Yasser Bourahla
email: yasser.bourahla@inria.fr

Manuel Atencia
email: atencia@lcc.uma.es

Jérôme Euzenat
email: jerome.euzenat@inria.fr

Knowledge Transmission and Improvement Across Generations do Not Need Strong Selection

Keywords: Multi-agent social simulation, Cultural evolution, Knowledge transmission, Agent generation, Cultural knowledge evolution

INTRODUCTION

In cultural evolution [START_REF] Luca | Cultural transmission and evolution: a quantitative approach[END_REF][START_REF] Richerson | Not By Genes Alone: How Culture Transformed Human Evolution[END_REF], concepts from biological evolution are applied to the culture of a society. This has been explored experimentally through multi-agent systems to evolve an agent population's behaviour [START_REF] Borenstein | Enhancing Autonomous Agents Evolution with Learning by Imitation[END_REF][START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF], language [START_REF] Steels | Experiments in cultural language evolution[END_REF] or knowledge [START_REF] Euzenat | Interaction-based ontology alignment repair with expansion and relaxation[END_REF] as their culture. The evolution of culture relies on its ability to display variations that can be selected and transmitted. Early work has identified different cultural transmission modes inspired by

Author version

Reference: Yasser Bourahla, Manuel Atencia and Jérôme Euzenat. Knowledge transmission and improvement across generations do not need strong selection. In P. Faliszewski, V. Mascardi, C. Pelachaud, M.E. Taylor (eds.), Proc. of the 21st International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2022), pp163-171, Online, May 9-13. 2022. epidemiology [START_REF] Boyd | Culture and the evolutionary process[END_REF][START_REF] Luca | Cultural transmission and evolution: a quantitative approach[END_REF]: vertical transmission is the transmission from parents to children, oblique transmission is the transmission from agents of the previous generation (think about education) to those of the next generation, and horizontal transmission is the transmission between agents of the same generation. Here, we will also use inter-generation transmission for the two former and intra-generation transmission for the latter.

Multi-agent work in which agents adapt to interactions among themselves [START_REF] Steels | Experiments in cultural language evolution[END_REF] can be considered as intra-generation transmission. This has proven to be efficient for reaching consensus and for sharing culture. Recently, it has been shown that agents that adapt their knowledge about the environment, expressed as ontologies, through social interactions in order to reach agreement are able to improve their ontology accuracy without necessarily adopting the same ontology [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF]. Thus, horizontal transmission is able to improve knowledge in a society of agents.

Vertical transmission, by transmitting culture from one generation of agents to another, may be seen as the occasion to shuffle the cards. It can introduce more variation or enforce (select) a dominant culture. This calls for assessing the respective roles of inter-generation and intra-generation transmission.

Another line of work considered exactly this and showed that inter-generation transmission allows agents to improve knowledge beyond what intra-generation transmission alone does [START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF]. In contrast, by disabling inter-generation transmission, agents have to start improving knowledge from scratch at each generation. In a similar setting, it was also found that intra-generation transmission generates variation and that inter-generation transmission performs selection [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF].

However, both works rely on strong conditions to ensure the faithful transmission of correct knowledge (using only the best part of the population as teachers, initialising agent ontologies from correct samples) or variation (adding noise in the learning process).

Here, we consider relaxing these assumptions to study the effects of horizontal and vertical culture transmission without selecting the best-performing agents and without starting with correct hints. This is achieved by offering a wider, yet differential, opportunity to breed and propagate knowledge to the whole agent society and by starting with random knowledge. This may eventually provide enough variation in the system.

To test this, we designed a new experimental framework building on these previous works. We performed experiments with intergeneration transmission through teaching [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF] and intra-generation transmission through interacting [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF], varying the extent of both transmission modalities and mating policies. We confirm the results of previous studies under these relaxed assumptions: intergeneration transmission increases the accuracy of knowledge obtained from intra-generation transmission. Moreover, we show that even if inter-generation transmission does not select the fittest parents, intra-generation transmission, if given enough time, can compensate for this, i.e. agents finally agree to select relevant pieces of knowledge.

The remainder of the paper is organised as follows: in Section 2, the related work is reviewed and more details on the two initial experiments are provided. Section 3 discusses the limitations of current settings and offers solutions to overcome them. Their actual implementation is precisely detailed in Section 4. Section 5 presents the performed experiments and Section 6 provides their results which are discussed in Section 7.

RELATED WORK

We first present work related to agents and cultural evolution generally before considering more precisely two experiments on which this work is based.

Agents and Cultural Evolution

Interactions between agents can serve as a mean of adaptation. Many approaches exploit them in multi-agent systems, for instance, to improve interoperability [START_REF] Atencia | An interaction-based approach to semantic alignment[END_REF][START_REF] Jurriaan Van Diggelen | ANEMONE: An effective minimal ontology negotiation environment[END_REF] or observe emergent behaviours [START_REF] Nolfi | Emergence of communication in embodied agents: Coadapting communicative and non-communicative behaviours[END_REF]. In some cases, by interacting with each other, agents may end up sharing and evolving a particular culture, e.g. knowledge about the environment, ways to interact, norms or conventions [START_REF] Gerard | Evolving Protocols and Agents in Multiagent Systems[END_REF][START_REF] Sen | Emergence of Norms through Social Learning[END_REF]. This is typically studied by observing a population of agents that interact with each other through a well-defined protocol. The state of the system is monitored until agents reach a stable state in which their culture does not change any more. The characteristics of this culture are then assessed [START_REF] Steels | Experiments in cultural language evolution[END_REF].

In this work, we are interested in the evolution of knowledge that agents use to behave. Cultural evolution has been applied to knowledge in the form of ontology alignments [START_REF] Anslow | Aligning experientially grounded ontologies using language games[END_REF][START_REF] Euzenat | Interaction-based ontology alignment repair with expansion and relaxation[END_REF]. It has also been applied to ontologies [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF] in which agents adapt their concept definitions to agree with each other. They improved their knowledge about the environment without necessarily sharing the same ontology. Agents in this setting learn from others by interacting with them, which is known as social learning [START_REF] Kendal | Social Learning Strategies: Bridge-Building between Fields[END_REF][START_REF] Rendell | Why Copy Others? Insights from the Social Learning Strategies Tournament[END_REF].

However, when the agents reach a full agreement, they stop adapting their knowledge. In a sense, they reach a local optimum with respect to the accuracy of their knowledge. Escaping this state may be obtained by either changing the environment or the agents.

Evolving different agent generations has been considered in evolutionary multi-agent systems [START_REF] Byrski | Evolutionary multi-agent systems[END_REF] in which agents are able to reproduce and may die. Although agents could be thought of as developing a culture, this has not been studied from that perspective. Introducing cultural mechanisms within agents has been developed in cultural algorithms [START_REF] Reynolds | An Introduction to Cultural Algorithms[END_REF]. However, this work has been mainly applied to optimisation problems.

It has been shown that culture transmission allows the discovery of behaviours that are inaccessible to genetic evolution [START_REF] Borg | Discovering and maintaining behaviours inaccessible to incremental genetic evolution through transcription errors and cultural transmission[END_REF][START_REF] Jolley | Analysis of social learning strategies when discovering and maintaining behaviours inaccessible to incremental genetic evolution[END_REF]. Multi-agent simulation of cultural evolution involving intrageneration and inter-generation transmission has been investigated in a series of experiments [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF][START_REF] Anzola | A model of cultural transmission by direct instruction: An exercise on replication and extension[END_REF][START_REF] Borenstein | Enhancing Autonomous Agents Evolution with Learning by Imitation[END_REF][START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF]. Based on neural networks for embodying knowledge, they implement connection weight communication [START_REF] Borenstein | Enhancing Autonomous Agents Evolution with Learning by Imitation[END_REF], supervised learning (imitation) [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF][START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF] or direct instruction [START_REF] Anzola | A model of cultural transmission by direct instruction: An exercise on replication and extension[END_REF] as a vertical transmission mechanism. Using the same imitation mechanism for horizontal transmission [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF], it was shown that the intra-generation culture transmission provided the variation that allowed the evolutionary process to be more effective than what it is with inter-generation transmission alone. This work is however based on a drastic selection of teachers from whom agents learn, both in oblique and horizontal transmission.

Below, we discuss more lengthly the experiments developed in [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF] and [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF] on which we will build.

