. ERSA 2010

It is to be noted that the services and the services sector is an economic reality rather unstudied [DJELLAL ET GALLOUJ, 2007]. Moreover, it is in the minds of many scientific considered as blur, which leads to the term of « services nebula ». However, in economics in particular some authors have addressed the issue. We can cite Hill and Gadrey, the "fathers" of the service economy, and more recently Djellal and Gallouj. It is on the theoretical perspective of these authors that we will base our approach to services.

It seems first necessary to deal with the many definitions of service and the realities that each covers. The first element of definition that comes to mind is that the service refers the tertiary sector. This statement is partly wrong with today's diverse activities that could potentially fall within the definition of service and the different discriminating criteria [DJELLAL ET [START_REF] Dessaint M.-P. ; Flammarion | Une retraite heureuse, ça dépend de vous[END_REF]. The borders are thus now widely blurred between service, agriculture (environmental services) and industries [START_REF] Veltz | Départs en retraite, précoces ou tardifs : à quoi tiennent les projets des salariés quinquagénaires[END_REF].

According to INSEE, an activity of service is characterized mainly by the provision of technical or intellectual capacity. Unlike an industrial activity, it can not be described only by the characteristics of a tangible property purchased by a customer. In a first approach to services, this definition of INSEE suits entirely to a technical triptych [DJELLAL ET [START_REF] Dessaint M.-P. ; Flammarion | Une retraite heureuse, ça dépend de vous[END_REF]: intangibility, interactivity and immediacy. Also according to INSEE, included in their broadest sense, the services cover a wide range of activities, from trade to administration, through transport, finance and real estate, business and individuals services, education, health and social action. This is the meaning generally given by the Anglo-Saxon term "services".

The term "service sector" is used more restrictively, since limited to business services and « lifestyle and home-care services (LHCS) »5 . The service sector is extremely diverse [GALLOUJ ET [START_REF] Gallouj | L'innovation dans les services[END_REF], even heterogeneous. Services to individuals within the meaning of INSEE include hotels and restaurants, recreation, cultural and sports services, and lifestyle and home-care services. We are particularly interested in this last category because retirees are "far more consuming LHCS than other population groups, without this increased consumption being only explained by dependency [START_REF] Gallouj | L'économie des services à la personne[END_REF]]. The LHCS encompass very heterogeneous activities such as housekeeping, meal preparation, assistance to people aged over 70 or disabled, home-delivery of meals, custody of children, slight gardening, "handymen" ... [COMMISSARIAT GÉNÉRAL DU PLAN, 2005]. A LHCS is thus a "service responding to individual or collective demands regarding the quality of the daily life, from a proximity, either objective becase rooted in a local limited space, or subjective, refering to the relational dimension of provision" (Definition of the Research Center for Solidarity and Social Innovation at UCL, quoted in [ [START_REF] Van Steenberge | Services de proximité : un premier regard critique[END_REF]). These services are defined as "quasi-collective" that is to say that, beyond the individual benefits for the users, they are also benefiting to the community, both in terms of jobs and social cohesion [BRANDELEER, 2008].

As for business services, they combine post and telecommunications; advice and assistance, operational services, and research and development. INSEE classifying market services according to their primary user, the telecommunication services, legal services, activities checks, technical analysis, ... are thus considered as business services, even when partially consumed by households.

In this study, not only will we retain the services sector as defined by INSEE (LHCS and business services) but also anything that relates to businesses that are also part of the tertiary sector. We also consider in this study the activities of construction for the private properties. Indeed, if based on the definition of a service by INSEE, an plumber or electrician for example, does not fit into the service sector and particularly in the services sector. However, a plumber deliver to the customer a technical capacity. So, here we reach the ERSA 2010 vision developped by [START_REF] Gallouj | L'économie des services à la personne[END_REF] about LHCS, that the "usual classifications (NAF or PCS) is inadequate to embrace the diversity of categories" and the activities involved within the term services.

