Ines Fragata

Diogo Prino-Godinho

Leonor R Rodrigues

Miguel A Cruz

Flore Zélé

Oscar Godoy

Sara Magalhães

Evolution in abiotic environments shapes coexistence between two spider mite species

Adaptation to novel environments have been documented at the population, phenotype and genotype level. However, the ecological consequences of this process are often ignored. For example, recent evolutionary history in different environments is expected to lead to increased growth rates and competitive abilities. These traits have been identified as key ingredients underlying species coexistence, which suggests that adaptation to new environments may shape species coexistence patterns. However, this hypothesis remains untested.

To tackle this issue, we performed experimental evolution of two herbivorous spider mite species (Tetranychus urticae and T. evansi) feeding on tomato plants grown under high or low cadmium concentrations. We combined phenotypic analyses with structural stability theory to show that both the cadmium environment and evolution in it changed the coexistence patterns of the two species by increasing niche differences. In fact, the presence of cadmium reduced interspecific competition and led to facilitation between the two herbivores, entailing stable coexistence independently of the previous evolutionary history. Evolution in the cadmium environment also reduced interspecific competition in the ancestral environment, producing stable coexistence. These results show that evolution in a new environment, even in absence of interspecific competitors, affects long-term species coexistence. Importantly, it highlights that biotic interactions (within or between populations) should be accounted for when describing adaptation to novel environments.

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Introduction

The recent development of theoretical frameworks such as modern coexistence theory or structural stability (1-3) has fostered our understanding of the mechanisms through which competing species coexist in ecological time. That is, species may coexist either through a reduction in niche overlap between species (i.e. low interspecific vs intraspecific competition) or via a reduction in fitness differences (i.e. the ability of species grow despite the presence of competitors) [START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF][START_REF] Barabás | Chesson's coexistence theory[END_REF].

Predictions on species coexistence are specific to a given environmental context. Indeed, the strength and signal of species interactions can be modified by the environment [START_REF] Chamberlain | How context dependent are species interactions?[END_REF][START_REF] Liu | Environmental context dependency in species interactions[END_REF], with implications for coexistence. For example, Matias et al [START_REF] Matías | An experimental extreme drought reduces the likelihood of species to coexist despite increasing intransitivity in competitive networks[END_REF] showed that extreme drought decreased fitness differences between plants species, but it also led to increased sensitivity to interspecific competition, reducing niche differences, thereby hampering coexistence [START_REF] Matías | An experimental extreme drought reduces the likelihood of species to coexist despite increasing intransitivity in competitive networks[END_REF]. It is thus key to evaluate both niche and fitness differences (and their underlying traits) in order to accurately predict species coexistence.

Exposure to a given environment over some generations may also affect species coexistence due to evolution-driven changes in trait values. For example, competition between and within species is a strong selective agent [START_REF] Bolnick | Intraspecific competition favours niche width expansion in Drosophila melanogaster[END_REF][START_REF] Dayan | Ecological and community-wide character displacement: The next generation[END_REF][START_REF] Pfennig | Evolution's Wedge Competition and the Origins of Diversity[END_REF][START_REF] Rodrigues | Integrating Competition for Food, Hosts, or Mates via Experimental Evolution[END_REF]. Theory predicts that the presence of competitors selects for the evolution of competitive ability [START_REF] Abrams | The evolution of traits that determine ability in competitive contests[END_REF][START_REF] Bernhardt | The evolution of competitive ability for essential resources[END_REF][START_REF] Sakarchi | The Evolution of Competitive Ability[END_REF]. This, in turn, is predicted to affect species coexistence, through mechanisms such as character displacement [START_REF] Brown | Character displacement[END_REF][START_REF] Germain | Moving Character Displacement beyond Characters Using Contemporary Coexistence Theory[END_REF][START_REF] Edwards | Evolutionarily stable communities: a framework for understanding the role of trait evolution in the maintenance of diversity[END_REF], neighbourdependent selection [START_REF] Vasseur | Eco-evolutionary dynamics enable coexistence via neighbor-dependent selection[END_REF] or a trade-off between competitive ability and the rate of adaptation in a fluctuating environment [START_REF] Yamamichi | Rapid evolution promotes fluctuation-dependent species coexistence[END_REF]. In line with these predictions, empirical, studies have shown that evolving with competitors can modify competitive traits [START_REF] Hart | Effects of rapid evolution on species coexistence[END_REF] and change coexistence patterns [START_REF] Lankau | Rapid evolution and mechanisms of species coexistence[END_REF][START_REF] Zhao | Evolution alters ecological mechanisms of coexistence in experimental microcosms[END_REF][START_REF] Hiltunen | Evolutionary contribution to coexistence of competitors in microbial food webs[END_REF][START_REF] Germain | Evolution of an inferior competitor increases resistance to biological invasion[END_REF].

An important, yet overlooked, potential role of evolution in species coexistence pertains to the fact that traits that affect coexistence may be selected even in the absence of competitors.

For example, species that arrive in an environment before their interspecific competitors will spend more generations in that environment. As population growth rate is highly correlated with fitness, it is expected that this exposure will lead to an increase in the value of this trait. This may either lead to local habitat monopolization, as in 'classical' inhibitory priority effects [START_REF] Urban | Community monopolization: Local adaptation enhances priority effects in an evolving metacommunity[END_REF][START_REF] Fukami | Historical Contingency in Community Assembly: Integrating Niches, Species Pools, and Priority Effects[END_REF][START_REF] Leibold | Regional neutrality evolves through local adaptive niche evolution[END_REF] or foster coexistence, if the species arriving first is the weaker competitor [START_REF] Fragata | Specific sequence of arrival promotes coexistence via spatial niche pre-emption by the weak competitor[END_REF]. For example, adaptation to temperature in an archaeon species resulted in increased growth rate in that environment. This, in turn, has led to this species being more resistant to invasion by a species that typically dominates at high temperatures [START_REF] Nadeau | Adaptation reduces competitive dominance and alters community assembly[END_REF].

Evolution in environments without interspecific competitors may also change traits affecting coexistence outcomes other than the growth rate. Indeed, evolution in environments with stressors, different intraspecific densities or under low concentrations of some nutrients has led to changes in the intraspecific competitive ability [START_REF] Fukano | Evolution of competitive traits changes species diversity in a natural field[END_REF][START_REF] Bernhardt | The evolution of competitive ability for essential resources[END_REF][START_REF] Limberger | Adaptation and competition in deteriorating environments[END_REF]. This, in turn, is expected to affect species coexistence [START_REF] Yamamichi | Intraspecific Adaptation Load: A Mechanism for Species Coexistence[END_REF]. Curiously, although some studies have shown that these evolutionary changes affected community composition [START_REF] Fukano | Evolution of competitive traits changes species diversity in a natural field[END_REF][START_REF] Low-Décarie | The effect of elevated CO 2 on growth and competition in experimental phytoplankton communities[END_REF], none has evaluated how evolution in the absence of interspecific competitors affects the growth rate, intra-and interspecific competition in the novel environment, which is required to predict coexistence and understand its mechanistic basis.

To fill this gap, we performed experimental evolution with two spider-mite species, Tetranychus urticae and T. evansi, feeding on tomato plants (Solanum lycopersicum) grown with and without cadmium. Previous studies from our group have shown that tomato plants can hyperaccumulate cadmium in their leaves, which strongly affects the performance of both spider-mite species [START_REF] Godinho | Effect of Cadmium Accumulation on the Performance of Plants and of Herbivores That Cope Differently With Organic Defenses Biological Materials and Rearing[END_REF][START_REF] Godinho | Concurrent herbivory and metal accumulation: The outcome for plants and herbivores[END_REF]. In addition, it is known that, in plants without cadmium, T. evansi is the superior competitor, excluding T. Urticae, unless it arrives first [START_REF] Fragata | Specific sequence of arrival promotes coexistence via spatial niche pre-emption by the weak competitor[END_REF]. However, we don't know the effects that cadmium accumulation and subsequent evolution in this environment can have in the coexistence of these two species. Here, we estimated competitive ability and intrinsic growth rate of the two species in the ancestral and high cadmium environments.

Combining these data with the structural stability framework, we predicted coexistence patterns between evolved and control populations of the two species in the two environments.

Our initial hypothesis was that evolution in a new environment would increase the intrinsic growth rate of both species. If this change was larger in the inferior competitor (T. urticae) then we expected a reduction in fitness differences. The opposite pattern in fitness differences would happen if the growth rate of T. evansi increased more than T. urticae. At the same time, we also expected that adaptation would decrease intraspecific competition, which could potentially decrease niche differences and reduce the possibility for coexistence. Finally, we also postulated that, if the performance of T. urticae was higher than T. evansi in cadmium environments, we would also see a shift in the coexistence predictions, with increased likelihood in coexistence, as we saw in previous studies. The impact of evolution on coexistence of the two species would then be determined by the magnitude of changes in fitness and niche differences, with coexistence more likely if equalizing mechanisms were stronger than destabilizing mechanisms.

Material and methods

Plant and spider-mite maintenance

Populations were maintained and experiments were performed using tomato plants (Solanum lycopersicum, var MoneyMaker) maintained in a climatic room (25:20 ºC, 65% of humidity, light:dark = 16:8). To maintain the original outbred populations, we used 5-week-old plants, having at least five fully expanded leaves, watered thrice per week. Plants used in the experimental evolution (see below) were watered twice a week with 100 mL of tap water for a duration of two weeks, then transplanted to new pots and watered each week with 100mL tap water and another time with either 100mL of distilled water or 100mL of 2mM cadmium chloride solution during another three weeks. This cadmium concentration of 2mM is highly detrimental to both spider-mite species [START_REF] Godinho | Effect of Cadmium Accumulation on the Performance of Plants and of Herbivores That Cope Differently With Organic Defenses Biological Materials and Rearing[END_REF].

Experimental evolution

Outbred populations, formed via controlled, one-on-one crosses of 200 individuals of 3 and 4 field populations of T. urticae and T. evansi spider mites (see details in [START_REF] Godinho | Creating outbred and inbred populations in haplodiploids to measure adaptive responses in the laboratory[END_REF]) were used to create experimental evolution populations and were maintained in boxes with detached leaves with stems inside a small pot containing water. Twice a week, old leaves were removed, and water and new tomato leaves were added.