Inter-Generation Culture Inheritance

Acerbi and Parisi [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF] designed an experiment in which agents use a neural network to navigate in their environment. The lifetime of agents spans 10 epochs of 50 games. At each game, the agent is presented with a situation and decides how to move. When it comes close to an edible food source, it receives a reward and when it comes close to a poisonous food source, it receives a penalty. In addition, a teacher discloses its decision to the agent, that it uses to adjust its network weights. This operation is repeated over 500 generations of 100 agents all replaced at once.

At birth, agents start with random weighted networks (𝑊 ). The first 6 epochs of their lifetime are dedicated to oblique transmission: they are taught their behaviour by agents of the previous generation. The next 4 epochs implements horizontal transmission: they are taught by agents from their generation (Figure 1, left). One key point is that in both cases they are only taught by the best 5% agents in terms of accumulated rewards. Teaching is achieved by constraining the output of the neural network. Teachers may add noise in their behaviour in order to generate variation.

Experiments are reported with oblique transmission only, horizontal transmission only, or both. In particular, results show that oblique transmission alone allows agents to improve (as measured by collected rewards) over generations, though horizontal transmission does not, because agents learn from novice agents. They also show that the introduction of noise is key to speed up improvement, and that horizontal transmission can provide it.

In these experiments, the selection of the 5% best performing agents in both transmission modes (20% for [START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF]) is a very strong bias because it gives little opportunity to general individuals to reproduce. This does not happen in human societies.

Intra-Generation Social Learning

Bourahla and colleagues [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF] designed an experiment in which agents live in an environment populated by objects identified by their features, e.g. 'can move' or 'has fangs', for which they have to make decisions, e.g. 'hunt' or 'hide'. Agents' goal is to agree with other agents on the decision to make. They follow a two-step experiment protocol (Figure 1, right). First, agents learn to make decisions about objects of their environments from a set of samples (𝑆). The output of this step is, in particular, a simple ontology (𝑂) allowing to classify objects and to determine the decision to make. Then, agents repetitively interact with each other two-by-two. They compare the decisions that they would make about objects. The interactions succeed when the agents agree on the decision; they fail otherwise. In the event of a failure, one of the agents adapts its ontology in order to adopt the decision of the other on this object. Experiments showed that agents are able to reach a state in which they always agree. The quality of their ontologies, as measured by its accuracy, increases on average, but not in every case, and does not necessarily reach full accuracy. Finally, though the distance between agents' ontologies decreases, agents do not necessarily end up with the same ontologies.

The success criterion for agents is to agree, not necessarily to make the correct decision. The correct decision to be made is unknown to the agents. It is used only in two occasions: (1) initially, agents are trained with a sample which is correct, but incomplete;

(2) the choice of which agent will adapt its knowledge is based on rewards that they have received on a (different) sample. Although (2) is legitimate, (1) is not. Hence, we relax this by using samples labelled by parents not knowing the correct decision.

TOWARDS AN INTEGRATED APPROACH TO KNOWLEDGE TRANSMISSION

We first discuss the limitations of the experiments presented before. Then we propose to combine them in a way addressing these limitations. This allows us to formulate our claims as hypotheses.

Limitations

The two experiments described in the last subsections have the merit to provide a model of cultural transmission in agents and to show that it has a positive effect on their efficiency. However, they do it with modalities which seem strong and unnatural:

• starting with correct samples does not correspond to what happens in real life;

• restricting the role of teachers to a very limited part of the population (5%, 20%) seems to go counter the idea of culture and its propagation.

Interestingly, these two modalities tend to enforce the faithful transmission of correct/fit culture, though the benefits of vertical transmission are supposed to come from the variation it provides. This is to the extent that [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF] introduces artificial noise in the model in order to increase variation. We conjecture that a less restricted opportunity to transmit knowledge, both across and within generations, provides enough variation to improve over horizontal transmission.

Combining the Two Experiments

Although the two experiments described above are about knowledge transmission, they differ on many notable features, such as:

• oblique and horizontal transmission vs. horizontal transmission;

• neural networks vs. ontologies and decision trees;

• selecting teachers vs. random interaction;

• positive and negative reward vs. agreement. Some of these differences are secondary, such as the choice of the representation, though others are more important, such as those affecting transmission modalities.

To test our conjecture, we combine both approaches of Figure 1 and relax these unwanted constraints. The resulting setting, as shown in Figure 2, is such that: intra-generation transmission is implemented by interaction exactly as in [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF].

inter-generation transmission is implemented through learning. As in [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF], a generation of agents is replaced by another generation. Instead of implementing oblique transmission, agents reproduce differentially with respect to a probability distribution and transmit their knowledge to their children. However, they do it with the modalities of [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF].

This should allow us to determine under which conditions agents can improve generation after generation, or if they reproduce their knowledge, thus behaviour, identically.

Relaxing Elitist Assumptions

For relaxing selection, the reproduction phase is implemented by parents having children. The probability to have children will be determined either equiprobably or relative to the income of the agents (denoting their success). Important changes concern vertical transmission. It is split into two steps: (a) the acquisition of an initial ontology by the children, and (b) the transmission of knowledge from the parents by first interacting predominantly with them and then progressively widening their interactions.

The initial ontology may either be empty, be random, be a merge of the parents' ontologies or be learned as in the first step above, from samples provided by the parents (Figure 2). Here, agents either start with random ontologies (suppressing the learning phase) or learn their ontologies under the supervision of their parents which provide the samples from which to learn.

This setting ensures a wide opportunity for agents to have children to which to transmit their knowledge. Moreover, the sample from which children learn may now be incorrect (because parents do not have fully correct knowledge and because samples are provided by both parents) and incomplete (because they do not cover the whole object space). They thus relax the first two identified limitations.

Of course, this setting is not exempt of bias: the most successful agents, which may not have the most correct knowledge, are more likely to have children and, during horizontal transmission, success will also play a role in which agent will learn from which other. However, this bias still allows a broad fraction of the propulation to reproduce and transmit knowledge.

Finally, no artificial noise is added to any agent behaviour. As mentioned above, the 'egalitarian' recruitment of parents and the incorrectness of samples provided by parents are already sources of variation during vertical transmission. The disconnection between ontology accuracy (the measure of knowledge quality) and agreement (the goal pursued by agents) is an additional source of variation during horizontal transmission.

Hypotheses

This framework will be used to test our claims experimentally. We aim at investigating primarily two directions. First, once agents reach a global agreement, they do not adapt their knowledge anymore. As shown in [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF], they may still agree on incorrect decisions and they preserve the diversity of their knowledge. The intergeneration transmission should introduce further variation allowing agents to discover new relevant pieces of knowledge. Accordingly, as in [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF][START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF], we hypothesise that (𝐻 1 ) vertical transmission allows new generations' knowledge to be more accurate than that of the previous generation.

According to [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF], agents are able to improve the correctness of their decisions when they adapt their knowledge to agree with each other. This suggests that the intra-generation knowledge transmission is able to select pieces of knowledge to preserve. Thus, we hypothesise that (𝐻 2 ), interaction, used as intra-generation transmission, can compensate for the absence of parent selection.

EXPERIMENTAL FRAMEWORK

In order to test the two proposed hypotheses, we have designed an experimental framework following the above principles with mechanisms for agents to mate, reproduce, die, and to transmit knowledge from parents to children.

Below we describe the general process (Section 4.1) and detail what differs from the original experiments:

• The agent life cycle (Section 4.2),

• How agents are selected to reproduce (Section 4.3),

• How agents transmit their knowledge to their children (Section 4.4).

Several questions can be raised on how these additions affect agents' knowledge. In this paper, we focus on the impact of knowledge transmission on knowledge accuracy.

Overall Process

In these experiments, we reuse the exact same

• environments and ontologies,

• ontology learning procedure,

• social learning procedure, and • evaluation measures, as in [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF]. The game is played with objects characterised by 4 features on which only one decision is valid among 6 possible ones. Experiment runs are made of periods split in two parts (Figure 3):

reproduction in which generation 𝑖 -1 (half of the population) is suppressed (dies) and generation 𝑖 +1 is added (is born), and agents of the new generation acquire their initial knowledge;

interaction in which agents use their ontologies to agree on decisions about objects and modify them in case of disagreement.

The agents of the initial population (generations 0 and 1) are initialised with random ontologies.

This process is illustrated in Figure 2 and precisely described below.

Agent Life Cycle

An agent is born at the beginning of a period and dies at the end of the next period (it lives for 2 periods). In the first period, the agent is considered a child. During the second period, the agent is considered an adult. Between these two periods, agents may reproduce according to precise modalities explained in Section 4.3.