Problematic: from the retiree consuming services to the retiree creating services

Until recently, territorial stakeholders perceived negatively aging population. The aging population was rather linked to concern than opportunity, and few urban and social planning documents really take into account this phenomenon, which is even often associated with the concept of "dependency" and "home maintaining". The image of the elderly given then by the local authorities approached that of societal burden.

Since the advent in the regional strategies of residential and presential economy [DAVEZIES ET [START_REF] Davezies | Un train peut en cacher un autre. Derrière l'économie productive, attention à l'économie présentielle[END_REF], which derives from the theory of the economic base, many authors have redefined the importance of the presence of seniors as an economic opportunity for the territories. The report of Godet and Mousli [2009] for the CAE 6 and DIACT 7 testifies an "officialization" by the government of the paradigm shift initiated by [START_REF] Vimont | Le nouveau troisième âge, une société active en devenir[END_REF], [START_REF] Guillemard | De la retraite mort sociale à la retraite solidaire : La Retraite, une mort sociale revisitée trente ans après[END_REF] Guerin [2002], Callois et al. [2003], Argoud et al. [2006], Kuntz [2007] ... etc. For policymakers, the elderly person becomes an active contributor to the economic and social development of the areas. The territories that will manage to play on the leverage that presential economy can be (attracting affluent retirees, young assets, encourage the development of activities) will be tomorrow's winning territories.

Moreover, the social value of older people has never been challenged, they are recognized for their investment in associations, their ability to create social links; but this was far outside the scope of public policy. For [START_REF] Guerin | Le grand retour des séniors[END_REF], the role of retirees in society is undeniable: they are the linchpins of associations, representing 30% of the mayors of France, involved in social life, school ... "The presence in our cities and our campaigns of various categories of senior citizens, opens the way for intervention by the market of new lifestyle and house-care services, new products to meet the specific demands of these populations to new and multiple expectations" [GUÉRIN, 2002].

Retirees can therefore be regarded as a source of jobs and may thus contribute to job creation in rural areas. Indeed, the high proportion of elderly in the population of some rural areas will guide the way to consider the development of these territories. We must therefore reckon with the opportunity they represent. Thus, mobilization to appeal and accommodate retirees in rural areas can be transformed into local development boosting the creation of lifestyle and home-care services and thus employment and local consumption [START_REF] Vollet | Les retraités : quel impact socio-économique sur les territoires, illustration à partir de la zone de Bourganeuf dans la Creuse, Région et Développement[END_REF].

In this context of aging population, and of the emergence of new demands for services in rural areas, we are wondering: how does the rise of retirees in the countryside influence the development of activities and more specifically the creation of services? The main hypothesis that we develop here 8 is that retirees can be creators of services in rural areas. Retirees are involved, stakeholders of the local economy. In addition to consuming the services offered, they create, while generating jobs. They will not only be (passive) users of services, but full participants in the process of creating activities and jobs in rural areas, taking advantage of the time of retirement to invest in and/or initiate locally emerging businesses. And we 8 The CreActE's research component dedicated to the link between aging and creating service activities considers the whole issue, both the creation and maintenance of services due to the presence and consumption of locally retirees but also the creation of employment generating activities by the retirees themselves that we are dealing with here. ERSA 2010 assume that some retirees will be driving and encourage the emergence of activities, including service activities.

CONCEPTUAL FRAMEWORK

A theoretical framework arising from the service economy

The approach developed by economists to address the issue of services allows to avoid the pitfalls of classification, where you would get in one hand industry and in the other tertiary sector, and takes into account the "material", "informational", "methodological" and "relational" functions of services [DJELLAL ET [START_REF] Dessaint M.-P. ; Flammarion | Une retraite heureuse, ça dépend de vous[END_REF]. [START_REF] Armand Colin | L'Âge de l'emploi : les sociétés à l'épreuve du vieillissement[END_REF] characterized the service as follows: " A service is a change in the condition of a person, or a good belonging to some economic entity, brought about as a result of some other economic entity, with the approval of the first person or economic entity". The definition is used by the author to construct typologies of services. He was able to distinguish between the services affecting the property and those affecting people. He also distinguished service permanent and temporary services, according to the time during which the change made would normally persist [AZNAR, 2002].

