domain: spi math phys

text:
G Pavlin

K B Laskey
email: klaskey@gmu.edu

F Mignet

F S Slijkhuis
email: filip.slijkhuis]@nl.thalesgroup.com

E Blasch

V Dragos

J P De Villiers

Lennard Jansen

Qualitative Models of Data Generation Processes: Facilitating Data-Intensive AI Solutions

AI-based decision support solutions require life cycles that adequately address critical steps, such as (i) finding suitable machine learning (ML) methods for the problem at hand, (ii) preparing and executing adequate data acquisition processes and (iii) tractable evaluation of the overall solution. Understanding the data generating processes is key in achieving this. Training and test data can be seen as a result of a causal data generation process, a sampling process in which the data is collected from different sources that are influenced by multiple interdependent phenomena. This is represented by a Qualitative Model of Data Generation Processes (QM-DGP), a causal graphical model. QM-DGP facilitates analysis of the complexity of the underlying data generating processes that can inform the development of trustable ML-based solutions in multiple ways. Firstly, this analysis is the basis for the determination of the required complexity of the ML models. Secondly, it facilitates the determination of the quantities of training data supporting good learning results. Thirdly, it can provide guidance for a systematic simplification of the models, supporting tractable solutions without significantly reduced performance. The construction of QM-DGP and the analysis benefit from sound theoretical concepts, such as dseparation and I-Maps. Experimental results with simulated data indicate that the approach can be effective in predicting the required quantities of training data and the determination of the modelling complexity using different types of models.

I. INTRODUCTION

Modern decision support systems require increasingly complex fusion solutions relying on Artificial Intelligence (AI) approaches that make use of Machine Learning (ML). The use of such technologies, however, introduces substantial challenges to the development, evaluation and deployment of mission critical fusion solutions [START_REF] Pavlin | Towards the rational development and evaluation of complex fusion systems: A URREF-driven approach[END_REF], [START_REF] Insaurralde | Uncertainty in avionics analytics ontology for decision-making support[END_REF], [START_REF]Situation awareness decision support system for air traffic management using ontological reasoning[END_REF], [START_REF] Sabatini | Application and certification challenges for ai/ml techniques in safety critical avionics systems[END_REF]. Some of the main challenges are the choice of the modelling approaches, machine learning methods and reasoning mechanisms. As emphasized in [START_REF] Pavlin | Towards the rational development and evaluation of complex fusion systems: A URREF-driven approach[END_REF], this is not trivial, and it critically influences the entire development life cycle as well as the properties of the resulting fusion solutions. Appropriately chosen representations, associated reasoning mechanisms and ML techniques facilitate the implementation and understanding of the required functions that perform within specific operational constraints. However, if the selected methods do not match the characteristics of the problem at hand, insurmountable obstacles can be introduced into the entire life cycle, impacting the development process as well as the system deployment. Given the complexity of the targeted problems, many aspects must be taken into account when making choices related to the modeling, ML and inference throughout the development life cycle. A URREF-driven life cycle [START_REF] Pavlin | Towards the rational development and evaluation of complex fusion systems: A URREF-driven approach[END_REF] approach was introduced to address these challenges. According to this approach, different representation and reasoning aspects must be evaluated in the inception, design, implementation, commissioning and operational phases. In the inception phase the following questions must be answered: What types of functions can in principle be automated? What types of models are suitable, given the operational conditions? Can models supporting sufficiently accurate inference be created for the given application? Can sufficient amounts of training data be obtained for achieving the needed accuracy? In the design phase, architects need answers to additional questions: What is the best model architecture that supports tractable ML and minimizes the required amounts of training data? How do we gather sufficient amounts of data for the given application? In the implementation and evaluation phases, developers need to answer questions, such as: Can we reliably estimate the expected accuracy of the resulting solutions? Does the training data reflect all situations under which the trained models will operate? Is the solution robust? Key to answering the above mentioned questions is understanding of the domain, in particular the mechanisms of the processes generating the data that is used for training of the models as well as inputs to the decision support functions at runtime. This paper proposes the concept of Qualitative Models of Data Generating Processes (QM-DGP) that describe causal dependencies between different phenomena influencing the generation of observations in a qualitative manner. The approach is inspired by the principles expressed in [START_REF] Pearl | The Book of Why[END_REF] and can be viewed as an extension of the Abstraction flow concepts introduced in [START_REF] Villiers | Uncertainty representation and evaluation for modeling and decision-making in information fusion[END_REF]. In particular, QM-DGP supports modelling of real world entities and processes (RWEPs), the basis for various types of abstractions and analyses throughout a system's life-cycle. The focus in this paper is complexity analysis of the correlations in the data as well as a coarse estimation of the quantities of data required for training of models that operate satisfactory under all relevant conditions. The QM-DGP approach is agnostic with respect to the adopted modelling paradigm and the ML methods. The paper shows how the approach facilitates evaluations in different phases of the URREF-driven life-cycle. Controlled experiments with synthetic data are used to demonstrate the effectiveness of the approach for both Bayesian network models and Neural Networks.

A. Example Use Case

The concepts in this paper will be illustrated with the help of a synthetic "ground truth" example data generating process (DGP) that gives rise to the observed data in a use case, which simulates aircraft being sensed by a radar. For the sake of clarity, we focus on a snapshot in time that is governed by a probability distribution P(V) over the set of random variables V = {Class, F light, P osition, Speed, RCS, W indDirection, Rain, V isibility, W indStrength}, defined as follows:

• States of Class represent airliners, small planes (general aviation) and helicopters. • RCS represents the radar cross section in three ranges.

• W indDirection represents easterly/westerly winds.

• States of Rain represent rain/no rain, respectively.

• Discrete variable V isibility has states good, low, fog.

• W indStrength represents normal, wind and storm. Fig. 1 shows the directed acyclic graph describing the dependencies in P(V) influencing the DGP. While the model is a severe simplification, it captures typical dependencies over the set of variables. The emphasis is on significant influences the context exerts on the distribution P(V). Various external conditions can change the DGP, resulting in major distribution shifts in the sampled data. E.g. the states of Speed directly depend on the Class and the flight phase F light. Moreover, P osition directly depends on the Class, the F light phase and the W indDirection. Airliners cruise at a much greater altitude than small planes. P osition also depends on the W indDirection that determines the landing and departure directions. RCS depends on the Class (the plane size and shape) and the relative position of the plane wrt. the radar. An airliner cruising at a high altitude will inevitably result in small values for RCS due to great distance between the radar and the plane. Small planes could have relatively great RCS when in the vicinity of the airport.

II. APPROACH

This paper assumes that the training data D train is a result of a causal data generation process (DGP) that can be seen as a sampling process from some distribution P (V) over correlated variables V. P (V) influences the frequencies of observations during the data sampling processes.

A. Complexity of Correlations

The complexity of a trained model M k defined over a set of variables V k ⊂ V can be expressed as the number of parameters required to specify the model. While M k should be as simple as possible, it must be rich enough, i.e. be defined through a sufficient number of parameters, to capture the relevant knowledge about the relations between variables V k from D train during an ML process. The required model complexity depends on the complexity of the relations between variables V reflected in P (V). The complexity of P (V), in turn, can be expressed with a Qualitative Model of a Data Generation Process (QM-DGP). This is a directed acyclic graph that captures the relations in the data generating process in a qualitative manner. That is, the model contains nodes representing the phenomena of interest and directed links representing direct dependencies between these phenomena; but no strength of these dependencies is considered. Figure 1 shows an example of such a model. A QM-DGP accurately represents a DGP over set of variables V if it is an Independence Map (I-MAP) of the underlying probability distribution P (V) [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF]. In that case we say that QM-DGP is faithful with respect to the underlying distribution P (V).

Given that a QM-DGP is faithful as a representation of the data generating process, its topology reveals useful information about the process complexity. An important pattern is a Collider, a variable X i associated with two or more parent variables π(X i ). Variables in π(X i ) directly influence the states of X i ; π(X i ) define the local context of X i . Colliders can greatly increase modelling complexity, i.e. a large number of parameters that often requires a large set of training data to learn with reasonable accuracy. Namely, a collider variable X i is associated with a set of parameters whose size increases exponentially with the number of its parent nodes π(X i ) unless modeling assumptions are imposed to control the number of parameters. For simplicity of exposition it is assumed initially that all variables are discrete. 1 In this case, we can assume that the DGP samples states of X i from a discrete distribution P (X i |π(X i )). The number of possible combinations of states n Xi over which the distribution is defined is expressed as:

n Xi = |X i | Yj ∈π(Xi) |Y j |, (1)
where |X i | and |Y j | denote the number of states of variables X i and Y j , respectively. This equation expresses the complexity of the model describing relations between X i and its parents π(X i ). In the model shown in Fig. 1, we can identify multiple colliders: Speed, P osition, Class and RCS for which (1) applies. Given the number of states of each of these variables and their parents, the estimation of the corresponding conditional probabilities: P (Speed|Class, F light, W indF orce), P (P osition|Class, F light, W indDirection), P (RCS|Class, P osition) and P (Class|Rain, V isibility, W indF orce)

requires observation of 144, 432, 108 and 6 different combinations of states, respectively. It is necessary to have a sufficient number of observations of each combination of state for reliable estimation of the real-valued parameters representing the models of such correlations. Section II-D considers this question.

B. Local Context

Parents π(X i ) define the local context of X i . That is, the sampled values of the parents π(X i ) determine the probability distribution from which X i is sampled. We call a specific combination of states of variables Y i ∈ π(X i ) a local context.

The cardinality of |π(X i )| and the number of states of each variable Y i ∈ π(X i ) and their correlations together determine the context complexity, i.e. the number of distinct contexts leading to manifestly different distributions over the states of X i . The number of local contexts c Xi can be expressed as a product c Xi = Yj ∈π(Xi)

|Y j | (2)
It is essential to train the models on data D train that was sampled under all relevant local contexts for each variable X i ∈ V.

Otherwise, the trained models are likely to fail/underperform when fed with data sampled in a context that was not considered at the collection of D train . The variable Class in Fig. 1 has 12 distinct local contexts, given the local context set {Rain, W indStrength, V isibility}. Without additional assumptions, accurately estimating P (Class|Rain, W indStrength, V isibility) would therefore require 12 times as much data as required for an estimation of the prior distribution P (Class).

