Eleni Nisioti
email: eleni.nisioti@inria.fr

Clément Moulin-Frier

Dynamics of niche construction in adaptable populations evolving in diverse environments

In both natural and artificial studies, evolution is often seen as synonymous to natural selection. Individuals evolve under pressures set by environments that are either reset or do not carry over significant changes from previous generations. Thus, niche construction (NC), the reciprocal process to natural selection where individuals incur inheritable changes to their environment, is ignored. Arguably due to this lack of study, the dynamics of NC are today little understood, especially in real-world settings. In this work, we study NC in simulation environments that consist of multiple, diverse niches and populations that evolve their plasticity, evolvability and niche-constructing behaviors. Our empirical analysis reveals many interesting dynamics, with populations experiencing mass extinctions, arms races and oscillations 1 . To understand these behaviors, we analyze the interaction between NC and adaptability and the effect of NC on the population's genomic diversity and dispersal, observing that NC diversifies niches. Our study suggests that complexifying the simulation environments studying NC, by considering multiple and diverse niches, is necessary for understanding its dynamics and can lend testable hypotheses to future studies of both natural and artificial systems.

Introduction

Biological organisms and their environments share a reciprocal relationship: organisms survive and reproduce under selection pressures present in their habitats and environments are modified by their inhabitants, with changes being inherited to the next generation and accumulating with evolutionary time [START_REF] Odling-Smee | Niche Construction: The Neglected Process in Evolution (MPB-37[END_REF]. The first process, natural selection, became the cornerstone of evolutionary theory in the early 20th century [START_REF] Provine | The Origins of Theoretical Population Genetics: With a New Afterword[END_REF] and, in both natural and artificial life studies, is often seen as synonymous to evolution. The second, niche construction (NC), was characterized as the neglected process in evolution in the early 2000s [START_REF] Odling-Smee | Niche Construction: The Neglected Process in Evolution (MPB-37[END_REF], as evolutionary theory assumed that NC's effect on selection pressures is negligible. Since then, studies of natural populations have shown that NC often affects selection pressures by helping species protect themselves from environmental uncertainty and accelerates evolution by complexifying environments [START_REF] Odling-Smee | Niche Construction: The Neglected Process in Evolution (MPB-37[END_REF][START_REF] Schwilk | Flammability Is a Niche Construction Trait: Canopy Architecture Affects Fire Intensity[END_REF][START_REF] Boivin | Ecological consequences of human niche construction: Examining long-term anthropogenic shaping of global species distributions[END_REF]. By now, NC is, at best, the elephant in the room of evolutionary synthesis: despite evidence for its existence, our understanding of it is too limited to enable its study in settings capturing the complexity of the real world.

Recent hypotheses studying major events in evolution point to environmental complexity [START_REF] Maslin | A synthesis of the theories and concepts of early human evolution[END_REF][START_REF] Potts | Hominin evolution in settings of strong environmental variability[END_REF]d'Errico et al., 2017). For example, the birth of our own lineage in East Africa occurred amidst large climatic instability that fragmented the landscape into patches of land differing in resource availability and separated by large lakes [START_REF] Maslin | East African climate pulses and early human evolution[END_REF]. Other hypotheses further emphasize the ability of natural landmarks such as deserts and oceans to form barriers that isolate populations [START_REF] Larrasoaña | Dynamics of Green Sahara Periods and Their Role in Hominin Evolution[END_REF]. A similar story is unfolding in artificial life: under Quality-Diversity optimization [START_REF] Pugh | Quality Diversity: A New Frontier for Evolutionary Computation[END_REF], the search space is divided into behavioral niches to evolve diverse solutions, a paradigm that challenged the dominant approach of training a single agent, as it proved more robust in real-world settings [START_REF] Cully | Robots that can adapt like animals[END_REF].

When in a heterogeneous environment, organisms can survive by: a) specializing in a niche to out-compete others, paying the cost that they are out-competed in other niches Nisioti and Moulin-Frier (2022); [START_REF] Grove | Evolution and dispersal under climatic instability: A simple evolutionary algorithm[END_REF] b) becoming phenotypically plastic: a plastic individual adapts its phenotype to its environment without genetic change and survive in diverse niches within its lifetime. On the downside, plasticity comes with fitness costs, so that plastic individuals are out-competed by specialists in their preferred niche [START_REF] Grove | Evolution and dispersal under climatic instability: A simple evolutionary algorithm[END_REF]Nisioti and Moulin-Frier, 2022) c) becoming highly evolvable: a high mutation rate enables quick adaptation at an evolutionary scale but comes at the cost of increased deleterious mutations [START_REF] Lynch | Genetic drift, selection and the evolution of the mutation rate[END_REF]Nisioti and Moulin-Frier, 2022). As both plasticity and evolvability enable adaptation we jointly refer to them as adaptability.

Although limited, our understanding of NC shows that it is influenced both by the adaptability of populations and the diversity of environments. For example, processes such as the invention of agriculture [START_REF] Zohari | The Origin and Early Spread of Agriculture in the Old World[END_REF] and cultural innovation [START_REF] Mesoudi | What is cumulative cultural evolution[END_REF] are both influenced by geography and our impressive social learning abilities [START_REF] Diamond | Guns, Germs, and Steel: the Fates of Human Societies[END_REF][START_REF] Migliano | Huntergatherer multilevel sociality accelerates cumulative cultural evolution[END_REF][START_REF] Migliano | The origins of human cumulative culture: From the foraging niche to collective intelligence[END_REF]. Explanations for this rely on the inter-play between a population's connectivity and its ability to accumulate solutions: spatial heterogeneity enforces isolation and, therefore, diversity within a population, while adaptability ensures that environmental barriers can be crossed and solutions spread, causing an intensification of NC [START_REF] Cantor | The interplay between social networks and culture: Theoretically and among whales and dolphins[END_REF][START_REF] Derex | Partial connectivity increases cultural accumulation within groups[END_REF]Nisioti et al., 2022).

In this work, we study the evolution of NC in environments divided in diverse niches where populations evolve their adaptability and niche-constructing behavior. Each niche is characterized by its environmental state, which determines how many agents it can fit, and consists of two components: the intrinsic state (which can for example model climatic variations uncontrollable by the agents) and the niche-constructed state, which is the product of nicheconstructing individuals inhabiting the niche. The nicheconstructed state is also inherited from the previous generation with some decaying applied to capture the fact that ecologically-inherited artifacts cannot persist indefinitely. Modeling NC as a process that changes the capacity of the environment is common [START_REF] Laland | Evolutionary consequences of niche construction and their implications for ecology[END_REF][START_REF] Krakauer | Diversity, Dilemmas, and Monopolies of Niche Construction[END_REF] and finds inspiration in natural behaviors, such as nest-constructing species. Genomes consist of four genes: preferred environmental state (the state at which their fitness is highest), plasticity (the variance in environmental state they can tolerate without a large impact on fitness), evolvability (the mutation rate) and niche construction (the amount by which they change the environmental state of a niche they inhabit). We consider two different mechanisms for selecting which agents will reproduce: a) under global competition we select them with a probability proportional to their average fitness across the niches they can survive in and reproduction stops when the environment's capacity is reached b) under local competition we consider reproduction in each niche independently: an agent is selected based on its fitness in each niche and reproduction stops when the capacity of that niche is filled. Thus, agents benefit from surviving in multiple niches. Our models of local and global competition have their equivalents both in previous studies in evolutionary computation (with Quality-Diversity algorithms representing local competition and classical algorithms global) and in the study of natural populations (where local adaptation considers that populations of the same species inhabiting different niches experience different natural selection pressures [START_REF] Leimu | A Meta-Analysis of Local Adaptation in Plants[END_REF]).

An agent may benefit from NC by: a) increasing the capacity of a niche, for example through nest-building, thus, reducing competition for resources b) reducing the capacity of a niche thus making it less desirable to others. This behavior, which we refer to as negative niche construction, is exemplified in nature by pines, which spread their needles to increase the probability of fire and out-compete not fire-resistant species [START_REF] Schwilk | Flammability Is a Niche Construction Trait: Canopy Architecture Affects Fire Intensity[END_REF] c) bringinf the environmental state closer to its preferred niche and further away from others For example, aquatic earthworms can inhabit earth soil only by changing its consistency [START_REF] Turner | The extended organism[END_REF]. But NC also comes at a cost: a) increasing the capacity of a niche may invite other species in and increase competition b) decreasing its capacity may make it uninhabitable c) changing the environmental state will require adaptability, which comes at its own cost d) multiple agents coinhabiting a niche can create high environmental uncertainty that can lead to mass extinctions if adaptability cannot increase enough to respond to it, a case that feels most relevant to our own evolution [START_REF] Boivin | Ecological consequences of human niche construction: Examining long-term anthropogenic shaping of global species distributions[END_REF][START_REF] West | Scale[END_REF].

