Infectious diseases are notorious for their complex dynamics, which make it difficult to fit models to test hypotheses. Methods based on state-space reconstruction have been proposed to infer causal interactions in noisy, nonlinear dynamical systems. These “model-free” methods are collectively known as convergent cross-mapping (CCM). Although CCM has theoretical support, natural systems routinely violate its assumptions. To identify the practical limits of causal inference under CCM, we simulated the dynamics of two pathogen strains with varying interaction strengths. The original method of CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies. This sensitivity vanishes with alternative criteria for inferring causality. However, CCM remains sensitive to high levels of process noise and changes to the deterministic attractor. This sensitivity is problematic because it remains challenging to gauge noise and dynamical changes in natural systems, including the quality of reconstructed attractors that underlie cross-mapping. We illustrate these challenges by analyzing time series of reportable childhood infections in New York City and Chicago during the pre-vaccine era. We comment on the statistical and conceptual challenges that currently limit the use of state-space reconstruction in causal inference. Identifying the forces driving change in natural systems is a major goal in ecology. Because experiments are often impractical and come at the cost of generalizability, a common approach is to fit mechanistic models to observations. Testing hypotheses through mechanistic models has a particularly strong tradition in infectious disease ecology –4. ModelX drives Y, information about X is embedded in the time series of Y. Examining the relationships between delay-embeddings of the time series of X and Y can reveal whether X drives Y, Y drives X, both, or neither. These approaches, which we refer to collectively as convergent cross-mapping (CCM), have been offered as general tools to analyze causation in nonlinear dynamical systems [An alternative approach to inferring causality is to examine the time series of potentially interacting variables without invoking a model. These methods face a similar challenge: they must distinguish correlated independent variables sharing a mutual driver from correlations arising from direct or indirect interactions. Many of these methods, including Granger causality  and othe systems –20.X(t) from the system can be mapped perfectly to the attractor in the full state space in the system by constructing a delay embedding, in which states of the full system are mapped to delay vectors, x(t) = {X(t), X(t − τ1), X(t − τ2), …, X X, then a newly observed x(t) can perfectly reconstruct the corresponding x(t) → Y(t) (x(t) increases, the reconstruction converges to small error, as observed points on the reconstructed attractor become close together [The mathematical foundations of CCM, and therefore its assumptions, lie in deterministic nonlinear systems theory. After sufficient time, the states of a deterministic dynamical system reach an attractor, which may be a point equilibrium, a limit cycle, or a higher-dimensional chaotic attractor. By Takens’ theorem, a one-dimensional time series ttractor . This ma) → Y(t) . As the together .With finite, noisy real data, the reconstruction is necessarily imperfect, and two operational criteria have been used to detect causality. The first criterion  is basedMany ecological systems undergo synchronized diurnal or annual fluctuations and thus raise doubts about the first criterion. Transient dynamics, demographic and environmental noise, and observation error—all ubiquitous in nature—raise general concerns, since they violate the theory’s assumption that variables are perfectly observed in a deterministic system. Variations of CCM have nonetheless been applied to such systems to test hypotheses about who interacts with whom , 23, 24.We investigated whether the frequently periodic, noisy, and transient dynamics of ecological systems are a current obstacle to causal inference based on state-space reconstruction. These factors have been addressed to varying degrees in different contexts –19 but nη. We also varied the strength of competition from strain 2 on strain 1 (σ12); strain 1, in contrast, never affected strain 2 (σ21 = 0). For each level of competition and process noise, we simulated 100 replicates from random initial conditions to stochastic fluctuations around a deterministic attractor. One thousand years of error-free monthly