Fortunately, structural properties of P(V) may permit estimation of the distribution using much less data. For example, when the local distribution of X i satisfies context-specific independence (CSI) [START_REF] Boutilier | Context Specific Independence in Bayesian Networks[END_REF], then subsets of different combinations of states of π(X i ) can be associated with the same distribution P (X i |π(X i )). Another example is independence of causal influence, or ICI [START_REF] Van Gerven | A generic qualitative characterization of independence of causal influence[END_REF]. Common ICI models include Disjunctive Interaction models (Noisy-OR/Noisy-MAX) [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF]. CSI and ICI are examples of parametric regression models in which the parent-child relationship is expressed as a parametric model. The amount of data required to estimate the parameters of a parametric model is often much less than required for a separate distribution per context.

In the DGP of Fig. 1, it reasonable to assume that the relationship of Class to its parents satisfies CSI. While there exist 12 possible state combinations for the set V isibility, W indF orce and Rain, they result in only three distinct distributions over states of the variable Class. Therefore, we need to ensure that we sample Class with sufficient representation from three these subsets, but ensuring sufficient representation from each combination of parent states in each subset is unnecessary.

C. Expressing the DGP complexity

This section provides a high-level analysis of the DGP complexity that serves as the basis of a heuristic approach to estimating the quantities of data required for learning adequate models for the task at hand. Let's assume a learning task to obtain a classifier using model M k defined over variables V k ⊆ V. The model relates X c ∈ V k and the observed variables X i ∈ O ⊂ V k , where O denotes the set of all observed features and V is the set of variables corresponding to the phenomena that occur in the underlying DGP. The classifier uses M k to predict the states of the classification variable X c given observations of the features represented by variables X i ∈ O.

Under the assumption that the QM-DGP is, to good approximation, a faithful representation of direct dependencies between the variables in V, it is possible to provide a rough estimate of the quantities of training data required for training of a model M k , for given variables X i ∈ V. To estimate the needed quantities of data for training M k , we must consider the complexity of the underlying DGP, i.e. P (V) from which the states of variables in V k are sampled. The positions of X c and the observed variables X i ∈ O in the QM-DGP graph reveal a lot about the complexity of the learning task at hand.

To understand the DGP complexity, we introduce the notion of DGP context variables. In common parlance, the term context refers to "the interrelated conditions in which something exists or occurs". 2 The DGP context variables C ∈ V in a QM-DGP are intended to represent the background conditions under which the process operates. Generally, a DGP context variable Y i ∈ C is either a root node in the DGP graph or, if not a root node, has no non-context nodes as parents. In addition, a DGP context variable will not be d-separated [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF] Moreover, for each V k we can obtain a reduced model from the full QM-DGP relating X i ∈ O, X c and C O . Fig. 2.b shows such a reduced model that was obtained from the QM-DGP in Fig. 2.a. In case the conditional probabilities for all relations in the QM-DGP were known, the model shown in Fig. 2.b could be obtained through marginalization of all latent variables along the paths connecting C O , X c and X i ∈ O in Fig. 2.a. If all context variables C O are removed from the reduced model, we obtain a core model defined over X c and O with joint probability distribution P (X c , O). In other words, P (X c , O) is embedded in the set of relevant DGP context variables C O ; i.e. there exist different versions of P (X c , O), each corresponding to a different context. In Fig. 2.b joint distribution P (X c , X 1 , X 2 ) over the core model is embedded in the set of relevant DGP contexts defined over variables

C O = {Y 1 , Y 2 , Y 3 , Y 4 , Y 5 }.
Let n core denote the number of combinations of states over which the P (X c , O) of a core model is defined. Then the number of different combinations of states n V k of X c , O and the relevant DGP context C O in the reduced model can be expressed as follows:

n V k = n core Yj ∈C O |Y j |, (3)
where |Y j | denote the cardinality of the discrete DGP context variables. Note that equation (3) takes into account different contexts which may not be observed. Still, these variables must be considered as their states drive the DGP and thus influence the observable variables.

In the case of a fully connected QM-DGP, n core is simply the product of the numbers of states of all variables X c and O. However, if the graph is sparsely connected, then fewer parameters are required to capture P (X c , O). Furthermore, if suitable learning methods are used, then subsets of the parameters could be learned independently of each other, requiring less training data. For example, consider a PGM M k whose topology is identical to the DGP model in Fig. 1, with the set of feature variables O = {Speed, RCS, P osition}. This is also a core model featuring two fragments defined over F 1 = {Class, RCS, P osition} and F 2 = {Class, Speed}, respectively. These two fragments are conditionally independent given the states of variable Class, i.e. they are dseparated. Fragments F 1 and F 2 are associated with 108 and 12 combinations of states, respectively. For a given context the parameters in each fragment can be learned independently. Except in special cases, it is likely that more training data is required to learn P (Class, RCS, P osition) than P (Class, Speed). Moreover, as each record d i ∈ D train contains observations of the states of variables from both fragments, i.e. O = {Speed, RCS, P osition}, the required number of data records is dictated by the more complex fragment. Therefore, in (3) we use n core = 108, the number state combinations of the more complex fragment F 1 . Thus far, we have considered only discrete variables with unconstrained probability distributions. Continuous variables are sometimes addressed with discretization, as was done for the model of Fig. 1. Here, we enounter a tension: a fine discretization improves accuracy of inference in the discretized model, but can dramatically increase the data required for learning an unconstrained distribution. This tension can be addressed using a suitable parametric model. Examples include the normal or exponential distribution, or mixtures thereof. Parametric models can generally be learned with many fewer data points than a fine discretization. Accuracy can sometimes be improved with mixtures of parameterized distributions. If discretization is needed, discretization can be performed after learning. Of course, this requires using an appropriate parameter estimation method. The methods of this paper assume unconstrained discrete distributions, but could be extended to parameterized continuous distributions.

D. Estimating the Required Data Quantities

The DGP complexity expressed with equation ( 3) is the basis for a heuristic approach to estimating the quantities of data required for learning adequate models for the classification task at hand. With equation ( 3) we can express a coarse estimate of the required size of the training set D train to train model M k :

|D train | = κ • n V k , (4)
where κ denotes the minimum number of occurrences of a specific combination of states of involved variables, such that the corresponding parameter can be estimated to the desired accuracy. Note that the choice of κ is heuristic, but it is often possible to make a rough estimate of the expected accuracy in advance of data collection. In this paper κ = 10, i.e. it is assumed that 10 • |X i | measurements are required for a variable with |X i | states for a given local context, i.e. a specific combination of states of X i 's parents π(X i ). As the number of states grows also the number of required observations grows, improving the chances of capturing multi-modal distributions that variables with many states can represent. Equation ( 4) is a very crude estimate as it does not consider the strength of correlations in P (V) from which DGP samples. It fails to account for the fact that some combinations of states might never materialize while other could be so rare that the chance of capturing a sufficient number of cases in the training data is very low. The distribution over these combinations depends on the phenomena corresponding to the X i 's ancestor variables in the QM-DGP. Ultimately, there exist one or more DGP context variables in C O that influence the values of X i ∈ O and all variables on the paths between C O and X i .

However, an improved estimate |D train | ′ for the required data can be obtained, if some amount of training data is already available at the time of the analysis. We introduce an auxiliary PGM M aux with the topology corresponding to the reduced QM-DGP, as for example the graph in figure 2.b. Such a M aux is trained on the currently available data using simple Maximum Likelihood estimation based on state counting 3 . The learned M aux encodes the frequencies of the state observations of all variables. For any context C(O) we can find the state combination with the smallest estimated probability. For each variable Y j ∈ C(O) we find the state with the smallest marginal probability P min (Y j ) and determine the probability of the least likely combination of states in C(O):

P min (C(O)) = Yj ∈C(O) P min (Y j ). (5)
With P min (C(O)) and n core we can compute factor c(V k ), a ratio between the number of required training cases to sufficiently cover all combinations of the states of the core model during learning and the expected number of occurrences of the least likely combination of C(O)'s states in D train :

c(V k ) = n core • κ/(|D train | • P min (C(O))). ( 6
)
This equation is relevant for simple learning approaches that cannot benefit from the underlying data structure during the training process. However, some training techniques can exploit structural properties of the graph and/or local distributions. If so, the analysis can be carried out on conditionally independent modelling fragments F i and we can investigate whether the frequency of observations of their state combinations can support good machine learning. A fragment F i is identified in M aux , given the class variable X c and observations. Examples are F 1 and F 2 identified in the graph from Fig. 1, given the Class variable (see section II-C). Such a fragment F i is associated with its relevant context C(O i ), where O i denotes the set of observed variables in F i . Like in the derivation of (5), we determine for each variable Y j ∈ C(O i ) the state with the smallest marginal probability P min (Y j ) and determine the probability of the least likely combination of states in C(O i ):

P min (C(O i )) = Yj ∈C(Oi) P min (Y j ). (7)
As next we determine the subset of variables F ′ i ⊆ F i that are directly influenced by at least one variable Y j ∈ C(O i ) in the fragment's context. The set F ′ i can be viewed as a hyper variable whose possible combinations of states n F ′ i can be determined as follows:

n F ′ i = Y k ∈F ′ i |Y k |. (8)
With P min (C(O i )) and n F ′ i we can compute factor c(F i ) for a specific fragment, a ratio between the number of required training cases to sufficiently cover all combinations of F i 's states for learning and the expected number of occurrences of the least likely combination of C(O i )'s states in D train :

c(F i ) = n F ′ i • κ/(|D train | • P min (C(O i ))). (9)
After executing this computation for all fragments in M aux , we take the greatest c(F i ) as a corrective factor to determine an adapted size of the training data considering the actual distributions of M G :

|D train | ′ = c max • |D train |.
If in fragment F i there exists a subset F ′′ i = F i \ F ′ i ̸ = ∅, then the same procedure can be repeated for F ′′ i , by using F ′ i as the context of F ′′ i . By recursively repeating this procedure for all fragments F i until F ′′ i = ∅, an improved estimate of the required training data size can be obtained, properly considering the dependencies throughout the DGP.