Taking into account these complex interactions between environmental heterogeneity, population adaptability and niche construction, we believe that studies of NC should depart from simplified settings with a single niche [START_REF] Laland | Evolutionary consequences of niche construction and their implications for ecology[END_REF][START_REF] Suzuki | Effects of Temporal Locality of Ecological Processes on Coevolution of Learning and Niche Construction[END_REF][START_REF] Chiba | Evolution of Complex Niche-Constructing Behaviors and Ecological Inheritance of Adaptive Structures in a Physically Grounded Environment[END_REF] and non-plastic populations [START_REF] Laland | Evolutionary consequences of niche construction and their implications for ecology[END_REF][START_REF] Krakauer | Diversity, Dilemmas, and Monopolies of Niche Construction[END_REF]. As we show in this work, rich models can offer interesting hypotheses about the dynamics of NC, such as that:

• having multiple niches is necessary for avoiding mass extinctions. We observed that, in a single niche, environmental uncertainty induced by NC becomes too high for adaptability to cope with;

• NC promotes adaptability and populations adapt differently depending on the selection mechanism: under global competition NC leads to higher plasticity while under local to higher evolvability;

• the population may niche-construct negatively for prolonged periods of time, making niches uninhabitable. Agents deal with this by evacuating the niche until it becomes inhabitable due to the decay of NC;

• under local competition NC increases genomic and environmental diversity

Related works

Previous studies have primarily modeled NC in two different ways: as an increase in the amount of resources that increases the environment's capacity [START_REF] Laland | Evolutionary consequences of niche construction and their implications for ecology[END_REF][START_REF] Krakauer | Diversity, Dilemmas, and Monopolies of Niche Construction[END_REF] and as a direct increase or decrease in fitness that does not affect capacity [START_REF] Suzuki | Effects of Temporal Locality of Ecological Processes on Coevolution of Learning and Niche Construction[END_REF]. We follow the first approach but also allow reductions in capacity. NC studies were at first primarily theoretical, employing differential equations to predict how NC affects evolution [START_REF] Laland | Evolutionary consequences of niche construction and their implications for ecology[END_REF][START_REF] Krakauer | Diversity, Dilemmas, and Monopolies of Niche Construction[END_REF]. Such models lent intuitive insights, such that NC can emerge without direct selection [START_REF] Laland | Evolutionary consequences of niche construction and their implications for ecology[END_REF] and that the ability to monopolize niches enables the emergence of NC [START_REF] Krakauer | Diversity, Dilemmas, and Monopolies of Niche Construction[END_REF] but come with limitations, such as the fact that niches are identical and agents are not plastic. [START_REF] Suzuki | Effects of Temporal Locality of Ecological Processes on Coevolution of Learning and Niche Construction[END_REF] study the co-evolution of plasticity and NC in an agent-based model and show that populations alternate between phases of high plasticity and NC, provided that agents niche-construct sequentially. This model differs from ours as the environment consists of a single niche, NC does not modify its capacity and evolvability is constant. Interestingly, when [START_REF] Suzuki | Effects of Temporal Locality of Ecological Processes on Coevolution of Learning and Niche Construction[END_REF] applied NC in parallel these patterns disappeared due to agents canceling out each other's behavior. Instead, the patterns in our analysis occur with NC applied in parallel. As we show, this becomes possible due to the presence of multiple niches that stabilize NC. Nisioti and Moulin-Frier ( 2022) studie the co-evolution of plasticity and evolvability in an environment with multiple niches, but do not consider NC.

Recent advents in deep reinforcement learning (DRL) and neuroevolution have enabled the study of complex behaviors in simulations, such as foraging and tool-use [START_REF] Pérolat | A multi-agent reinforcement learning model of common-pool resource appropriation[END_REF][START_REF] Hamon | Ecoevolutionary Dynamics of Non-episodic Neuroevolution in Large Multi-agent Environments[END_REF][START_REF] Baker | Emergent Tool Use From Multi-Agent Autocurricula[END_REF]. [START_REF] Chiba | Evolution of Complex Niche-Constructing Behaviors and Ecological Inheritance of Adaptive Structures in a Physically Grounded Environment[END_REF] leverage such techniques to study NC in a 2D environment where agents can construct artifacts useful for avoiding predation. Our study can lend insights to this direction, as we can view DRL as the mechanism that underlies the behavioral plasticity considered in our model.

Modeling and methodology

We now separately discuss our model of the environment and genomes, the evolutionary algorithm and the set of metrics we use to monitor evolution.

Modeling the environment

The environment, illustrated in Figure 1, is divided into N niches arranged in a simple latitudinal model: we consider a reference niche at n = 0, N/2 "northern" niches indicated with positive indexes n ∈ (0, N/2] and N/2 -1 "southern" niches with negative indexes n ∈ (-N/2, 0) . Each niche is characterized by its environmental state e g n which is the sum of two elements:

• an intrinsic state i n that remains constant with evolutionary time and depends on the location of the niche. Specifically, the state of niche n at generation g is i n = i 0 +ϵ•n, where i 0 is the state of the reference niche and ϵ is a constant capturing the difference between adjacent niches.

• the niche-constructed state b g n , capturing the modifications that agents inhabiting the niche cause. These modifications are carried over generations but are discounted by a factor γ. Formally, the niche-constructed state b g n of niche n is equal to b g-1 n

• γ, with γ < 1, plus the total amount of NC applied by all agents that reproduced in this niche in generation g. We denote this latter amount as k∈Kn a g k , where K n is the subset of all agents that reproduced in niche n and a g k is the amount of niche construction by a single agent (we later explain how agents niche-construct).

Thus, the general equation describing the evolution of niche n with generations g is:

b g n = b g-1 n • γ + k∈Kn a g k e g n = i 0 + ϵ • n + b g n (1)
As we explain later, the environmental state determines the fitness of an agent based on its genome and the capacity of the niche c g n as: c g n = e g n C N , where C N is the reference niche capacity. Thus, higher environmental states can support larger populations and are termed "high-quality". To ensure that the maximum population size is independent of the number of niches we define C N = C ref /N , where C ref is equal to the desirable maximum population size. An assumption of this model is that there is spatial smoothness, i.e, nearby niches are similar. Note that C ref is independent of niche-constructing behavior: by niche-constructing the population can exceed this capacity. We, therefore, further bound the population size by randomly discarding agents if the population exceeds a value K max .

Modeling the genome

We model plasticity through tolerance curves, a tool developed in ecology [START_REF] Lynch | Environmental tolerance[END_REF] and previously employed in simulation environments [START_REF] Grove | Evolution and dispersal under climatic instability: A simple evolutionary algorithm[END_REF]Nisioti and Moulin-Frier, 2022). A tolerance curve is a normal distribution with mean µ g k , indicating the environmental state of highest fitness for an individual k at generation g, called the preferred state, and standard deviation σ g k that captures how quickly the fitness of the genome drops as the environmental state varies from its preferred state. Genomes with large σ g k are indicative of plastic individuals (we illustrate the tolerance curves of a plastic and a non-plastic individual in Figure 2).

To model niche construction we introduce a nicheconstructing gene a k ∈ [-N/K max , N/K max ] where we bound the amount an agent can niche-construct to ensure that agents inhabiting large environments have limited capabilities. The niche-constructing gene is expressed in the niche an agent reproduces in by modifying its environmental state. Thus, at each generation, niche n is constructed by an amount k∈Kn a k , where K n denotes the subset of agents that reproduced in it. The genome o g k also includes the mutation rate r g k . Thus the complete form of a genome is

o g k = [µ g k , σ g k , r g k , a g k ]
and, upon reproduction, it mutates as:

µ g+1 k = µ g k + N (0, r g k ) σ g+1 k = σ g k + N (0, r g k ) a g+1 k = [c g k + N (0, r a )] N/Kmax -N/Kmax r g+1 k = r g k + N (0, r g k ) (2)
where N (x, y) denotes a normal distribution with mean x and variance y and we have highlighted that the niche-constructing gene is bounded. Note also that, for stability reasons, we employ a different mutation rate for the nicheconstructing gene, r a , that remains constant.