Experimental evolution populations were created by transferring 220 adult females from the outbred populations to a box with four tomato leaves, again with their stems in a small pot (2 pots per box), which was replenished every week. Each box contained leaves 2, 3, 4 and 5, each from a different plant. We created 5 populations for each of two selection regimes: cadmium and control, corresponding to mites exposed to leaves from plants watered with a 2mM cadmium) solution or only with water (see above). Every two weeks (corresponding to a mite generation), 220 adult females were transferred by aspiration to a new box containing four new tomato leaves. The remaining mites were kept to form generation T-1. These mites were used as a back-up when less than 220 females were found in the box. If still this did not reach 220 mites, females from the base population were added until 220 adult females were reached (see protocol details in [START_REF] Godinho | Creating outbred and inbred populations in haplodiploids to measure adaptive responses in the laboratory[END_REF]). Populations were thus maintained in discrete generations, in two selection regimes (mites exposed to plants with or without cadmium), each replicated 5 times.

Prior to experiments, individuals from all regimes were placed in a common garden of cadmium-free tomato leaves during two generations. For that, 100 females from each population were transferred to a new box with two tomato leaves. Two weeks later, a new leaf was added. After three weeks, six cohorts of 50 adult females were transferred to petri dishes with cotton soaked in water and two tomato leaflets. Females were left to oviposit for 4 days, and then killed. An additional leaflet and water were added three days later. Adult females for the experiment were collected after one week.

Estimation of competitive ability and intrinsic growth rate

Replicate 2 of T. urticae evolving on leaves with cadmium did not produce enough individuals and was thus not used in trait measurements.

To test if evolution on plants with or without cadmium affected the probability of coexistence between T. urticae and T. evansi in each of these environments we estimated competitive ability and the intrinsic rate of increase for each experimental regime (control and evolved) in the water and cadmium environments, in order to estimate parameters to be used in the theoretical analyses (cf. below).

To estimate the intrinsic growth rate, the intra-and interspecific competitive abilities, we followed the methodology described in Hart et al [START_REF] Hart | How to quantify competitive ability[END_REF]. For that, we cut leaf disks (18mm diameter) from tomato plants grown with or without cadmium and placed one focal female with 1, 3 or 9 females of either the same or species or the competitor species. Leaf discs were placed in a square petri dish on water saturated cotton, with each box containing one disc of each treatment (4 densities and 4 selection regimes, amounting to 16 treatments). Females were left to oviposit for four days and then were removed. After two weeks, the number of adult females per patch was counted. 10 replicates per intra-or intraspecific treatment were done for each of the five experimental populations. The experiment was done in six blocks, the first three with replicates one to three and the last three with replicate populations four and five.

Theoretical estimation of competition and growth parameters

Data collected in the competitive ability experiment was used to parameterize a model, from which we can quantify niche and fitness differences and predict the outcome of competition between the two spider mite species. We assume that the population dynamics in our experiment can be described by Ricker's competition model [START_REF] Fowler | Density dependence as related to life history strategy[END_REF]. This model accounts for positive interactions, unlike the often-used Beverton-Holt model [START_REF] Beverton | On the Dynamics of Exploited Fish Populations[END_REF], and initial data scrutiny suggested these to occur in our system. In addition, this model has also been used in a previous study with spider mites [START_REF] Bisschop | The Demographic Consequences of Adaptation: Evidence from Experimental Evolution[END_REF]. Ricker's model is described by the following equation (equation 1):

(1) 𝑁 𝑖,𝑡+1 𝑁 𝑖,𝑡 = 𝜆 𝑖 𝑒 -𝛼 𝑖𝑖 𝑁 𝑖,𝑡 -𝛼 𝑖𝑗 𝑁 𝑗,𝑡

Where Ni,t+1 is the number of individuals of species i in the next generation, 𝜆 𝑖 the intrinsic growth rate of species i in absence of competitors, 𝛼 𝑖𝑖 is the intraspecific competitive ability describing the per-capita effect of species i on itself, 𝛼 𝑖𝑗 is the interspecific competitive ability describing the per-capita effect of species j on species i, and Ni,t, Nj,t are the number of individuals of species i and j, respectively, in the current generation,. To fit this model, we used the cxr package [START_REF] García-Callejas | cxr: A toolbox for modelling species coexistence in R[END_REF] in R to estimate , ii and ij. We used the function cxr_pm_multifit to obtain the estimation of parameters for all selection regimes per replicate population at the same time Initial parameters were set at i = 1, ii=0.1 and ij=0.1 for all replicates and confidence intervals were estimated using 200 bootstrap samples.

To predict the outcomes of species interactions in our system, we used the structural stability approach [START_REF] Saavedra | A structural approach for understanding multispecies coexistence[END_REF][START_REF] Allen-Perkins | bioRxiv[END_REF][START_REF] García-Callejas | Non-random interactions within and across guilds shape the potential to coexist in multitrophic ecological communities[END_REF]. This approach generates a feasibility domain representing the range of species interactions (including competition and facilitation) that allow for coexistence, based on their intrinsic growth rate.

Using the above-mentioned parameters, we estimated the structural niche differences (), defined as the normalized solid angle of the cone that represents the feasibility domain of a system (Saavedra 2017):

(2) Ω = )

and structural fitness differences (), as the angle between the vector of intrinsic growth rates of the species (r) and the centroid of the feasibility cone (rc):

(3) θ = 𝑎𝑟𝑐𝑜𝑠 ( r * 𝑟 𝑐 ‖𝑟‖ * ‖𝑟 𝑐 ‖ )

For a system to be feasible (that is, for coexistence to occur) the angle has to be lower than 45º. This corresponds to individuals of each species affecting more conspecifics than heterospecifics and fitness differences being smaller than niche differences. Note that these are also the conditions for coexistence to occur in MCT.

To measure each species' vulnerability to exclusion, we tested how coexistence is resistant to perturbations. Following an approach from [START_REF] Allen-Perkins | bioRxiv[END_REF][START_REF] Medeiros | Observed ecological communities are formed by species combinations that are among the most likely to persist under changing environments[END_REF], we estimated the minimal distance between the vector of intrinsic growth rates (r= [I, j]) and the edges of the feasibility cone (vectors corresponding to either [0,

𝛼 22 𝛼 12
] or[0,

𝛼 21 𝛼 11
]) as a proxy for how strong a perturbation should be to change the coexistence outcome in each system. To calculate the distance between the vector of intrinsic growth rates and the edges of the cone of feasibility, we applied the following formula:

(4)

𝑑𝑖𝑠𝑡 𝑖 = cos -1 [ 𝜆 𝑖 𝜆 𝑗 ] . [ 𝛼 21 𝛼 11 ]

Data analyses

Environmental and evolutionary effects on competition

To test the impact of cadmium and of evolution in this environment on the competitive abilities and intrinsic growth rates, we performed the following linear models per species:

( all other factors, but the interaction was not significant in any model, and was thus excluded (data not shown). To compare how evolution in cadmium affected the response to competitors a posteriori contrasts were done between selection regimes of each species using the testInteractions function from the phia package [START_REF] Rosario-Martinez | phia: Post-Hoc Interaction Analysis[END_REF].

To test if evolution in cadmium changed the competitive ability or intrinsic growth rate in that environment, a linear model similar to equations 5 and 6 was performed. These models included only the cadmium environment; thus, the Environment factor was removed.

All analyses were done using R (47), statistical analysis were done using the package "lme4" [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF] and graphical representation was done using "ggplot2" [START_REF] Wickham | ggplot2: Elegant Graphics for Data Analysis[END_REF].

Results

All populations (had reduced intrinsic growth rate on plants with cadmium, as compared to on plants with water only (Figure 1, Table S1). This was also observed in the interspecific competitive ability, with an overall decrease in competition for all selection regimes (Figure 2, Table S2). In fact, competition with heterospecifics in the ancestral environment switches to no competition (overlap with 0) or even facilitation (negative values) for almost all regimes in the environment with cadmium (Figure 2). This is not the case of intraspecific competition, which is not affected by the presence of cadmium (Figure 3, Table S3).

Evolution in the environment with cadmium did not change the intrinsic growth rate of T. urticae (F1,6 = 1.583, P-value=0.255) or T. evansi 's (F1,6 = 1.5, P-value=0.267), nor interspecific competition values for most of the evolved populations (Figure 2, Table S4), in cadmium. However, there was a decrease in interspecific competition for T. urticae in the ancestral environment when both species evolved in cadmium, although it is only marginally significant (Fig. 2, Focal Control vs Focal Evolved: F1,1 = 3,698, P-value=0.064). Interestingly, evolution in cadmium led to an increase in intraspecific competition for T. evansi populations environment (F1,6 = 6.839, P-value=0.039). This was not the case for T. urticae (F1,6 = 0.686, P-value=0.439).

,. This was (Fig 2).Long-term predictions of coexistence patterns for both ancestral regimes (Figure 4, upper left panel) showed a clear shift from exclusion of T. urticae in two of the replicates in the water environment, to coexistence of both species in cadmium, mostly due to changes in structural niche differences. This is in accordance with the observed reduction of interspecific competition in the cadmium environment (Fig 4). This shift was also observed for the combination of T. urticae ancestral and T. evansi evolved regimes (Figure 4, upper right panel), and T. urticae evolved regime with T. evansi control regime (Figure 4, lower left panel).

However, for both evolved regimes, coexistence was possible both in water and cadmium environments, with strong facilitation in the latter environment (Figure 4, lower right panel, structural niche differences above 1 indicate facilitation). In presence of, irrespective of past evolutionary history of the vector of intrinsic growth rates fact, the vectors of intrinsic growth rates were always inside of the feasibility cone in the cadmium environment (Figure S1), which does not happen in the water environment, except when both species evolved in cadmium. The increased stability of coexistence in the cadmium environment is also inferred from an increase in the minimal distance between the vector of intrinsic growth rates and the edges of the feasibility domain (Figure S2), with higher values indicating more stable coexistence. In the water environment, even when coexistence is predicted, the short distance to the edges of the cone suggest that small perturbations could change the dynamics of the system, except when both species evolved in cadmium.