It may be that some of the context variables are controllable, either by setting them to particular values (e.g., choosing a setting on a sensor) or by collecting data when they are in certain states (e.g., waiting to collect data until given weather conditions occur). In such cases, if we determine that some combinations of conditions have insufficient data for reliable estimation, we can collect additional data for those circumstances and adjust the learned probabilities accordingly.

Also, the problem complexity can be controlled through the resolution of the variables used in the trained model. While reducing the resolution of variables results in smaller |D train |, we might be losing some precision and accuracy.

III. EXPERIMENTAL RESULTS

This section illustrates how the QM-DGP based analysis can facilitate the determination of the model architecture and the estimation of the required training data volumes. Known ground truth models M i G were used to sample training and testing data. This enabled objective comparison of different modelling paradigms with respect to the modelling complexity and the requirements for training good quality models.

A. Model Complexity

The QM-DGP provides guidance on the determination of the architecture, complexity and resolution of different types of ML-based models. To illustrate this different models were used. M 1 , M 2 and M 3 were PGMs whose topology is shown in Fig. 3. Their architecture was obtained from the graph in Fig. 1 by adding a ContextSummary variable between the Rain, W indStrength, V isibility and Class. ContextSummary is a latent variable introducing the knowledge that there exist three groups of local contexts of Class. Also M 4 was a PGM whose topology was defined over a subset of the nodes indicated by emphasized frames in Fig. 3. The PGMs were trained by using the Expectation Maximization (EM) algorithm. Moreover, M 5 was a Multi-Layer Perceptron (MLP) with 3 hidden layers of 16 neurons each and leaky ReLU activation. While QM-DGP directly provides guidance on the suitable topology of the PGMs, there is no easy way of translating QM-DGP to a Neural Network architecture. Still, the QM-DGP can be helpful in finding a good model. Namely, by being able to estimate the necessary size |D train |, we know that the search of the architecture and subsequent optimization of a neural network M 5 is carried out on a data set that is likely to carry information from all relevant types of situations in which M 5 will operate; i.e. the model will be exposed to all relevant contexts during the training sufficiently often. Thus, M 5 was obtained by training different architectures on the same D train and choosing the simplest architecture that was also yielding the smallest cross entropy loss given a large validation set of a fixed size.

For the sake of completeness, also a full Joint Probability Distribution (JPD) model M 6 was used. M 6 was defined over all variables shown in Fig. 3 and its parameters were obtained through Maximum Likelihood parameter estimation based on simple counting of state combinations.

B. Adequate Quantities of Training Data

A series of experiments confirmed that the presented QM-DGP approach can provide useful information on the quantities of training data that increase the chances of learning a good model. The experiments were carried out with three versions of ground truth model M 1 G , M 2 G and M 3 G . All versions had the topology shown in Fig. 1 and the same conditional probabilities, where P (P osition|Class, F light) varied between 0.032 and 0.47, P (Speed|, F light, Class) varied between 0.048 and 0.89 while P (RCS|Class, P osition) varied between 0.05 and 0.88. M 1 G used a set of prior probabilities for the context variables: P (Rain = true) = 0. P (V isibility = good) = 0.7, P (V isibility = low) = 0.2, P (W indF orce = normal) = 0.9, P (F light) varied between 0.1 and 0.5 while P (W indDirection = east) = 0.5. M 2 G used priors that were the same as M 1 G , except that P (W indF orce = normal) = 0.97. In M 3 G all priors over the context variables were uniform.

Each M i G was used to sample (i) a large test set D test with 500000 records and (ii) a series of training data sets D train of increasing sizes. For each set of training data D train the experiments were repeated ten times. The averages of the error rates were plotted for different data set sizes allowing visual determination of the point |D train | f lat after which no significant improvements of the error rates took place. This point corresponded to error f lat . Each ground truth model M i G was also used for optimal classification yielding the smallest possible error rate error min , given the underlying distribution represented by M i G . Moreover, as there was a significant class imbalance, the F1 score was monitored. In all experiments the F1 score improved with the overall accuracy.

In each experiment the required quantities of training data were estimated in two steps: (i) estimate initial |D train | using equation ( 4) with κ = 10 and (ii) train M aux and compute |D train | ′ using (9) for the PGMs and the MLP and (6) for the full JPD model, respectively. The M aux 's architecture corresponded to the topology shown in Fig. 3 and its parameters were obtained via Maximum Likelihood parameter estimation, i.e. simple counting of state combinations in a training set of 10000 records. ContextSummary in M aux was a deterministic function of the states of the context variables. By running inference algorithm, marginal distribution over the sates of ContextSummary was estimated, providing the inputs for [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF]. Multiple scenarios were investigated:

• Exp 1: Sampling on M 1 G , n core = 108, n V1 = 3888. • Exp 2: Sampling on M 2 G , n core = 108, n V2 = 3888. • Exp 3: Sampling on M 3 G , n core = 108, n V3 = 3888. • Exp 4: Sampling on M 1 G , n core = 12, n V4 = 216. • Exp 5: Sampling on M 3 G , n core = 432, n V5 = 15520. • Exp 6: Sampling on M 3
G , n core = 432, n V6 = 15520 As table I shows, the initial estimates |D train | using (4) indicated the right order of magnitude for the needed data quantity in all cases. Also the corrected |D train | ′ resulting from the analysis of the auxiliary PGM was a safe estimate as |D train | ′ ≥ |D train | f lat . Except in Exp 2, the classifier achieved close to optimal performance when the size of the training set was close to the estimated |D train | ′ . In Exp 2 , |D train | ′ was almost two times larger than |D train | f lat . This is likely a consequence of very small probability of certain state combinations, such that even in the cases of suboptimal parameter estimation these cases did not have a significant impact on the overall classification accuracy. It is also evident that the MLP model in Exp 5 requires significantly more training data to achieve close to optimal performance than the PGM models. This is a consequence of the training method which does not fully benefit from the data structure as is the case with the EM algorithm. Still, the MLP learning seems to be able to exploit some structure in the data, as the required quantities of training data were still significantly smaller than in Exp 6. The hypothesis is that the MLP approach could not use the conditional independence between fragments F 1 and F 2 , but it could exploit the d-separation between RCS disc and the rest of the variables via the observations of Class, Speed and P osition. This is supported by the fact that for the MLP, accurate |D train | ′ was obtained by using ( 9) on the entire core model (a single fragment). Exp 6 clearly demonstrates the consequences of ignoring the data structure, resulting in huge quantities of training data to achieve close to optimal classification performance. In this case |D train | ′ was accurately predicted by using equation [START_REF] Villiers | Uncertainty representation and evaluation for modeling and decision-making in information fusion[END_REF] .

IV. USING QM-DGP IN LIFE CYCLES

The presented approach can play an important role at multiple stages of a system life cycle involving components obtained through machine learning. It provides support for informed decisions throughout a life-cycle. In particular, this paper assumes a URREF-driven life cycle [START_REF] Pavlin | Towards the rational development and evaluation of complex fusion systems: A URREF-driven approach[END_REF] that puts the evaluation of uncertainty representations and reasoning mechanisms at the center of all stages of system development and operation. At a high level, the URREF life-cycle can be subdivided into three main phases: (i) Inception, (ii) Design, implementation and Testing, and (iii) Operation. In each phase the choices are based on different types of evaluations [START_REF] Pavlin | Towards the rational development and evaluation of complex fusion systems: A URREF-driven approach[END_REF] that can be supported by the presented QM-DGP based analysis.

A. Inception

In the Inception phase of a URREF-driven life cycle the viability of AI-based solutions is investigated and decisions are made about the use of specific AI techniques and the data acquisition processes. This is the phase in which the QM-DGP graph is constructed by using qualitative knowledge of the dependencies between the relevant variables. Such knowledge is likely to be available if the data is produced by (i) processes whose physical properties are understood at a high level or (ii) by processes that are governed by clear protocols. Examples of the former are human made cyber-physical systems where direct influences between different data producing components are known. An example of the latter is the presented aviation use case, where it is known that the air crews use clear rules in different flight phases establishing direct dependencies between the flight phases, the speed, and the location. Also, we know that the RCS depends on the distance from the sensor and the aircraft type. Moreover, it is known that there are three weather situations, such that a.) only jetliners can fly, b.) small planes and helicopters are rare and c.) all three types of aircraft are likely. Even when the DGP is not known exactly, it can often be specified to good approximation through expert judgemnt. In such cases, the approximate QM-DGP can still be useful to provide a rough guide to the necessary number of training samples.

The developed QM-DGP graph supports the initial assessment of the relevant variables that should be explicitly modeled in M k . Based on the QM-DGP graph, we can see the relevance of variables for the task at hand and assess the complexity of correlations. This step is an example of the evaluation of Expressivity, Relevance and Weight Of Information criteria from the URREF ontology and provides guidance for the type and the architecture of the model M k . For example, if the nodes in the QM-DGP indicate different types of (discrete) observations correlated in complex ways, a Probabilistic Graphical Model (PGM) approach could be a good choice. On the other hand, if the nodes represent multi dimensional continuous measurements, such as images or other raw signals, Neural Networks may be preferred. In some cases, the M k complexity can be estimated in terms of required numbers of parameters as a consequence of the QM-DGP topology and the choice of the discretization, which is straightforward if PGMs are used. Moreover, the assessment of |D train | based on equation (4) provides useful input in the Inception phase. By knowing |D train | and the relevant variables in the QM-DGP, the viability of the data acquisition process can be evaluated, a data collection plan prepared and the initial estimate of its costs can be made. Thus, at an early stage in the life cycle we can see whether certain parts of the system can be automated in reliable and economical ways. This is an example of an evaluation that contributes to the Correctness criterion from the URREF ontology.