In the tradition of [START_REF] Armand Colin | L'Âge de l'emploi : les sociétés à l'épreuve du vieillissement[END_REF][START_REF] Hill | Tangibles, intangibles and services: a new taxonomy for the classification of output[END_REF], some economists consider the service as a particular social relationship between production and use, assuming that the service is not limited to the interpersonal dimension [START_REF] Gadrey | Les enjeux de la société de service[END_REF]. Thus, according to [START_REF] Gadrey | Services : la productivité en question[END_REF] and his triangle of services, "a service is a transaction involving a change of state of a reality C, possessed or used by a consumer (or customer, or user) B, produced by a provider A at the request of B, often in relationship with him, but not resulting in the production of goods that could economically circulate independently of the support of the service C (otherwise it would amount to production of goods)". As part of the triptyque made by Lenain, [START_REF] Revol | Création d'activités et d'emplois dans les espaces ruraux : état des lieux des approches et des postures. XLVIe colloque ASRDLF, Entre projets locaux de développement et globalisation de l'économie : quel équilibre pour les espaces régionaux ?[END_REF] for CreActE, we consider the creation activities as a co-construction involving the creator, the accompanying structures and the territory. "As a system, the territory [as we consider it in our study] is an [personal] intellectual, moving, evolutionary, fuzzy construct [...], whose characteristics fully correspond ERSA 2010

to those that can be attributed more generally to the principle of complexity [...]. It consists in a whole, composed of subsystems, of components, and especially of multiple relationships, including positive or negative feedback loops, which change over time." [START_REF] Moine | Le territoire comme un système complexe : un concept opératoire pour l'aménagement et la géographie[END_REF]. The diagram of the service economy, as defined by Gadrey, does not explicitly introduce this notion of territory, whereas a service is a representative subsystem of an action taking place within a territory. Also, we tried to territorialise this pattern, and to consider scalability in time, focusing on the creator of service and his environment. We thus propose to construct a second model of analysis emerging from the triangle of services [START_REF] Gadrey | Services : la productivité en question[END_REF], and from the polygon of services proposed by [START_REF] Gallouj | L'économie des services à la personne[END_REF] (Figure 2). The concept of territory as defined above being unique to each individual and subjective, the territorialisation of the polygon service requires to distinguish between the vision of the provider of service from the one of the addressee receiving the service.

Indeed, during a given period, will provide services to recipients. The provider will change (in a different or identical way, depending on the type of service provided) the support of the service, that is to say, the territorial realities of the recipients . We add here the notion of 'territorial' linked to the reality for which owns property right and that is about to change, because the service will (more or less) act upon a set of mechanisms and in-place relationships, related to , and thus his territory. Therefore, it is part of the territorial reality of that will be affected by the action of the provider .

However, the service will also change the environment of . Indeed, the fact that provides a service for each will reduce his available time, his stock and thus his potential further provision of services. The every will therefore also impact on the reality of (and that might be compensated financially as part of a market service). We call this reality modified by the every the "territory of action" of (schematically shown by the red stripes on Figure 2). This territory is included in a broader territory (always in the sense of an organized entity) covering all the systems to which belongs. We call this territory the "territory of fullfilment" of the provider (that is to say the territory "where the service provider fulfils himself"). This is the territory where the provider is evolving, both with the services it offers and its users , its relations with suppliers and other services necessary for his business, but also for the support and regulation organisations.

The activity of the service provider will undergo a constant evolution, from its setting-up to beyond its end. Thus, the territorial configuration (or "territory of fulfilment") of this activity will change according to needs and decisions of the creator (or willingness to see his territory of action modified), and/or being subject to external constraints (human, natural, economic, regulatory factors...).