During the first period of their lives, (child) agents learn from their parents through inter-generation knowledge transmission detailed in Section 4.4. They gradually get detached from their parents and start interacting with other individuals of the society. During the second period of their lives, some agents have become parents and transmit their knowledge to their children. They still interact with the other individuals of the society and may adapt their knowledge.

At the end of each period, 𝑋 2 agents die and 𝑋 2 agents are born. This means that each generation is composed of 𝑋 2 agents and that the whole population is composed of 𝑋 agents (𝑋 being even and greater than 4).

To keep the number of agents in the population constant, the initial population is composed of 𝑋 agents. Half of this population, considered generation 0, dies at the end of the first period and does not reproduce. The other half, generation 1, behaves like the rest of the generations starting from the second period. Figure 3 shows the evolution of a society through 3 generations.

Agent Mating

In order to reproduce, (adult) agents behave along the following rule: 𝑣 = 2 parents are selected randomly following a distribution 𝑠 to have 𝑐 = 1 child. As a consequence, individuals may have between 0 and 𝑋 2 children, with between 1 and 𝑋 2 -1 partners. The probability to mate follows a distribution 𝑠 that may be:

• Maximal (100%) for the 𝑣 agents having gathered the most income and minimal (0%) for the other agents,

• Proportional to the income gathered from doing their tasks,

• Proportional to their success rate in interactions, • Inversely to the ontology distance with other agents,

• Equiprobable. Here, we will only test the maximal (𝑏𝑒𝑠𝑡), the income-based (𝑖𝑛𝑐𝑜𝑚𝑒) and the equiprobable (𝑟𝑎𝑛𝑑𝑜𝑚) distributions. The maximal strategy is introduced as a strong selection baseline, instead of [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF]'s selection. It corresponds to 10% selection. Figure 4 shows these probability distributions. In the case of the performed experiment, income-based is very different from maximal and closer to equiprobable.

In [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF], it is reported that only oblique and not vertical transmission is tested. However, the setting may be interpreted as vertical transmission of the 𝑣 = 𝑋 2 ×5% agents with largest income (𝑠 = 𝑏𝑒𝑠𝑡) having together 𝑐 = 𝑋 2 children.

Knowledge Transmission

The transmission process goes through two steps (Figure 3).

Initial vertical transmission.

In the first stage, each agent of the new population acquires knowledge directly from its 𝑣 parents. Children may have an initial ontology that is empty, random, the result of merging their parents' ontologies, or the result of being taught by their parents. Although all options are possible, we only experiment with either random ontologies (abusively denoted by 𝑟 = 0) or ontologies learnt from the parents reusing the technique of [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF]. More precisely, 𝑟 % of all objects with distinct properties (object types) are randomly selected. Each parent labels half of these objects with the decisions it would make with respect to its own ontology (which may be incorrect). This set of labelled objects is presented to the child as a training sample (𝑆) from which it learns its ontology.

Interactions. Once this initial transmission has been performed, agents interact with other agents following the protocol of [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF]. The interactions are constrained such that agents are initially biased towards more interactions with their parents: At its 𝑖 𝑡ℎ iteraction, each agent has probability 𝑃 𝑖 to interact with one of its parents selected randomly. The probability of restricting the agent interaction depends on 𝑖 and the restricted interaction reduction rate 𝜖 < 1. It is determined by:

𝑃 𝑖 = max(0, 1 -𝑖 × 𝜖)
Thus, the bias is maximal at the first interaction, decreases as interactions increase and has no effect after interaction ⌈ 1 𝜖 ⌉. This mimics agents progressively broadening their social circles. In the experiments, we use 𝜖 = .01. Hence, for each child, this bias disappears after 100 interactions.

When agents are adult, they can interact with anyone:

• their children (vertical transmission),

• the children of others (oblique transmission),

• other agents of their generation (horizontal transmission).

Given the non-oriented character of transmission, it is possible that an adult learns knowledge from a child, as this occurs in real life and contrary to genetic transmission. This learnt piece of knowledge may even be transmitted to future generations if it goes again to the next generation through vertical or oblique transmission. Agents adapt their ontologies with an operator (split) which splits a concept in two according to the description of the object for which both agents do not agree [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF].

EXPERIMENTS

We perform two experiments to test each of the hypotheses introduced in Section 3.4. They use the same modus operandi, only a few independent variables differ. Table 1 summarises the parameter values considered in these experiment plans. Values of 𝜏 end by 1, in order to compute measures at the 𝜏 -1 iteration, i.e. before the population is replaced. Each combination of parameter values is run 10 times.

Experiment 1: Effect of Inter-Generation Transmission on Ontology Accuracy

As mentioned in Section 2.3, intra-generation transmission converges towards a stable state in which agents always agree on the same decision. However, this decision may not be the correct one but, without feedback from the environment, agents have no reason to know it. Hence the accuracy of their ontology is not maximal. Typically, this situation may evolve through changing the conditions (adding new agents, modifying the environment). The introduction of new agents, which have to learn their ontologies from imperfect ones (either starting with a random ontology or learning from an imperfect and incomplete sample provided by their genitors), introduces variations in the system.

The first experiment, aims at assessing the effects of introducing agent generations. Thus, we focus on the variables affecting vertical knowledge transmission: the proportion of instances covered by the training sample and the length of population life span, because it constrains the amount of interactions with parents.

As a consequence, we vary the transmission percentage 𝑟 which corresponds to how complete and how imperfect the inter-generation transfer is. When the transmission sample ratio is 0, agents start with random ontologies. We also vary the length of the period 𝜏 which corresponds to agents' half-life. When the period length is greater than the number of iterations (𝜏 > 𝑛), the experiment happens within one generation (no variation of agent knowledge).

Hypothesis 𝐻 1 can thus be rephrased as Adding inter-generation transmission leads to higher accuracy than intra-generation transmission alone.

Experiment 2: Interaction Between Selection and Interaction Length

Selection mechanisms are assumed to provide a reproductive advantage: the most accurate ontologies will provide higher fitness which itself provides to their bearers the possibility to reproduce more. Such ontologies may spread more in further generations. Previous results confirmed this assumption and showed that selection played an important role in such a spreading (Section 2.2). In this second experiment, we test the less selective policies. More specifically, we investigate whether intra-generation transmission, a typical cultural evolution mechanism, may compensate for the reduction or absence of parent selection.

This experiment focuses on (1) how parents are selected for reproduction, and (2) how long an agent generation lives: because agents need time to agree with each other on which pieces of knowledge to adopt. Thus, we vary the parent selection policy 𝑠 as 𝑟𝑎𝑛𝑑𝑜𝑚, 𝑖𝑛𝑐𝑜𝑚𝑒 and 𝑏𝑒𝑠𝑡 and the period length 𝜏 as in the first experiment. We also perform the experiment for agents which do not adapt their knowledge after interaction (𝑜𝑝 = 𝑛𝑜𝑛𝑒), fully discarding horizontal transmission. To that extent, the adaptation operator 𝑛𝑜𝑛𝑒 is introduced, the operator 𝑠𝑝𝑙𝑖𝑡 being that of [START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF].

Hypothesis 𝐻 2 can thus be tested as with sufficient intra-generation transmission, accuracy obtained with or without selection is similar.

Ontology Accuracy

For each experiment, we report the ontology accuracy which is used to test the hypotheses. The accuracy of an ontology is computed as the proportion of object types, i.e. feature combinations, for which the correct decision is made by the ontology. It is averaged over the 𝑋 ontologies of all agents at a particular iteration and averaged over 10 runs. The test of the hypotheses themselves applies to the final state of the experiment (iteration 𝑛). We display the evolution of the measure over all iterations.

RESULTS

In the following, the results for the two experiments are presented.

For each of them, we first show how the results answer the associated hypothesis. Additional details are discussed regarding the interaction of the different parameters with the results.

Inter-Generation Transmission Improves Ontology Accuracy

To test Hypothesis 𝐻 1 , we compare the average final accuracy of experiments with only one generation (𝜏 = 200001) to experiments with multiple generations (of different period lengths). Figure 5 shows this evolution. By performing an ANOVA (Analysis of Variance) test, the accuracy at the end of the experiment when intergeneration transmission occurs at periods of length 10001 and 20001 is different from when it does not occur at all. Post-hoc, tuckey-hsd (honestly significant difference) test shows, that the difference is significant (𝑝 ≪ 0.01) for both 10001 and 20001 periods compared to a single generation (200001). Thus, Hypothesis 𝐻 1 is accepted with 𝜏 ≥ 10001 when the period is long enough.