B. Design, Implementation and Testing

The second phase of the URREF-driven life cycle consists of multiple iterations of design, implementation and testing steps. In this phase the QM-DGP provides guidance for the determination of the model architecture and the model resolution. As it explicitly encodes the qualitative dependencies between the variables that are also represented in M k , it can provide guidance for systematic architectural simplifications leading to models with fewer parameters, without jeopardizing the overall classification performance. For example, given the direct dependencies in the example QM-DGP in Fig. 1, it is obvious a Naive Bayes model is likely to be inadequate. [START_REF] Jansen | Context-based vessel trajectory forecasting: A probabilistic approach combining dynamic bayesian networks with an auxiliary position determination process[END_REF] provides an example where such a technique was used to obtain significantly simpler models for vessel track forecasting by introducing latent variables. While the direct dependencies often cannot be ignored, the complexity of the models can be controlled by choosing a lower resolution for discretization of variables or use of parametric models, thus reducing the number of parameters. This is an example of the evaluation of the Expressivity criteria according to the URREF ontology. As illustrated with the MLP experiment, in case of model types for which the architecture cannot be directly derived from the QM-DGP, the training data of sufficient size increases the chances that the search for suitable architectures will produce models that can cope with all major settings under which the input data is produced during operation.

An important step in this phase is the preparation of adequate training data sets that cover all major operational conditions. As the data is obtained, corrected |D train |' can be estimated according to equation ( 9) or ( 6), dependent on the training method. In this way the forecast of the data acquisition costs can be re-estimated and the chances of training a good model can be improved.

V. CONCLUSIONS

Life-cycles of decision support solutions involving AI technologies must include the following critical development steps:

• Choosing suitable AI techniques.

• Acquisition of sufficient amounts of training data.

• Determining the complexity of the models, such that the key knowledge can be extracted from the available data. The presented qualitative causal models of the Data Generating Processes (QM-DGP) facilitate the above mentioned steps. The QM-DGP's topology exposes the complexity of the relations between different phenomena in a data generating process (DGP). This provides the guidance for the determination of (i) the model's complexity capable of absorbing the key information during the ML process, (ii) the volumes of training and testing/validation data required for the extraction of adequate models and (iii) the types of data the acquisition process should focus on. Based on the dependencies encoded in the QM-DGP, simple analysis rules enable coarse estimation of the data volumes enabling the training of good quality models. It should be noted that the QM-DGP based approach is agnostic to the used AI paradigm. Controlled experiments using synthetic data sampled from known ground truth models were carried out with Bayesian Networks and Neural Networks. The results suggest that the approach could indeed provide useful guidance for the preparation of the training data and generation of models covering all major contexts. For the used experimental setup, near perfect models could be trained with the data quantities estimated with the presented method. The experimental results are consistent over different parametrizations of the ground truth model. However, the ground truth model always had the same topology. Moreover, the approach can be viewed as a tool that is used throughout a system life cycle. In particular, the paper shows how the method supports critical evaluations in a URREF-driven life cycle. Such evaluations provide critical feedback for the technical choices and guidance for the planning of activities, making different phases of the life cycle more efficient and making high-quality results more likely.

The future work will focus on multiple aspects of the presented approach. Firstly, the effectiveness of the approach will be validated with more experiments based on a variety of ground truth models. While no special modelling "tricks" were used when building the ground truth model used in this paper, it might still be biased, due to unintended special structural and parametric properties. Secondly, the exploitation of assumptions allowing the use of parametric distributions as well as simplifications based on Context-Specific Independence and Independence of Causal Influence will be further investigated. In this way the estimates of the required sizes of the training data sets could get closer to the true required data set sizes.

Fig. 1 .

 1 Fig. 1. A directed acyclic graph encoding dependencies between phenomena.

  from X c or X i ∈ O by other context variables. This means it has an influence on the class and/or feature variables that is not accounted for by the other context variables. The set of DGP context variables satisfying this condition for the set of observable variables O is called the DGP relevant context C O ⊆ C, i.e. for any Y j ∈ C O there exists at least one path between Y j and X c or X i ∈ O. Such context variables influence the occurrence of the states of the variables that are represented in the trained model M k . Fig. 2.a shows an example where O = {X 1 , X 2 } and the corresponding relevant DGP context is defined over C O = {Y 1 , Y 2 , Y 3 , Y 4 , Y 5 }. Note that the architecture of the trained model M k could explicitly represent only X c and the observed variables X i ∈ O, i.e. it would not contain variables from C O which are explicitly represented in the QM-DGP. Yet, whether included in M k or not, the variables in C O drive the QM-DGP by influencing distributions at different places in the causal process, thus influencing the frequencies of combinations of observed states of X c and X i ∈ O. Thus, possible combinations of states in C O and states of variables in the trained model M k must be explicitly considered when estimating the required size of the training sets.

Fig. 2 .

 2 Fig. 2. a.) An example QM-DGP describing dependencies in V. The black nodes correspond to the variables that are relevant for the estimation of the complexity of the relations between the class variable Xc and the observed variables X 1 and X 2 in the trained model M k . Gray nodes are observed context and feature variables that are irrelevant for inference over Xc. b.) A reduced model explicitly relating only X i ∈ O, Xc and C O .

Fig. 3 .

 3 Fig. 3. Topology of the basic PGM model defined over variables V captured by the QM-DGP shown in Fig. 1. Variable ContextSummary was added as it was known that there are three types of contexts influencing Class.

ESTIMATED

  1, TRAINING DATA VOLUMES |D train | AND |D train | ′ VS. THE SUFFICIENT DATA VOLUMES |D train | f lat .

	Exp	|D train |	|D train |'	|D train | f lat	error f lat	error min
	1	38880	36000	≈ 36000	15.47%	15.33%
	2	38880	72000	≈ 40000	16.06%	15.98%
	3	38880	42300	≈ 40000	7.02%	6.92%
	4	2160	6000	≈ 6000	23.63%	23.54%
	5	155200	172000	≈ 160000	7.02%	6.92%
	6	155200	540000	≈ 540000	7.04%	6.92%
				TABLE I

We consider relaxing this assumption later.

https://www.merriam-webster.com/dictionary/context

Note that Mauxis not supposed to be used in the classification task.


Giovanni Bortolami

Nathalie Ferrer

Kendra Baumgartner

Sylvain Delzon

David Gramaje

Laurent J Lamarque

Gianfranco Romanazzi

Gregory A Gambetta

Chloé E L Delmas
email: chloe.delmas@inrae.fr

Esca grapevine disease involves leaf hydraulic failure and represents a unique premature senescence process

Keywords: Hydraulic failure, magnesium deficiency, senescence, tyloses, vascular disease, Vitis vinifera

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

INTRODUCTION

The enormous anatomical diversity of flowering plants is a visual representation of their evolution and adaptation to different living environments [START_REF] Crang | Plant Anatomy: A Concept-Based Approach to the Structure of Seed Plants[END_REF].

Plants can modify the anatomy of their cells, tissues and organs based on different environmental conditions and in response to abiotic and biotic stresses (e.g. [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF][START_REF] Trueba | The three-dimensional construction of leaves is coordinated with water use efficiency in conifers[END_REF]. Xylem vascular occlusions are considered a functional anatomical trait that result in response to a broad range of environmental and biotic factors [START_REF] De Micco | Tyloses and gums: a review of structure, function and occurrence of vessel occlusions[END_REF]. They can be caused by gels (or gums), formed by amorphous extracellular materials [START_REF] Rioux | Immunocytochemical evidence that secretion of pectin occurs during gel (gum) and tylosis formation in trees[END_REF], and tyloses, which are expansions of parenchyma cells inside the vessel lumen [START_REF] Zimmermann | The discovery of tylose formation by a viennese lady in 1845[END_REF]).

Vascular occlusions have been identified during senescence process induced by different causes, such as tissue aging [START_REF] Dute | Tyloses in abscission scars of loblolly pine[END_REF][START_REF] Salleo | Changes in stem and leaf hydraulics preceding leaf shedding in Castanea sativa L[END_REF], wounding [START_REF] Sun | Ethylene and not embolism is required for wound-induced tylose development in stems of grapevines[END_REF][START_REF] Sun | Wound-induced vascular occlusions in Vitis vinifera (Vitaceae): Tyloses in summer and gels in winter[END_REF], flooding [START_REF] Davison | The effect of waterlogging on seedlings of Eucalyptus marginata[END_REF], and vascular diseases [START_REF] Pouzoulet | Modeling of xylem vessel occlusion in grapevine[END_REF][START_REF] Mensah | Physiological response of Pinus taeda L. trees to stem inoculation with Leptographium terebrantis[END_REF]. In general, vascular occlusions are formed to hydraulically isolate specific regions of the plant, contributing to wound or pathogen compartmentalization [START_REF] Pearce | Antimicrobial defences in the wood of living trees[END_REF], and increasing decay resistance and mechanical support during heartwood formation [START_REF] De Micco | Tyloses and gums: a review of structure, function and occurrence of vessel occlusions[END_REF]. The consequences of these occlusions have been largely studied in woody perennial organs, where they are thought to contribute to plant resistance to vascular pathogens [START_REF] Venturas | Heritability of Ulmus minor resistance to Dutch elm disease and its relationship to vessel size, but not to xylem vulnerability to drought[END_REF][START_REF] Park | Ceratocystis smalleyi colonization of bitternut hickory and host responses in the xylem[END_REF][START_REF] Rioux | First extensive microscopic study of butternut defense mechanisms following inoculation with the canker pathogen Ophiognomonia clavigignentijuglandacearum reveals compartmentalization of tissue damage[END_REF]. However, they sometimes can lead to decreased hydraulic conductivity [START_REF] Mcelrone | The role of tyloses in crown hydraulic failure of mature walnut trees afflicted by apoplexy disorder[END_REF][START_REF] Deyett | Assessment of Pierce's disease susceptibility in Vitis vinifera cultivars with different pedigrees[END_REF][START_REF] Mensah | Physiological response of Pinus taeda L. trees to stem inoculation with Leptographium terebrantis[END_REF][START_REF] Fanton | Pathogen-induced hydraulic decline limits photosynthesis and starch storage in grapevines (Vitis sp.)[END_REF], and many theoretical articles have hypothesized that excessive production of vascular occlusions during disease could lead to lethal impairment in plant water transport [START_REF] Fradin | Physiology and molecular aspects of Verticillium wilt diseases caused by V. dahliae and V. albo-atrum[END_REF][START_REF] Yadeta | The xylem as battleground for plant hosts and vascular wilt pathogens[END_REF][START_REF] Oliva | The effect of fungal pathogens on the water and carbon economy of trees: implications for drought-induced mortality[END_REF].