incidence were output to give CCM the best chance to work. For each combination of parameters (competition strength σ12 and process noise η), we examined whether strain interactions were correctly inferred. When σ12 > 0, strain 2 should be inferred to “drive” (influence) strain 1. Because σ21 = 0, strain 1 should never be inferred to drive strain 2.To assess the reliability of CCM, we began by simulating the dynamics of two strains with stochastic, seasonally varying transmission rates . In largρ, which is the correlation between reconstructed values of Y, given the reconstructed attractor of X. We use p < 0.05 to identify significant differences in these correlations because we are interested in situations in which the null hypothesis of no change in correlation, and thus no interaction, is rejected. Criterion 1 [To detect interactions, for each individual time series, we identified the delay-embeddings  and applterion 1 , 19 measterion 1  infers aρ with observation library size L, frequently detected interactions that did not exist. In all cases where strain 2 had no effect on strain 1, CCM always incorrectly inferred an influence (σ12 = 0 and η = 0.05), strain 1 often oscillated with a period that was an integer multiple of the other strain’s  because of noise-induced oscillations  and false positives (σ12 = 0) were detected than when surrogates were used only for the putative cause  and interactions in noisy systems . Results for annual data were similar  and one strongly drives the other (σ12 = 1), the direction of the interaction cannot be detected when the dynamics are nearly deterministic (η = 10−6) (If two variables  = 10−6) . Causal ρ be positive and peak at a negative lag [η = 0.01), the false positive rate depended on correlation strength and the quantity of data. When using 100 years of monthly incidence, the false positive rate varied non-monotonically with correlation strength, with a minimum (5%-6%) at a correlation of 0.75 and its highest values, near 24%, at correlations of 0 and 1 , that the cross-map correlation tive lag . Process 0 and 1 . Using 1 0 and 1 . The bes 0 and 1 . Thus, tβ1 ≠ β2) when one strain strongly drives the other (σ12 = 1) and its dynamics resemble the seasonal driver. In this case, even with perfectly correlated process noise, correct interactions are consistently inferred (η = 0.01): as shown earlier, higher levels hurt performance . We tesσ12 = 0.5), causal inference is compromised, even when process noise is low  with two strains, little noise near the attractor, and 1000 years of observations, we investigated whether the method might shed light on the historic dynamics of childhood infections in the pre-vaccine era. Time series analyses have suggested that historically common childhood pathogens may have competed with or facilitated one another , 29. We le tests . Polio dle tests . The infp = 0.055), polio drove measles. In these cases, the maximum cross-map correlation ρ was not only positive but also increased at negative lag. Requiring that ρ only be positive at negative lag, polio also drove pertussis, measles drove mumps and varicella, and mumps drove scarlet fever. Except in one case, all negative lags occurred at more than one year  can lead to erroneous conclusions whenever strains fluctuated at similar frequencies. A related approach intended to control for periodic behavior also fared poorly . ApplyinL , avoids Oscillations are common in nature, especially in infectious diseases, and suggest that one of the criteria for causal inference (Criterion 1), including a method that tries to control for periodic behavior, could routinely mislead. Climatic and seasonal cycles, driven by such factors as school terms, El Niño, and absolute humidity, pervade the dynamics of many pathogens and influence the timing of epidemics , 31–33. Assuming the stronger criterion for causality , under wIf an ecologist were confident that observed dynamics reflected dynamics near a fixed, deterministic attractor , uncertainties in the methodology of attractor reconstruction still suggest caution. We tested four different methods of selecting the lag-embedding. Even near an attractor, they gave different results . DecadesOf the many factors that might explain the contrasting results for childhood infections in two cities, biological explanations thus seem the least likely. Although there is evidence that measles increases suceptibility to other pathogens , and thaDetecting causality remains challenging in the face of real data from a complex world. With limited data and