Global and local selection

At the end of a generation agents are selected for crossover based on their fitness. Each chosen individual has two offspring and the next generation consists only of offspring. To compute the fitness of an individual k in generation g we first detect the niches in which it can survive as:

n ∈ {1, • • • , N } | e g n ∈ [µ g k -2σ g k , µ g k + 2σ g k ] (3)
and compute its fitness in each one of them as

f g k,n = pdf (µ g k , σ g k , e g n )
, where pdf denotes the value of the normal probability density function with mean µ g k , and variance σ g k at location e g n . We study two selection mechanisms:

• under global selection all agents in the population are ranked based on their average fitness across the niches they can survive in and reproduce with a probability proportional to it. Agents reproduce until the capacity of the environment is filled.

• under local selection we apply the same criterion but independently for each niche: we detect which agents survive in a niche and reproduce them with a probability proportional to their fitness. Thus, agents that can survive in multiple niches have higher chances of reproduction under this mechanism. Again, agents reproduce in a niche until its capacity is filled.

Thus, at the end of a generation a new population is formed that consists of the offspring of agents from the previous population that were chosen for reproduction, based on their fitness and the environment's capacity. Note that the niche is not inherited from parent to offspring: the offspring will inhabit the niches its genome describes (as in Eq. 3). We present the pseudocode of our algorithm in Algorithm 1 and 2, provided in our online repo due to limited space.

Metrics

In addition to population-wide averages of the genome values and environment-wide averages of the intrinsic and niche-constructed states we monitor the following metrics:

1. X g = k X g k , the number of extinctions. We denote the survival of individual k in niche n at generation g as a binary variable:

s g k,n = (e n,g ∈ [µ g k -2σ g k , µ g k + 2σ g k ]) (4)
Thus, an individual goes extinct (X 2. V g µ , the diversity of the population defined as the standard deviation of the population's preferred state, namely

V g µ = σ µ g (5)
This metric captures the genetic diversity of the population computed for the gene of preferred state.

3. D g , the dispersal of the population, computed as the number of niches over which at least one individual survives for a temporal window of at least w generations. Formally,

D g = N n=1 d g n,w
, where d g n,w denotes the persistence of the population in a given niche for the required time window and is computed as

d g n,w = 1 if g g ′ =g-w s g ′ n = w 0 otherwise (6)
where s g n is indicates the survival of at least one individual in a given niche and is computed as

s g n = 1 if K k s g k,n > 1 0 otherwise (7)
with s g k,n defined in Eq. ( 4). 4. H g , the competition for reproduction within the population. We count, for each niche, the number of agents that survived in it and were fit enough to be chosen for reproduction but did not reproduce because its capacity was reached and, then, sum over all niches.

Results

We now examine the behavior of agents under different settings. First, we compare behaviors under global competition between environments with different number of niches. After, we consider only heterogeneous environments (N = 100) niches and we contrast the behavior across two dimensions: a) whether NC takes place or not (where we force all niche-constructing genes to be zero) and b) whether selection is local or global. In all simulations we set the discount factor γ to 0.5, the intrinsic state of the reference niche i 0 to 0.6, ϵ (the difference between adjacent niches) to 0.01, the reference capacity to C ref = 1000, the maximum population size to K max = 5000 and the mutation rate of the niche-constructing gene, r c , to 0.0003. As we discuss later it would be interesting to study the effect of some of these hyper-parameters. For this study we note that the values of ref , K max where chosen to limit computational complexity, increasing them further should not qualitatively change our conclusions. Also regarding r c , setting it to too low a value will disable NC and setting it too high may destabilize NC. We performed ten independent trials and present in plots median values and 95% confidence intervals. When studying niche-constructing behaviors we do not average across trials but present them individually, as differences would average out and conceal information.

Spatial heterogeneity stabilizes niche construction

In Figure 3 we compare the behavior under global competition for different number of niches (N ∈ {1, 50, 100} for a single trial. We observe that, for N = 1, the agents are niche-constructing positively (third row), which pushes the environment state to higher values and more variability (first row). We see that the the population reacts by adapting its preferred niche (second row), increasing its plasticity (fourth row) and keeping its evolvability high (fifth row). Despite that, the population goes extinct around generation 250, after experiencing many booms and busts (sixth row). This behavior was consistent across all trials for N = 1, with half of the trials experiencing a mass extinction due to negative NC and half due to positive NC (as in Figure 3).

In the heterogeneous environments, on the other hand, the population survives for the whole simulation. We see that the average NC among agents (E(a)) is similar to that of the homogeneous environment but that this leads to less niche construction in the environment (evident through the environmental state). This is because the population in the heterogeneous environment spreads over multiple niches and often migrates collectively out of a niche (we will take a look at this behavior in the next section), leading to a decrease to the accumulation of NC due to its discounting. In contrast, when N = 1 NC accumulates in a single niche. We also observe that NC in N = 100 does not increase continuously but experiences oscillations, which suggests that some agents are niche-constructing negatively or reducing their positive NC. As a result, the environment experiences lower oscillations which enables the population to reduce its evolvability. Plasticity remains relatively high but much lower than in the homogeneous environment. We also mea- sured the number of mass extinctions for environments with different number of niches and observed that even a small number of niches is useful and increasing the number of niches continuously decreases the probability of extinction (10/10 went extinct for N = 1, 4/10 for 20, 3/10 for 50 and 2/10 for 100). Thus, the presence of multiple niches was necessary for the survival of the niche-constructing population. Next, we will look into how adaptability interacts with NC to give rise to this behavior. As we hypothesize that the presence of niches matters, we will focus on how agents disperse and niche-construct differently in different niches.

Niche construction promotes adaptability

We now compare a niche-constructing population (denoted as R N C ) and a population that cannot niche -construct (R).

We examine populations under global selection in Figure 4 and under local selection in Figure 5. We observe that both populations increase their adaptability but do so differently. Under global selection, the R N C population increases its plasticity but keeps its evolvability low. Dispersal is a bit higher and genomic diversity is initially high but, by the middle of the simulation, reaches the low level of the R population. We also see that R N C has a smaller population size early in the simulation. As extinctions are low, this is due to NC reducing the capacity of the environment. Near the end of the simulation we see that R N C reaches and, in some trials, surpasses the size of the R population. This indicates that positive NC has increased the environment's capacity. Under local selection R N C has very high evolvability but plasticity is at similar level to R. We observe that some extinctions persist throughout evolution but the population size is relatively stable. Why did the niche-constructing population prefer to adapt through evolvability rather than plasticity? As we will see more closely in our analysis of specific trials, agents in a niche-constructing population manage to coordinate their NC behavior within a niche. This would not have been possible under high plasticity, as agents would stochastically niche-construct in different niches and increase environmental uncertainty.

Niche construction can cause an arms race

In Figure 6 we analyze one of the trials for the nicheconstructing population under global competition through heatmaps that show the amount of NC at each generation and niche. Populations are initialized with diverse genomes, so that at the beginning they are dispersed in all niches. Then, global competition leads to a decrease in plasticity and quickly wipes out the diversity of the population, gathering all agents in the same narrow stripe of niches. Around generation 50, the population starts positively niche-constructing in the middle niche, then starts moving to the north and, once it reaches the end of the environment (around generation 150), stays there and oscillates between phases of positive and negative NC. On the top plot, we see that this population has adapted its preferred state to the last niche and that as soon it reaches it, plasticity stops decreasing and the population size stops increasing. The trial depicted in Figure 6 is representative of 4 out of the 10 trials. In another five trials the same pattern occured, but in the south instead of the north. In contrast, we observed that populations without NC do not gather at the edge of the environment but stay in a random niche near the center. Thus, NC under global competition leads to a "geographic" arms race due to the following dynamics: once the agents have been gathered to a narrow stripe of niches, they begin niche-constructing, initially randomly. Then, NC will, by random chance become slightly positive or negative. As all agents are competing in the same niche, this will force them to adapt their preferred state towards the direction that the sum of agents is constructing to. This enables inhabiting the adjacent niche, where the agents will niche-construct towards the same direction. Eventually, the population will reach the end of the environment. Why doesn't the population continue increasing its niche construction to the same direction instead of experiencing cycles? We believe that this is not possible as the mutation rate is low and, therefore, the preferred niche cannot be adapted anymore.