Inter-generation transmission needs long interaction periods. It can be observed, in the early iterations of Figure 5, that each generation improves its accuracy over the previous one. In particular, the accuracy obtained at 2𝜏 is strictly superior to the accuracy at 𝜏. This confirms that agents with vertical transmission are able to reach a higher accuracy than horizontal transmission alone. However, when the interaction period is not long enough, agents do not have time to spread relevant knowledge widely. Hence, vertical transmission suffers from the low accuracy of the transmitted knowledge and the short period only allows to recover from this. This explains why, when the period length is 5001, the accuracy does not improve.

Short interaction periods can be compensated for by larger transmission percentage. Complete transmission percentage harms variation in long interaction periods. In contrast, when the period is long (10001 or 20001), the transmission percentage only affects accuracy when it is complete (𝑟 = 1.0). Then accuracy is lower. This might be because faithful transmission reduces variation. As long as there is a small variation, agents improve. When the transmission percentage is small, agents compensate for it by transmitting through interaction.

Transmission percentage and period length interact. Figure 6 compares the accuracy of agents with (𝑟 ≠ 0) and without (𝑟 = 0) initial vertical transmission, under different period lengths (𝜏 = 5001 and 𝜏 = 20001). When the period is short (𝜏 = 5001), a higher transmission percentage (𝑟 = .8) yields better results than a lower transmission percentage (𝑟 = 0 and 𝑟 = .2 provide very close final results). On the contrary, with a long period (𝜏 = 20001), the best results are obtained without initial vertical transmission (𝑟 = 0), those with initial vertical transmission being very close to each other. This is explained by the capacity of intra-generation transmission to spread accurate knowledge to the whole population. This knowledge has a chance to be transmitted even with low 𝑟 and even in absence of initial vertical transmission (𝑟 = 0) because it can be transmitted from parents through interaction. In this case, a low 𝑟 provides the variation allowing to further increase accuracy. On the contrary, if there is not enough intra-generation transmission (short 𝜏), the perpetuation of knowledge benefits from a more faithful initial vertical transmission. This shows the delicate balance to be found between 𝑟 and 𝜏 to ensure knowledge improvement.

Intra-Generation Transmission can Compensate for the Lack of Selection

To test Hypothesis 𝐻 2 , we first show that the selection of parents without the intra-generation transmission does actually improve knowledge accuracy. Then, we show that this effect does not exist when there is intra-generation transmission. Intra-generation transmission compensates for the lack of selection. As it can be observed in Figure 7, the evolution of agent accuracy when there is intra-generation transmission (solid lines), is significantly higher than when it is not present (dashed lines). Furthermore, contrary to having inter-generation transmission only, when the intra-generation transmission is present, the way parents are selected has little impact on the final accuracy. In the presence of intra-generation transmission (𝑜𝑝 = 𝑠𝑝𝑙𝑖𝑡), ANOVA returns no significant difference between the three parent selection methods (𝑝 = 0.34). In this case, Table 4 shows that the difference between no selection (𝑟𝑎𝑛𝑑𝑜𝑚) and maximal and income-based selection policies is close to 0, though it is significantly larger without intrageneration transmission. Thus, we accept Hypothesis 𝐻 2 : intrageneration transmission compensates for the lack of selection.

𝑜𝑝 \ 𝑠 𝑖𝑛𝑐𝑜𝑚𝑒 𝑏𝑒𝑠𝑡 𝑛𝑜𝑛𝑒 -0.115 ± 0.035 -0.165 ± 0.035 𝑠𝑝𝑙𝑖𝑡 -0.01 ± 0.04 0.005 ± 0.035

DISCUSSION

Such results provide a better understanding of transmission parameters which warrant a proper cumulative cultural evolution.

We have shown that the combination of vertical and horizontal transmission of knowledge over generations of agents improves knowledge accuracy. This confirms previous results [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF][START_REF] Denaro | Cultural evolution in a population of neural networks[END_REF] under broader conditions: initial knowledge is not necessarily correct, no drastic selection of teachers is applied, no artificial noise is introduced to boost variation. We have also shown that a very important factor in the cumulative improvement of knowledge is the population life span.

Thus this paper can be read as a confirmation, using a different framework and relaxed constraints, of [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF]'s results about the efficiency of vertical transmission for improving agent knowledge. It can also be seen as a rebuttal that strong parent selection is an important factor for observing such effects.

In fact, the wider a culture is shared in a population, the less important the selection. The obtained results show that spreading quality knowledge requires time. If agents have a short life span and no selection, then knowledge will not improve because the fittest one will have little chance to be passed to the next generation. But if they have enough time to spread accurate knowledge, then it will improve over generations without parent selection.

It can be questioned whether evolution without selection is still evolution. This is the specificity of cultural evolution that, to the selection of individuals by the environment, is added the selection of culture by these individuals, occurring during horizontal transmission. [START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF] showed that (1) the intra-generation transmission can introduce variation in culture and (2) its selection occurs in the inter-generation transmission. Contrary to that, we showed how (1) inter-generation transmission can be the one introducing variations (which allow agents to improve further their accuracy as shown in Section 6.1) and (2) intra-generation transmission can select the knowledge that spreads in the agent population (Section 6.2). Contrary to genes, even if parents do not provide the best cultural assets, children are able to acquire them from peers or other sources. These results show the robustness of cultural evolution in which the two transmission modes can balance each other.

The social import of such results is that it is not necessary to have a drastic selection of agents for the society's culture to improve over generations. The good news is that if we are too ignorant, there is hope that our children can catch good knowledge. Of course, there should be a minimal transmission of what is improved for the evolution to be cumulative. But this is also ensured when efficient culture is widely spread, as culture should be.

Figure 1 :

 1 Figure1: Experimental frameworks of[START_REF] Acerbi | Cultural Transmission Between and Within Generations[END_REF] (left) and[START_REF] Bourahla | Knowledge Improvement and Diversity under Interaction-Driven Adaptation of Learned Ontologies[END_REF] (right). (𝑊 =neural networks weights, 𝑆=training sample, 𝑂=ontology). In spite of structural similarities, the mechanisms for transmitting knowledge are different: both intergeneration mechanisms are supervised learning, but intrageneration transmission is different.

+ 1 Figure 2 :

 12 Figure2: Combination of the mechanisms of Figure1: horizontal transmission of knowledge is achieved through agents interacting; initial vertical transmission involves parents generating samples (𝑆) from their ontologies (𝑂) from which children will learn their initial ontology (𝑂).

Figure 3 :Figure 4 :

 34 Figure 3: Evolution of a society through 3 agent generations.

Figure 5 :

 5 Figure 5: Average accuracy (over 𝑟 ) by period lengths.

8 Figure 6 :

 86 Figure 6: Average accuracy with (red and brown) or without (blue) initial vertical transmission (blue).

Figure 7 :

 7 Figure 7: Average accuracy by parent selection with (plain lines) and without (dashed lines) horizontal transmission.

Table 1 :

 1 Table 2 shows the final accuracy of agents per period length and transmission percentage. When the Independent variables and experiment values. period length is 5001, the accuracy gets higher as the transmission percentage gets larger. This is because the shorter the period, the smaller the transmission achieved by interaction. If the initial training sample is small, then agents do not receive enough knowledge from their parents to perpetuate what has been gained during the previous period.

			Meaning Number of Iterations Size of the Population Period Length Transmission Percentage Parent Selection Number of Parents Adaptation Operator Rest. Inter. Reduction Rate	Variable 𝑛 𝑋 𝜏 𝑟 𝑠 𝑣 𝑜𝑝 𝜖	Experiment 1 5001, 10001, 20001, 200001 200000 40 0 = 𝑟𝑎𝑛𝑑𝑜𝑚, 20, 40, 60, 80, 100 𝑟𝑎𝑛𝑑𝑜𝑚 2 𝑠𝑝𝑙𝑖𝑡 0.01	Experiment 2 5001, 10001, 20001 40 𝑖𝑛𝑐𝑜𝑚𝑒, 𝑟𝑎𝑛𝑑𝑜𝑚, 𝑏𝑒𝑠𝑡 𝑠𝑝𝑙𝑖𝑡, 𝑛𝑜𝑛𝑒
	period length (𝜏)	5001 10001 20001 200001	Transmission percentage (𝑟 ) 0 (random) 0.2 0.4 0.6 0.8 1.0 0.63 0.63 0.66 0.72 0.73 0.82 0.91 0.91 0.91 0.86 0.90 0.82 0.95 0.91 0.89 0.94 0.91 0.86 0.86 0.86 0.84 0.81 0.83 0.81

Table 2 :

 2 Final average accuracy grouped by experiment parameter values. In bold, the highest values of the column.

Table 3

 3

	summarises these results. Results reported below are those with 𝜏 = 20001, the same results are obtained with 5001 and 10001 (20001 provides the least favourable figures).