complex dynamics, mechanistic models are always misspecified to some extent, and the use of other lines of evidence to motivate the choice of model structure is necessary for good inference –12. But Prediction, in contrast, is epistemologically straightforward and useful without knowledge of the true underlying system. It does not require deciding a priori what the best method is : the proof is in the prediction. Model-free prediction methods, including those based on state-space reconstruction , 54, 55,Beyond its statistical practicalities, the prospect of applying state-space reconstruction to causal inference touches on unsettled questions in ecology. Are systems approximately deterministic and settled on static attractors, and how can we tell? Although CCM does not require that dynamics follow an identifiable model, it does require sufficient coverage of a fixed state-space . We propSi), infected (Ii), or recovered and immune (Ri) to each strain i. The deterministic model has the form:We modeled the dynamics of two pathogen strains under variable amounts of competition and process noise . The stai through the birth (and death) rate μ. They leave through infection with strain i (Si → Ii), infection with strain j that elicits cross-immunity to i (Si → Ri), or death. The per capita transmission rate, βi(t), depends on a mean strain-specific rate, βi, and a forcing function that is shared by all strains. This function has a sinusoidal form and represents a shared common driver, such as seasonal changes in susceptibility or transmission from school-term forcing. The forcing function is defined by a shared period ψ and amplitude ϵ. Infected hosts recover at rate νi (Ii → Ri). The immune host class grows through these recoveries and also from the fraction of susceptible hosts, Si, contacting infected hosts, Ij, who develop cross-immunity, σij (0 ≤ σij ≤ 1). Immunity of this form has been described as “polarizing” because σij of hosts Si contacting infecteds Ij become completely immune (non-susceptible) to strain i, while 1 − σij remain completely susceptible. This cross-immunity is a form of competition that determines the directions of interaction between strains: when σij > 0, strain j drives strain i. We assume σii = 1: hosts acquire perfect immunity to a strain from which they have recovered  for convenience, is given by the difference in cumulative cases:The observations consist of the number of new cases or incidence over some interval. Cumulative cases The equations were solved numerically using the Euler-Maruyama method with a fixed step size. The step size was chosen to be less than the smallest within-run harmonic mean step size across deterministic, adaptive-step size pilot runs performed across the range of parameter space being studied. When numerical errors arose during transients, the step size was reduced further until the numerical issues disappeared.Except where noted, the model was simulated with random initial conditions, and 1000 years of monthly observations were obtained from stochastic fluctuations around the deterministic attractor. The use of random initial conditions minimizes arbitrary bias in the simulated dynamics. From visual inspection of dynamics, the transient phase lasted much less than 1000 years. Time series were obtained from years 2000–3000.E-dimensional system, the attractor for the state space represented by delay vectors in a single variable X, x(t) = {X(t), X(t − τ1), X(t − τ2), …, X(t − τE−1)}, is topologically equivalent to the E-dimensional attractor for variables X1, …, XE. In the limit of infinite data, the full E-dimensional attractor can be reconstructed perfectly from a one-dimensional time series. Therefore, because x(t) contains complete information about the system’s dynamics, if Y is part of the same system and thus causally drives X, observations of x(t) → Y(t − ℓ), for a fixed lag ℓ, can be used to reconstruct unobserved values of Y(t) from new observations of x(t) (Convergent cross-mapping (CCM) is a method for inferring causality in deterministic systems via delay embedding . Takens’ of x(t) .Y drives X, we construct “libraries” of observations of x(t) → y(t − ℓ). For a particular library, we treat each value of Y(t) as unobserved, and reconstruct its value E + 1 nearest neighbors to x(t) in the library, x(ti), for t1, …, tE + 1, and calculating e. Weights are calculated from the Euclidean distances di between x(t) and x(ti), with wi proportional to d0 is the distance to the nearest neighbor [To evaluate whether neighbor .