During the setting up of the project, and where no service delivery has begun, the creator is to work on the delineating of his "theoretical territory of action", that is to say define exactly the set of services that he will be able to propose, and the general public he will be targetting. The services that he will be able to offer depend on previously acquired skills that he is going to call for (training, work experience ...), on the financial capital will be able to invest, and ideological and personal choices that will govern the creation of his activity ... In addition to these elements proper to the creator, other external factors are playing a part, namely the size and the distance (in terms of time and cost) to potential consumers, consumers' propensity to resort to his services (cost / benefit, publicizing the service, quality of service) or the existence of local competition for the proposed service ... From the beginning and during provision, the theoretical territory of action evolve because of changes in the financial, material and human capitals of the company. For example, suppliers will feed his potential territory of action (increased stock, equipment ...), as well as increase social capital (new encounters, exchanges), cultural capital (training, identifying of new potential) financial capital (capital gains, paid services), they might also help to develop his business and therefore his theoretical territory of action. However, because of the confrontation with the reality of the constantly changing market, the actual territory of action of A, will be somewhat ERSA 2010 limited compared to his theoretical territory of action. The theoretical territory of action is often larger than what the provider of services can actually provide.

Moreover, in addition to the direct effect of the creator on his territory of action, it will have an indirect effect on his territory of fulfilment, because of his mere presence on the territory, the creator, as a stakeholder, will contribute to general economic dynamism and more widely to the territorial attractiveness by his integration into the local life of the territory and his social capital that he will call on there.

Hypotheses of work around the triptyque of co-creation

The triptyque of co-creation highlighted and described under the PSDR CreActE [START_REF] Revol | Création d'activités et d'emplois dans les espaces ruraux : état des lieux des approches et des postures. XLVIe colloque ASRDLF, Entre projets locaux de développement et globalisation de l'économie : quel équilibre pour les espaces régionaux ?[END_REF] that involves the creator of activity (A: the active retiree), structures that support the creation of activities and the territory where the activity is located (namely the territory of fulfilment) can thus help in the evolving version of the polygon of services of Gallouj we are proposing.

The relationship between the various elements of the triptyque of co-creation leads us to four assumptions:

-Hypothesis 1: we assume a complex framework, system of activities, marketing methods, forms of reception, under specific motives in each case (family, home, hopes ...). This complexity interacts with the local specificity of each small territory. Thus each process requires bespoke approach that support structures have to take into account.

-Hypothesis 2: Active retirees creating services would possess some relational abilities and would be multi-skilled.

-Hypothesis 3: There exist very important networks between active retiree, contacts and territory. The creators mobilize a wide variety of networking contacts from the family, friendly, professional, neighbourhood environment, which "bypass" the network of elected people. However, there are strong differences of figuration between elected representatives (very conformist vision / clichés / assumed curbs) and creators (values "terroir" value, informal support). The universes of the institutional and authoritative bodies of an area would be out of touch with those of the creators, much more open but also confidential ... Hence the need to take an interest in providing support.

-Hypothesis 4: the creators and their activities are "embedded" in networks of relationships and structures (the territory of fulfilment) that play a role on the success and maintain of the activity. The active retiree providing services would thus be "embedded" in the territory thanks to his many networks, whether formal or informal. It would be the same for his activity.

In an attempt to test our hypotheses regarding the active role that could hold retirees in the economic development of rural areas, we looked through the literature for first clues for answer and apply to a concrete situation on a field of study: the plateau of Cézallier.

RESULTS : THE ACTIVE RETIREE: A POTENTIAL CREATOR OF ACTIVITIES AND EMPLOYMENT?

4.1 First clues through scientific litterature Callois et al. [2003], recognize that the migration of retirees may be considered as "bringing to the region an external income and generating Keynesian-like effects through the demand for local goods and services". However, people retiring are likely to "slow down consumption compared to their working lives because of their reduced income or loss of expenditure due to professional activity". In addition, the strong presence of pensioners in an area may be causing "a representation of the territory as economically and even socio-cultural sluggish". Conversely, it can "attract investors specializing in the needs of retirees" [CALLOIS et al., 2003]. ERSA 2010

Many authors have addressed the issue of the impact of retirees on economic development. [START_REF] Day | Economic Impact of Retirement Migration on the Texas Hill Country[END_REF] have conducted a study on 34 Texan counties. They demonstrate that "the impact of the retired population is often low on the job itself, but positive about creating activities (new facility), including services, healthcare, retail and construction". Li and MacLean [1999] show that changes in the population of retirees in Saskachewan "has a significant impact on the growth of cities and activity in the services sector." From multiplier models, some authors have been able to estimate the precise economic impact of retirees.