Discussion

Here, we used structural stability theory to predict the impact of the environment (tomato plants with or without cadmium) and evolution in coexistence patterns between two closelyrelated mite species. We found that coexistence was possible in presence of cadmium, irrespective of the evolutionary history of populations. In contrast, on plants without cadmium, coexistence was only possible when the two species had evolved on plants with cadmium.

We find that coexistence is more likely in the presence of cadmium. In fact, feeding in plants that accumulate cadmium entails a major reduction in interspecific competition (irrespective of evolutionary history), leading to a large increase in niche differences in this environment, hence to an increase in the feasibility domain. Interestingly, this reduction in interspecific competition then leads to facilitation between species. Facilitation has been understudied mechanism involved in species persistence [START_REF] Bruno | Inclusion of facilitation into ecological theory[END_REF] and can be particularly important in harsh environments [START_REF] Bruno | Inclusion of facilitation into ecological theory[END_REF][START_REF] Callaway | Competition and Facilitation: A Synthetic Approach to Interactions in Plant Communities by the Ecological Society of America COMPETITION AND FACILITATION: A SYNTHETIC APPROACH TO INTERACTIONS IN PLANT COMMUNITIES[END_REF][START_REF] Bulleri | Facilitation and the niche: Implications for coexistence, range shifts and ecosystem functioning[END_REF]. Possibly the ability of T. evansi and T. urticae to suppress plant defences [START_REF] Kant | Intraspecific variation in a generalist herbivore accounts for differential induction and impact of host plant defences[END_REF][START_REF] Sarmento | A herbivorous mite down-regulates plant defence and produces web to exclude competitors[END_REF][START_REF] Alba | Spider mites suppress tomato defenses downstream of jasmonate and salicylate independently of hormonal crosstalk[END_REF][START_REF] Godinho | Down -regulation of plant defence in a resident spider mite species and its effect upon con -and heterospecifics[END_REF] facilitates growth in cadmium environments. However, this ability was

shown not to interact with the ability to cope with metal-based defences on plants with cadmium [START_REF] Godinho | Effect of Cadmium Accumulation on the Performance of Plants and of Herbivores That Cope Differently With Organic Defenses Biological Materials and Rearing[END_REF]. Still, it is possible that this facilitation has a stronger effect on interspecific competition in cadmium-accumulating plants in comparison to plants without cadmium. We also see a clear reduction in intrinsic growth rates for both species in the cadmium environment, which is in accordance with a previous study using this system [START_REF] Godinho | Concurrent herbivory and metal accumulation: The outcome for plants and herbivores[END_REF]. Changes in the growth rate and interspecific competition were also found in other studies that used modern coexistence theory [START_REF] Matías | An experimental extreme drought reduces the likelihood of species to coexist despite increasing intransitivity in competitive networks[END_REF][START_REF] Wainwright | Distinct responses of niche and fitness differences to water availability underlie variable coexistence outcomes in semiarid annual plant communities[END_REF][START_REF] Grainger | Applying modern coexistence theory to priority effects[END_REF] and/or structural stability frameworks [START_REF] Song | Disentangling the effects of external perturbations on coexistence and priority effects[END_REF][START_REF] Granjel | Nitrogen enrichment and foliar fungal pathogens affect the mechanisms of multispecies plant coexistence[END_REF] to predict coexistence in novel environments. In general, it seems that more stressful environments foster coexistence by equalizing fitness differences and/or reducing interspecific competition.

One of our initial expectations was that evolution in the cadmium environment enhanced population performance. However, intrinsic growth rate did not change in evolved populations of both species., which is in line with a previous study on life-history traits that underlie the growth rate (61). We did, however, observe an increase of intraspecific competition in the T.

evansi populations that evolved in cadmium when in this environment, as compared to populations that evolved in water. This finding is puzzling, as an increase in intraspecific competition is maladaptive, reducing the overall population growth. However, it suggests that resource uptake when together with conspecifics has increased during evolution, despite the fact that there were no changes in intrinsic (individual) growth rate. Zhang et al [START_REF] Zhang | Evolution of increased intraspecific competitive ability following introduction: The importance of relatedness among genotypes[END_REF] also observed an increased intraspecific competitive ability in introduced populations of Alternanthera philoxeroides, without changes in growth rate. The authors suggest that this could happen in invasive genotypes due to reduced herbivory pressure, allowing for the plant to invest resources and become more competitive (following the theory of a trade-off between competition and defense in plants, [START_REF] Herms | The Dilemma of Plants : To Grow or Defend[END_REF]). One possible explanation for the results observed in our study is that the suppression of plant defences by T. evansi requires a certain number of individuals in order to be effective. In fact, most studies quantifying suppression of defences in spider mites use between 5 (55) and 45 [START_REF] Knegt | Tetranychus evansi spider mite populations suppress tomato defenses to varying degrees[END_REF] females, suggesting that plant defence suppression might be only seen in larger cohort of individuals. This highlights that studies addressing evolution in new environment (via experimental evolution) should consider measuring traits that are expressed in presence of conspecifics, and not only individual traits such as fecundity and survival when alone [START_REF] Kawecki | Experimental evolution[END_REF].

Most studies addressing the impact of evolution on coexistence compare populations that have evolved with or without an interspecific competitor [START_REF] Hart | Effects of rapid evolution on species coexistence[END_REF][START_REF] Germain | Evolution of an inferior competitor increases resistance to biological invasion[END_REF]. While this is clearly of great relevance, it is also important to note that competition is generally an indirect interaction, hence how the interaction between organisms with their resources evolves is bound to affect the outcome of competitive interactions as well. However, little is known about this. In our study, we observe no changes in the interspecific competition in the evolved regimes in the new environment. However, we see a marginal reduction in interspecific competition for T.

urticae's evolved regime, when competing in the ancestral environment with the evolved competitor. This suggests that this trait is correlated to others that have been selected in the novel environment. In fact, theory has considered the possibility of a trade-off between growth and resistance to interspecific competition, with important consequences for coexistence [START_REF] Wittmann | Eco-Evolutionary Buffering : Rapid Evolution Facilitates Regional Species Coexistence despite Local Priority Effects[END_REF].

Other empirical studies have shown that evolution of a single species in a new environment can change interspecific competitive ability [START_REF] Limberger | Adaptation and competition in deteriorating environments[END_REF][START_REF] Low-Décarie | The effect of elevated CO 2 on growth and competition in experimental phytoplankton communities[END_REF][START_REF] Bach | Rapid evolution of highly variable competitive abilities in a key phytoplankton species[END_REF] . However, most of them do not predict the impact of changes in interspecific competition in coexistence of species. In our study, we find that evolving in cadmium favours coexistence in its absence, due to an increase in niche differences in the ancestral environment. This may be due to a slight reduction (marginal significance) in interspecific competitive ability for the inferior competitor (T. urticae) after evolution in cadmium and a slight increase (non-significant) in the superior competitor in the ancestral environment. Despite the small magnitude of these changes, their combined effect has an important impact on species coexistence. While the mechanisms through which this shift occurs are unclear, this type of pattern has been observed previously in the same system.

Indeed, niche preemption by the inferior competitor (T. urticae) can shift the outcome of competitive interactions between the two species, from extinction to stable coexistence [START_REF] Fragata | Specific sequence of arrival promotes coexistence via spatial niche pre-emption by the weak competitor[END_REF].

Thus, several mechanisms (ecological and evolutionary) may affect coexistence between species. Specifically, it will be important to incorporate trait changes in response to selective pressures and how this affects interactions between species, when predicting coexistence, both in empirical [START_REF] Lankau | Rapid evolution and mechanisms of species coexistence[END_REF][START_REF] Zhao | Evolution alters ecological mechanisms of coexistence in experimental microcosms[END_REF][START_REF] Hiltunen | Evolutionary contribution to coexistence of competitors in microbial food webs[END_REF][START_REF] Germain | Evolution of an inferior competitor increases resistance to biological invasion[END_REF] and theoretical studies [START_REF] Yamamichi | Integrating eco-evolutionary dynamics and modern coexistence theory[END_REF][START_REF] Yamamichi | Rapid evolution promotes fluctuation-dependent species coexistence[END_REF].

Our study highlights that it is important to combine experimental evolution with ecological theory to be able to fully predict species persistence and to understand the mechanisms through which species adapt to a new environment. On one side, there has been an increase in the attention to how species interactions evolve in response to a new environment [START_REF] Bolnick | Intraspecific competition favours niche width expansion in Drosophila melanogaster[END_REF][START_REF] Fukano | Evolution of competitive traits changes species diversity in a natural field[END_REF][START_REF] Bernhardt | The evolution of competitive ability for essential resources[END_REF][START_REF] Limberger | Adaptation and competition in deteriorating environments[END_REF][START_REF] Low-Décarie | The effect of elevated CO 2 on growth and competition in experimental phytoplankton communities[END_REF].

However, these studies generally quantify evolution by measuring life-history traits of individuals when alone [START_REF] Kawecki | Experimental evolution[END_REF][START_REF] Garland | Experimental Evolution: Concepts, Methods and Applications of Selection Experiments[END_REF] and this may not reflect the conditions in which populations evolve [START_REF] Chippindale | The devil in the details of life-history evolution: instability and reversal of genetic correlations during selection on Drosophila development[END_REF], masking the mechanisms involved in adaptation. On the other side, ecological studies have also to gain when incorporating past evolutionary history to understand how species interact and coexist [START_REF] Urban | Community monopolization: Local adaptation enhances priority effects in an evolving metacommunity[END_REF][START_REF] Leibold | Regional neutrality evolves through local adaptive niche evolution[END_REF][START_REF] Yamamichi | Intraspecific Adaptation Load: A Mechanism for Species Coexistence[END_REF][START_REF] Wittmann | Eco-Evolutionary Buffering : Rapid Evolution Facilitates Regional Species Coexistence despite Local Priority Effects[END_REF]. Currently, it is well established that quick evolution can operate in ecological times [START_REF] Carroll | Evolution on ecological time-scales[END_REF] and that ecological interactions can shape evolutionary trajectories [START_REF] Hendry | Eco-evolutionary dynamics[END_REF], the next step is to merge theoretical frameworks from both fields to predict how eco-evolutionary interactions affects persistence of communities and design well informed empirical studies to test them.