Negative niche construction reduces competition

In Figure 7 we analyze another trial for the nicheconstructing population under global competition, where a different behavior emerged: the population niche-constructs negatively, which pushes it to the low-index niches. There we see an interesting pattern: the population is gathered in a narrow stripe of niches where it niche-constructs negatively and with increasing intensity. Then the population leaves this stripe and moves to the adjacent northern and southern niches. This is possible due to the maintained plasticity and does not require an adaptation of the preferred niche. Then, the same behavior happens until the population moves back to the previous stripe and we see many cycles of moving back and forth. This switching behavior is caused by the fact that, once the population niche constructs negatively in a niche for some time, then this niche becomes uninhabitable, so that the population needs to move out until it becomes inhabitable again. Eventually, some positive NC happens, which leads to an extinction, as evolvability is too low to enable adaptation. This indicates that negative niche construction is not stable in the long-term.

Niche construction diversifies the environment

We now move to local selection, where we saw in Figure 5 that NC leads to a more evolvable population. In Figure 8, we analyze a typical trial where we see that NC is positive and high in northern niches and negative in more southern niches. Thus, the majority lives in the north (this can be inferred from the preferred state E(µ) = 0.8 surpassing the state of the reference niche i 0 = 0.6). The population experiences many changes, with niches often switching between being positively and negatively niche-constructed. We also measured the variance of NC within a niche and found that it is two orders of magnitude smaller than the one under global selection. This suggests that local selection enables agents to coordinate their niche construction within a niche, which diversifies the environment and leads to the higher genomic diversity observed in Figure 5.

An intriguing question is why populations under global selection adapt by increasing their evolvability but keep their plasticity at even lower levels than without NC. We believe that this is due to the interplay between NC and plasticity: very plastic agents could niche-construct in many niches, which would make it difficult to maintain low variance in NC within a niche. By monopolizing a limited number of niches and quickly changing niche through mutations these populations can better coordinate their NC.

Discussion

We have shown that the evolution of niche construction is contingent on the number of niches in the environment and the selection mechanism. We explained this by looking into the interplay between adaptability and NC, in particular their effect on the population's and environment's diversity and dispersal patterns. Populations are impressive in their ability to self-regulate themselves: NC remains bounded, even though we do not introduce an explicit cost for it. Populations fail to coordinate their NC and go extinct only when the environment has a single niche.

Our empirical study could be extended in multiple ways. First, we could study the effect of additional hyperparameters. For example, we could allow the intrinsic state to vary with time, following a noisy or periodic signal (Nisioti and Moulin-Frier, 2022). We could also consider that NC is plastic: currently an agent's gene determines its NC independently of the environmental state while we could imagine scenarios where agents niche-construct differently for different states. Finally, we believe that our empirical observations should be tested in grounded environments with RL agents, such as grid-worlds where a population forages or avoids predation [START_REF] Hamon | Ecoevolutionary Dynamics of Non-episodic Neuroevolution in Large Multi-agent Environments[END_REF][START_REF] Chiba | Evolution of Complex Niche-Constructing Behaviors and Ecological Inheritance of Adaptive Structures in a Physically Grounded Environment[END_REF].

We hope that our work will contribute towards incorporating NC in future studies of collective adaptation. We think this is particularly relevant for the Artificial Intelligence community, which recently focused on agents that can generalize to diverse environments, the importance of environmental complexity and multi-agent dynamics [START_REF] Reed | A generalist agent[END_REF][START_REF] Jaderberg | Open-Ended learning leads to Generally Capable Agents[END_REF][START_REF] Nisioti | Grounding an Ecological Theory of Artificial Intelligence in Human Evolution[END_REF][START_REF] Moulin-Frier | The Ecology of Open-Ended Skill Acquisition[END_REF]. As we show here, niche construction, which can be seen as a meta-learning mechanism [START_REF] Constant | A variational approach to niche construction[END_REF], can prove promising in complexifying environments and population dynamics and bring us closer to artificial agents with behaviors reminiscent of natural ones.

Figure 1 :

 1 Figure1: Our model of the environment: each niche n is characterized by its environmental state e g n which is the sum of the intrinsic state i n (in blue) and the niche-constructed state b g n (in red). i n depends on the state of the reference niche (e 0 ), the offset ϵ and n. b g n is the sum of the nicheconstructed state at the previous generation discounted by γ plus the sum of the niche-constructing behavior of agents that reproduced in this niche in the current generation.

Figure 2 :

 2 Figure 2: Modeling plasticity as a normal distribution N (µ k , σ k ). A non-plastic individual (k) has small σ k and a high peak at their preferred niche, while a plastic individual (k ′ ) has large σ k and a lower peak at their preferred niche. Fitness in a given niche n is computed as the probability density function of the distribution at the environmental state e n . This figure also illustrates the cost and benefit of plasticity, assuming that µ k = µ ′ k . If e n = µ k (the actual environmental state is identical to the preferred niche of both individuals) the plastic individual has lower fitness (cost of plasticity). If e n differs significantly from µ k (the actual environmental state differs from the preferred one) the plastic individual has higher fitness (benefit of plasticity).

Figure 3 :

 3 Figure 3: Comparison between a homogeneous (N = 1) and a heterogeneous environment (N = 100) under global competition

  Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal/35/63/2149048/isal_a_00668.pdf by guest on 20 December 2023

Figure 4 :

 4 Figure 4: Comparison between populations with (R N C ) and without NC (R) under global competition.

Figure 5 :

 5 Figure 5: Comparison between populations with (R N C ) and without NC (R) under local competition.

Figure 6 :

 6 Figure 6: Analyzing one trial for global competition with niche-constructing population where an arms race emerged (Top) evolution of metrics (Bottom) Heatmap with rows corresponding to niches, columns to generations and value/color of cell to the sum of niche construction of all agents in a given niche and generation.

Figure 7 :

 7 Figure 7: Analyzing one trial for global competition with niche-constructing population where negative niche construction emerged.

Figure 8 :

 8 Figure 8: Analyzing a typical trial for local competition with a niche-constructing population.

We provide an online repo for reproducing our simulations at https://github.com/eleninisioti/ NicheConstructionModel/tree/main

Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal/35/63/2149048/isal_a_00668.pdf by guest on 20 December 2023

Acknowledgements This research was partially funded by the French National Research Agency (https://anr. fr/, project ECOCURL, Grant ANR-20-CE23-0006). This work also benefited from access to the HPC resources of IDRIS under the allocation 2020-[A0091011996] made by GENCI.


Keywords: cleft palate, secondary alveolar bone graft, biomaterial, bioglass

The secondary alveolar bone grafting (SABG) step restores the continuity of the alveolar bone necessary for dentition. Faced with the complications of autografts, synthetic biomaterials such as Bioglass (BG) 45S5 have been proposed. The objective was to evaluate the success rate of SABG with the addition of BG 45S5 and to highlight the prognostic factors. Patients operated on between 2015 and 2021 and had follow-up CBCT were analyzed. Multivariate analysis was performed to determine factors influencing radiographic success. 102 SABG were analyzed. They were unilateral total cleft lip and palate (49, 48.0%). The mean age of surgery was 9.32 ± 3.09 years. They were performed mainly outside a syndromic context and without a family history after orthodontic preparation. The radiographic success rate at 1 year was 80.4%. Mixed dentition stage (OR = 7.3, p = 0.024), absence of syndromic context (OR = 20.7, p = 0.024) and female sex (OR = 4.88, p = 0.021) were predictive factors for surgical success.

The use of BG 45S5 instead of autograft is relevant for SABG with a one-year success rate of over 80%. The stage of mixed dentition, the absence of syndromic context and the female sex were factors of good prognosis.

Bioglass 45S5, a relevant alternative to autogenous harvesting for secondary alveolar grafts in clefts?

Retrospective study of one hundred surgeries.

Introduction

Cleft lip and palate is the fourth most common congenital malformation and the first craniofacial anomaly [START_REF] Ysunza | Cleft Palate, Interdisciplinary Diagnosis, and Treatment[END_REF]. Cleft lip and/or palate (CL/P) are divided into two groups: isolated cleft palate, and cleft lip without or with cleft palate [START_REF] Merritt | Part 1. Understanding the Embryology and Genetics of Cleft Lip and Palate[END_REF][START_REF] Shkoukani | Cleft Lip -A Comprehensive Review[END_REF]. In France, the incidence of CL/P in all clinical forms is 1 per 700 to 1000 births (CCMR MaFace and Filière de santé maladies rares TeteCou 2021).