The report "Pensioners in Massif Central" [2003] identifies through literature a multiplier effect generating from 0.2 jobs per retiree received on a territory [S SHIELDS, STALLMAN ET [START_REF] Shields M | Stimulating the economic and fiscal impacts of highand low-income elderly on a small rural region[END_REF][START_REF] Shields M | Stimulating the economic and fiscal impacts of highand low-income elderly on a small rural region[END_REF], to 0.5 jobs [START_REF] Hodge | The Economic Impact of Retirees on Smaller Communities[END_REF] or 0.55 [START_REF] Deller | Economic Impact of Retirement Migration[END_REF]. But the economic impact is only "one of the component of the impact of retirees on the dynamics of local development" [CALLOIS et al., 2003]. However, the presential economy is not the only solution for the development in the countryside because it can not allow economic development to small scale [GODET ET MOUSLI, 2009]. This is where active retirees may have a card to play.

Apart from the references listed above, the participation of retirees in local rural areas is still an aspect fewly studied by scientists. Early works on this issue emerged in the 70s from the Anglo-Saxon. Lénel [2003] recall them, distinguishing the three theories about the behaviour of retirees and that the report on "Pensioners in Massif Central" [2003] clarify:

-The theory of disengagement: the removal of the individual from society, an idea of irretrievable decline. "This theory is challenged in recent years because it does not correspond well with the common idea [...] of flourishing senior citizens, free from occupational onstraints, finally yielding to passions they had always restrained."

-The theory of activity: it is the subject of much research and crowns the archetype of "dynamic retiree, invested in the social life, anxious to avoid apathy.

-The theory of continuity: "a retiree living-style, keeping the rhythms of working life, kind of activity but not necessarily a great social involvement."

In line with these three theories, many authors have developed their own typology of retirees. A profile of retiree seems to appear from these types, opening new possibilities of investigation. It is delineated by some authors under different terms: committed retirees [CALLOIS ET AL., 2003) or BooBos [GUERIN]. From our side we call them active retirees [START_REF] Dessaint M.-P. ; Flammarion | Une retraite heureuse, ça dépend de vous[END_REF], or "working retirement" [START_REF] Perrin- | Etre vieux et être à la retraite : La fin d'une tautologie[END_REF].

Two main theories currently stand about aging. First, the "pessimistic" thesis [START_REF] Longino | The Gray Peril Mentality and the Impact of Retirement Migration[END_REF] compares the period of retirement to a lack of capacity to innovate, to upgrade with the development of human services that are mostly low value added jobs economically speaking. Some even speak of "papy-crash". Thus, according to Guchez and Frossard [2001], "We have been pleased to give an optimistic view of retirement assets". This view is simplistic, but in addition, it hardly corresponds to rural areas "more influenced than other by activities more closely linked with family or friends." Assimilate retired to a "silver gold", source of employment and local development, seems wrong for some authors, or at least simplistic. "Focus development strategy on attracting retirees may have a number of perverse effects: increased land prices, the possibility of generational conflicts blocking local development, increased extraterritorial competition [CALLOIS et al., 2003] That is what [START_REF] Longino | The Gray Peril Mentality and the Impact of Retirement Migration[END_REF] calls the "gray peril".