Acknowledgments:

5 )

 5 YF= Environment + Focal Selection Regime +  (6) YF= Environment + (Focal Selection Regime * Competitor Selection Regime) +  Where YF corresponds to either intrinsic growth rate and intraspecific competitive ability (equation 5) or interspecific competitive ability (equation 6) of T. urticae or T. evansi, Environment to a fixed factor with two levels (cadmium and water) and Focal Selection Regime to a fixed factor with two levels (control, evolved) corresponding to the selection regime of the focal species, Competitor Selection Regime to a fixed factor with two levels (control, evolved) corresponding to the selection regime of the competitor species and  to the residual error. Models were initially tested including the interaction between Environment and

FiguresFigure 1 -

 1 Figures

Figure 2 -Figure 3 -

 23 Figure 2 -Interspecific competitive ability for T. urticae and T. evansi depending on focal and competitor selection regime, in cadmium (A, B) and water (C, D) environments.Boxplots represent variation across the five (or four in case of T. urticae evolved regime) experimental replicates. Note that the scales are different between the two panels.

Figure 4 -

 4 Figure 4 -Map of structural niche and fitness differences according to the focal and competitor selection regime, in water (blue shapes) and cadmium (red shapes) environment. Standard error represents the variation of the five population replicates (or four in the case of the T. urticae evolved regime). Smaller points represent the value from each experimental replicate.

  MINECO) and by the European Social Fund through the Ramón y Cajal Program (RYC2017-23666). The authors acknowledge stimulating discussion with all members of the Mite Squad and Raul Costa-Pereira, which have significantly improved the experimental design and interpretation of the results, and Marta Artal and Liesbeth de Jong for invaluable infrastructure at meetings in Sevilla.

	This work was financed by an ERC (European Research Council) consolidator grant
	COMPCON, GA 725419 attributed to SM and by FCT (Fundação para Ciência e Tecnologia)
	with the Junior researcher contract (CEECIND/02616/2018) attributed to IF. OG
	acknowledges financial support provided by the Spanish Ministry of Economy and
	Competitiveness (

Competing interests: Authors declare no competing interests.

T. evansi T. urticae

Intrinsic growth rate B) Water environment

Supplementary Figures

Figure S1 -Feasibility domain for the different combinations of evolved and control regimes of T. urticae (Tu) and T. evansi (Te). The arrow represents the vector of intrinsic growth for the two populations and the edges of the cone represent the area under which the isoclines cross at positive abundances. In order for coexistence to occur, the vector of intrinsic growth has to fall within the cone. Red isoclines correspond to T. evansi and green isoclines to T. urticae.

Figure S2

-Minimum distance between the vector of intrinsic growth rate and the edges of the feasibility domain for water (blue) and cadmium (red) environments. Triangle shape


Ilhem Slama

Oussama Ben-Ammar

Simon Thevenin

Alexandre Dolgui

Stochastic approaches for multi-echelon disassembly lot-sizing under random lead times

Keywords: Reverse logistic, disassembly lot-sizing, random lead time, stochastic programming

With the increasing focus on environmental issues, manufacturers are facing pressure to adopt end-of-life item collection practices and maximize the reuse of components or sub-assemblies to their fullest potential. The decision-making processes for disassembly planning and components inventory management become critical as they directly impact a company's production costs and service level. In this particular context, Reverse Material Requirements Planning (RMRP) is a widely utilized method to determine the optimal lot sizes of endof-life (EoL) products for disassembly, ensuring sufficient component supply. Traditionally, these lot sizes are calculated based on deterministic and dynamic demand assumptions when disassembly lead times are either zero or deterministic. However, in this work, we investigate optimization approaches for RMRP systems that consider disassembly lead time uncertainties, in a disassembly multi-echelon lot-sizing problem. We proposed stochastic programming models based on a Monte Carlo simulation approach whose performance is validated that are validated Their performance is validated on several numerical tests.

Introduction and related publications

Environmental and energy issues are becoming increasingly big issues. Product recovery processes have become an indispensable focus of attention for the industry and for the reverse logistics management research community. There have been numerous papers on this issue, with a strong focus on reverse logistics supplychain optimization problems due to their role in reducing environmental impacts [START_REF] Kim | Multi-period disassembly levelling and lot-sizing for multiple product types with parts commonality[END_REF]. Here we investigate disassembly systems, which are one of the key links in the reverse logistics network. The disassembly process is a methodical extraction of valuable components. The scholarship has considered a number of disassembly optimization problems, including the disassembly line balancing problem, the disassembly sequencing problem, and the disassembly lot-sizing problem, etc. The disassembly lot-sizing (DLS) problem is examined in this study. Finding the best lot sizes for various time periods while reducing the expenses of the disassembly system constitutes a DLS challenge. These lot sizes are typically calculated based on deterministic and dynamic demand assumptions when disassembly lead times are zero or deterministic.

Many researchers have applied stochastic, [e.g., 2, 3, 4] and deterministic algorithms [e.g., [START_REF] Slama | New mixed integer approach to solve a multi-level capacitated disassembly lot-sizing problem with defective items and backlogging[END_REF][START_REF] Kim | Capacitated disassembly scheduling: minimizing the number of products disassembled[END_REF] to determine the optimal disassembly scheduling of complex end-of-life (EoL) product. Managing disassembly operations under the uncertainty of the disassembly process is very challenging in practice, due to the lack of planning and control systems for the remanufacturing systems. When an EoL product is disassembled, it is fundamental to ensure that it is the right model to be supplied. Owing to the complexity of the disassembly operation that is done manually, the workforce is often the major factor that provokes the uncertainly of the disassembly process in terms of its timing, and then, the disassembly operation of EoL product faces stochastic disassembly lead times. However, due to the uncertainty of the disassembly process, it is very hard to determine the availability CIE50 Proceedings, October 30-November 2, 2023 American University of Sharjah, UAE of a specific component. This uncertainty may be caused also by technical problems (absenteeism, limited disassembly capacity, quality problem, etc.). In this paper, the uncertainty of lead time is modeled through scenarios over the planning horizon.

The multi-echelon disassembly lot-sizing problem is taken into account. To address the static and dynamic decision frameworks, a two-stage and multi-stage model is created, respectively. Many solution approaches are suggested because two-stage and multi-stage stochastic algorithms are not practical in large-scale applications. First of all, for the static framework, we proposed a new reformulation of the inventory constraint that greatly lowers the overall number of scenarios and enables real-time static judgments. Second, we created heuristics for the dynamic framework, combining them with a Monte Carlo sampling method. Finally, we use a rolling horizon implementation for the dynamic framework.

Problem description

The case of a multi-echelon disassembly system and one type of end-of-life product is studied. Over the planning horizon, there will be a certain amount of demand from customers for disassembled items (the last level of the BOM). We make the loosely general assumption that there is no external demand for the subassemblies items (intermediate level). However, the parent item i (can be root item and sub-assembly item) that has been disassembled is available after a stochastic lead time L i . These stochastic lead times are the intervals between the beginning of the disassembly process and the availability date of each parent item that has been disassembled. The disassembled quantity of the parent item i is thus available in period t + L i if any disassembly operation begins in period t.

For each parent item, i at each time t, the probability distribution of the disassembly lead time is known and is bounded over predetermined intervals [L - i , L + i ]. Additionally, a setup cost is incurred in that period if any disassembly order for the parent item is released, and the disassembly capacity is considered to be unlimited over the planning horizon. Finally, we offer a scenario-based stochastic optimization formulation in the current study.

For each item, an inventory holding cost is considered if the amount of disassembled items received exceeds the demand. Conversely, a backlog cost is paid when the demand for the leaf item in a period is backlogged (it can be satisfied in the next periods). The backlog quantity at the end of the horizon can be interpreted as the lost sale and a penalty cost is incurred. In order to meet all leaf item requests and reduce overall system costs, including setup, inventory, lost sales, and backlog expenses, it is necessary to determine the best disassembly order and quantity for each parent item.

Solution approaches

As mentioned early, two decision frameworks, known as static and dynamic are developed in this paper. The static decisions framework can be represented by a Two-Stage stochastic Mixed Integer Linear Program formulation (TS-MILP). The first stage variables correspond to the decisions made in period 0 before observing the disassembly lead time. These decisions are the setup and disassembly quantity for each item in each period. The second stage variables, also called recourse decisions, correspond to the inventory, backlog, and lost sale levels of each item at the end of each period. These decisions are observed after the realization of the disassembly lead time for each scenario. The proposed two-stage model describes the random lead time through all possible scenarios. However, the size of the scenario set increases exponentially with the number of periods, and the resulting program requires too much time and memory resources to be solved. Consequently, we developed a new formulation of the inventory constraint that significantly reduces the number of scenarios. The resulting model significantly improves the effectiveness of the approach.

The main drawback of the TS-MILP is that it does account for dynamic decision-making over multiple periods of the planning horizon. To extend the two-stage stochastic programming model by allowing revised CIE50 Proceedings, October 30-November 2, 2023 American University of Sharjah, UAE decisions in each period, we model the dynamic decision framework with a multi-stage stochastic Mixed Integer Linear Program model (MS-MILP). Because the proposed MS-MILP, is based on all possible scenarios, it is intractable. To make it tractable, an approach coupling Monte Carlo (MC) simulation and the MS-MILP is suggested. Finally, a rolling horizon strategy coupled with a multi-stage is developed to deal with the dynamic decision frameworks. The disassembly decisions are updated in each period of the planning horizon after observing the value of the lead time up to that period. As far as we are aware, there is no efficient approach available for this particular version of the stochastic multi-stage disassembly lot-sizing model.