In leaves, xylem occlusions have been studied during natural autumn senescence [START_REF] Salleo | Changes in stem and leaf hydraulics preceding leaf shedding in Castanea sativa L[END_REF] and induced premature senescence by the bacterium Xylella spp. [START_REF] Fritschi | Scanning electron microscopy reveals different response pattern of four vitis genotypes to Xylella fastidiosa infection[END_REF][START_REF] Choat | The effects of Pierce's disease on leaf and petiole hydraulic conductance in Vitis vinifera cv. Chardonnay[END_REF]), but their functions or effects on leaf physiology are still unknown. In addition, published reviews on leaf senescence (defined here as the degradation of the cellular structures and transition in cellular metabolism, [START_REF] Woo | Plant leaf senescence and deathregulation by multiple layers of control and implications for aging in general[END_REF]) have focused on molecular mechanisms, rather than the anatomical and physiological changes that occur in the xylem [START_REF] Lim | Leaf senescence[END_REF][START_REF] Schippers | Living to die and dying to live: the survival strategy behind leaf senescence[END_REF], probably because vascular occlusions are frequently observed at the late stages of the senescence process [START_REF] Chaffey | Presence of Tyloses at the Blade/Sheath Junction in Senescing Leaves of Lolium temulentum L[END_REF]. In this context, exploring the underlying origins of xylem occlusions and their effects on plant physiology may improve our understanding of their functional role in leaf senescence resulting from different environmental factors.

Recently, we have associated vascular occlusions with in vivo quantification of xylem hydraulic failure in midribs, petioles, and stems during the development of leaf symptoms caused by the grapevine trunk disease esca [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF](Bortolami et al. , 2021a)).

The wood-infecting fungal pathogens damage the host's vascular system, through enzymatic decomposition of woody cells/tissues and/or production of phytotoxin metabolites [START_REF] Lecomte | New insights into esca of grapevine: the development of foliar symptoms and their association with xylem discoloration[END_REF][START_REF] Gramaje | Managing grapevine trunk diseases with respect to etiology and epidemiology: current strategies and future prospects[END_REF]. Strikingly, vascular occlusions in esca symptomatic leaves or stems were observed at a distance from pathogen infection localized in the trunk or wounds [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF](Bortolami et al. , 2021a)). This fatal disease impacts grape yield and quality worldwide [START_REF] Mondello | Grapevine trunk diseases: a review of fifteen years of trials for their control with chemicals and biocontrol agents[END_REF], and while its severity appears to have a relationship with climate (Bortolami et al. 2021b), the mechanisms behind leaf (and plant) death are largely unknown [START_REF] Claverie | Current knowledge on Grapevine Trunk Diseases with complex etiology: a systemic approach[END_REF].

In grapevine, premature or age-dependent leaf senescence induced by different stressors leads to similar physiological responses and leaf symptom phenotypes that are sometimes hard to distinguish. Esca leaf symptoms consist of partial and total leaf discoloration and scorching, followed by leaf fall [START_REF] Calzarano | Grapevine leaf stripe disease symptoms (esca complex) are reduced by a nutrient and seaweed mixture[END_REF], similar to some mineral deficiencies and naturally occurring autumn senescence. Moreover, a decrease in stomatal conductance was observed during autumn senescence [START_REF] Douthe | Whole-plant water use in field grown grapevine: seasonal and environmental effects on water and carbon balance[END_REF][START_REF] Gowdy | Estimating bulk stomatal conductance in grapevine canopies[END_REF], premature senescence induced by magnesium deficiency [START_REF] Rogiers | Potassium and magnesium mediate the light and CO2 photosynthetic responses of grapevines[END_REF], and esca (Bortolami et al. 2021b). Therefore, we hypothesized that grapevine leaves affected by different stresses would be associated with similar responses of xylem anatomy, namely, the presence of vascular occlusions. In this study, we compared midrib vascular occlusions during leaf symptom development from esca versus leaf senescence induced by magnesium deficiency and autumn in grapevine (Vitis vinifera L.). In addition, we focused on esca leaf symptoms, comparing occlusion production in leaves from esca-infected vineyards across different climatic regions and cultivars. Finally, we followed the progression of vascular occlusions during esca symptom development and, through the use of noninvasive visualization of embolism, we quantified the xylem hydraulic integrity in the blade.

MATERIALS AND METHODS

Plant material and symptoms of senescence

To quantify xylem occlusions during different senescence types, we sampled leaves from V. vinifera cultivars (cv) in the Vitadapt experimental plot [START_REF] Van Leeuwen | An update on the impact of climate change in viticulture and potential adaptations[END_REF]. This plot includes 52 cultivars grafted onto the Selection Oppenheim 4 (SO4) rootstock and planted in 2009 in the Bordeaux region (France, 44°47'23.8"N 0°34'39.7"W). As presented in Table 1,in August 2018, we sampled seventeen healthy (control) leaves, twenty-two esca symptomatic leaves, and six magnesium-deficient leaves from five grapevine varieties. In October 2018, we sampled from the same varieties twenty-one leaves with phenotypes of autumn senescence (Table 1).

Examples of the sampled induced senescence leaf symptoms are presented in Fig. S1 for a white (Chenin) and a red (Castets) cultivar. Single leaves presented partial or total discoloration, or scorched tissue in between the major veins, and we were able to distinguish the different stresses by the whole-plant symptom pattern. Esca leaf symptoms were identified by the so-called 'tiger-stripe' leaves, as described in [START_REF] Lecomte | New insights into esca of grapevine: the development of foliar symptoms and their association with xylem discoloration[END_REF], in the entire length of the stems. We identified the magnesiumdeficiency phenotype in plants with leaves with discolorations only located in the lower part of the canopy and with no scorching. We identified autumn senescence in leaves with total or partial discoloration at the end of the growing season.

To further explore leaf xylem anatomy during esca symptom development, symptomatic and healthy (control) leaves were sampled from eight cultivars (Castets, Chenin, Grenache, Mourvedre, Sangiovese, Sauvignon blanc, Tempranillo, and Tempranillo blanco) from different countries (France, Italy, Spain, and California in the United States). The exact number of replicates per country and variety is presented in Table1. In France, we sampled thirty-nine leaves from five cultivars of the Vitadapt plot in August 2018 as described above. In Italy (Carassai, Ascoli Piceno Province, 43°02'18.07"N 13°39'39.41"E), leaves were sampled in June 2019 from two V. vinifera cultivars , planted in 1989, grafted onto Kober 5BB rootstock. In Spain (La Rioja region, 42°26'19.7"N 1°49'30.5"W), leaves were sampled in late August 2019 from three V. vinifera cultivars, planted in 2013, grafted onto the 110 Richter (110R) rootstock. In California (in the North Coast regions, 39°00'15.1"N 122°51'08.3"W), leaves were sampled in August 2020 from one V. vinifera cultivar , planted in 2000, grafted onto the Teleki 5C (5C) rootstock.

To explore the evolution of occlusion formation over time during esca symptom development, we monitored esca leaf symptoms and sampled leaves on eight potted plants from June (day of the year, doy=172) to September 2018 (doy=262). The experimental setup is described in [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF]. Briefly, 30-year-old V. vinifera cv Sauvignon blanc vines, grafted onto the Millardet de Grasset 101-14 (101-14 MGt) rootstock, were uprooted from the field in February 2018 and transferred into 20L pots. We sampled, over the experimental season 2018, forty-five leaves from three control asymptomatic plants and five esca symptomatic plants. Leaf sample size was as follows: eight control, thirteen asymptomatic leaves before the plant expressed esca symptoms, nine asymptomatic leaves from plants with symptomatic leaves, and fifteen esca symptomatic leaves. In September 2017 and 2018, we brought control and symptomatic plants to synchrotron SOLEIL (PSICHE beamline), and scanned leaf midribs with X-ray microCT, as described in [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF]. The same midribs analyzed in [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF] are reported on here, but we report only novel data on the percentage of occluded vessels quantification (in number), and not the theoretical loss of hydraulic conductivity (PLC).

Light microscopy and occlusion quantification

On each leaf, a one-centimeter section of midrib was cut at one centimeter from the petiole point. Samples collected in France were directly put in a FAA solution composed of 0.64% paraformaldehyde, 50% ethanol, 5% acetic acid, and 44.36% water (v/v). After one to three days in the FAA solution on a shaker at 90 rpm, samples were dehydrated using a graded series of alcohol (80%, 100%, 100% for 30' each) and stored at 4 °C until analysis. Samples collected in California, Italy, and Spain were put directly in 80% alcohol, mailed to France and stored at 4°C until analysis. After one night in the FAA solution, samples were dehydrated using the same graded series (80%, 100%, 100% v/v for 30' each). Samples were then embedded using a graded series of LR White resin (Agar scientific, 33%, 50%, and 66% LR White v/v in ethanol solution for 120' each, and 100% three times for 7 hours each). Finally, samples were polymerized in capsules at 60 °C for 24-48 hours. Transverse sections of 1.8 to 2 µm thickness were cut using an Ultracut S microtome (Reichert) equipped with a glass knife at the Bordeaux Imaging Center, a member of the France Bio Imaging national infrastructure (ANR-10-INBS-04). Cross sections were stained with 0.05% (w/v) Toluidine Blue O. Stained sections were dried and photographed with a DS-Fi3 camera (Nikon, France) mounted on a stereo microscope SMZ1270 (Nikon, France).

By the use of Toluidine blue O dye, we identified the nature of vascular occlusions, which includes gels (i.e. amorphous extracellular material, mainly composed by pectins and polysaccharides, Fig. 1B,D) and tyloses (i.e. expansions of the neighbourvessels parenchyma cells, Fig. 1B,D).

Xylem vessels were identified and quantified in one entire cross-section per leaf using imageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]) and categorized as empty vessels or occluded vessels (presenting gel or tyloses). In addition, we observed a deposition of crystals in vessels of 93% of the samples and thus quantified their presence. To confirm that vascular occlusions were equally distributed within a sample (i.e. in the one-centimeter segment), we quantified vascular occlusions in three cross-sections along the segment (i.e., subsamples) for 29 (over the one-hundred seventy-seven analyzed) midribs. We found that the presence of occlusions did not significantly differ among cross-sections within a sample (F55,12498=0.97, P=0.54, treating repetition, sample identity, and their interaction as fixed effects in an independent linear model, with a binomial distribution for presence/absence of an occlusion, in SAS using the GLIMMIX procedure).