Selection is efficient. Figure

7

shows in dashed lines the evolution of agent accuracy with only the inter-generation transmission comparing maximal (𝑏𝑒𝑠𝑡), income-based (𝑖𝑛𝑐𝑜𝑚𝑒) and equiprobable (𝑟𝑎𝑛𝑑𝑜𝑚) selection policies. In the absence of intra-generation

Table 3 :

 3 Accuracy improvement in function of selection (𝑠) and horizontal transmission (𝑜𝑝). In absence of horizontal transmission (𝑜𝑝 = 𝑛𝑜𝑛𝑒), maximal and income-based selection improves final accuracy; with horizontal transmission (𝑜𝑝 = 𝑠𝑝𝑙𝑖𝑡), all strategies provide a higher improvement.

		1
	ontology accuracy	0.2 0.4 0.6 0.8			𝑟𝑎𝑛𝑑𝑜𝑚 -𝑛𝑜𝑛𝑒 𝑟𝑎𝑛𝑑𝑜𝑚 -𝑠𝑝𝑙𝑖𝑡	𝑖𝑛𝑐𝑜𝑚𝑒 -𝑛𝑜𝑛𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 -𝑠𝑝𝑙𝑖𝑡	𝑏𝑒𝑠𝑡 -𝑛𝑜𝑛𝑒 𝑏𝑒𝑠𝑡 -𝑠𝑝𝑙𝑖𝑡
		0	0	50000	100000	150000	200000
					iteration (𝜏 = 20001)

Table 4 :

 4 95% confidence intervals of mean difference between random and the other selection methods with (𝑜𝑝 = 𝑠𝑝𝑙𝑖𝑡) and without (𝑜𝑝 = 𝑛𝑜𝑛𝑒) intra-generation transmission.

ACKNOWLEDGMENTS

This work has been partially supported by MIAI @ Grenoble Alpes (ANR-19-P3IA-0003).

DATA AVAILABILITY

All experiments were performed in the Lazy lavender software environment [START_REF]Lazy lavender[END_REF]. Settings, output and data analysis notebooks are made available at [START_REF] Bourahla | DOTG: Knowledge is transmitted between agents and across generations[END_REF] and [START_REF] Bourahla | DOTG: Knowledge is transmitted between agents and across generations with different parent selection methods[END_REF].


Florent Macé
email: florent.mace@u-bourgogne.fr

Christine Peyron

Carine De Vriese

Marjorie Nelissen-Vrancken

Martine Ruggli

Mélanie Brülhart

General Practitioners-CommunityPharmacists practice groups: Analysis of the potentialities and limits of this practice through its implementation in several European countries

Keywords: Community pharmacist, general practitioner, quality circle, interprofessional collaboration, general practice, primary care organization

Practice groups involving general practitioners and community pharmacists have been developed in several European countries (Belgium, the Netherlands, Switzerland) since the 1980s. Each country has implemented this practice using a different model with similarities but also specificities. Each model has encountered different dynamics during its implementation thanks to a significant and even growing participation of professionals in the Netherlands and Switzerland and, to a lesser extent, in Belgium. According to the research that has studied the implementation of these models, the potential of this practice is important in terms of improving the quality of drug prescription and in its cost effectiveness and better collaboration between physicians and pharmacists. However, the parameters associated to individual professionals' practices and to the healthcare system concerned may have influenced the implementation of this practice in these different countries. A generalization of this practice to other countries with similar challenges is appropriate but different considerations linked to the individual practices of professionals and healthcare systems must be analyzed before large-scale implementation is possible.

Introduction

While practice groups between General Practitioners (GPs) have been established in many European countries, the concept of practice groups between GPs and Community Pharmacists (CPs) has been developed in fewer of these countries [START_REF] Rohrbasser | Use of quality circles for primary care providers in 24 European countries : an online survey of European Society for Quality and Safety in family practice delegates[END_REF] . This practice can be defined as meetings between GPs and CPs from the same territory which are regularly organized with the aim of improving the practices associated with pharmacotherapy. However, as each country has different healthcare organizations but also healthcare and pharmaceutical issues, each country has implemented this practice using a different model with similarities but also specificities. Through the study of the implementation of this practice in three European countries (Belgium, the Netherlands, and Switzerland), we analysed what were the potentialities of this practice as well as the levers and limits inherent in each of these countries in order to identify the conditions favorable to the generalization of GPs-CPs practice groups in other healthcare systems. This analysis was carried out through a literature review as well as through feedback from persons attached to the structures supporting this practice in these various countries.

1) Overview of the implementation of this practice in Belgium, the Netherlands and Switzerland

1.1) Establishment and objectives

In Belgium, the Netherlands, and Switzerland, the implementation of practice groups between GPs and CPs has been carried out in different ways according to different associated issues. The Netherlands was the first country where this practice was established by pioneers around 1986, then officially taken over by the government in 1992 under the name of « Pharmacotherapy Audit Meetings » (PTAM) [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF] . This practice was introduced later in Switzerland (1997) and Belgium (2000) respectively with the designation « Physician-Pharmacist Quality Circles » (QC) and « Medico-Pharmaceutical Concertations » (MPC) [START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF] . The introduction of these models was supported by different promoters depending on the country. In fact, while the PTAMs and QCs were initially carried by pioneers then supported by a political willingness to rationalize drug expenditures for the PTAMs and by an umbrella organization for Swiss pharmacists (pharmaSuisse), the MPCs were set up by a joint initiative of several professional and institutional structures a without being initially associated with a Scientific Society of Francophone Pharmacists (SSPF), the General Inspection of Pharmacy, the Belgian Center for Pharmacotherapeutic Information (CBIP) and the Scientific Society of General Medicine (SSMG) were the initial promoters health policies [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF] . However, the objective of these practice groups was the same. It was to integrate the expertise of the two professions, through the exchange of information and practices, in order to contribute to an optimization of GPs prescriptions with respect to quality, safety and economy [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF][4] .

Improving relationships between physicians and pharmacists at the local level was another explicit objective pursued by these three models [START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF]4 .

1.2) Similarities and differences in the running of practice groups

Each country has implemented this practice using a different model with similarities but also specificities concerning the professionals authorized to lead meetings, support for meeting leaders, integration of prescription data, etc. As mentioned, the general principle of this practice is characterized by organizing regular exchanges between GPs and CPs and even specialists from the same territory in order to exchange scientific, clinical, therapeutic and economic-data, adapted to their daily practice about defined themes [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF][4][START_REF] Bugnon | Cercles de qualité médecins-pharmaciens, pour une responsabilité partagée de la liberté de prescription[END_REF][START_REF] Philbet | Cercles de qualité médecins-pharmaciens. Déjà 20 ans, mais toujours aussi innovants[END_REF] . Depending on the model, the practice groups are made up of 1 to 3 pharmacists and 5 to 15 physicians who meet on average 3 to 6 times a year [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF] Bugnon | Cercles de qualité médecins-pharmaciens, pour une responsabilité partagée de la liberté de prescription[END_REF][START_REF] Van Mil | Pharmaceutical Care in Community Pharmacy: Practice and Research in the Netherlands[END_REF] . Moreover, although this is more or less systematic depending on the model, the provision of prescription data from participating GPs is a common feature of these models b 2,5,8,9 . These models are also characterized by the support of a supporting structure, whether institutional such as the Dutch Institute for Rational Use of Medicine (IVM) c for the PTAMs and the National Institute for Health and Disability Insurance (NIHDI) for the MPCs, or professional with pharmaSuisse for the QCs. The purpose of these structures is to accompany professionals in this process through, according to the model, its financing, the provision of prescription data, training of meeting leaders and/or the provision of programs or working materials for the meetings 2,4,5 . However, these models differ in certain characteristics concerning the setting up of the meetings. Indeed, while the preparation and animation of QCs are exclusively carried out by one or more pharmacists, a joint approach by physicians and pharmacists is planned within the PTAM or MPC models in order to make the meetings more focused on the practical aspects of the two professions d 2,4,5 . On the other hand, the methodology of QCs provides for a uniform method for setting up sessions in particular through the preliminary training of meeting leader pharmacists e , while that of CMPs and PTAMs is more flexible of this model before its takeover in 2012-2013 by the National Institute of Health and Disability Insurance (NIHDI) to contribute to its development. b The provision of prescription data is systematically made available within the QCs while it is not systematically made available within the CMPs and the PTAMs, depending on the quality level of the latter (see comment 6) 4,8 . c IVM is an institute for the proper use of medication that benefits from an institutional grant from the Dutch Ministry of Health [START_REF]Informatiepagina over IVM[END_REF] . d However, local CMP project teams can use meeting leaders previously trained (e.g., from programs, but also from other organizations) to lead their meetings. e The meeting leader pharmacists must follow a specific continuing education program provided by pharmaSuisse for each topic which includes basic training (50h) followed by continuing training (updates 16h / year) in order to master the topics discussed. Each training includes a broad review of literature associated with the topic discussed. in terms of preparation methods f due to a level of requirement and quality that may differ between groups g 4,5,8 . Moreover, the participation of professionals in this type of practice, whether they are meeting leaders or participants, is not recognized in the same way. Indeed, while a maximum budget of 2,500 euros is allocated per MPC to finance the entire local project, only some professionals are paid within the other two models, meeting leader pharmacists under certain conditions within the QCs h and participants involved in the higher-level groups for some PTAMs i 9 . Likewise, CPs and GPs can have their participation in these three models recognized within their continuing training but through specific modalities in each country [START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF] . Table 1 describes more explicitly the similarities and differences between these different models.