Conclusion

The use of stochastic optimization in the disassembly lot-sizing problem is investigated in this paper. First, in a static and dynamic decision context, we propose a two-stage and a multi-stage model for the multi-echelon uncapacitated lot-sizing problem. Disassembly quantities in the two-stage model are constant throughout the whole horizon. On the other hand, the multi-stage model takes into account the dynamic decision framework in which the disassembly amounts for each period are gradually defined. Second, we suggest effective scenario aggregation, a Monte Carlo sampling technique, and a framework for rolling horizon solutions to cope with large-scale occurrences. Third, we show the effectiveness and performance of the suggested stochastic optimization approaches through numerical experiments. The results show that the stochastic optimization for the disassembly lot-sizing problem is considerably more beneficial in a dynamic setting because the generated plans are significantly less expensive and take up less CPU time than those made by conventional methods. Finally, future research on this topic would be interesting if it took into account other actual model characteristics like consumer demand and yield from disassembly as stochastic. Furthermore, only stochastic programming techniques are considered in this work; nonetheless, a robust model might be recommended.


Dr Soroush Naseri
email: soroush.naseri@unige.ch

Dr Inès Taarit
email: ines.taarit@unige.ch

Dr Hélène Bolvin

Jean-Claude Bünzli

Dr Alexandre Fürstenberg

Dr Laure Guénée

Dr Giau Le-Hoang

Dr Mohsen Mirzakhani

Dr Homayoun Nozary

Dr Arnulf Rosspeintner

Prof. Dr Claude Piguet
email: claude.piguet@unige.ch

Dr J.-C Bünzli

Symmetry and Rigidity for Boosting Erbium-Based Molecular Light-Upconversion in Solution

Keywords: molecular upconversion, erbium, heteroleptic complexes, single molecule

Previously limited to highly symmetrical homoleptic triple-helical complexes [Er(Lk)

where Lk are polyaromatic tridentate ligands, single-center molecular-based upconversion using linear optics and exploiting the excited-state absorption mechanism (ESA) greatly benefits from the design of stable and low-symmetrical [LkEr(hfa)3] heteroleptic adducts (hfa - = hexafluoroacetylacetonate anion). Depending on (i) the extended -electron delocalization, (ii) the flexibility, and (iii) the heavy atom effect brought by the bound ligand Lk, the nearinfrared (801 nm) to visible green (542 nm) upconversion quantum yield measured for [LkEr(hfa)3] in solution at room temperature can be boosted by up to three orders of magnitude.

Introduction

The conversion of low-energy photons toward higher energies, much beyond the standard thermally-activated vibrational Stokes' shifts, is referred to as light upconversion. It remains challenging in both physics and chemistry since it suggests some apparent deviations from the well-accepted law of energy degradation. [START_REF] Prasad | Introduction to Nonlinear Optical Effects in Molecules & Polymers[END_REF] Such process was theoretically predicted by Goeppert-Mayer in 1931 [START_REF] Goeppert-Mayer | [END_REF] when considering the consequences of the non-linear dependence of the refractive index on incident light. [3], [4] Indeed, the polarization of the macroscopic medium produced by an intense electric field at  frequency results in a linear response at the same frequency (= linear optics), together with additional oscillating polarizations of the medium at twice (2, second order polarization) and thrice (3, third order polarization) the incident frequency (= non-linear optics, NLO). [START_REF] Prasad | Introduction to Nonlinear Optical Effects in Molecules & Polymers[END_REF] A related approach applies for molecules characterized by linear  polarizability (linear response) together with first and second  hyperpolarizabilities (non-linear response at higher frequencies). [START_REF] Prasad | Introduction to Nonlinear Optical Effects in Molecules & Polymers[END_REF] However, even for modern optimized polarized materials, [5], [6] the non-linear responses are so weak (typically / = 10 -8 for first-order and / = 10 -12 for second-order hyperpolarizabilities) that NLO upconversion had to wait the discovery of intense coherent laser excitation beams in the early sixties [7] to be experimentally demonstrated. [8], [9] Nowadays, the easy access to intense pulsed-femtosecond lasers (incident power intensity P  10 9 Wꞏcm -2 ) may compensate for the inherent inefficiency of NLO materials, leading to modern applications as deeply penetrating beams for addressing biological probes [10]- [START_REF] Bui | [END_REF] or as optical limiting devices. [14]- [16] Scheme 1. a) Kinetic scheme and b) associated differential matrix equations depicting the modeling of the one-ion excited-state absorption (ESA) process occurring upon off-resonance irradiation into the activator-centered absorption band where

  exc A i j
k  (in s -1 ) corresponds to the excitation rate constants (eq 1) [57] and A j i k  stands for the global (sum of radiative and nonradiative contribution) decay rate constant of level j into level i. [18] With this in mind, detectable light-upconversion induced under weak excitation power intensities compatible with normal lamps or solar irradiance (P  0.1-1.0 Wcm -2 ) is limited to the exclusive use of linear optics (Scheme 1a). [17] An initial photon absorption reaches a real intermediate excited state with a long lifetime (A* in Scheme 1), which is exploited as a relay

A A * 0 1 2 A ** Energy exc(1 2) A k  exc(0 1) A k  1 0 A k  2 1 A k  2 0 A k  ESA a) b)     0 0 exc(0 1) 1 0 2 0 A A A A A 1 1 exc(0 1) exc(1 2) 1 0 2 1 A A A A A A 2 2 exc(1 2) 2 1 2 0 A A A A A 0 dN dt N k k k dN dt k k k k N dN dt N k k k                                                     
for the absorption of a second photon leading to a higher excited state A ** . An ultimate radiative relaxation to the ground state A, as quantified by its intrinsic radiative quantum yield

  2 0 2 1 2 0 A A , r a d A A k k k      
, completes the light-upconversion process (Scheme 1). [17] A first hint based on successive absorptions relying on linear optics was proposed by Bloembergen for the potential design of infra-red quantum counters. [19] For addressing this challenge, chemists logically focused on systems possessing long-lived intermediate excited states, i.e., triplet states in polyaromatic organic molecules [20], [21] or 2S+1 LJ spectroscopic levels in f-block trivalent centers doped in low-phonon ionic solids. [22], [23] Due to the strict respect of the spin selection rule in polyaromatic scaffolds (negligible spin-orbit coupling), there is no chance to reach a strongly emissive singlet state via the absorption of a second photon by an intermediate longlived triplet excited state in pure organic chromophores (ESA mechanism). Consequently, organic-based (linear) upconversion exploits the alternative triplet-triplet annihilation mechanism (TTA), which requires the diffusion and collision of two excited aromatic triplet acceptors. [24]- [26] This methodology is thus mainly [27] limited to intermolecular processes occurring in solution, rubbery polymeric materials, or solid matrices. [28], [29], [30] This constraint is removed for 4f-block elements since their considerable spin-orbit coupling constants relax the spin rule. However, the lanthanide-based excited-state absorption (ESA) upconversion mechanism remains limited by the weak absorption coefficients accompanying the parityforbidden forced electric dipole transitions

(   exc A i j
k  in Scheme 1). A clever bypass, referred to as Energy Transfer Upconversion: ETU, considers the use of additional strongly absorbing sensitizers (S) as partners for feeding the lanthanide activator (A) via successive SA energy transfers. [17], [23], [31] . [32] Using plasmon surfaces [29], [33]- [35] or organic dyes [29], [36], [37] as sensitizers for lanthanide activators in doped ionic solids or nanoparticles opened the door toward applications [29] with upconversion quantum yields overpassing 10% and large associated brightness. [38]- [40] Miniaturization to reach the molecular level in lanthanide coordination complexes is hindered by the drastic reduction of the lifetimes of the intermediate excited relays ( 1

1 0 A A 1 k    in Scheme 1
) due to a massive increase in non-radiative relaxation processes produced by the considerable thermal vibrational bath found in molecules. [41] Consequently, the few dozens of lanthanide-containing molecular complexes displaying detectable (linear) light upconversion under weak excitation intensity powers (P ≤ 40 Wcm -2 ) [18], [42]- [49] relied mainly on ETU [50]- [53] or on related multicenter cooperative upconversion (CU) processes. [54]- [56] However, the synthetic difficulties associated with the non-statistical combination of sensitizers and activators within a single molecular entity for programming ETU or CU mechanisms, particularly when both partners are open-shell labile lanthanide cations, [48], [54]- [56] pave the way for the single-center excited-state absorption mechanism (ESA) to rise as the ultimate fully controlled upconversion process programmed at the molecular level in the absence of statistical doping. [57]- [60] For boosting the ESA mechanism, the first criterion concerns the f-f absorption cross sections A i j   , which should be rationally programmed in the target coordination complexes to maximize the excitation rate constants exc( ) A i j k  under reasonable pump intensities P (in Wcm -2 ) as modeled in eq (1). [61] exc( ) 21 P P A A A 3.8 10

i j i j i j k P P hc hc            ( 1 )
p is the pump wavelength (in cm), h is the Planck constant (in Jꞏs), and c is the speed of light in vacuum (in cmꞏs -1 ). The absorption cross section of the activator A i j   (in cm 2 ) is related to its decadic molar absorption coefficient  ij (in L/molcm) with 21 3.8 10

i j i j       
. [62] Solving the differential matrix equation pertinent to the single-center ESA mechanism (Scheme 1b) for the steady-state (S-S) conditions

               2 2 0 A,rad A,S-S up A 0 1 exc 0 1 exc 1 2 A A , S -S A A , S -S exc 1 2 2 0 A A , r a d exc 1 2 exc 1 2 1 0 2 1 2 0 2 0 A A A A A A 2 0 exc 1 2 A,rad A 1 0 2 1 2 0 A A A
Total emitted photons time unit Total absorbed photons time unit

k N k N k N k k k k k k k k k k k k k                            1 2 21 1 2 2 0 P A A A,rad A A,ESA A 3.8 10 P k hc                     ( 2 )
Under weak incident excitation power used for inducing linear upconversion in molecular complexes (P = 0.1-40 Wꞏcm -2 ), [18], [42]- [59] the rate constants of the excitation processes