ρ measures how well values of Y can be reconstructed from values of X, and is defined as the Pearson correlation coefficient between reconstructed values Y(t) across the entire time series [L and lag ℓ, we generate a distribution of cross-map correlations ρ by bootstrap-sampling libraries mapping delay vectors x(t) to values Y(t − ℓ) and then computing the cross-map correlation for each sampled library. We use the bootstrap distribution of cross-map correlation as the basis for statistical criteria for causality.The cross-map correlation e series . Given lρ [ρ increases with L for a fixed lag ℓ; (2) whether ρ is positive and maximized at a negative temporal lag ℓ. We also consider a weaker alternative to the first criterion, testing simply whether ρ is positive, and a method intended to control for seasonal behavior based on randomizing seasonal anomalies [We infer causality using two primary criteria involving the cross-map correlation ρ , 18: (1)nomalies .Y drives X, then increasing the library size L should improve predictions of x(t) as measured by ρ [ρ with L. We calculate ρ at Lmin = E + 2, the smallest library that will contain E + 1 nearest neighbors for delay vectors x(t), and at Lmax, the total number of delay vectors x(t) in the time series. An increase in ρ is indicated by a lack of overlap between the distributions at Lmin = E + 2, the smallest library that will have E + 1 neighbors for most points, and Lmax, the largest possible library given the time-series length and delay embedding parameters E and τ.If red by ρ  for fixeY strongly drives X, cross-map correlation at ℓ = 0 may yield a false positive when testing for X driving Y, but because information is transferred forwards in time from Y to X, the cross-map correlation should be maximized at a negative lag ℓ [Y drives X, the cross-map correlation ρ be maximized at a negative cross-map lag ℓ and be positive. In other words, not only must X contain information about Y, but this information must be greatest for past states of Y, reflecting the correct temporal direction for causality.If ve lag ℓ . The secY drives X in the absence of noise, the correlation ρ between the reconstructed and observed states of Y should converge to one with infinite samples of X. In practice, if X and Y share a complex  attractor, time series of X may not be long enough to see convergence [The theory underlying CCM assumes completely deterministic interactions and infinite data. If vergence .ρ from ever reaching 1. Nonetheless, a detectable increase in the correlation ρ with the library length L (for Criterion 1), or a maximum and positive correlation at negative lag (for Criterion 2), may suffice to demonstrate that X drives Y in natural systems. It is important to note that we have no formal theoretical justification for such statistical heuristics.The presence of observation and/or process noise violates the deterministic assumptions and prevents ρ(L), we perform a nonparametric test of whether ρ(Lmax), obtained at the largest library length is greater than ρ(Lmin), obtained at the smallest libary length. The p-value for this test is calculated as the probability that ρ(Lmax) is not greater than ρ(Lmin), and calculate the p-value directly from the sampled distributions (the fraction of bootstraps in which ρ(Lmax) < ρ(Lmin)). We also consider a weaker alternative, testing simply whether ρ is significantly positive.Our statistics are based on the distributions obtained from bootstrapping. For Criterion 1, which tests for an increase in ρ to a null distribution based on randomized seasonal anomalies [ρ for the original time series is less than ρi for a random surrogate time series i.We also test a proposed method for controlling for periodic behavior by comparing nomalies . Specifi(−) with the highest median correlation, ρ(ℓ(−)) as well as the nonnegative cross-map lag ℓ(0+) with the highest median correlation. The p-value for this test is calculated as the probability that ρ(ℓ(−)) is not greater than ρ(ℓ(0+)).For Criterion 2, which tests whether the best cross-map lag is negative and thus indicates the correct causal direction in time, we perform a similar nonparametric test. We identify the negative cross-map lag ℓp < 0.05 for all tests.We use a significance threshold of E-dimensional projection of a one-dimensional time series, which can be generated in many ways from lags of the time series. In simulated, deterministic models, E can be known perfectly, but the best projection may be system-dependent. In systems with process noise, unknown dynamics, and/or finite observations, there is no clearly superior method to select the appropriate projection [The theory underlying attractor reconstruction works with any ojection , 60–62.