The "optimistic" thesis view retirement as a period of intense activity (tourism, further work, organisational and cultural commitment) which boosts the economy and society. In fact, once retired, the former active would be freed from the burden that weighed on his activity. "The mood of the retiree is to have a greater freedom of mind. He may therefore be useful for society, whether in his original business or in another activity, to bring his experience, which became his competence in the current world's " [START_REF] Vimont | Le nouveau troisième âge, une société active en devenir[END_REF]. Between the time of retirement and that of death "runs a life to live only part of which is marked by difficulties associated with old age." Though retirees and seniors are weighing on public finance, they ERSA 2010 can sometimes be a lever: it concerns income from pensions or the creation of local jobs [IAURIF, 1999]. Thus, for [START_REF] Vimont | Le nouveau troisième âge, une société active en devenir[END_REF], the occupation of the elderly is a trend that will grow in the years to come. And this in many forms: a mixture of retirement and activeness, volunteer and salaried, in different sectors (social, cultural ...). "The third age will become a laboratory for new forms of economic and social activity. Longer life expectancy and a better state of health, are of course components that form the base of changing conditions of life of the "third age". Thus, this age is promoted to the forefront of innovation within the twenty-first century's society and it is going to play a new role in the economic, social and family life " [START_REF] Vimont | Le nouveau troisième âge, une société active en devenir[END_REF]. And this even if the activity of the elderly collides several reviews: older workers are taking the place of youth, they have a low yield ... statement far from being fully testified

This "optimistic" vision is favored by the pension system that is beginning to be much more flexible concerning the extension of professional careers, leaving the opportunity for older workers which have completed all their quarters, and that would want to, to pursue a gainful activity. In France, three incentive mechanisms exist so: the bonus, which increases the amount of future retirement pension by combining the trimesters beyond the maximum cumulative; gradual retirement, which allows a part-time while receiving a part retirement, the last device, widespread, combining work wile benefiting from pension, which allows retirees who have accumulated as many quarters as necessary, to a maximum rate, to increase income by taking up employment. If the remaining quarter is not reached, the additional income derived from combining work and retirement pension is capped. Moreover, a study from the National Pension Fund [GUILLAIN et al., 2009] amounted to 206,887 the number of retirees who left before 2008 that cumulate employment and retirement, or 1.9% of the 2007 retired population. This figure is steadily increasing from year to year, and the gradual easing of its application seems to have made the device more attractive.

First descriptive results on two federations of municipalities in the Massif of Cézallier

A methodology based on case studies

Many French rural areas are facing a demographic (and socioeconomic) imbalance. So is the Massif Central. In 2006, 21% of the inhabitants of the Massif Central were over 65 yearsold, 11% were over 75, compared to respectively 17% and 8% in overall France. This demographic imbalance across the Massif Central is actually due to a triple movement: the overall aging of the population, the outmigration of many young people linked to an increasing concentration of employment in urban areas, and arrival / return of population in retirement age in large numbers. The proportion of pensioners in the population is growing.

As such, the Massif Central is an interesting field of study for our issue.

Within the space Massif Central, Auvergne (NUTS 2 region), following this heavy trend of an aging population with a median age over 44 years-old for two of its NUTS 3 regions (namely Allier, Cantal) and 41-43 years for two others (knowing the median age in France is 38 years). We selected three territories dimensionally variable in this region: a Pays 9 (Pays des Combrailles), a Federation of municipalities (Billom -Saint-Dier) and a geographically united area (Plateau Cézallier).

Semi-structured interviews were conducted with the three main types of actors defined in the co-creation triptique: the retiree creating services, support structures for business creation and territorial authorities potentially involved in the creation of service activities (eg Federation of Municipalities). 9 In France, apart from its "country" meaning, a Pays is an area whose inhabitants share common geographical, economic, cultural, or social interests, who have a right to enter into communal planning contracts under a law known as the Loi Pasqua or LOADT (Loi d'Orientation pour l'Aménagement et le Développement du Territoire; English: Directive law concerning territorial planning and development)," http://en.wikipedia.org/wiki/Pays_(France)

The modified triangle of services proposed in Figure 2 will allow us to identify the main stakeholders involved in the creation of rural service in much the same way as Gallouj in his work on the LHCS [2008]. We will thus be able to identify different configurations of creations of services made by retirees, and as such identify the most favourable ones not only among the different actors involved but also from the place each of them takes in the creation of service. These configurations will be declined on each of the fields of study and built upon the same basis of semi-structured interviews.