(   exc A i j k  )
    exc 1 2 up 1 0 A A A A k k       , where   1 1 0 A A 1 k   
is the lifetime of the intermediate excited relay level 1 and A corresponds to the intrinsic quantum yield of the final upconverted emissive level 2 . In solution at room temperature, where lanthanide complexes exist as isolated molecular species, the ESA mechanism has been implemented mainly in erbium complexes [46]- [18], [60] possessing 4 I13/2 excited relay with microsecond lifetimes and intrinsic emission quantum yield Er  10 -5 for the emissive Er( 4 S3/2) level (Figure 1). [59] Combined with the limited excitation rate constants

  exc 1 2 A k   10
s -1 computed with eq (1) at P = 25 Wcm -2 , [59] the upconverting quantum yields reported for the molecular Er 10 -9 for the homoleptic triple-stranded complex [Er(Et-bzimpy)3] 3+ (Figure 1). [59] complex (taken from the crystal structure of [Er(Et-bzimpy)3](ClO4)3ꞏ2C2H3N) [69] and b)

proposed Excited-state Absorption (ESA) mechanism responsible for the red (801 nm)-to-green (520-540 nm) light upconversion observed in solution at room temperature. [59] In our quest for pushing single-center molecular upconversion within acceptable efficiency limits, we hypothesized that lowering the symmetry around the Er(III) ion would lead to larger transition probabilities and, furthermore, rigidifying the ligands would lesser vibrational quenching. Subtle correlations exist between the intensities of the forced electric dipole 4f-4f transitions and the nature and geometry of the coordination spheres in lanthanide complexes due to the mixing between 4f N states with opposite parity intra-metal excitation configurations (such as 4f N-1 5d or 4f N-1 5g following the Judd-Ofelt theory), or with intra-ligand excitation configurations via the crystal field generated by the oscillating induced dipole moments on the ligands following the dynamic coupling model. [START_REF] Görller-Walrand | Handbook on the Physics and Chemistry of Rare Earths[END_REF], [START_REF] Hatanaka | [END_REF] Being aware of these effects, we moved from highly symmetrical triple-helical [ErL3] 3+ complexes illustrated in Figure 1a [59] toward heteroleptic [LkEr(hfa)3] adducts based on the substituted tridentate 2,6bis(benzimidazole)pyridine scaffolds (hfa -= hexafluoroacetylacetonate). [65]- [68] The reported adducts are unique examples of fully characterized and stable heteroleptic lanthanide complexes for which the single-center NIR to visible upconversion ESA mechanism is boosted by two to three orders of magnitude at room temperature in diluted solutions. ). [66]- [68] The heteroleptic [LkEr(hfa)3] adducts (Lk = L1-L9, Figure 2a) have been designed paying particular attention (i) to rationally introduce bromine substituents for exploring the heavy atom effect due to spin-orbit coupling (L1L2 and L3L4L5), (ii) to modulate rigidity and Ln-N bond distances while controlling the crystal-field effects and the magnitude of J-splitting (L1L6-L8L9) [59] and (iii) to extend the aromatic -electron delocalization for lowering the energies of the ligand-based excited states and thus increasing dynamic coupling (L1-L5 and L9L6-L8). [START_REF] Hatanaka | [END_REF] All heteroleptic erbium [LkEr(hfa)3] complexes were obtained as stable mononuclear adducts ( 90% of the ligand speciation at 10 -6 M, Table S1) from 1:1 host-guest reactions between Lk and [digEr(hfa)3] [65] (Tables S1-S2, Figure S1) conducted in dichloromethane. [66]- [68] The molecular structures for [LkEr(hfa)3], taken from the associated published crystal structures [66]- [68] together with the complementary data collected for [L2Er(hfa)3] (Tables S3-S5, Figure S2), are gathered in Figure 2b. They show low-symmetry nine-coordinate [LnN3O6] coordination spheres that evolve from muffins for ligands L3-L6 toward spherical capped square antiprisms for L1-L2 and L9 (Figure S3 and Table S6). In the solid state, the most compact, rigid, and preorganized adduct [L7Er(hfa)3] is unique for approaching the spherical tricapped trigonal prism geometry, previously found for the triplestranded [Er(Et-bzimpy)3] 3+ complex and its analogues. [59] It is worth stressing here that the idealized D3h symmetry, approached by the latter [ErN9] coordination sphere in [Er(Etbzimpy)3] 3+ , is automatically reduced to idealized C2v for the

Results and discussion

Synthesis

[ErN3O6] unit in [L7Er(hfa)3]
because of the heteroleptic nature of the adduct possessing N and O donor groups.

The pertinent νLn-N and νLn-O bond valences [70] are dominated by series of 1 πi*← 1 π transitions characteristic for 2,6bis(benzimidazole)pyridine-type units. [71] For the non-conjugated ligands L1-L5 and L9, which possess localized 10+6+10 π-electrons systems (bzim-py-bzim) according to Clar's rule of aromaticity, [START_REF] Clar | The Aromatic Sextet[END_REF], [START_REF] Sola | [END_REF] the main 1 *← 1 π absorption band centered around 31000 cm -1 (Figures 4a andS6a) is split upon complexation to Er(hfa)3 to give an additional lower energy band around 28000 cm -1 (Figures 4b andS6b), which is diagnostic for the formation of the [LkEr(hfa)3] adducts in solution. [66], [74] Obviously, the absorption spectra of all [LkEr(hfa)3] integrate the and result in (i) a ca. 1000 cm -1 red-shift of the main 1 π2*← 1 π absorption bands and (ii) the appearance of an additional vibrationally-structured 1 π1*← 1 π transition at lower energy (0-0 origin at 22000 cm -1 with 1400 cm -1 progression, Figures 4a andS7a). [START_REF] Solà | Aromaticity and Antiaromaticity: Concepts and Applications[END_REF] Since the rigid preorganized ligands L6-L8 retain their shape and their aromatic character upon coordination to a metallic center, the absorption spectra of the resulting [LkEr(hfa)3] adducts are essentially comparable with those of the pertinent unbound ligands (Figures 4 andS7). This similarity is accompanied by an apparent redshift of about 1200 cm -1 , which can be assigned to the Lewis acid nature of bound trivalent lanthanides. [L1Er(hfa

) 3 ] [L9Er(hfa) 3 ] [digEr(hfa) 3 ] [L7Er(hfa) 3 ] L1 L9 L7 a) b) 1 π 2 *← 1 π 1 π 3 *← 1 π 1 π 1 *← 1 π 1 π 2 *← 1 π 1 π 3 *← 1 π 1 π 1 *← 1 π ε /10 4 L/molcm
At the low concentrations used, the low-intensity Laporte-forbidden f→f transitions could not be detected. Concomitant measurements using concentrated solutions (~5 mM) indeed allowed the assessment of weak Er( 2S+1 LJ 4 I15/2) absorption transitions (ε ≈ 1-80 L/molꞏcm) covering the 6000-20000 cm -1 spectral window (Figures 5 andS8). Besides these transitions, the absorption spectra exhibited bands arising from the second and third overtones of C-H vibration frequencies around 6000 and 8500 cm -1 , respectively (Figure S8). A look at the Er-centered absorption spectra of [LkEr(hfa)3] confirms that the energies of f-f transitions are globally not affected by the nature of the tridentate heteroaromatic chromophore bound to the Er(III) center, but the contrasting change in intensity and in shape of the pseudo-hypersensitive Er( 2 H11/2← 4 I15/2) transition (which mixes with the 'true' hypersentitive high-energy Er( 4 G11/2← 4 I15/2) transition by spin-orbit coupling), [START_REF] Görller-Walrand | Handbook on the Physics and Chemistry of Rare Earths[END_REF], [START_REF] Hatanaka | [END_REF] does highlight some differences in going from a homoleptic D3-symmetrical [Er(Et-bzimpy)3] 3+ triple helical complex toward C2vsymmetrical [LkEr(hfa)3] complexes (Figures 5 andS8). The latter point can be quantified by the estimation of the radiative lifetime ' ' rad rad 1

J J J J k    
for each Er( 2S+1 LJ) excited level using the Strickler-Berg eqs (3)-( 4), according that its luminescent transitions terminate onto the ground Er( 4 I15/2) level (Table S10). In eq (3),

( )d v v
    is the integrated spectrum of the incriminated absorption transition recorded in solution (in M -1 •cm -2 ), J and J' refer to the ground (J = 15/2) and excited states, respectively, n is the refractive index of the medium, NA is Avogadro's number (in mol -1 ), c is the speed of light in vacuum (in cm•s -1 ), and m v  is the barycenter of the transition (in cm -1 ) given in eq. ( 4). [START_REF] Strickler | [END_REF], [77]

2 2 ' m rad ' rad A 8 (2 1 ) 1 2303 ( )d (2 1) J J J J cn v J k v v N J                ( 3 ) m ( )d ( )d v v v v v v             ( 4 )
The experimental ' 1 5/2 rad J J    extracted for the Er( 2S+1 LJ´) excited levels located within the 6000- 20000 cm -1 domain cover the 0.02-13 ms range in agreement with the symmetry-forbidden character of the intrashell f-f electric dipole transitions (Figures 5 andS8). As expected from the dependence of the Einstein coefficient for spontaneous emission with m v  , [78] the radiative lifetimes globally decrease with increasing energy gaps (Table S10), but their abrupt drop for the pseudo-hypersensitive Er( 2 H11/2← 4 I15/2) transition reflects some extreme sensitivity of the latter transition to (i) local symmetry affecting the mixing between 4f N states and the opposite parity intra-metal excitation configurations (Judd-Ofelt theory), [START_REF] Görller-Walrand | Handbook on the Physics and Chemistry of Rare Earths[END_REF] and/or mixing with intraligand excitation configurations (dynamic coupling). [START_REF] Hatanaka | [END_REF] In this context, one notes that the shortest radiative lifetimes 0.02 ≤ rad( 2 H11/2← 4 I15/2) ≤ 0.04 ms are obtained for [LkEr(hfa)3]

with the extended 30 -electrons polyaromatic ligands L6-L8 (Table S10), which display lowenergy intra-ligand excitations (Figure 4b). The latter complexes are therefore good candidates for maximizing the target green Er( 2 H11/2 4 I15/2) and Er( 4 S3/2 4 I15/2) (upconverted) emissions. transitions and the associated radiative lifetimes (in ms) between parentheses. spectra at 293 K show the tridentate ligand-centered singlet 1 π1*→ 1 π emission in the UV-Vis region (Figure S9), together with minor Er-centered emission following intramolecular ligandto-metal energy transfers (Figures S10-S12). The global 5000 cm -1 red-shift of the 1 π1*→ 1 π transitions observed in going from the 'broken' 10+6+10 -electrons polyaromatic ligands (L1-L5, L9, 27000-22000 cm -1 , Figure S9) to the extended 30 -electrons systems (L6-L8, 23000-16000 cm -1 , Figure S9a) mirrors the related drift observed in the absorption spectra (Figure 4).