ρ for each interaction. Three of the four methods use uniform embeddings, identifying E and a fixed delay τ, and the other uses a nonuniform embedding, identifying a series of specific delays τ1, τ2, etc., whose length determines E.We accommodated this uncertainty by using four different methods. Two methods infer the best delay-embedding for each interaction by maximizing the ability of one variable, the driven variable, to predict itself . ThUnivariate prediction method: By default, for each causal interaction (Ci → Cj), E and τ are chosen to maximize the one-step-ahead univariate prediction ρ at Lmax for the driven variable (Cj) based on its own time series.Maximum cross-correlation method: As an alternative, E and τ are chosen to maximize the mean cross-map correlation ρ at Lmax for each causal interaction being tested, for each time series.Random projection method: A recently proposed method based on random projection of delay coordinates sidesteps the problem of choosing optimal delays [E, all delays up to a maximum delay τmax are projected onto an E-dimensional vector via multiplication by a random projection matrix. E is chosen to maximize the cross-map correlation ρ.l delays . InsteadNonuniform method: For each driven variable Cj, starting with τ0 = 0, additional delays τ1, τ2, … are chosen iteratively to maximize the directional derivative to nearest neighbors when the new delay is added [is added . The delis added . This meis added .https://github.com/cobeylab/pyembedding. The complete code for the analysis and figures is publicly available at https://github.com/cobeylab/causality_manuscript; individual analyses include references to the Git commit version identifier in the ‘pyembedding’ repository. The simulated time series on which the analyses were performed are available from the authors on request.Code implementing the state-space reconstruction methods is publicly available at Time series were obtained from L2-level data maintained by Project Tycho . All avaS1 Figρ with library length L indicated a causal interaction. Each analysis is based on 1000 years of data. (A) Annual incidence, (B) prevalence strobed annually, (C) first-differenced annual incidence, and (D) monthly incidence without seasonal forcing.Heat maps show the fraction of 100 replicates significant for each inferred interaction for different parameter combinations. A significant increase in cross-map correlation (PDF)Click here for additional data file.S2 Figρ with library length L indicated a causal interaction. Each analysis is based on 100 years of monthly data. Delay-embeddings were chosen by (A) nonuniform embedding, (B) random projection, or (C) maximizing the cross-map correlation ρ.Heat maps show the fraction of 100 replicates significant for each inferred interaction for different parameter combinations. A significant increase in cross-map correlation (PDF)Click here for additional data file.S3 Figρ at a negative lag was required for inferring causal interaction. (A) 1000 years of annual incidence, requiring that the maximum ρ be positive. (B) 100 years of monthly incidence, requiring that the maximum ρ be increasing. (C) 100 years of monthly incidence with identical strains (β1 = β2 = 0.3), requiring that maximum ρ be positive.Heat maps show the fraction of 100 replicates significant for each inferred interaction for different parameter combinations. A maximum cross-map correlation (PDF)Click here for additional data file.S4 Figρ at a negative lag was required for inferring causal interaction. 100 years of monthly (A) and 1000 years of annual (B) incidence, requiring that the maximum ρ be positive. (C) 100 years of monthly incidence, requiring that maximum ρ be increasing.Heat maps show the fraction of 100 replicates significant for each inferred interaction. A maximum cross-map correlation (PDF)Click here for additional data file.S5 Figρ at a negative lag and ρ > 0 were required for inferring causal interaction. Results are shown for 5, 10, 25, 50, and 100 years of monthly incidence.Heat maps show the fraction of 100 replicates significant for each inferred interaction. A maximum cross-map correlation (PDF)Click here for additional data file.S6 FigHeat maps show the fraction of 100 replicates significant for each inferred interaction in simulations using distinct strains and seasonal forcing. (A) Surrogate time series generated for putative cause and putative effect. (B) Surrogate time series generated for putative cause only.