4.2.2

The Cezallier: a territory with unknown potential of active retirees From the first interviews on the two main Federations of Municipalities located on the Plateau of Cézallier (namely "Ardes Communauté" and "Cezallier"), it is possible to provide first descriptive results concerning the creation of services by retirees.

The Plateau of Cezallier is a geographical entity grouping 37 municipalities, located inbetween three NUTS 3 regions: Puy-de-Dôme (North), Haute-Loire (East, 2 municipalities concerned) and Cantal (South). According to INSEE data [2009], it had 7,811 inhabitants in 2006 with a heterogeneous density of 7.9 inhabitants per square km and over one third of retirees in its total population. Its economy is mainly based on agriculture with 15.8% of its active population working in the primary sector and 864 farms especially oriented in (cattle) breeding. According to INSEE services alone represent 56% of market businesses of the territory. In 2008, there are essentially creations of activities in this sector which constitutes 73.1% of salaried jobs in this federation of municipalities.

For territorial Cézallier, retired as such do not seem to be a driving force. Indeed, whether the federations of municipalities authority or the Pays to which the federation belongs, neither of these local authorities do spontaneously see retirees as potential business creators of services but rather as consumers of services. Very few project holders are identified and identifiable in this area and the creation of services observed in the last 5 years are primarily public kind of creations (Services for Nurses at Home in "Ardes Communauté" for example). There might also be support structures to project holder wishing to set up service in the area.

From the support structures for creating service activities side, we may figure out the Platform for Local Initiative that are tools elaborated by the Chambers of Commerce and Industry (CCI) to accompany the creation of projects and / or resumption of business in various industries: crafts, industry, trade, services. As such, the PFLI has already been accompanying active retirees wishing to settle in the Cézallier and more specifically in the craft. There are also supporting structures dedicated to project holders at the departmental level (such as Appuy Créateur in Puy-de-Dôme), they also accompany active pensioners, but they seem to focus in urban area (Clermont-Ferrand) or even in suburban areas rather than in rural area. The local authorities seem less "armed" with respect to the potential of retirees because they have "no visibility on the needs of those retirees but also on who are retired" on their territory.

The main point that we can take out from these initial very descriptive results is that authorities are lacking stock-taking and accurate data to know what is happening in terms of creation of services by retirees on their territories. The support structures, seem already aware of the phenomenon of retirement assets and begin to accompany some. It seems that in rural areas, they are rather ex-workers who create craftshop while in urban areas, are more former executives opting for consulting services companies.

CONCLUSION

From the observation that the creation of activity generating employment is the result of a joint construction between the creator, the support structures and the territory, we attempt to identify the impact of a structural phenomenon -aging population -on the territorial configuration holding the emergence of activity in rural areas. Indeed, rural areas are more affected by aging than urban. Moreover, this global aging is accompanied by an increase of ERSA 2010 life expectancy and improving the overall health of the population. Therefore, while forty years ago, retirement was considered as a "social death" [START_REF] Guillemard | De la retraite mort sociale à la retraite solidaire : La Retraite, une mort sociale revisitée trente ans après[END_REF], at the time of retirement, there remains nowadays retirees with some energy and motivation to pursue their careers and build their business, that the relaxation of French rules for combining work with pension simplified.

Following the generic definition proposed by the service economy, which manages to encompass the concept of service in its entirety, [START_REF] Gadrey | Services : la productivité en question[END_REF] and [START_REF] Gallouj | L'économie des services à la personne[END_REF] proposed a diagram summarizing service provision on the basis of a triangle declined into a polygon. From the point of view of the creator of service activities, the emergence of his activity does not depend solely on local demand, but of all socio-spatial configurations in which he operates and fulfils, in a more or less conscious and voluntary way. The retiree -serviceentrepreneur is thus embedded in a multiscalar and evolving territory in which the support structures and characteristics of the territory play determining roles. That is what we have begun to outline on the Plateau of Cézallier.