The same conclusion holds for frozen solutions at 77 K, while some additional broad ligandcentered emission residues, assigned to 3 π1*→ 1 π phosphorescence boosted by the heavy atom effect, [79] could be detected at lower energy for the brominated [L4Er(hfa)3], [L5Er(hfa)3], and [L9Er(hfa)3] complexes (Figure S9b). In this context, the improved 1  *  3  * intersystem crossing operating in the latter complexes favors energy transfer onto the erbium emitter which exhibits visible Er( 2 H11/2→ 4 I15/2) and Er( 4 S3/2→ 4 I15/2) emissions in the 500-580 nm range (Figures 6a andS10a). [START_REF] Sabbatini | Handbook on the Physics and Chemistry of Rare Earths[END_REF], [START_REF] Moore | [END_REF] We took advantage of this improved green luminescence for the challenging determination of 1, column 3) by using pulsed ligand centered excitation at ex = 355 nm followed by time-dependent detection at em = 542 nm ( 4 S3/2 4 I15/2). This rare experimental data updates 4 3/2 S tot  = 40 ns previously reported [82] for the triple-helical complex [GaErGaL3](CF3SO3)9 in the solid state at 3 K and [L2Er Calculated by taking τtot = 20 ns measured for the model complex [GaErGaL3] 9+ (see main text). [82] [b] Calculated by taking τtot = 3.5 ns.

Interestingly, the red Er( 4 F9/2 4 I15/2) emission was never observed for the [LkEr(hfa)3] under steady-state UV excitation, which implies that the non-radiative process from 4 S3/2 to 4 F9/2

(energy gap  3500 cm -1 ) lacks efficiency as previously reported for erbium cations bound to other rigid multidentate polyaromatic ligands. [44], [47], [58]- [60] An ultimate look at the emission spectra of [LkEr(hfa)3] shows emission bands assigned to Er( 4 IJ 4 I15/2) electronic transitions occurring within the ground state 4 I atomic term (Scheme 2, Figures 6b,c and S11-S12). The associated excitation spectra (em = 1531 nm, Figure S13) perfectly match the absorption spectra. This demonstrates that all ligand-based excited state levels contribute to the antenna effect, which eventually induces the well-known microsecond infrared Er( 4 I13/2 1, column 9). [83], [84] Scheme 2. Jabłoński diagram summarizing the excitation processes (straight upward arrows), energy transfers (dashed arrows), non-radiative multi-phonon relaxation (undulating arrows) and radiative emission processes (straight downward arrows) operating in the heteroleptic complexes [LkEr(hfa)3] (Lk = 1-9). Ligand-to-metal energy transfers arising from both singlet and triplet states are considered. To summarize, moving from homoleptic D3-symmetrical [ErL3] 3+ complexes (idealized D3h-

    ≤ 10 -3 , Table
[ErN9] coordination environment, Figure 1) [59] to heteroleptic C2v-symmetrical [LkEr(hfa)3] adducts (idealized C2v-[ErN3O6] coordination environments) maintains similar Er-based photophysical properties. However, the tunable electronic nature of the bound tridentate polyaromatic ligands L1-L9 can be exploited to influence (i) the sensitization possibilities via -aromatic delocalization and (ii) the final ligand-centered and erbium-centered emission output of the complexes via the control of intersystem crossing (heavy atom effect) and of intramolecular ligand-to-erbium energy transfers (phonon-assisted mechanism, Scheme 2 S17). The complete lack of residual ligand-centered 1,3 π*→ 1 π emission bands following NIR excitation at 801 nm (Figures 7, S14-S15) rules out the possibility for ligandcentered non-linear two-photon absorption processes. [85][86] Furthermore, at these reasonable incident power intensities (1-25 Wꞏcm -2 ), there is no realistic option for the operation of competitive non-linear Er-centered processes. [87], [88] Quantitative data for the upconversion processes are based on the upconversion quantum yields up tot  (Figure 8 and Table S11, column 6) obtained by laser excitation of [LkEr(hfa)3] at λexc = 801 nm with incident pump intensity of 1 W focused on a spot size of ≈ 0.07 cm 2 in dichloromethane solutions [59] and using indocyanine green (ICG) as the standard (λexc = 801 nm, P = 5 mW focused on a spot size of ≈ 0.07 cm 2 , Φs = 0.132 in ethanol at 293K, [89] see Appendix 1 for details). The trend in the upconversion quantum yields (Figure 8) mirrors the upconverted intensities (Figure 7), and one immediately notes that going from the homoleptic D3-symmetrical complex [Er(Et-bzimpy)3] 3+ ( up tot  = 1.7(2)10 -9 normalized at 25 Wcm -2 ) [59] to the flexible heteroleptic C2v-symmetrical [LkEr(hfa)3] adducts (Lk = L1-L5 and L9) results in a gain in upconversion quantum yield by roughly one to two orders of magnitude (1.6(2)10 -8 ≤ up tot  ≤ 3.0(3)10 -7 normalized at 25 Wcm -2 ). The simultaneous extension of the delocalized - aromatic system and rigidity in the preorganized [LkEr(hfa)3] complexes (Lk = L6-L8) further The energies of the level are taken for the free ions. [START_REF] Brik | Theoretical Spectroscopy of Transition Metal and Earth Ions: From free State to Crystal Field[END_REF] First considering the ESA mechanism in Scheme 3, in which Er( 4 I13/2) works as the longlived excited relay (microsecond range, Table 1, column 8) returns 410 3 ≤ 1 2 Er   ≤ 510 5 L/molcm with eq (5) for the second absorption event (Table S11, column 8). These huge absorption coefficients are out of the accessible range theoretically computed for the incriminated 4 S3/2 4 I13/2 second excitation, [59] and, more generally, for any internal 4f4f transitions (1-500 L/molcm). [START_REF] Görller-Walrand | Handbook on the Physics and Chemistry of Rare Earths[END_REF] We conclude that the microsecond luminescent Er( S10), which usually prevent their detection in molecules possessing high-energy vibrations and thus efficient non-radiative relaxation pathways. Although the latter emission intensities were too weak to record reliable experimental lifetimes for the Er( 4 I11/2) and Er( 4 I9/2) levels in these complexes with our setup, one notices that the incriminated energy gap E = 3600 cm -1 separating the Er( 4 I11/2) and Er( 4 I13/2) levels, fairly matches the related 3500 cm -1 energy separation between Er( 4 S3/2) to Er( 4 F9/2) levels in [LkEr(hfa)3] (Scheme 3, right). [START_REF] Brik | Theoretical Spectroscopy of Transition Metal and Earth Ions: From free State to Crystal Field[END_REF] The lack of efficient phonon bath in this energy range, which prevents the observation of red Er( 4 F9/2 4 I15/2) emission in these complexes, [60] may similarly drastically limit non-radiative Er( 4 I11/2) to Er( 4 I13/2) relaxation with the consequent existence of long-lived Er( 4 I11/2) excited relays and the operation of an efficient ESA mechanism depicted in Scheme 3. [START_REF] Ferrier | [END_REF] With this in mind, it is probably worth stressing here that the largest upconversion quantum yield of up tot  = 1.0(1)10 -6 is observed for [L7Er(hfa)3] (normalized at 25 Wcm -2 , Figure 8), being the only complex devoid of high-energy C-Haliphatique stretching vibrations around 3000 cm -1 (Figure S5).

P k h c                     ( 5
This suggests that overlap between the putative Er( 4 I11/2 4 I13/2) emission and the vibrational

  are largely dominated by the relaxation rate constants ( A j i k  ), and a negligible number of molecules exist in the excited levels (

Figure 1 .

 1 Figure 1. a) Synthesis and molecular structure of the triple-stranded helical [Er(Et-bzimpy)3] 3+

  , structures and stabilities of the heteroleptic complexes [LkEr(hfa)3] (Lk = L1-L9).

Figure 2 .

 2 Figure 2. a) Polyaromatic tridentate receptors L1-L9 used for hosting [Er(hfa)3] units to give nine-coordinate [LkEr(hfa)3] adducts. b) Synthesis and molecular structures of [LkLn(hfa)3]adducts (crystal structure: Ln = Er for L1, L2, L7 and L9; Ln = Eu for L3-L6).[66]-[68]

  computed for the Er-N and Er-O bond lengths in the crystal structures of [LkEr(hfa)3] (eq A1-2 in Appendix 1, Tables S7-S9, FigureS4) show similar Ln-Nbzim and Ln-O bond strengths, which are indeed larger than Ln-Npy when the flexible ligands L1-L5 and L9 are bound to Ln(III) (Figures3 and S4). The situation is reversed for the rigid polyaromatic ligands L6-L7, where the drop of νLn-Nbzim observed in the associated [LkLn(hfa)3] adducts implies an unfavorable match between the preorganized ligand cavity and the entering [Ln(hfa)3] metal container. Finally, to further highlight the unusual design of L7, one should realize that it is the only ligand of the series that does not possess alkyl groups (CH2 or CH3). This limits the contribution of high-energy vibrations to some weak C-Harom stretching bands around 3030 cm -1 in the IR spectrum (FigureS5). For all other ligands, the weak C-Harom stretching bands are completed with broader and more intense C-Haliph stretching bands covering the 2800-2950 cm -1 range.

Figure 3 .