1.3) The situation of the current implementation of this practice in these countries

Due to a different anteriority and a distinct dynamic, the implementation level of these practice groups is currently different in the three countries analyzed. In the Netherlands, this practice was rapidly and noticeably established among GPs and Dutch CPs 2 . Thus, since 1995, almost all Dutch GPs and CPs (up to 95%) participate in these practice groups, which would represent more than 800 PTAMs in 2022 [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF] Van Mil | Pharmaceutical Care in Community Pharmacy: Practice and Research in the Netherlands[END_REF][START_REF] Teichert | How useful are prescribing indicators based on the DU90% method to distinguish the quality of prescribing between pharmacotherapy audit meetings with different levels of functioning?[END_REF] . In 2022, there are about one hundred QCs (which represent approximately 800 physicians and 100 pharmacists), established in Switzerland, but they are not not homogeneous throughout the country j 11 . Compared to the Netherlands, the participation of professionals in QCs is lower but the figures illustrate a growing and consolidated presence in certain cantons where this model has been established since its beginnings (for example Canton of Vaud) k11 . In Belgium, with only 386 local projects approved since 2015, while the budgets allocated to its financing were planned to support 800 local projects per year until the end of the year 2018, the development of CMPs seems modest [START_REF] Damiaens | General practitioners and community pharmacists' collaboration in primary care : small steps for a major change[END_REF] .

Moreover, this model seems to have different dynamics between the French and Dutch-speaking parts of the country with a more developed implantation on the Dutch-speaking side where the establishment of 322 local projects has been recorded since 2015, against respectively 48 and 16 in the French-speaking part and Brussels area.

f The preparation of the sessions depends on the topics and the tools available for their realization. These tools can be prescription data from GPs but also working materials (powerpoint, etc.) which are made available to meeting leaders, whether by IVM for PTAMs or by promoters of quality promotion programs whose programs have been previously validated by NIHDI for MPCs. g For the PTAMs, the quality level is classified into four levels. It is assessed by IVM using six criteria: number of PTAMs performed, average duration of meetings, joint preparation of CP and GP, use of prescription data, drafting of agreements on the choice of drugs, verification of adherence decisions made with prescription data [START_REF] Teichert | How useful are prescribing indicators based on the DU90% method to distinguish the quality of prescribing between pharmacotherapy audit meetings with different levels of functioning?[END_REF] . Not all groups are assessed annually. Some groups that operate at a higher level (Level 4) and are paid annually by certain health insurers, are only reviewed once every two or three years. h In order to be paid, each meeting leader pharmacist must meet several conditions such as leading at least 3 meetings per year, integrating GPs' prescription data, making an annual report, etc. i Not all higher level groups are paid. Only groups that have (a majority of) patients from certain health insurers are paid. j Indeed, after being introduced in a few cantons, this model has gradually spread throughout Switzerland, mainly within the Roman cantons but also within Italian and even German-speaking parts of Switzerland. In the German-speaking part, this practice is very little developed (less than 5 QCs), this can be explained by the existing competition between GPs and CPs within this region where GPs have also the right to dispense medication. k Indeed, most of the QCs are located in the French-speaking part of Switzerland, where in 2019 in the canton of Vaud, nearly a third of the QCs were counted (30 QCs including 228 physicians and 34 pharmacists) [START_REF] Herzig | Cercles de qualité : pour optimiser la prescription médicamenteuse et l'interprofessionnalité?[END_REF] .

2) Results in terms of prescriptions and pluriprofessional relationships

These practice groups have been evaluated using 3 main outcome criteria: the quality of drug prescription, its cost effectiveness and the collaboration between GPs and CPs.

2.1) Regarding the quality of drug prescription

Studies on the implementation of these three models have highlighted an overall positive effect of this practice on the quality and safety of drug prescription by the participating GPs, in particular in relation to the choice of drugs prescribed. These studies show that these practice groups have contributed to improving the quality of drug prescription for specific pharmacotherapeutic management, such as reducing the use of benzodiazepines or prescription antibiotics more appropriately for respiratory disorders in adults and adolescents (in the Netherlands) [START_REF] Vervloet | Reducing antibiotic prescriptions for respiratory tract infections in family practice: results of a cluster randomized controlled trial evaluating a multifaceted peer-group-based intervention[END_REF][START_REF] Nelissen-Vrancken | Minimale interventiestrategie voor stoppen met benzodiazepinen[END_REF] , or in managing cardiovascular diseases or diabetes (in Switzerland) [START_REF]Rédaction Prescrire. Cercles de qualité médecins-pharmaciens suisses : intérêt confirmé[END_REF][START_REF] Niquille | Impact des Cercles de qualité médecins pharmaciens pour la prescription médicamenteuse entre 1999 et 2010[END_REF] . Moreover, even if not all the studies are consensual concerning the correlation between the quality level of PTAMs and the quality of the prescription, it appears nevertheless that the PTAMs contribute globally to an improvement of the quality of drug prescription by the GPs involved, especially if the quality level of PTAM is high [START_REF] Teichert | How useful are prescribing indicators based on the DU90% method to distinguish the quality of prescribing between pharmacotherapy audit meetings with different levels of functioning?[END_REF][START_REF] Eimers | Leidt een goed FTO tot beter voorschrijven?[END_REF][START_REF] Florentinus | The Effect of Pharmacotherapy Audit Meetings on Early New Drug Prescribing by General Practitioners[END_REF][START_REF] Muijrers | Differences in prescribing between GPs: impact of the cooperation with pharmacists and impact of visits from pharmaceutical industry representatives[END_REF][START_REF] Kroneman | Netherlands : Health System Review[END_REF][START_REF] Meulepas | Relatie tussen FTO-niveau en score op voorschrijfindicatoren[END_REF] . Although the Belgian model has not been extensively studied on this issue, the only published study showed that this model has led, for some of these groups, to the elaboration of consensus, such as the notification of kidney function on prescriptions l 12 . However, although most of these groups did not consider tracking the effect of this consensus on practice, these results nonetheless show a first step that could contribute to an improvement in the quality of prescription of the participating GPs 12 .