Cleft palate is characteristic of over 200 well-defined congenital malformation syndromes [START_REF] Ysunza | Cleft Palate, Interdisciplinary Diagnosis, and Treatment[END_REF]. Nearly 70% of cases are considered non-syndromic [START_REF] Stanier | Genetics of Cleft Lip and Palate: Syndromic Genes Contribute to the Incidence of Non-Syndromic Clefts[END_REF]. At present, the described etiologies are multifactorial and involve genetic and environmental factors [START_REF] Dixon | Cleft Lip and Palate: Understanding Genetic and Environmental Influences[END_REF][START_REF] Martinelli | Non-Syndromic Cleft Palate: An Overview on Human Genetic and Environmental Risk Factors[END_REF]).

It is not yet possible to completely prevent the onset of these embryopathies which, if left untreated, have a considerable impact on the quality of life of children [START_REF] Rando | Oral Health-Related Quality of Life of Children with Oral Clefts and Their Families[END_REF][START_REF] Karki | Validating and Assessing the Oral Health-Related Quality of Life among Hungarian Children with Cleft Lip and Palate Using Child-OIDP Scale[END_REF][START_REF] Manuel | Quality of Life in Early Age Spanish Children Treated for Cleft Lip and/or Palate: A Case-Control Study Approach[END_REF]. In France, to optimize the care pathway, a national diagnosis and care protocol (PNDS) was published in November 2021 (CCMR MaFace and Filière de santé maladies rares TeteCou 2021). The goal of cleft lip and palate repair is to restore oral anatomy and velum function (L. Ma et al. 2021). It takes place through three surgical steps.

The first step is primary cheilo-rhinoplasty associated with intraveloplasty. It takes place between three and six months. The second step is the closure of the residual bone gap, scheduled between 12 and 18 months. The third step, called secondary alveolar bone grafting (SABG), takes place between 4 and 6 years of age after orthodontic preparation. This key step provides support to the maxillary arch for dentition and mastication by preventing transverse collapse [START_REF] Weissler | Alveolar Bone Grafting and Cleft Lip and Palate: A Review[END_REF]X.-L. Liu et al. 2017).

The use of bone grafts or synthetic substitutes is described. They can be of natural origin, such as autografts or allografts. Autogenous harvesting can come from different sites: the most common is the iliac crest, but the tibia, mandible or skull can also be used [START_REF] Thuaksuban | A Comparison of Autogenous Bone Graft Combined with Deproteinized Bovine Bone and Autogenous Bone Graft Alone for Treatment of Alveolar Cleft[END_REF]. The inconvenience is due to the complications related to the harvesting: postoperative pain, difficulty in walking, nerve damage, hematoma and infections [START_REF] Cricchio | Donor Site Morbidity in Two Different Approaches to Anterior Iliac Crest Bone Harvesting[END_REF][START_REF] Sbitany | Continuous Bupivacaine Infusion in Iliac Bone Graft Donor Sites to Minimize Pain and Hospitalization[END_REF][START_REF] Hayes | Continuous Bupivacaine Infusion Post-Iliac Crest Bone Graft Harvesting in Pediatric Cleft Surgery: Role and Comparison with Ketorolac[END_REF][START_REF] Chang | Influence of Standardized Orientation on Patient Perception of Perioperative Care Following Alveolar Cleft Repair: A Survey Based Study of Patients Treated in a Large Academic Medical Center[END_REF][START_REF] Sequera-Ramos | Continuous Transversalis Fascia Plane Catheter Infusion in a Pediatric Patient Undergoing Alveolar Cleft Repair With Iliac Crest Bone Graft: A Case Report[END_REF][START_REF] Tache | Pain Management at Iliac Donor Sites after Grafting of Alveolar Clefts[END_REF].

In this context, alternatives were sought [START_REF] Liang | Alternatives to Autologous Bone Graft in Alveolar Cleft Reconstruction: The State of Alveolar Tissue Engineering[END_REF][START_REF] Wu | Grafting Materials for Alveolar Cleft Reconstruction: A Systematic Review and Best-Evidence Synthesis[END_REF]. Researchers are proposing the use of various bone substitutes: β-tricalcium phosphate (TCP), bioactive silicates, calcium phosphate, recombinant human bone morphogenic proteins-2 and 7 (rhBMP-2 and rhBMP-7) 4, [START_REF] Osorio | Evaluation of Density, Volume, Height and Rate of Bone Resorption of Substitutes of Autologous Bone Grafts for the Repair of Alveolar Clefts in Humans: A Systematic Review[END_REF][START_REF] Brézulier | The Challenge of 3D Bioprinting of Composite Natural Polymers PLA/Bioglass: Trends and Benefits in Cleft Palate Surgery[END_REF]). Among bioactive silicates, Bioglass® (BG) 45S5 provides promising results in a study of 58 cases [START_REF] Graillon | Bioactive Glass 45S5 Ceramic for Alveolar Cleft Reconstruction, about 58 Cases[END_REF].

However, literature is poor on its use in SABGs.

The primary aim of this study was to determine the success rate of SABG with BG supply. The secondary objectives were to test the predictive value of different parameters on the success of this approach by uni-and multivariate models.

1 Materials and methods Exclusion criteria were: (1) absence of pre-or postoperative three-dimensional X-ray imaging at 1 year, (2) unreadable postoperative three-dimensional imaging at the six sites evaluated,

(3) use of another type of graft, and (4) incomplete medical records.

Studied variables

The variables were divided into six blocks. The first described the sample: patient's age at SABG, gender, syndrome, history of familial clefts.

The second described the characteristics of the operated cleft: type, laterality.

The third described the dental data in relation to the cleft: orthodontics, formula (normal, lateral incisor agenesis, supernumerary tooth), stage of dentition at the time of SABG (temporary, mixed, adolescent), temporary teeth in the cleft and time of their extraction (preor per-operative), preoperative fistula.

The fourth one reported on the surgical procedure: fistula closure, operator, ambulatory character, anesthesia by supra-zygomatic block.

The fifth part consisted of postoperative data: residual fistula, antibiotics, infections.

The sixth section, which develops the radiographic data, is presented below.

Radiographic evaluation and definition of the operative result

The last set of variables was composed by measurements on CBCTs at 1 year. The three planes, orthogonal, 2 mm thick, were selected as follows (Figure 1). A first plane connected the two teeth adjacent to the cleft. A second described the long axis from the mesial tooth to the cleft.

A third traveled the cleft path on an anteroposterior axis.

Scoring by thirds (apical, medial, cervical) was performed in the horizontal and vertical dimensions. Therefore 6 sites were evaluated. The score was a discrete variable with three modalities: "1" for the absence of detectable bone in the area of interest, "2" in the presence of bone not filling the area on either side, "3" in the presence of bone filling the area of interest. In case of artifacts or blurring making the area non-evaluable, the score "NA" was assigned.

Inter-and intra-examiner reproducibility was assessed on 11 CBCTs by 4 practitioners (OA, TDB, DB, and AS) using Fleiss kappa and Cohen's kappa. It was complemented by reproducibility analyses by pair of examiners. Postoperative CBCTs were then all read separately by the two practitioners with the highest inter-rater reproducibility. Examinations with score discrepancies were re-evaluated by the two examiners associated with a third in a joint reading.

From these measurements, the outcome of the surgical procedure was defined by a binary variable taking the modalities: "failure" if the number of sites with score "1" was greater than or equal to 3 out of 6; "success" in all other cases.

Statistical analysis

Data were compiled in a Microsoft Excel® spreadsheet. Statistical analysis was performed with RStudio® software v1.4.1103 (RStudioTeam) in R language v4.0.2 (RCore Team). Categorical data were reported as proportions and counts. c 2 tests were performed for comparison.

Univariate and multivariate logistic regression analyses were performed. Covariates from the univariate analysis were entered into top-down stepwise multivariate regression analyses. A p value ≤ 0.05 was considered significant.

Results

Descriptive analysis of the sample

Characteristics of surgical procedures

The study included 124 SABG surgeries with BG 45S5 performed on 97 patients. 22 were excluded: 16 had no control CBCT at 1 year and for 6, it was unusable (6 of the 6 sites were "NA"). This left a sample of 102 procedures in 79 patients, performed by two experienced operators with a ratio of 3:7. Of this sample, 95 (93.1%) procedures were a primary SABG procedure and 7 (6.9%) were a revision. The procedures were performed at a mean age of 9.32 ± 3.09 years and carried out 34 times in girls and 68 times in boys, i.e., 33.3% and 66.7% respectively. In 96 (94.1%) procedures, the cleft was isolated and 85 (83.3%) had no family history. The majority of the procedures were performed under general anesthesia on an outpatient basis (96 cases; 94.1%) with suprazygomatic block for 82 cases (80.4%). The majority of cases received 1 cubic centimeter of bioglass (99 cases; 97.1%), the remaining cases required 2 cc. These procedures were almost all under antibiotic coverage (99 cases; 97.1%). Three procedures (2.9%) developed a postoperative infection. The mean age of the follow-up CBCT for this study was 1.58 ± 0.94 years.