(PDF)Click here for additional data file.S7 FigC2 drives C1 , the maximum cross-correlation ρ for C1 cross-mapped to C2 occurs at a positive lag, and the reverse at a negative lag, leading to the conclusion that C1 drives C2, and C2 does not drive C1. Sample dynamics include process noise (η = 0.01) but no seasonal forcing (ϵ = 0).Cross-map correlations at different lags for a sample 100-year time series with monthly sampling (inset). Lines represent bootstrap medians; gray ribbons represent the middle 95% of the bootstrap distribution. Although (PDF)Click here for additional data file.S8 Fig(PDF)Click here for additional data file.S9 Fig(PDF)Click here for additional data file.S10 Fig(PDF)Click here for additional data file.S11 Fig(PDF)Click here for additional data file.


In the glucose units of tree-ring cellulose of 12 tree species, we detected large differences in 13C/12C ratios (>10‰) among carbon atoms, which provide isotopically distinct inputs to major global C pools, including wood and soil organic matter. Thus, considering position-specific differences can improve characterisation of soil-to-atmosphere carbon fluxes and soil metabolism. In a Pinus nigra tree-ring archive formed from 1961 to 1995, we found novel 13C signals, and show that intramolecular analysis enables more comprehensive and precise signal extraction from tree rings, and thus higher resolution reconstruction of plants’ responses to climate change. Moreover, we propose an ecophysiological mechanism for the introduction of a 13C signal, which links an environmental shift to the triggered metabolic shift and its intramolecular 13C signature. In conclusion, intramolecular 13C analyses can provide valuable new information about long-term metabolic dynamics for numerous applications.Measurements of carbon isotope contents of plant organic matter provide important information in diverse fields such as plant breeding, ecophysiology, biogeochemistry and paleoclimatology. They are currently based on  However, there are major uncertainties in earth system models due to incomplete characterisation of soil microbial, biogeochemical, plant physiological, and climatic processes. Notably, estimation of soil-to-atmosphere CO2 fluxes based on δ13C analysis is impeded by  lack of knowledge about 13C fractionations by soil microbes3. Similarly, simulated C exchange fluxes between the atmosphere and biosphere are insufficiently constrained due to limited understanding of CO2 fertilization effects4, i.e., the increase in plant carbon sequestration associated with rising atmospheric [CO2].In-depth understanding of the earth system is required to preserve intact ecosystems and protect biodiversity, maintain food supplies and secure other resources in the context of ongoing environmental change. Measurements of stable carbon isotope ratios  fractionation and post-Rubisco (PR) fractionation. DR fractionation refers to the 13C fractionation by CO2 diffusion from ambient air into plant chloroplasts and Rubisco-mediated CO2 fixation2, previously called photosynthetic fractionation10. The rationale for the change in nomenclature is outlined below. Rubisco adds a single carbon from CO2 to ribulose-1,5-bisphosphate. Therefore, DR fractionation cannot cause intramolecular 13C variation, i.e. it is not position-specific. In contrast, PR fractionation denotes 13C fractionation by enzymes acting downstream of Rubisco. This type of fractionation is known to occur at individual C positions within metabolites11, i.e. it is position-specific. PR fractionation occurs at metabolic branch points9. Theoretically, events such as changes in metabolite allocation at an isotope-sensitive branch point will change the intramolecular 13C pattern. Thus, intramolecular 13C distributions should carry signals reflecting such shifts in metabolic branching.To analyse effects of intramolecular 13C distributions in the glucose units of tree-ring cellulose of an annually resolved Pinus nigra tree-ring series. The samples originate from a moisture limited site, and cover the period 1961–1995. We then conducted a comparative time-series analysis with conventional whole-molecule and intramolecular 13C/12C ratios. Furthermore, we measured the same distributions in samples of six angiosperm and five additional gymnosperm species from globally distributed sites.To explore the potential of the intramolecular level, we measured intramolecular 13C distributions show intramolecular differences of