Non-invasive optical determination of xylem functionality

To investigate the extent to which esca impacts xylem functionality and leaf embolism resistance, the onset and propagation of embolism were evaluated in four leaves from three different control asymptomatic plants and in eleven leaves from four different esca symptomatic plants, using the optical vulnerability (OV) technique [START_REF] Brodribb | Visual quantification of embolism reveals leaf vulnerability to hydraulic failure[END_REF]) during a dry-down experiment. In every leaf the region of interest (i.e. the scanned area) included the midrib (at 3-5 cm from the apex of the leaf) in the middle of the scan and approximately 10x3 cm around it. The experiment took place over two weeks (in September 2019) on > 2-m long stems of potted V. vinifera cv Sauvignon blanc plants uprooted in February 2019 from the same plot as the one used for the leaf midrib sampling for occlusion quantification (INRAE, Bordeaux). In the early morning, stems were cut under water at their base, put inside dark plastic bags with humid paper and rapidly transported to the lab. Once at the lab, the abaxial side of intact leaves was fixed on a scanner (Perfection V800 Photo, EPSON, Suna, Japan) using a transparent glass and adhesive tape. Brightness and contrast as well as leaf scanned area were adjusted to optimize visualization of embolisms. Imaging of 991 ± 90 mm 2 (average ± SE) of each leaf was automatically performed every 5 min throughout plant dehydration using a computer automation software (AutoIt 3). Upon completion, the stacks of images, consisting of 1,800 to 2,000 scans per leaf, were analyzed to highlight embolism events revealed as changes in light transmission through the leaf xylem. Analyses were carried out using ImageJ software and following instructions from http://www.opensourceov.org. Briefly, total embolism was quantified by subtracting pixel differences between consecutive images (i.e. pixel values that did not change resulted in a value of zero). In these series, white pixels represented leaf embolism. Noise was removed using the ImageJ outlier removal, and pixel threshold was used to extract embolism from any background noise remaining. The embolism area per image was calculated as the sum of non-zero pixels on the total scanned surface (mm²) or on green leaf surface only (mm², excluding the symptomatic tissue).

We considered the veins that embolized as functional (i.e. containing water under tension), while the remaining veins were considered as non-functional (i.e. containing any combination of air, occlusion, or static water). As stems dehydrated, stem water potential (Ψstem) was simultaneously monitored every 30' using psychrometers (ICT Internationale, Armidale, NSW, Australia), which were installed in the middle of the stem prior to the start of the experiment (i.e. when stems were fully hydrated). The accuracy of psychrometer readings was assessed periodically with a Scholander pressure bomb (SAM Precis, Gradignan, France), using leaves adjacent to the scanned ones and that had been covered for at least 2h with aluminum foil and wrapped in a plastic bag.

Esca leaf symptom severity

Each leaf was photographed before sampling for the leaf xylem anatomy and OV measurements during esca symptom development. We quantified the percentage of green tissue on the upper face of each leaf using ImageJ in order to estimate leaf esca symptom severity. On samples used for OV measurements, this estimation was done on the scanned area only, not on the whole leaf surface. We first detected the green hue ranges on RGB pictures of control-asymptomatic leaves using the color threshold in ImageJ, and then used these green ranges to select and quantify the green pixels in each photo. We finally reported these values to the total leaf surface and obtained a percentage of green tissue per leaf or area analysed. In every cultivar we covered the esca symptom severity spectrum (from low to high percentage of green tissue) as much as possible in order to avoid sampling bias.

Statistical analysis

We investigated whether induced senescence types and cultivars are associated with the probability of occlusion formation in xylem vessels using multiple generalized linear mixed models to compare control versus esca symptomatic plants (fixed effect). Prior to analysis the data (bounded between 0.0001 and 1) were transformed using a logit function as appropriate for analyzing proportions [START_REF] Warton | The arcsine is asinine: the analysis of proportions in ecology[END_REF]. In order to use the logit function the lowest value of 0.0001 was assigned to samples with no presence of occlusions. We investigated whether esca symptomatic and control leaves presented different response in embolized surface during decreasing ΨStem using a generalized linear mixed model with the plant treated as random effect and the interaction between symptom presence and ΨStem as a fixed effect. The relationships between the percentage of occluded vessels and esca symptom severity (expressed in percentage of leaf green tissue) were tested using linear regression models. The effect of the age of symptom on the amount of vascular occlusion was tested with a general linear mixed model on symptomatic leaves, using the sampling date as fixed effect, and the plant as random effect. All statistical tests were performed using the SAS software (SAS 9.4; SAS Institute). We used the GLIMMIX procedure for generalized linear mixed models, and the REG procedure for regression analyses.

The normality of the response variables was tested using a Kolmogorov-Smirnov test implemented in the UNIVARIATE procedure, prior to analyses.

RESULTS

Anatomical diversity of vascular occlusions and presence of crystals

In each sample, we categorised the vessels as occluded by gels and/or tyloses, with depositions of crystals, or with an absence of any structure (Fig. 1). Crystals (both druse and prismatic) were present inside some vessel lumen (in 15% of vessels on average, Fig. 1C). These crystals were more often present in samples from which occlusions were absent (on average, 21% of vessels with crystals in control leaves, versus 10% in esca symptomatic leaves, Fig. S2). We showed that control (asymptomatic) leaves (almost) never had occlusions (in 2% of vessels on average, Fig. 234), and that under microCT X-ray scans (data from [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF]) and optical visualizations (Fig. 5) they were almost fully functional. This relationship suggests that crystals are likely present in functional rather than occluded vessels (see supplemental discussion SD1 for details). Consequently, to evaluate the impact of different stresses on xylem anatomy and water transport, we reported here only the percentages of occlusions, and not of crystals, in different experiments and comparisons.

Vascular occlusions in senescing leaves

To investigate the presence of occlusion during the autumnal or premature leaf senescence induced by different causes, we compared midribs from control, esca symptomatic, magnesium deficient, and autumn senescent leaves (Fig. 2). The amount of vessel occlusions in midribs significantly differs among the four leaf categories (F3,62=19.4, P<0.0001). Midribs in esca-symptomatic leaves presented the highest percentage of occluded vessels (27% ± 4, average ± SE) comparing to autumn-senescent leaves (4.0 ± 1%), control leaves (2.9 ± 1%) and magnesiumdeficient leaves, which had the lowest percentage of occluded vessels (0.53 ± 0.5%).

However, two autumn-senescent midribs, that were statistical outliers, had over 15% occluded vessels (Fig. 2).

Vascular occlusions in esca symptomatic leaves from different cultivars and countries

We quantified the percentage of occluded vessels in esca symptomatic and control (asymptomatic) leaf midribs from four different countries (France, Italy, California in the USA, and Spain) in eight cultivars: Castets, Chenin, Grenache, Mourvedre, Sangiovese, Sauvignon blanc, Tempranillo, and Tempranillo blanco (Fig. 3, Fig. S3, Table S1). Our results show that esca symptomatic leaves presented a significantly higher presence of occlusions compared to controls (F1,93=85.93, P<0.0001), see Table S1 for the detailed comparisons within varieties and countries. Cultivars had significantly different levels of occlusions among the symptomatic samples (F7,48=13.55, P<0.0001 Fig. 3A). However, the variability was high, ranging from no occlusion in symptomatic Grenache midribs to 52 ± 5% of occluded vessels in symptomatic Tempranillo blanco midribs (Fig. 3A). Leaf symptom severity (quantified as the percentage of green leaf tissue) had no significant effect on the leaf occlusion level within symptomatic leaves, except for Sangiovese (Fig. 3B, Table S2).

Nevertheless, the most occluded leaves (above 40%) had the most severe symptoms (less than 40% of green tissue), and among the mildly symptomatic leaves (more than 60% of green tissue) the occlusions rarely occupied more than 30% of the vessels (Fig. 3B). When considering the control leaves (entirely green) in the statistical analysis, the percentage of occluded vessels was significantly related to the percentage of leaf green tissue (R 2 =0.31, P<0.0001).

Vascular occlusion evolution during esca symptom appearance

During one experimental season, we monitored esca leaf symptoms on eight potted plants from June (doy=172) to September 2018 (doy=262, Fig. 4). The symptoms developed at the same time in the season; hence, using 'doy' as a good comparison to evaluate the effect of symptom age on occlusion formation. Using light microscopy, we found that control plants always had low levels of occlusions inside their midribs, as was the case for the majority of asymptomatic leaves both before and after symptoms appeared on other leaves on the same plant (<7% of occluded vessels, Fig. 4). Ten out of fifteen symptomatic leaves had a higher level of occlusions (>14%) compared to controls, as well as two leaves before symptom appearance, and one asymptomatic leaf from a symptomatic plant (Fig. 4). Overall, we found a significant effect of the presence of esca symptoms on the amount of vessel occlusions (i.e. comparing the four leaf categories in Fig. 4, F3,35=9.36, P=0.0001), but there were no changes in the occlusion level over time within the symptomatic leaves (F5,5=1.19, P=0.43), suggesting that occlusions do not increase with symptom age. Scanning midribs with X-ray microCT, we found higher average occluded vessels (compared to light microscopy) both in control and symptomatic midribs (15.2 ± 4% and 62.7 ± 7%, average ± SE, respectively, Fig. 4).