2.2) Concerning to the cost effectiveness of the prescription

The most convincing results in terms of medico-economic efficiency, were highlighted by studies which evaluated the Swiss QC model. The last evaluation conducted between 1999 and 2010 noted that QCs contributed to a significant reduction in the cost of prescription with a 40% difference in annual drug costs per patient for physicians involved in QCs m [START_REF] Niquille | Impact des Cercles de qualité médecins pharmaciens pour la prescription médicamenteuse entre 1999 et 2010[END_REF] . In 2016, the savings made with the QCs were evaluated at 27 euros n for a patient followed by a physician member of a QC [START_REF] Philbet | Cercles de qualité médecins-pharmaciens. Déjà 20 ans, mais toujours aussi innovants[END_REF] . This represents a saving of 40 735 euros per physician per year. Extrapolating this figure to all GPs working in Switzerland ( around 21,000), the potential savings would be approximately 855 million euros per year [START_REF] Philbet | Cercles de qualité médecins-pharmaciens. Déjà 20 ans, mais toujours aussi innovants[END_REF] . A study financed by a fund for joint quality (pharmacists-insurers) is currently planned in Switzerland in particular to assess the effectiveness, economics and adequacy of QCs. In l The notification of kidney function on prescriptions was in particular part of one of the measures agreed between participants in order to inform the CP of the patient's kidney function during dispensing [START_REF] Damiaens | General practitioners and community pharmacists' collaboration in primary care : small steps for a major change[END_REF] . m This evaluation focused on the overall cost of expenses incurred per patient as well as those relating more specifically to five pharmacological classes from the category of cardiovascular drugs, in particular with regard to the level of generics and the choice of molecules [START_REF] Niquille | Impact des Cercles de qualité médecins pharmaciens pour la prescription médicamenteuse entre 1999 et 2010[END_REF] . n In this article, we have used the conversion of the beginning of the year 2022 which is 1 euro = 1.03 CHF to express the amounts mentioned in the Swiss evaluations.

the Netherlands, there are no large-scale studies demonstrating economic advantage from the creation of PTAMs. However, data indicates that the implementation of this model has allowed some territories to decrease their health expenditures, for example the city of Asten (about 16,000 inhabitants) where the expenditure for drugs in primary care was lower by 600,000 euros in 2018, than what would be expected for a community of the same size [START_REF] Stolk | Succesvol farmacotherapeutisch overleg leidt tot efficiënt voorschrijven[END_REF] .

2.3) Concerning the collaboration between physicians and pharmacists

The satisfaction of the professionals, meeting leaders or participants, has been demonstrated by various studies, particularly with regard to the improvement of the collaboration between the physicians and pharmacists who participated in these groups. These studies showed an increase in satisfaction and an enrichment for physicians and pharmacists who work together in this practice [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF] Philbet | Cercles de qualité médecins-pharmaciens. Déjà 20 ans, mais toujours aussi innovants[END_REF][START_REF] Damiaens | General practitioners and community pharmacists' collaboration in primary care : small steps for a major change[END_REF] . Thus, these studies have shown that this practice has contributed to improving their relationship through better mutual knowledge, a better understanding of the way in which tasks should be shared between them, as well as an enrichment of their professional practices [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF] Philbet | Cercles de qualité médecins-pharmaciens. Déjà 20 ans, mais toujours aussi innovants[END_REF][START_REF] Damiaens | General practitioners and community pharmacists' collaboration in primary care : small steps for a major change[END_REF] . CPs, for their part, mentionned that they were much more likely to contact a GP when they had a question [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF] . In a survey carried out in November 2017 in Switzerland, a large majority of the meeting leader pharmacists (84%) considered that it was worth setting up QCs because even if the investment in time was important, it allowed them to improve patient care (70%) while increasing collaboration with physicians (88%) [START_REF] Philbet | Cercles de qualité médecins-pharmaciens. Déjà 20 ans, mais toujours aussi innovants[END_REF] .

The evaluations carried out during the implementation of this practice with regard to these three models have led to positive results concerning these three criteria. However, each model has faced or is currently facing different challenges in terms of development or maintenance. These challenges may be specific, related to the particularities of each of these three healthcare systems, but they may also refer to the barriers (and levers) that any implementation of these practice groups might face.

3) Analysis and perspectives of generalization in other countries

The cross-analysis carried out between the dynamics encountered by these three models with their own characteristics and those of their implementation context allows us to identify the factors that may have facilitated or limited the implementation of these models, whether they are related to the individual practices of professionals or to the context of the country of establishment.

3.1) Barriers and levers associated with the individual practices of professionals

Whether it is the meeting leaders or the participants, various factors associated with the individual practices of these professionals can condition their adherence to this practice. These factors include the suitability of this practice to their needs and expectations, the integration of this practice into their respective availability, but also the consistency of this practice with their professional logic.

The response to the expectations and needs of the participating professionals, both in terms of enrichment of their practice and in terms of improving collaboration between physicians and pharmacists are factors that have allowed the implementation of these models, more particularly in the Netherlands and Switzerland 2,6 . Indeed, the constitution of groups integrating professionals from the same territory as well as dealing with topics related to the current practices of professionals or public health campaigns in the country has facilitated the implementation of this practice. However, depending on the anteriority of the model, the expectations of professionals seem to evolve. First, the participants seem to seek to improve communication with others professionals and exchange about medical information and their prescribing behaviour, then aim to implement effective measures within their respective practices [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF][START_REF] Damiaens | General practitioners and community pharmacists' collaboration in primary care : small steps for a major change[END_REF] .

On the other hand, the modalities of implementation of these models being different, both in terms of the frequency of the meetings and the preparatory methods, the availability of the professsionals may represent a limit to the integration of this practice. Indeed, while the contribution of the participants is rather modest because mainly represented by their simple participation in the meetings o , that of the meeting leaders is much more important p and may represent a limit to the implementation of this practice. The role played by the supporting structure is then all the more important in order to facilitate the setting up of meetings, notably by accompanying the meeting leaders, by the provision of various tools ( prescription data, working materials, training modules for meeting leader pharmacists, etc.) [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF]4,[START_REF] Bugnon | Cercles de qualité médecins-pharmaciens, pour une responsabilité partagée de la liberté de prescription[END_REF] . Moreover, the initial accompaniment of Dutch professionals by advisers attached to IVM, at the time of the establishment of the PTAMs, were measures that facilitated their establishment and could be one of the possible levers for the development of MPCs in Belgium if the same arrangements could be made [START_REF] Kocken | Medication discussion groups in the Netherlands : Five years of experience[END_REF] .

Furthermore, consistency between the involvement of professionals in this practice and the modalities put in place to recognize this involvement is another parameter which may encourage professionals to participate to this type of practice. Indeed, in the countries where the majority of these professionals are self employed, the recognition of their participation, whether financial or as a professional, is one of the factors that can facilitate their participation in this practice. So, although there was funding from o Regarding the participants of these 3 models, it is not generally expected that they perform work for the preparation of meetings which generally take place over a period of 2 hours. However, for PTAMs for example, depending on the topic, participants sometimes need to do homework that can vary from preparing prescribing data from their own information system, researching specific patients, collecting information materials to following an online training before the meeting. In addition, meeting leaders differ between meetings. So each participant prepares a meeting once in a while (pharmacists more often than GPs). p The preparation time for a session depends on the subject, the meeting leader and the preparation methods for the session (provision of prescription data, working materials, etc.). Thus, according to pharmaSuisse, it takes about 40 hours to prepare a QC meeting. For PTAMs, the results of a recent survey conducted by IVM in 2019 reported that the average preparation time was: 1-2 h (15%), 2-3 h (26%), 3-4 h (27%), >4h (30%). Although official information could not be provided by NIHDI on this subject, it would seem that the hourly volume associated with the preparation of a MPC is similar to that associated with the preparation of an PTAM meeting. health insurers at the beginning of the PTAMs q , the non-systematic funding of professionnals doesn't represent a totally limiting factor with regard of the current implementation of this practice in the Netherlands.

) Barriers and levers associated with the context of the country of implementation

The context within the country of implementation may also influence the setting up of this practice because of the type of the GPs and CPs practice, the healthcare and professional policies led in this country as well as the links between professionals and funders.

First, a primary health care organization such as the one in the Netherlands, in which the majority of GPs participate in peer groups, practice in group structures r and work with the expertise of the pharmacist, is a favorable context that can promote the implementation of this practice, explaining in part the rapid and significant implantation of PTAMs in the Netherlands [START_REF] Rohrbasser | Use of quality circles for primary care providers in 24 European countries : an online survey of European Society for Quality and Safety in family practice delegates[END_REF][START_REF] Van Mil | Pharmaceutical Care in Community Pharmacy: Practice and Research in the Netherlands[END_REF][START_REF] Bourgueil | Médecine de groupe en soins primaires dans six pays européens[END_REF] . On the other hand, the characteristics of the Belgian primary healthcare organization where most GPs still practice alone s and CPs do not contribute enough to new services as they use all of their expertise in patient care (medication review, service for asthma patients) represent a limiting context for the development of MPCs in spite of the development of coordinated exercise in this country [START_REF] Rohrbasser | Use of quality circles for primary care providers in 24 European countries : an online survey of European Society for Quality and Safety in family practice delegates[END_REF][START_REF] Bourgueil | Médecine de groupe en soins primaires dans six pays européens[END_REF][START_REF] Lelubre | Implementation study of an intermediate medication review in Belgian community pharmacies[END_REF][START_REF] Tommelein | Revue de la médication par le pharmacien d'officine en Belgique : pourquoi, comment et situation actuelle[END_REF][START_REF] Gordon | Coordination et intégration sont au centre des réformes[END_REF] . Thus, the collaboration between Belgian GPs and CPs seems not to be very developed, each profession seeming to want to free up time for its own activity to the detriment of the time available for this type of collaborative practice. Moreover, the observation of an implementation with opposite dynamics in different regions of the same country, as is the case in Switzerland and Belgium, may explain or suggest that differences in professional practices between regions (interprofessional practice, dispensing medication by GPs in German-speaking part of Switzerland, etc.) may condition the implementation of these practice groups in the same country.