the order of 10‰. Second, while a signal due to DR fractionation is present at some C positions of Pinus nigra tree-ring glucose, it is attenuated or even absent at other positions. Third, the intramolecular approach enables better description and prediction of environmental variables. Fourth, Hierarchical Cluster Analysis revealed PR signals at several C positions. Fifth, environmental drivers control PR fractionation. Finally, we propose an ecophysiological mechanism for the origin of a PR signal linking an environmental shift with a defined metabolic shift, which leaves its isotopic signature in the tree-ring archive. We conclude that intramolecular 13C analysis greatly extends the information that can be extracted from tree-ring archives.We report six findings. First, 12. Photosynthesis involves the action of several fractionating enzymes, e.g. Rubisco, transketolase, and aldolase13, but the term photosynthetic fractionation usually refers exclusively to fractionation by CO2 diffusion and Rubisco-catalysed carboxylation. Fractionations occurring downstream of Rubisco carboxylation have been called post-carboxylation fractionation, but other fractionating carboxylases occur in plants. Robust understanding of high-resolution intramolecular 13C fractionation requires unambiguous terminology. Therefore, we here introduce the terms DR and PR fractionation, which allow the classification of plant 13C fractionations into non-position-specific and position-specific processes.As described above, we distinguish here between diffusion-Rubisco (DR) and post-Rubisco (PR) fractionation. Synonyms for DR and PR fractionation are photosynthetic fractionation, and post-photosynthetic or post-carboxylation fractionation, respectively13C discrimination, a measure of the 13C fractionation in plants, has been defined14 as:a and Rp are the 13C/12C ratios of a carbon source and plant sample, respectively. To screen for intramolecular 13C signals, suitable isotope parameters are required. In analogy to Δ, we define positional 13C discrimination as:pi is the 13C/12C ratio at carbon position i of a plant metabolite  of Pinus nigra. Both distributions show non-random patterns with intramolecular differences exceeding 10‰ . We obtained similar intramolecular 13C distributions for six angiosperm and five additional gymnosperm species from different sites with global coverage .Above, we show that tree-ring glucose exhibits a pronounced intramolecular 13C time series would exhibit autocorrelation signals. Therefore, we tested all 13C time series  for autocorrelation, applying temporal lags of one to three years (see SI). We found no evidence of autocorrelation, showing that interannual carryover of signals is negligible. Thus, all subsequent analyses focused on conditions during the year of tree-ring formation.A tree ring formed in a particular year may have had significant input of stored glucose monomers from previous years. If so, 19. It is routinely evaluated by measurements of whole-molecule 13C discrimination, Δ20. An underlying assumption is that DR fractionation controls Δ. To search for the most influential environmental variable, we correlated Δ with air vapour pressure deficit, precipitation, soil moisture, air temperature, and global radiation during the growing season . VPD was found to be most strongly correlated with Δ . The strong negative VPD dependency is consistent with expectations for a moisture-limited site, published relationships and the well-established mechanisms underlying DR fractionation19. Thus, the variability of DR fractionation is reflected by the variability of VPD in the first approximation. This establishes VPD as a proxy of DR fractionation under given conditions.DR fractionation may be affected by diverse environmental variables13C discrimination, Δi′ (see above). We tested this by analysing the linear relationships between Δi′ and VPD. We found that VPD signal strengths vary among Δi′ . Thus, the VPD signal is stronger in Δ1′ than in Δ, and undetectable in Δ4′, which implies that the DR signal is transmitted into tree-ring glucose in a position-specific manner.If DR fractionation was the only temporally variable fractionation process in plants, its signal strength should be equal at all positional time series of Δi′ Fig. . The lar4′ Figs.  and S3. 