The hydraulic consequences of xylem occlusions

Using a non-invasive optical vulnerability technique, we were able to quantify the embolism spread in control and esca symptomatic leaf veins (Fig. 5,6). At the end of dehydration, when no supplemental embolism formation was detected, we summed all the embolism events within a sample (red vessels, Fig. 5). We found that almost all the veins embolized in control leaves (Fig. 5 A-D), whereas the veins did not embolize in wide portions of the leaf blade in esca symptomatic leaves (Fig. 5 E-M), especially in between the main veins where the leaf was yellow and scorched. In two symptomatic leaves no embolism event was observed (Fig. 5 N,O). In most symptomatic leaves, the primary and secondary order veins readily embolized, whereas the tertiary or above order veins did not. Plotting the embolism spread versus the decrease in stem water potential, we found that control leaves had a final embolized area of 25.1 ± 7 x 100 pixels mm -2 on the entire scanned area, compared to 5.2 ± 2 x 100 pixels mm -2 in symptomatic leaves (Fig. 6A). When only the green surface of the leaves was considered (i.e. excluding the symptomatic discolored and scorched tissues; Fig. 6B), control leaves had the same embolized area evolution (they were completely green), whereas symptomatic leaves had a final embolized area of 13.0 ± 4 x 100 pixels mm -2 (Fig. 6B). We found a significant effect of esca both considering the whole scanned surface (F2,456=219.05 P<0.0001) or only the green area (F2,456=128.80 P<0.0001). In control leaves, embolism events were detected between -1.9 and -3.3 MPa (Fig. 6A,B), whereas in symptomatic leaves these events appeared across a larger range of ΨStem (i.e. between -1.3 and -4.9 MPa, Fig. 6A,B).

Finally, it is worth noting that the total embolized area of symptomatic leaves was almost always less (21 ± 0.1%) than half that of the control leaves (noted with the horizontal line in Fig. 6B).

DISCUSSION

In this study, we highlight the uniqueness of esca leaf symptoms compared to other induced senescence processes. We demonstrated that only esca symptomatic leaves had significant levels of occluded vessels in their midribs compared to those of leaves with magnesium deficiency or undergoing autumn senescence. We investigated esca leaf symptoms in detail and demonstrated that the percentage of occlusion: (i) varied among cultivars; and (ii) were similar among symptomatic leaves collected throughout the season (i.e. occlusions did not increase over time). Finally, using the optical vulnerability (OV) technique, we explored the hydraulic integrity in esca symptomatic leaves. Our finding of non-functional vessels across large portions of esca symptomatic leaf blade, compared to the highest density of functional xylem vessels in the midrib, suggests that vascular occlusions are localized near the scorched and discolored areas of the leaves in between the major veins and at the margins of the leaf.

Esca, a unique senescence process

Comparing different leaves with different senescence types, esca leaf symptoms had the highest levels of vessel occlusion. Both magnesium deficiency and autumn senescence types share in common with esca a leaf chlorosis and a decrease in stomatal conductance (Salleo et al. 2002, Brodribb and[START_REF] Brodribb | Stomatal closure during leaf dehydration, correlation with other leaf physiological traits[END_REF] for autumn senescence, [START_REF] Tränkner | Magnesium deficiency decreases biomass water-use efficiency and increases leaf water-use efficiency and oxidative stress in barley plants[END_REF][START_REF] Rogiers | Potassium and magnesium mediate the light and CO2 photosynthetic responses of grapevines[END_REF] for magnesium deficiency, and [START_REF] Lecomte | New insights into esca of grapevine: the development of foliar symptoms and their association with xylem discoloration[END_REF], Bortolami et al. 2021b for esca). Given that occlusions were absent from leaves with magnesium deficiency, it is likely that the impacts of magnesium deficiency on leaf gas exchange are not related to a loss of leaf xylem hydraulic conductivity. During autumn senescence, occlusions have been detected in parts of the leaf we did not examine, namely the petioles and the stem-petiole junction [START_REF] Chattaway | The development of tyloses and secretion of gum in heartwood formation[END_REF][START_REF] Salleo | Changes in stem and leaf hydraulics preceding leaf shedding in Castanea sativa L[END_REF][START_REF] De Micco | Tyloses and gums: a review of structure, function and occurrence of vessel occlusions[END_REF]. Indeed, during autumn, the hydraulic conductivity decreases in petioles, but not in leaf blades [START_REF] Salleo | Changes in stem and leaf hydraulics preceding leaf shedding in Castanea sativa L[END_REF]. This difference in the spatial distribution of occlusions suggests that the visible similarities between esca-symptom leaves and autumn senescence (described above) are due to different mechanisms. In the most prominent hypothesis of esca leaf symptom formation, toxins are translocated from the fungal biomass (the pathogens reside in the woody tissues) out to the leaves through the vascular system [START_REF] Claverie | Current knowledge on Grapevine Trunk Diseases with complex etiology: a systemic approach[END_REF]). Previously, using microCT X-ray we showed that more basal organs (stems, Bortolami et al. 2021a) are less occluded than distal organs (petioles and midribs, [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF]). Here we show that occlusions are more frequent in the leaf blade than in the midribs (Fig. 5), supporting the hypothesis that fungal toxins are expected to accumulate, and thus initiate a host response in the form of xylem occlusions, where the water flow ends (i.e. peripheral veins). In contrast, during autumn senescence the hormones that initiate the senescence process are synthesized in situ [START_REF] Schippers | Living to die and dying to live: the survival strategy behind leaf senescence[END_REF], suggesting a more local response in the vasculature (for example, only at the abscission point in petioles).

Exploring the vascular occlusions and hydraulic integrity during esca leaf symptoms

Comparing esca symptomatic leaves among cultivars and countries, we found significant levels of occlusion in the majority of the symptomatic leaves analyzed. It has been previously demonstrated that Sauvignon blanc vines (30 year-old plants transplanted from the vineyard into pots and grown in a greenhouse) suffer from occlusion-driven hydraulic failure during esca leaf symptom expression [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF](Bortolami et al. , 2021a)). Here, we demonstrated that occlusions (and subsequent hydraulic failure) are also associated with esca in the field, and this finding is not particular to one specific climate or cultivar (or to our previous greenhouse experiment). However, the range of occlusion levels among cultivars is noteworthy and suggests differences between genotypes regarding the extent of vascular occlusion. This is consistent with the fact that, during other vascular diseases, occlusions can be considered beneficial up until the point at which they impact plant function. In the first case, occlusions efficiently compartmentalize pathogens and limit the spread of infection within a plant [START_REF] Clérivet | Tyloses and gels associated with cellulose accumulation in vessels are responses of plane tree seedlings (Platanus × acerifolia) to the vascular fungus Ceratocystis fimbriata f. sp. platani[END_REF][START_REF] Rioux | First extensive microscopic study of butternut defense mechanisms following inoculation with the canker pathogen Ophiognomonia clavigignentijuglandacearum reveals compartmentalization of tissue damage[END_REF][START_REF] Pouzoulet | Behind the curtain of the compartmentalization process: Exploring how xylem vessel diameter impacts vascular pathogen resistance[END_REF]; in the second case, occlusions interfere with water movement, generating hydraulic failure with detrimental consequences for the plant [START_REF] Sun | Vascular occlusions in grapevines with pierce's disease make disease symptom development worse[END_REF][START_REF] Mensah | Physiological response of Pinus taeda L. trees to stem inoculation with Leptographium terebrantis[END_REF]. When a xylem vessel is occluded, we cannot separate these two consequences. Especially in the case of esca, where the subsequent reduction in water flow should reduce the spread of pathogen-derived toxins as well, while suppressing xylem functionality by hydraulic failure. More studies are needed to test this hypothesis and relate vascular occlusion rates to plant mortality relative to the degree of esca susceptibility in each cultivar.

Following occlusions in leaves from symptomatic plants throughout the season, we observed that esca symptomatic leaves had a higher proportion of occluded vessels than asymptomatic leaves from the same plants and healthy leaves from control plants. Moreover, levels of occlusions were similar throughout the season, indicating that the number of occlusions does not increase over time, but is coincident with the onset of symptoms. In three out of twenty-two samples, occlusions were present in asymptomatic leaves from plants with other symptomatic leaves (light and dark green dots above 10% in Fig. 4). At the same time, we also observed that visual symptoms were sometimes (in five out of fifteen samples) associated with low levels of occlusions (red dots in Fig. 4). These results are also consistent with the comparison among and within cultivars, where the level of occlusions was not related to symptom severity (Fig. 3B). We could explain this variability by the fact that we analyzed 2 µm-thick crosssections on midribs, which can reach 20 cm in length, and as such, we may have underestimated occlusions. Indeed, if we quantified more non-functional vessels using microCT X-ray it is also because we could explore 1cm volume in each sample, increasing the probability of observing occlusions. The comparison with the optical embolism visualization supports this hypothesis, as the midribs are not uniformly functional (or non-functional) along their length. From optical visualizations, we considered each vein with an embolism event during dehydration (i.e. containing water under tension) as functional. We observed that midribs are the most functional parts in symptomatic leaves (Fig. 5) and that many regions of leaf blade were already nonfunctional before we started the dry-down experiment. We can conclude that occlusion-driven hydraulic failure may have a stronger impact on the total leaf hydraulic conductivity than what was previously estimated by X-ray scans in midribs [START_REF] Bortolami | Exploring the hydraulic failure hypothesis of esca leaf symptom formation[END_REF]. Moreover, even when only the remaining green asymptomatic part of the leaves was considered, we quantified that the relative embolized surface was lower in symptomatic leaves compared to controls, reinforcing the hypothesis that vascular occlusions strongly affect the leaf xylem functionality of grapevines with esca.

Conclusions

In this study, we showed that esca leaf symptoms are associated with anatomical modifications that are unique to its proper premature leaf senescence process. Indeed, no vascular occlusions were detected in leaves with magnesium deficiency or autumn senescence. This result reinforced the particularity of esca over other induced senescence types, highlighting the need to understand the underlying physiological S1. (B) Relationship between the percentage of occluded vessels and esca symptom severity (expressed in percentage of green tissue per leaf). Control leaves were excluded from the statistical analysis but are represented on the graphics as blue filled circles for illustration. The colors and markers are the same as panel A: circles for Grenache, squares for Tempranillo, stars for Mourvedre, diamonds for Castets, plus for Chenin, pentagons for Sauvignon blanc, upside-triangles for Sangiovese, and downside-triangles for Tempranillo blanco. The regressions for each cultivar are presented in Table S2, where a significant relationship was found only for Sangiovese.

(

  and pathological) mechanisms of esca pathogenesis. Importantly, this work confirms that vascular occlusions in leaves during esca are associated with hydraulic failure in the leaf blade. The different cultivar (and climatic) susceptibility in occlusion formation during esca could also open new perspectives regarding the use of occlusion quantification to characterize plant resistance to the disease.

FIGURESFigure 1 .

 1 FIGURES

Figure 2 .

 2 Figure 2. Percentage of occluded vessels in Vitis vinifera midribs of control leaves and

Figure 3 .