The healthcare and professional policies that tend to define the place of the pharmacist and of their practice in primary health care are also parameters that may condition its implementation. Indeed, historically focused on the preparation and dispensing of drugs, the pharmacist's missions in all these countries have evolved towards the concept of pharmaceutical care which represents an activity more focused on pharmaceutical expertise towards the patients and the physicians. Thus, anteriority of the political measures taken to legislate this evolution as well as its effective evolution within these countries may have conditioned the implementation of these models, notably through a practice of pharmaceutical care much older and developed in the Netherlands than in Belgium [START_REF] Van Mil | Pharmaceutical Care in Community Pharmacy: Practice and Research in the Netherlands[END_REF][START_REF] Lelubre | Implementation study of an intermediate medication review in Belgian community pharmacies[END_REF] . In addition, the willingness of pharmaceutical professional organizations, such as pharmaSuisse, to promote this q In the early years of PTAMs, all participants received a financial incentive from health insurers to stimulate their participation. This incentive consisted of compensation in the form of a small fixed annual amount for each patient. r In the Netherlands, 90% of Dutch GPs work in medical practices or health centers [START_REF] Rohrbasser | Use of quality circles for primary care providers in 24 European countries : an online survey of European Society for Quality and Safety in family practice delegates[END_REF] . s Despite the evolution of the mode of practice of Belgian GPs, the majority of Belgian GPs still practice in a solo exercise (60% in 2015 versus 70% in 2007) 1,22 . practice in Switzerland by its development and a rigorous evaluation, has allowed this practice to be recognized by politicians and funders and to be integrated into Swiss policies, using the expertise of pharmacists in the search for efficiency in its healthcare system. In Belgium, the support of professional institutions such as the SSPF for the preparation and the animation of meetings, the development of the financing of MPCs by the NIHDI and the recent legislation governing their implementation (2015), are also measures that illustrate the professional and political willingness to develop this model in Belgium [START_REF]03 avril 2015 fixant les conditions et les modalités de la mise en oeuvre de la concertation médico-pharmaceutique[END_REF][START_REF]Projets locaux. Les "projets CMP[END_REF] . However, the non-systematic provision of prescription data during these meetings, which makes it difficult to measure the impact of CMPs, and the fact that priority is given more to exchanges between physicians and pharmacists rather than to the expected results, seem to lead to a less ambitious policy orientation towards this practice in Belgium. In the Netherlands, public policies have accompanied the development of PTAMs and still consider PTAMs as an important tool for optimizing drug therapy. So, the government still finances the development of independent working materials to which the Dutch College of General Practitioners and the Royal Dutch Pharmacists Association contribute. These professional institutions promote PTAMs because they see PTAMs as an important tool for the implementation of their guidelines (concerning pharmacotherapy) and as an implementation tool for successful interventions in primary care. In addition, PTAMs are also part of the training program for pharmacy students and to a lesser extent for medical students in general practice (depending on the university).

As mentioned previously, the funding of professionals who participate in practice groups is a parameter that can facilitate their implementation. However, the relationship between funders and professionals, depending on the nature of the funder, may be able to condition the implementation of this practice within a healthcare organization. Indeed, depending on the country, the financing of professionals for their practice can be undertaken by a state organization (as in France for example) or entrusted to health insurers, as is the case for the three countries we are studying. However, based on these three examples, the nature of the funder does not seem to lead to the same objectives and the same issues for professionals. Indeed, the remuneration of professionals by health insurers for their contribution to practice groups has contributed to introduce financial incentives for professionals in return for more selective measures. The remuneration of participants in some higher-level PTAMs as well as that of meeting leader pharmacists who fulfill the pre-established conditions are examples of this. This negotiation relationship between health insurers and professionals requires pharmaSuisse to assess the medico-economic efficiency of the QCs practice in Switzerland in order to negotiate the remuneration of meeting leader pharmacists and to make the model sustainable. These negotiations are all the more difficult as pharmaSuisse is currently encountering difficulties in obtaining good quality medico-economic data, that can be easily manipulated and discussed by the QCs. On the other hand, the financing of this practice by a public body responsible for the general management and control of healthcare insurance through the NIHDI in Belgium, has led to the implementation of strategies intended to be less intrusive and more incentive based for all professionals, as is the case with the funding of local projects with less significant counterparties than the previous examples. These examples underline that the relationship between funders and professionals is a parameter that can influence the implementation of this practice because it will not generate the same objectives and the same issues for professionals.

3.3) Perspectives of generalization to other countries

The impact of drug expenditure and the proper use of drugs are important issues in many developed countries. In addition, healthcare organizations in most countries are currently moving towards an increasingly coordinated exercise. Thus, as illustrated above, this type of practice, through its effects on the quality of drug prescription, cost effectiveness and collaboration between physicians and pharmacists, represents a potential for these healthcare organizations to respond to these different challenges. However, this practice cannot be generalized without taking into account the specificities of each country beforehand. Indeed, multiple factors associated to individuals' professional practices such as how this practice answers their needs, their availability and their professional logic, as well as those related to the context of country, such as the mode of practice of professionals, health and professional policies and the links between professionals and funders, can condition the implementation of this type of practice. Thus, a generalization of this model to other countries is entirely appropriate, but these considerations must be taken into account because they can represent both levers and barriers to the implementation of this type of practice. Thus, before considering a larger scale implementation in other country, setting up an experiment, which was the case recently in France, is an essential step in order to analyze the appropriateness of the model implemented and the specific limits of the healthcare organization in order to facilitate its further development [START_REF] Macé | Les cercles de qualité médecins-pharmaciens, un mode de collaboration vertueux expérimenté en France[END_REF] .

Conclusion

Through this analysis, we can say that group practices between GPs and CPs have been established with different modalities and dynamics in the three countries we have just studied. We can emphasize that this practice has been implemented successfully more particularly in the Netherlands and Switzerland where we can see an important or increasing participation of GPs and CPs. However, although the modalities which contributed to the implementation of these models present similarities but also differences, the general results of this practice have been positive, particularly in terms of quality of drug prescription, cost effectiveness and improving physician-pharmacist collaboration. Despite these encouraging results, various parameters associated to the individual practices of professionals or the context of the country are likely to condition its implementation. Thus, before considering a generalization of this practice in other countries, all these considerations must be taken into account in order to facilitate its implementation.

Acknowledgements

The authors gratefully acknowledge IVM, NIHDI and the INNOVATION department of pharmaSuisse for providing information and data on the three respective practice group models.

Funding This work was supported by a French Government grant managed by the French National Research Agency under the program Investissements d'Avenir (reference ANR-11-LABX-0021-01-LipSTIC Labex») and by grants from the Conseil Régional de Bourgogne-Franche-Comté and the Fonds Europeen de Developpement Regional. The French Institute for Public Health Research (IReSP) and the Unity of Continuing Professional Development in Healtcare from the University of Burgundy (UMDPCS) also supported this work.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Belgium The Netherlands Switzeralnd

Profession of meeting leaders

General practioners (GP), Community Pharmacists (CP)

General practioners, Community Pharmacists

Community Pharmacists

Profession of participants

GPs, CPs and even hospital physicians and pharmacists GPs, CPs and even hospital practitioners Depending on the subject, participants can be for instance also practice nurses, specialists geriatric medicine, district nurses.

GPs, CPs and even physician specialists in internal medicine and pediatricians

Average number of participants

We do not have precise data but we can suggest 2 to 3 CPs and 5 to 15 GPs

Topic discussed

Topics based on quality promotion programs validated by the NIHDI Free choice of subjects, although most PTAMs groups choose topics that are related to new/renewed guidelines of the profession.

Topics on the themes of the training modules, whose the number of these is significant

Average frequency of meetings

No fixed frequency 4 to 6 per year 3 to 4 per year

Duration of meetings

Professional recognition

For GPs and CPs For GPs and CPs For GPs and CPs