Characteristics of operated clefts

The majority of the surgeries involved unilateral clefts (57.8%) located on the left in 66 (64.7%) cases. They involved 49 (48.0%) unilateral CLP, 4 (3.9%) bilateral CL, 10 (9.8%) unilateral CL, 4 (3.9%) asymmetrical bilateral CLP and 35 (34.3%) symmetrical CLP.

An orthodontic preparation phase preceded 96 (94.1%) of the surgeries. For all of them and to avoid contraction of the fragments after the graft, the patients were fitted with a Hawley plate or a trans-palatal arch or quad'helix after the surgery. In 40 (39.2%) patients, the maxillary lateral incisor was agenesic. In contrast, 15 (14.7%) cases had supernumerary teeth or odontomas near the cleft. 36 (35.3%) cases had a primary tooth in the cleft path. Moreover, in 12 (11.8%) surgeries, a tooth near the cleft was extracted.

Oral-nasal fistulas were visible before the operation in 51 cases (50.0%). They were either closed before the procedure (3 cases; 5.9%) or during the procedure (48; 94.1%). Also, two fistulas (3.9%) of incidental discovery were closed during surgery, leading to 53 closure procedures.

Assessment of surgical success rate

Firstly, each rater read 11 CBCTs twice, one month apart. Intra-rater reproducibility ranged from 0.77 to 0.89. Intra-group reproducibility by Fleiss kappa was 0.71. The pair with the best reproducibility (0.85) then evaluated all CBCTs.

At the end of the inter-examiner consensus, 9 (1.52%) evaluated sites had artifacts, 8 in the horizontal dimension (1 apical, 2 medial, 5 cervical) and 1 in the vertical (cervical). They were found in 5 patients, respectively 2, 2 and 1 subject with 1, 2 or 3 missing values. For the further analysis, the score "1" was assigned to the artifactual sites.

Scores 2 and 3 were most often attained in both dimensions with one exception in the cervical third, with the minimum score (1) most present in the horizontal dimension (Table 1).

Using the definition of surgical outcome described previously, 82 (80.4%) procedures were successful and 20 (19.6%) were failures. More precisely, among the 95 first operative steps, 77 (81.1%) were successful and among the 7 revision surgeries, 5 (71.4%) were successful (p = 0.6).

Considering the orthodontic aspect and the possibility of moving teeth within the graft zone, only 59 of the patients in the cohort were now old enough to receive braces. Of these, 39 (66.1%) are currently being treated without any particular complication regarding tooth displacement.

Univariate analysis of factors impacting success

Initially and after exclusion of the only case with a median cleft (surgical success), a univariate analysis was conducted to explain a successful outcome of SABG using the factors: sex, laterality of the cleft, type of cleft (transformed into "cleft lip/alveolar" or "cleft palate"), syndromic context, surgical step, family history, number of teeth, extraction of teeth, repair of a fistula, and stage of dentition (Table 2). The univariate analysis approach reported no parameters affecting success.

Multivariate analysis of factors impacting success

Initially, a complete model was used to conduct the multivariate analysis (Figure 2). Factors predictive of radiographic success were ( 1

Discussion

The anterior iliac crest is the preferred donor site for SABG [START_REF] Schaaf | Donor Site Morbidity after Bone Harvesting from the Anterior Iliac Crest[END_REF][START_REF] Gjerde | Patient Experience Following Iliac Crest-Derived Alveolar Bone Grafting and Implant Placement[END_REF]). However, postoperative pain is reported in 38% of cases. Some patients report walking difficulties, haematomas, paresthesias and infections [START_REF] Eufinger | Iliac Crest Donor Site Morbidity Following Open and Closed Methods of Bone Harvest for Alveolar Cleft Osteoplasty[END_REF][START_REF] Nkenke | Morbidity of Harvesting of Bone Grafts from the Iliac Crest for Preprosthetic Augmentation Procedures: A Prospective Study[END_REF][START_REF] Swan | Morbidity at the Iliac Crest Donor Site Following Bone Grafting of the Cleft Alveolus[END_REF][START_REF] Hernigou | Morbidity of Graft Harvesting versus Bone Marrow Aspiration in Cell Regenerative Therapy[END_REF][START_REF] Jessop | The Challenge for Reconstructive Surgeons in the Twenty-First Century: Manufacturing Tissue-Engineered Solutions[END_REF][START_REF] Brudnicki | Secondary Alveolar Bone Grafting in Cleft Lip and Palate: A Comparative Analysis of Donor Site Morbidity in Different Age Groups[END_REF]. This leads to 4.3 ± 3.5 days of hospitalization and 20.2 ± 18.5 days of work absence [START_REF] Gjerde | Patient Experience Following Iliac Crest-Derived Alveolar Bone Grafting and Implant Placement[END_REF]). Ultimately, it degrades patients' quality of life [START_REF] Reissmann | Impact of Donor Site for Bone Graft Harvesting for Dental Implants on Health-Related and Oral Health-Related Quality of Life[END_REF].

The benefits of using a biomaterial are multiple: no donor site, no limited quantity of material [START_REF] Janssen | Tissue Engineering Strategies for Alveolar Cleft Reconstruction: A Systematic Review of the Literature[END_REF], reduction in operating time and the ambulatory nature of general anesthesia. The use of BG 45S5 makes the surgical protocol studied here completely innovative. This synthetic material is a silicate network (45 wt% SiO2) incorporating 24.5 wt% Na2O, 24.5 wt% CaO, and 6 wt% P2O5 [START_REF] Hench | The Story of Bioglass®[END_REF]. It binds rapidly to bone and promotes osteoblasts differentiation. Its dissolution fluids is responsible for the creation of a suitable pH for the nucleation of hydroxyapatite [START_REF] Sanders | Mechanisms of Glass Corrosion[END_REF]. BG 45S5 also has an inhibitory effect on the activity of osteoclasts ("Abstracts of the 35th European Symposium on Calcified Tissues" 2008). This biochemistry makes it an excellent candidate for surgical applications with a limited cost [START_REF] Graillon | Bioactive Glass 45S5 Ceramic for Alveolar Cleft Reconstruction, about 58 Cases[END_REF][START_REF] Tamami | Tolerance and Safety of 45S5 Bioactive Glass Used in Obliteration Procedures during Middle Ear Surgery: Preliminary Results[END_REF]. One of the problems with this type of substitute is its granular form, which does not ensure good mechanical properties. An orthodontic follow-up is therefore necessary.