 3 Figure 3. Occluded vessels [%] in different cultivars from different countries in Vitis

Figure 4 .

 4 Figure 4. Evolution of occluded vessels [%] over the season (July to September) in

Figure 5 .

 5 Figure 5. Visualization of embolism formation during dehydration of Vitis vinifera cv

Figure 6 .

 6 Figure 6. Embolism formation in leaf blade from Vitis vinifera cv Sauvignon blanc from

Acknowledgments

We thank Mark Gowdy and Agnès Destrac-Irvine from UMR EGFV (INRAE) for providing technical help in the Vitadapt plot. We thank the team of UMR SAVE (INRAE) for the technical support in the greenhouse experimentations. We thank Patrick Leger and Regis Burlett from UMR BIOGECO (INRAE) for help with the optical vulnerability method implementation and the SOLEIL synchrotron facility (HRCT beamline PSICHE) for providing the materials and logistics.

Funding

This work was supported by the French Ministry of Agriculture, Agrifood, and Forestry (FranceAgriMer and CNIV) within the PHYSIOPATH project (program Plan National Dépérissement du Vignoble, 22001150-1506) and the LabEx COTE (ANR-10-LABX-45) "Projet Caviplace Platform".

Supplementary data

The following Supplementary Data are available for this article: Table S1. Effect of esca leaf symptoms on the presence of occluded vessels in Vitis vinifera.

Table S2. Linear relationships between the percentage of occluded vessels and esca symptom severity (expressed in percentage of green tissue per symptomatic leaf, control leaves were excluded from the analysis) for each Vitis vinifera cultivar.

Supplementary References

Conflict of interest

None declared.

Author's contributions


domain: sde sdv

text:
Diego Penaranda
email: diego.penaranda-sandoval@inria.fr

; Morales

; Freddy

Guihéneuf

; Bernard

LCA for technologies at low technological readiness level: A case study on microalgae cultivation system

Keywords: Eco-design, Emerging technologies, Microalgae, Sustainable production, TRL (Technology readiness level) Eco-diseño, Tecnologías emergentes, Microalga, Producción sustentable, Nivel de madurez tecnológica Ecodesign, Tecnologias emergentes, Microalgas, Produção sustentável

Appropriate choices in the early technology development phase of a process can avoid large impacts on its future environmental performance. LCA can support efficient eco-conception, driving the development of immature technologies by identifying environmental hotspots and proposing alternatives with reduced impact. This work introduces an LCA-based methodology with an eco-design approach that aims to quantitatively demonstrate the importance in the selection of design parameters on the environmental impacts. The overall environmental impacts are evaluated for different functional units, extending the analysis to identification of process hotpots with iterative sensitivity analysis of the associated parameters. A case study based on an innovative Rotating Algal Biofilm (RAB) technology for microalgae (algae meal) production is presented to illustrate this methodology. The ecodesign parameters were spotted from the process modelling through an iterative analysis. The resulting eco-designed technology was compared with classical approaches for producing protein sources (soymeal and fishmeal), and with other microalgae cultivation technologies (ORP and rotating carpet biofilms). Results show that the NH3 emission factor, fabric support properties and electricity consumption turned out to be the crucial eco-design parameters. The impacts of the new eco-designed technology were reduced in a range from 25% to 88.3%. Algae meal from rotating algal biofilms outperformed the environmental footprint of the other conventional aquafeeds (fishmeal and soymeal). The proposed methodology can guide technology developers to understand the implications of design choices on the future environmental impacts. Since economic allocation was chosen, the evaluated impacts remain highly sensitive to the future price of these products.

Introduction

LCA is a useful tool to reduce the environmental impacts of a product at its design stage [START_REF] Eksi | Life cycle assessment of combined bioheat and biopower production: An eco-design approach[END_REF], by quantifying the relation between the parameters and the environmental impacts. However, traditionally, LCA has been used to evaluate mature technologies [START_REF] Moni | Life cycle assessment of emerging technologies: A review[END_REF]. The limited data, uncertainties and scale up issues of low Technology readiness level (TRL 2-5) technologies, make it very challenging to carry out a standard LCA. Thus, methodological advances in the current LCA framework are required [START_REF] Moni | Life cycle assessment of emerging technologies: A review[END_REF]. Early decisions in the technology design phase can strongly reduce its future impacts, e.g., it has been estimated that around 80% of the total environmental impacts are related to the design phase (Tischner and Deutschland, 2000). We propose an eco-design approach based on LCA to improve the design and further reduce the environmental impacts of a promising and emerging rotating cylinder biofilm technology used to produced two products (microalgae biomass and protein powder). Biofilm systems demonstrated multiple benefits in comparison to conventional cultivation systems, such as photosynthetic efficiency and areal productivity, while considerably reducing the cost for harvesting [START_REF] Wang | The difference in effective light penetration may explain the superiority in photosynthetic efficiency of attached cultivation over the conventional open pond for microalgae[END_REF]Morales et al., 2020). This study identifies the key parameters in the design of the rotating cylinder biofilm system and their influence on the resulting environmental burdens. Finally, we compare the ecodesigned technology with other protein sources, such as soymeal and fishmeal, and with other microalgae cultivation technologies, such as open raceways and rotating carpet biofilms.

Material and methods

The research methodology was carried out including three main stages: i) Process modelling, ii) Environmental assessment, and iii) Selection of eco-design parameters. In the first stage (Process modelling), a preliminary process design is proposed by using specific data from the Inalve S.A. company (France). These data are complemented by literature information for technologies not yet implemented. An excel-based tool was used for the estimation of mass and energy balances of the large-scale algal cultivation and downstream processing steps. The second stage (Environmental assessment) is based on the process modelling outputs (inventory data), which are evaluated in the LCA. A pond-to-gate LCA is performed. This system boundary is divided into four subsystems (1-Water treatment and fertilizer addition, 2 -Cultivation, 3 -Cell disruption and 4 -Protein recovery). Three functional units (FU) are considered: FU1 = 1kg biomass, FU2 = 1 kg algae meal and FU3 = 1000 WNDS (weight nutrient density score). Environmental footprint (EF) and Cumulative Energy demand (CED) methods are used to perform the impact assessment. The EF categories included in the study are Climate change (CC), Particulate matter (Respiratory inorganics, RI), Acidification (terrestrial and freshwater) (A), Land use (LU), Eutrophication terrestrial (ET) and Water scarcity (WS). Finally, in the third stage (Selection of eco-design parameters), the relevant process steps were identified based on the environmental impacts, i.e., process steps with contributions higher than 10% of the total impact in each impact category. The relevant parameters for the hotspots process steps were then identified and evaluated in a sensitivity and iterative analysis. Finally, the eco-designed process was also compared with conventional protein meals (soybean meal and fishmeal) and with other microalgae cultivation technologies (open raceways (ORP) and rotational carpet system (RCAB)).

Results and Discussion

The main contributors on all assessed impact categories are subsystems 1 and 2, around 99%, while only 1% are attributed to subsystems 3 and 4. Processes with contributions above 10% are NH4NO3 production (in subsystem 1), contributing to fossil CED, CC and RI; P2O5 production (in subsystem 1) affecting LU; Cotton production (in subsystem 2) critical process for fossil CED, CC, LU and WS; Polyester production (in subsystem 2), which negatively affects fossil CED; Plastic production (in subsystem 2), representing an adverse effect on fossil CED; Electricity consumption of rotary engine (in subsystem 2) affecting the total CED category; Electricity consumption of blower engine (in subsystem 2) contributing to the total CED category; NH3 emissions (in subsystem 2) affecting the ET, RI and A categories. The parameters selected for the eco-designed system, after sensitivity analysis were: 'Nfertilizer source: NH4NO3', 'P-fertilizer source: P2O5', 'Fabric lifetime: 8 years', 'Fabric material: 100% Oleofin', 'Plastic lifetime and thickness: 8 years and 0.5 mm', 'Rotator power: 0.03 kW', 'Blower power: 0.025 kW', 'PVC lifetime: 25 years' and 'NH3 emission factor: 90 g NH3/kg N'. When comparing the environmental impacts to produce 1 kg of algae biomass (FU1), the lowest is the algae meal produced through rotational cylinder biofilm (where eco-designed technology reports the less impacting option), followed by rotating carpet biofilm, while open raceways have the highest environmental loads. Considering the more refined FU3 (weight nutrient density score), the lowest impacts are reached with the eco-designed process in all the evaluated impact categories. The ecodesigned technology achieves reduction higher than 25% in comparison to before eco-design and higher than 34% with respect to RCAB. When comparing to conventional protein meals (fish meal and soybean), improvements higher than 70.8% are reached for eco-designed algae meal in comparison to fishmeal and soymeal for CC, RI, A, E and CED. However, analyzing LU and WS, reductions higher than 99.7% are obtained by eco-designed algae meal in comparison to soymeal, in the same range of the ones obtained by the fishmeal.

Conclusions

This study proposes an LCA methodology for eco-designing new technologies, in their early design stages. The subprocesses with the highest environmental impact and the most influential parameters were identified. Nutrient production, cylinder production, electricity consumption, greenhouse production and gas emission are the processes with environmental loads higher than 10%. Then, by implementing a sensitivity analysis, the most influential parameters in the environmental design were identified, such as the lifetime and thickness of the plastic used in the cylinder, the power of the blower, the NH3 emission factor, the lifetime of the fabric and its source. Comparing the rotational cylinder cultivation technology (before and after eco-design) showed lower impacts in all impact categories than the other cultivation technologies (open raceway pond and rotational carpet systems). The same result is obtained when comparing algae meal with other protein sources (fish meal and soybean meal). The eco-design approach reduces the environmental impact in all the categories. The ecodesigned system compared to the system before eco-design is 65.7% less impacting for category LU, 88.3% for WS, between 25% and 27.6% for categories CC, RI, A and ET, and 50.3% for CED. The methodology used in this work can be adapted and implemented to analyze other technologies with low TRLs at early design stages, through the analysis, identification and selection of key parameters according to their environmental loads.

Acknowledgements

The authors acknowledge the support of the ANR Photobiofilm Explorer Project-ANR-20-CE43-0008 and of the Région Sud Grant funding the PhD of D. Penaranda.