 3 Figure 3. Average vEr-Nbenzimidazole (green), vEr-Npyridine (blue), and average vEr-O(hfa) (red) bond valences [70] calculated with eq (A1-2) for the molecular structure of complexes [LkEr(hfa)3] (Lk = L1, L2, L7 and L9) in their crystalline state. Standard deviations of the average are shown with vertical error bars. The dashed traces are only guides for the eyes.

  *← 1 π transition centered on the bound hfa -anions at 33000 cm -1 (identified for [digEr(hfa)3] with black traces in Figures4b, S6b, and S7b). In contrast, the delocalized 30 π-electrons aromatic backbones characterizing the rigid ligands L6-L8 extend the π-systems

Figure 4 .

 4 Figure 4. Selected UV-Vis absorption spectra of a) ligands L1, L7 and L9, and b) corresponding [LkEr(hfa)3] and [digEr(hfa)3] complexes (510 -6 M in CH2Cl2, 293 K).

Figure 5 .

 5 Figure 5. Visible to near-infrared absorption spectra of [L1Er(hfa)3] (5 mM in CH2Cl2) and triple-stranded [Er(Et-bzimpy)3] 3+ (3 mM in CH3CN) at 293 K showing the Er( 2S+1 LJ← 4 I15/2)

Figure 6 .

 6 Figure 6. Emission spectra (λexc = 350 nm) recorded for [L5Er(hfa)3] in dichloromethane solution (C ≈ 510 -6 M) highlighting the spectral windows associated with Er-centered transitions at room temperature. Excitation of [LkEr(hfa)3] in solution at 350 nm limits sensitization via the bound N-donor tridentate ligands and excludes contribution from the hfa -co-ligands. The resulting emission

  ns, which corresponds to the total lifetime of the Er( 4 S3/2) excited level in [L4Er(hfa)3] (dichloromethane at 293 K, Table

  ns measured at 293 K for [GaErGaL3] 9+ in acetonitrile with our novel setup. The faint associated intrinsic quantum yields 10 -hfa)3] complexes (Table1, columns 4-5) represent a severe handicap to the implementation of efficient NIR-to-Visible (green) upconverted signals induced in erbium(III) molecular complexes in solution (eq 2).

Figure 7 .

 7 Figure 7. Upconverted visible Er( 2 H11/2→ 4 I15/2) and Er( 4 S3/2→ 4 I15/2) emissions observed for [LkEr(hfa)3] complexes recorded upon laser excitation of the Er( 4 I9/2← 4 I15/2) transition at λexc = 801 nm (ṽexc = 12284 cm -1 ) and using incident pump intensity P = 14.3 Wꞏcm -2 in dichloromethane solution (5 mM) at (measurements for [L2Er(hfa)3] and [Er(Etbzimpy)3] 3+ complexes were performed in CH3CN under the same conditions).

) Scheme 3 .

 3 Scheme 3. Jabłoński diagram summarizing the possible mechanisms (1-3) of the Er-centered upconversion processes operating in the complexes [LkEr(hfa)3] upon excitation of the Er( 4 I9/2← 4 I15/2) transition at 801 nm. Excitation (upward arrows), non-radiative multiphonon relaxation (undulating arrows) and emission (downward arrows). The energies of the level are

  of the CH quenchers in this energy range plays a crucial role. The intense CH3-stretching vibrations measured in the 3000 cm -1 range for the [LkEr(hfa)3] adducts possessing alkyl groups should therefore contribute more efficiently to the non-radiative relaxation of the Er( 4 I11/2) relay compared with the much weaker aromatic CH vibrations (FigureS5).ConclusionMoving from idealized D3h-symmetrical triple-helical [ErN9] chromophores, found in [Er(Etbimpy)3] 3+ (Figure1), toward idealized C2v-[ErN3O6] units in C2v-symmetrical [LkEr(hfa)3] adducts (Figure2) boosts the efficiency of the ESA upconversion mechanism by 2-3 orders of magnitude (Figure8), which makes molecular-based ESA a concurrent to multicenter ETU and CU processes. Detailed photophysical studies strongly suggest that the origin of this remarkable effect finds its root in the existence of a long-lived Er( 4 I11/2) level resulting from the specific lack of efficient relaxation processes in the 3500 cm -1 range accompanying the concomitant binding of perfluorinated hfa -co-ligands and rigid polyaromatic Lk guests to Er(III) in [LkEr(hfa)3]. An ultimate proof for the dominance of mechanism operating in these mononuclear complexes is currently under investigation with the technical development of ultra-sensitive time-gated NIR detection following intense pulsed NIR excitation of Er( 4 I9/2 4 I15/2) at 801 nm and of Er( 4 I11/2 4 I15/2) at 966 nm.

Table 1 .

 1 Radiative lifetimes (τrad) for the Er( 4 S3/2→ 4 I15/2) and Er( 4 I13/2→ 4 I15/2) transitions computed with eqs (3)-(4), experimental excited-state lifetimes (τtot) for the Er( 4 S3/2) and Er( 4 I13/2) levels and associated intrinsic quantum yields (

		2 +1 Er S	J L			2 +1 tot S	J L		2 +1 rad S	J L	) in [LkEr(hfa)3] and [Er(Et-

  ).

	Single-center NIRVIS light upconversion in heteroleptic complexes [LkEr(hfa)3] in
	solution. Having established that (i) at least one of the intermediate Er( 4 IJ) excited states (J =
	9/2, 11/2 or 13/2) possesses a lifetime long-enough to potentially act as emitter for
	downshifting, or as relay for upconversion in the heteroleptic [LkEr(hfa)3] complexes, and (ii)
	the Er( 2 H11/2), Er( 4 S3/2), and Er( 4 I13/2) excited levels are luminescent, it is not so surprising that
	direct continuous 801 nm diode laser excitation into the Er( 4 I9/2← I15/2) transition (molar
	absorption coefficients 0.10 ≤ ε801 ≤ 0.30 L/molꞏcm, Table S11, column 2) reveals dual
	downshifted infrared Er( 4 I13/2→ 4 I15/2) emissions (1540 nm) induced by linear one-photon
	processes (slope n = 0.95(1)-1.02(3) for the log(IDS)-log(P) plots, Figures S14-S15), and
	challenging two-photons visible upconverted Er( 2 H11/2→ 4 I15/2) and Er( 4 S3/2→ 4 I15/2) emissions
	depicted in Figure 7 (slope n = 1.26(6) -2.16(7) for the corresponding log(IUC)-log(P) plots,
	Figures S16-

   4 I 15/2 ) Er( 4 S 3/2  4 I 15/2 ) level kinetic model of the ESA mechanism (Scheme 1), correlates ESA with the second excitation process characterized by its decadic molar absorption coefficient1 2 Er   (eq 5).

					Wavelength /nm
			510	525			545	578
	Er,ESA	4 Er 3/2 up Er S	Intensity /a.u. exc 1 2 Er( 2 H 11/2   Er 1 0 Er 3.8 10 k	21	P	1 2 Er	1 Er
			19.8	19.3	18.8		18.3	17.8	17.3
				Wavenumber /10 3 cm -1

  LkEr(hfa)3] should be considered as potential long-lived relays. This is supported by the detection of Er( 4 I11/2 4 I15/2) and Er( 4 I9/2 4 I15/2) radiative emission upon ligand-based excitation (Figures 6b and S11) despite their long radiative lifetimes (4-12 ms, Table

						4 I13/2) level
	does not contribute significantly as a relay for the erbium-based ESA upconversion in these
	complexes (ESA mechanism			in Scheme 3), a claim further confirmed by the lack of
	correlation between Er,ESA and		4 Er	13/2 I	(Figure S18) despite the theoretical link predicted in eq
	(5). Alternatively, the Er( 4 I11/2) level (ESA mechanism	in Scheme 3) and/or Er( 4 I9/2) level
	(ESA mechanism	in Scheme 3) in [

Acknowledgements

This work is supported from the Swiss National Science Foundation (grant 200020_207313).

Data Availability Statement

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

boosts the upconversion quantum yield, which culminates at up tot  = 1.0(1)10 -6 for [L7Er(hfa)3] (normalized at 25 Wcm -2 , Figure 8). The latter value compares well with the best reproducible molecular-based upconversion quantum yield of up tot  = 9(1)10 -7 (normalized at 25 Wcm -2 ) reported for a doped single-emitter TbYb9 hetero-nonanuclear cluster obeying the multicenter cooperative upconversion (CU) mechanism upon 980 nm excitation in CD3OD. [54] Figure 8. Upconversion luminescent quantum yields (Φ UC ) calculated for single-centered mononuclear complexes [LkEr(hfa)3] upon laser excitation of the Er( 4 I9/2 4 I15/2) transition at λexc = 801 nm (ṽexc = 12284 cm -1 ) at 293 K normalized to P = 25 Wꞏcm -2 for comparison purpose. All samples were measured in dichloromethane solutions (C ~ 5 mM) with respect to indocyanine green in ethanol, except for [Er(Et-bzimpy)3] 3+ [59] and [L2Er(hfa)3], which were measured in acetonitrile solutions (C ~ 10 mM).

Considering the minor intrinsic Er( 4 S3/2) quantum yield (10 S11, column 7), which overpass by two orders of magnitude ESA = 1.1(2)10 -4 previously reported for the homoleptic [Er(Etbzimpy)3] 3+ complex. [59] A straightforward reorganization of eq (2), which stands for the three-



Conflict of Interest

The authors declared no conflict of interest.


domain: sdv info

text:
A large-scale exploration of cell-free compositions to maximize protein production using active learning

Lysate-based cell-free systems have become a major platform to study gene expression 1-3 but batch-to-batch variation makes protein production difficult to predict 4 . Here we describe an active learning approach 5 to explore a combinatorial space of ~4,000,000 cell-free compositions, maximizing protein production and identifying critical parameters involved in cell-free productivity. We also provide a one-step-method to achieve high quality predictions for protein production using minimal experimental effort regardless of the lysate quality.

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  Borkowski O*, Koch M*, Zettor A, Pandi A, Batista AC, Soudier P, Faulon J-L in cell-free platforms