The main objective of this study was to establish the success rate of SABG with BG 45S5. As this technique is not yet widely used, a retrospective analysis was chosen as it is faster, economic and easier to implement. This primary objective requires a reliable outcome measure. Although the clinical criterion of success is the placement of teeth in the operated area, a radiographic evaluation is imperative, in particular to argue the need for a surgical revision. The evaluation of the success of the graft have been discussed for a long time, reflecting its complexity due to the radiographic technique and the growth of patients [START_REF] Kamperos | A Novel Success Scale for Evaluating Alveolar Cleft Repair Using Cone-Beam Computed Tomography[END_REF]Shaheen et al. n.d.;Stasiak, Wojtaszek-Słomińska, and Racka-Pilszak 2021;[START_REF] Chen | Progressive Comparison of Density Assessment of Alveolar Bone Graft in Patients with Unilateral and Bilateral Cleft[END_REF]). Bergland's two-dimensional classification method is historically the most widely used [START_REF] Bergland | Elimination of the Residual Alveolar Cleft by Secondary Bone Grafting and Subsequent Orthodontic Treatment[END_REF][START_REF] Witherow | A New Scale to Assess Radiographic Success of Secondary Alveolar Bone Grafts[END_REF][START_REF] Hynes | Assessment of Secondary Alveolar Bone Grafting Using a Modification of the Bergland Grading System[END_REF]. It gives excellent results (majority of graft height > 50% of the cleft height) [START_REF] Newlands | Secondary Alveolar Bone Grafting in Cleft Lip and Palate Patients[END_REF][START_REF] Matic | Evaluating the Success of Gingivoperiosteoplasty versus Secondary Bone Grafting in Patients with Unilateral Clefts[END_REF]. However, it does not take into account the sagittal dimension where most of the resorption takes place [START_REF] Dissaux | Evaluation of Success of Alveolar Cleft Bone Graft Performed at 5 Years versus 10 Years of Age[END_REF]. Three publications point out that 2D evaluation overestimates results [START_REF] Van Der Meij | Bone Volume after Secondary Bone Grafting in Unilateral and Bilateral Clefts Determined by Computed Tomography Scans[END_REF][START_REF] Hamada | Application of Limited Cone Beam Computed Tomography to Clinical Assessment of Alveolar Bone Grafting: A Preliminary Report[END_REF][START_REF] Feichtinger | Three-Dimensional Evaluation of Secondary Alveolar Bone Grafting Using a 3D-Navigation System Based on Computed Tomography: A Two-Year Follow-Up[END_REF]). These findings make 3D diagnostics an appropriate tool for this purpose. Specifically, cone-beam CT (CBCT) is preferred over CT because of its lower radiation dose [START_REF] Amirlak | Volumetric Analysis of Simulated Alveolar Cleft Defects and Bone Grafts Using Cone Beam Computed Tomography[END_REF]. The evaluation of a percentage or volume of reconstruction during SABG remains extremely complex. First, because percentage ratios do not provide a spatial assessment of the architecture of the bone bridge [START_REF] Zhang | Evaluation of Alveolar Bone Grafting Using Limited Cone Beam Computed Tomography[END_REF][START_REF] Dissaux | Evaluation of Success of Alveolar Cleft Bone Graft Performed at 5 Years versus 10 Years of Age[END_REF][START_REF] Stasiak | Current Methods for Secondary Alveolar Bone Grafting Assessment in Cleft Lip and Palate Patients -A Systematic Review[END_REF][START_REF] Liu | An Accurate Volumetric Analysis Method for Evaluating Outcomes of Alveolar Cleft Reconstruction[END_REF]. Secondly, because this type of evaluation requires defining anatomical landmarks, which are non-standardized criteria and delicate to implement in a growing patient [START_REF] Feng | A New Method of Volumetric Assessment of Alveolar Bone Grafting for Cleft Patients Using Cone Beam Computed Tomography[END_REF]). Based on these findings, our study replicated the Suomalainen protocol [START_REF] Suomalainen | Cone Beam Computed Tomography in the Assessment of Alveolar Bone Grafting in Children with Unilateral Cleft Lip and Palate[END_REF]. It allows the precise localization of the graft in three dimensions. It has been used in a recent study [START_REF] Padwa | Cone Beam Computed Tomographic Analysis Demonstrates a 94% Radiographic Success Rate in 783 Alveolar Bone Grafts[END_REF]. The evaluation was conducted on CBCT taken on average 1 year after surgery as recommended in the literature [START_REF] Stasiak | Current Methods for Secondary Alveolar Bone Grafting Assessment in Cleft Lip and Palate Patients -A Systematic Review[END_REF]. Taking all of these elements into account, the success rate of SABG varies from 32% to 95%. This wide variability is due to the different definitions of success [START_REF] Tan | Secondary Alveolar Bone Grafting -Five-Year Periodontal and Radiographic Evaluation in 100 Consecutive Cases[END_REF][START_REF] Kumar | Secondary Bone Grafting of Alveolar Clefts: A Review of Outcome at Two Centres in Australia and the UK[END_REF]. It is also due to the length of follow-up. Studies conducted in the short term, less than one year, show a higher success rate. A study using the same protocol showed a 94% success rate [START_REF] Padwa | Cone Beam Computed Tomographic Analysis Demonstrates a 94% Radiographic Success Rate in 783 Alveolar Bone Grafts[END_REF]. According to a 2022 meta-analysis, the total percentage of SABG success in the follow-up period of at least 1 year according to the Bergland index was 76.52% and the total percentage of bone filling after 1 year and according to CBCT was approximately 63.38% [START_REF] Jahanbin | Long-Term Stability of Alveolar Bone Graft in Cleft Lip and Palate Patients: Systematic Review and Meta-Analysis[END_REF]).

The protocol with BG 45S5 led here to a success rate of 80%, higher than that found in the literature for this type of procedure with autogenous graft. Moreover, this score should be weighted by the fact that the artifactual sites were given a score of "1" by default, which leads to an underestimation of the success rate. In addition, the very low complication rate is significantly lower than reported with autografts. Only one other study used the same surgical protocol. In a smaller sample (58 patients) and with an assessment of bone continuity on CBCT at 1 year by linear measurements, the success rate was fewer than ours [START_REF] Graillon | Bioactive Glass 45S5 Ceramic for Alveolar Cleft Reconstruction, about 58 Cases[END_REF].

From an orthodontic point of view, the young age of the cohort meant that no reliable longterm conclusions could yet be drawn. However, the first 39 cases showed that it was possible to move teeth through the grafted area.

Secondly, we sought to establish the parameters influencing the outcome. A univariate and then multivariate approach was conducted. It is regularly used in medicine for these purposes [START_REF] Bell | Univariate and Multivariate Analyses of Preoperative Factors Influencing Symptomatic Outcomes of Transoral Fundoplication[END_REF][START_REF] Mishra | Multivariate Approach in Analyzing Medical Data with Correlated Multiple Outcomes: An Exploration Using ACCORD Trial Data[END_REF]). Nevertheless, a preliminary description of the sample is essential. Concerning the gender of the patients, 66.7% of the interventions concerned boys, which is comparable to a systemic review (Li Ma et al. 2021). The mean age of 9.32 years at the time of surgery has been found in another study [START_REF] Chen | Progressive Comparison of Density Assessment of Alveolar Bone Graft in Patients with Unilateral and Bilateral Cleft[END_REF]. The majority of the clefts were located on the left, in agreement with the literature. One of the particularities here is the high proportion of bilateral clefts (42.2%), since the incidence of unilateral clefts is normally double that of bilateral ones [START_REF] Martelli-Junior | Prevalence of Nonsyndromic Oral Clefts in a Reference Hospital in the State of Minas Gerais, Brazil, between 2000-2005[END_REF]. As in the literature, clefts were associated with a syndrome in 5.9% of cases ("Prevalence at Birth of Cleft Lip with or without Cleft Palate: Data from the International Perinatal Database of Typical Oral Clefts (IPDTOC)" 2011). Van der Woude syndrome was the most common in this sample. It is the leading cause of syndromic cleft lip and palate. It associates clefts, fistulas of the lower lip and sometimes hypodontia [START_REF] Ural | Van Der Woude Syndrome With a Novel Mutation in the IRF6 Gene[END_REF].