The fieldwork on the northern Cézallier described above remained confined for now to supporting structures of the territory. The specificity of the retiree creator is not for the time identified by the support structures, however, they have access to all measures available for creators. Local communities have not integrated the active retired creator of activities in their development policies, and continued to consider them through medico-social policies, housing and personal assistance, in direct link with their loss of autonomy. However, our first interviews seem to depict a dynamic constrained by the socio-geographical specific down this rural area. Personal investment and provision of service by retirees of the territory will result in investment in local associations (associations of home care, elder club ...) and municipal (electoral mandate, participation in recreation committee). Volunteers, those retirees will be more motivated by community spirit than by providing market services for profit. Finally, the difficulty in identifying people both providing locally paid services and pensioners partly explains the lack of interest, from the support structures, in this category of pensioners, still economically dynamic and volunteers. The analysis started in the southern part of Cézallier located in the Cantal department reveals the same initial findings on the limited number of active retirees identified and accompanied, and also little enthusiasm for the opportunity they might be in this rural area.

It is now to seek and meet those retirees -creators and restated to know the factors that fostered their installation locally and their motives, and particularly the role played by the level of their pension in their personal choice, as it seemed to be, according to support structures and technicians working for local authorities, a key motivation that would drive a retiree to continue working.

6

  CAE : Conseil d'Analyse Economique -Economic Analysis Council 7 DIACT: Délégation Interministérielle à l'Aménagement et la Compétitivité des Territoires; now DATAR: Délégation à l'Aménagement du Territoire et à l'Action Régionale -Delegation for Planning and Regional Management

Figure n°1 :

 n°1 Figure n°1 : Triangle of service, translatedfrom[START_REF] Gadrey | Services : la productivité en question[END_REF]

  , BESSAC G., et DAURE P.-H., 2006, Territoires et vieillissement, Les Annales de la recherche urbaine, n°100, pp.29-32. BARNAY T., SERMET C. (sous la direction de), 2007, Le vieillissement en Europe : aspects biologiques, économiques et sociaux. Paris, La Documentation française. BRANDELEER C., 2008, Vieillissement et services à la personne en Europe, Association Pour la Solidarité, 15 p. CALLOIS J. M., MAZUEL L., ROUSSEL V., SENCEBE Y., VOLLET D., (avec la collaboration de Farghen F., Géraud C., Guyot C., Laporte A., et Petitdan M.), 2003, Les retraités et les espaces ruraux du Massif Central, Cemagref-Enesad-Enita, 136 p.

  3 and INSEE 4 [INRA etINSEE], retirees are less subject to spatial constraints previously attributed to the necessary location near his place of work, and may well more easily migrate and settle in rural areas.

	It now has more
	free time, without a priori temporal constraints, but will get more as long as his personal
	investments increase (associations, cultural…) and the pace of his « new » life moves on
	[GUÉRIN, 2002; GUILLEMARD, 2002]. In addition, he has an average living standards roughly
	equivalent to that of active population (although with the recent stagnation of narrowing gaps
	up to now) [OBSERVATOIRE NATIONAL DE LA PAUVRETÉ ET DE L'EXCLUSION SOCIALE, 2010,
	P. 99 ; CONSEIL D'ORIENTATION DES RETRAITES, 2009], a relative financial security, plus an
	proper capital accumulated throughout life [GIRARDOT-BUFFARD

« Pour et Sur le Développement Régional (PSDR), « Création d'Activités nouvelles et d'Emploi » (CreActE)

A recent TNS Sofres[2009] survey showed that a "baby boomer" is a person of 56 years-old, a "senior" is a person about 58 years of age, a "senior" is a person of about 61, a "veteran" is a person about 68, a "former" is a person about 72, a "senior" is someone around 74, and an "old people" is about 76. But the meaning of these names is very relative: people do not associate the same age to each of those terms depending on how old each surveyed is, and the two vary correlatively.

INRA : Institut National de la Recherche Agronomique -National Institute for Agricultural Research

INSEE : Institut National de la Statistique et des Etudes Economiques -National Institute for Statistics and Economic Studies

Translation of « service à la personne » given by the ANSP (Agence Nationale pour le Service à la Personne -National Agency for Lifestyle and Home-Care Agency)