The univariate analysis approach reported no parameters influencing surgical success. The data were then included in a multivariate model. The syndromic context was then shown to be an unfavorable element for the success of SABG. The literature on this subject is not abundant. The vast majority of studies exclude patients with syndromes [START_REF] Chetpakdeechit | Cleft Size and Success of Secondary Alveolar Bone Grafting-A Systematic Review[END_REF][START_REF] Thiruvenkatachari | Reducing the Burden of Orthodontic Care for Children with Clefts: Evaluating the Effectiveness of Pre-Alveolar Bone Graft Orthodontics in Unilateral Non-Syndromic Cleft Patients (PABO Study)-A Study Protocol for a Multicentric Randomised Controlled Trial[END_REF]. Concerning the Van der Woude syndromes, a recurrent inflammatory context complicate the care [START_REF] Dissemond | The Van Der Woude Syndrome: A Case Report and Review of the Literature[END_REF][START_REF] Etöz | Isolated Lower Lip Fistulas in Van Der Woude Syndrome[END_REF]. Another parameter that emerged from this approach was the stage of dentition reached at the time of surgery. The stage of mixed dentition, i.e. after evolution of the permanent lateral incisor but before eruption of the canine, offered the best prognosis [START_REF] Ozawa | Factors Influencing Secondary Alveolar Bone Grafting in Cleft Lip and Palate Patients: Prospective Analysis Using CT Image Analyzer[END_REF][START_REF] Zhang | Evaluation of Alveolar Bone Grafting Using Limited Cone Beam Computed Tomography[END_REF][START_REF] Borba | Predictors of Complication for Alveolar Cleft Bone Graft[END_REF]. The eruption of the lateral incisor would initiate osteoinductive activities resulting in better bone formation and less resorption [START_REF] Ozawa | Factors Influencing Secondary Alveolar Bone Grafting in Cleft Lip and Palate Patients: Prospective Analysis Using CT Image Analyzer[END_REF]. In parallel, rapid closure of the space and eruption of the canine through the grafted area were associated with maintenance of the thickness and width of the bone volume [START_REF] Feichtinger | Evaluation of Bone Volume Following Bone Grafting in Patients with Unilateral Clefts of Lip, Alveolus and Palate Using a CT-Guided Three-Dimensional Navigation System[END_REF]2007;[START_REF] Elhaddaoui | Timing of alveolar bone graft and sequences of canine eruption in cases of cleft lip and palate: a systematic review[END_REF][START_REF] Miller | Retrospective Review of 99 Patients with Secondary Alveolar Cleft Repair[END_REF]. A 3D analysis showed a higher success rate of bone grafting around 5 years of age [START_REF] Dissaux | Evaluation of Success of Alveolar Cleft Bone Graft Performed at 5 Years versus 10 Years of Age[END_REF]). This age is younger than the study cohort. With the first ones dating back to 2015, orthodontic expansion was complex. The age of surgery is decreasing as advances in orthodontics make it easier to manage very young patients. The impact of the adjacent tooth is essential and directly influences the success rate of the bone graft, regardless of age [START_REF] Feichtinger | Evaluation of Bone Volume Following Bone Grafting in Patients with Unilateral Clefts of Lip, Alveolus and Palate Using a CT-Guided Three-Dimensional Navigation System[END_REF]2007;[START_REF] Pinheiro | Comparison of Early and Conventional Autogenous Secondary Alveolar Bone Graft in Children with Cleft Lip and Palate: A Systematic Review[END_REF]. Finally, male sex was found to be a predictive factor for failure. Our hypothesis is that young boys have poorer oral hygiene control and inflammatory conditions around the graft. Girls brush their teeth more often and tend to have better oral hygiene and dental care [START_REF] Vallejos-Sánchez | Sociobehavioral Factors Influencing Toothbrushing Frequency Among Schoolchildren[END_REF][START_REF] Angelopoulou | Oral Hygiene Facilitators and Barriers in Greek 10 Years Old Schoolchildren[END_REF][START_REF] Costa | Early Childhood Factors in the Development of Oral Health Behaviours in Adolescence: A Structural Equation Modelling Approach[END_REF]). Although we did not collect this parameter from patients, several studies have associated poor hygiene with SABG failure [START_REF] Jabbari | Optimization of Dental Status Improves Long-Term Outcome after Alveolar Bone Grafting in Unilateral Cleft Lip and Palate[END_REF][START_REF] Lundberg | Outcome after Secondary Alveolar Bone Grafting among Patients with Cleft Lip and Palate at 16 Years of Age: A Retrospective Study[END_REF][START_REF] Chalien | Predictive Factors for Secondary Alveolar Bone Graft Failure in Patients with Cleft Alveolus[END_REF].

Despite the reported success rate of about 80%, the limitations of this study should be noted.

First of all, radiographic success does not predict clinical success, especially the good evolution of the teeth in the grafted areas with a healthy aspect of the periodontal mucosa. Secondly, the histo-physiology of the newly formed bone remains unknown. Further work in this area is required.

Conclusion

We can affirm that the innovative approach to clefts using BG 45S5 substitute offers a very interesting success rate, greater than 80%. A multivariate analysis retained the following predictive factors for a favorable outcome: mixed dentition stage, absence of syndromic context and female gender. The earlier the SABG was performed, the more favorable the outcome, always before the evolution of the permanent canines. To reinforce these good results, we believe it is essential to implement appropriate oral hygiene measures.

Captions

Complete model

Reduced model

1. 1

 1 Study Design and Participants A retrospective cross-sectional observational study was conducted according to the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) recommendations. The approval of the Ethics Committee of the Hospital of Rennes was obtained (opinion n°22.31). Data collection took place from November 2021 to July 2022. Data from 124 SABG with BG 45S5 (GlassBone, Noraker, France), consecutively conducted in the pediatric surgery department of the South Hospital of the University Hospital of Rennes between July 2015 and 2021, by two surgeons, were used in the study. The surgical technique was always the same. First, a vestibular approach allows exposure of the bony cleft. The nasal mucosal plane is closed tightly in case of a fistula, whether it is known or discovered during surgery. The palatal fibromucosal plane is then closed tightly. The bone margins are then enhanced by corticotomies. Briefly, corticotomies are performed with the tip of an 11-blade scalpel on both bone margins, at a distance from the dental germs, until blood suffusion is obtained, but without bone avulsion. The bony cleft is filled with BG, followed by gingivoperiostoplasty to ensure tight closure. Inclusion criteria were: (1) SABG of a facial cleft; (2) with a BG 45S5 bone substitute (GlassBone, Noraker, France); (3) performed in patients with a complete medical and radiographic record.

  ) mixed dentition stage (OR = 7,30, IC = 1,67-42,5, p = 0,024); (2) non-syndromic status (OR = 20,7, IC = 1,48-393, p = 0,024); and (3) female gender (OR = 4,88, IC = 1,26-23,2, p = 0,021). The Hosmer-Lemeshow test concluded that the model had good predictive value (c 2 = 10.55; p = .23). In a second step, the stepwise top-down selection technique was used to simplify the explanatory model, generating a reduced model (p = 0.74). Only the factors: dentition stage, sex and syndrome were retained in this model. It had an Akaike Information Criterion (AIC) of 100.33 versus 112.32 for the full model. Pour ce modèle le test de Hosmer-Lemeshow reached (c 2 = 1.10; p = .998).

Figure 1 :

 1 Figure 1: Positioning of 2mm-thick CBCT slices in vertical and horizontal dimensions.

Figure 2 :

 2 Figure 2: Complete multivariate analysis model and reduced model using the step-down

Table 1 :

 1 Distribution of scores on the six sites evaluated on CBCTs at 1 year after SABG in the vertical and horizontal dimensions at the apical, medial, and cervical thirds. Unreadable or artifactual sites were given a score of 1.

Table 2 :

 2 Univariate regression analysis for successful 1-year radiographic outcome of SABG.

			Vertical			Horizontal
	Score	1, N = 76 1	2, N = 129 1	3, N = 101 1	p-value 2	1, N = 84 1	2, N = 149 1	3, N = 73 1	p-value 2
	Thirds				<0.001				<0.001
		17	39	46		18	52	32
	Apical
		(16.7%)	(38.2%)	(45.1%)		(17.6%)	(51.0%)	(31.4%)
		16	47	39		16	61	25
	Medial
		(15.7%)	(46.1%)	(38.2%)		(15.7%)	(59.8%)	(24.5%)
		43	43	16		50	36	16
	Cervical
		(42.2%)	(42.2%)	(15.7%)		(49.0%)	(35.3%)	(15.7%)

1 n (%) 2 Pearson's Chi-squared test Parameters N Event N

OR 1 95% CI 1 p-value

	Mixed		33	-	-
	Sex Adolescent	101	12	0.36 0.07, 1.75	0.16
	Female Temporary		29 36	-0.36 0.09, 1.16 -
	Male		52	0.45 0.12, 1.36
	Laterality of the cleft	101				0.97
	Right		28	-	-
	Left		53	1.02 0.35, 2.79
	Type of cleft	101				0.56
	Cleft lip		12	-	-
	Cleft lip and palate		69	0.64 0.09, 2.63
	Syndrom	101				0.086
	No		78	-	-
	Yes		3	0.22 0.04, 1.26
	Surgical step	101				0.56
	#1		76	-	-
	#2		5	0.59 0.12, 4.36
	Family history	101				0.68
	No		68	-	-
	Yes		13	0.76 0.23, 2.99
	Number of teeth	101				0.59
	Normal		35	-	-
	Lateral incisor agenesis		33	1.48 0.52, 4.46
	Supernumerary tooth or odontoma	13	2.04 0.46, 14.4
	Tooth extraction	101				0.64
	None		72	-	-
	Per-operative		9	0.71 0.19, 3.44
	Oral-nasal fistulas reparation	101				0.80
	Pre-operative		2	-	-
	None		37	1.90 0.08, 21.9
	Per-operative		41	2.28 0.10, 26.4
	Stage of dentition	101				0.20

1 OR = Odds Ratio, CI = Confidence Interval