1′~VPD relationships are similar . Thus, simple linear regression modelling provided no indications that Δi′ is superior to Δ as a proxy of environmental variables. Therefore, we tested the feasibility of capturing a higher-quality VPD signal using Δi′ in a more sophisticated modelling approach. Combining multiple linear regression modelling with automatic model selection, we generated a Δi′ model that describes VPD more precisely than the corresponding Δ model . In contrast to R2, model evaluation by adjR2 takes the number of explanatory variables into account, enabling comparison of models with different numbers of explanatory variables. Next, we tested the predictive abilities of both models by 10-fold cross-validation. We found that the Δi′ model predicts VPD more precisely . These findings show that the intramolecular approach enables more precise description and prediction of VPD, and suggests that Δi′ might allow for improved climate reconstructions.Correlation coefficients for the Δ~VPD and Δi′, and have had varying effects in the 31-year tree-ring series. To confirm this implication, we screened for position-specific signals by hierarchical cluster analysis of Δi′. We found four clusters: Δ1′ to Δ2′, Δ3′, Δ4′, and Δ5′ to Δ6′ . As Δ1′ and Δ6′ as well as Δ2′ and Δ5′ are uncorrelated , detected common signals are independent of each other. Thus, PR fractionations introduce 13C signals on top of the DR fractionation signal. Moreover, independence among clusters implies that intramolecular 13C patterns of tree-ring glucose vary on interannual timescales.Due to the single carbon addition by Rubisco, DR fractionation equally affects all carbon entering photosynthesis (see above). However, the results presented above show that the DR signal is not equally distributed over all carbon positions of the downstream metabolite tree-ring glucose Figs.  and S3, Δ6′ Fig. . Cluster13C signals implies that Δ is a composite of several signals with distinct physiological origins, and raises questions about the relative importance of DR and PR fractionation for Δ and Δi′. To address these questions, we first estimated the error variances in Δ and Δi′, which reflect random components of variance caused by finite measurement precision, which differs strongly between Δ and Δi′. Then, we calculated explainable components of variance, which may theoretically be linked to specific ecophysiological processes through modelling21. We then de-convoluted the explainable variance into a component explained by growing season air VPD and an unexplained component. With VPD as a proxy of DR fractionation (see above), this approach enables estimation of the relative importance of DR versus PR fractionation.Observation of multiple intramolecular i′, from 0.45‰ for Δ4′ to 3.37‰ for Δ1′  is one of the largest global C pools3 and the isotopic composition of soil substrates. For instance, soil cellulose decomposition occurs under both aerobic and anaerobic conditions via several metabolic pathways27. Because of the non-random 13C distribution of wood glucose , CO2 with approximately 2.5‰ more positive δ13C values will be released . Although this reasoning neglects fractionation effects of decarboxylation reactions, it illustrates the association of distinct breakdown pathways with substantial 13C differences in respired CO2. Thus, it shows that considering positional 13C differences in soil organic matter will enable better characterisation of C turnover pathways and quantification of heterotrophic soil respiration. This, in turn, will help reduce uncertainties in regional- to global-scale models of terrestrial productivity, and earth system models28.Isotopes are powerful tools for analysing soil C turnover and associated phenomena. However, their use requires information about both fractionation effects of microbial communities13C patterns; more specifically, interannual variation in the 13C patterns of glucose derived from Pinus nigra tree rings  obtained by attempts to model Δ rarely exceed 50%. This, in turn, suggests that multiple intramolecular signals are generally present in 13C datasets, and that intramolecular 13C analysis offers considerable scope to improve the resolution and robustness of 13C analyses.Our analyses show that intramolecular le Figs. . This ma13C ratios clearly offer more information than whole-molecule ratios , Δ2′  and Δ3′ . However, as shown in Figure i′ decline in the order Δ1′ (b1′ = −0.0226 ± 0.0046SE ‰ Pa−1), Δ2′ (b2′ = −0.0156 ± 0.0052SE ‰ Pa−1) and Δ3′ (b3′ = −0.0116 ± 0.0037SE ‰ Pa−1). DR fractionation is not position-specific, and can therefore only introduce regression slopes of equal size. Significant VPD correlations suggest that the DR signal is present at Δ1′ to Δ3′. Above-average explainable variance, a strong common signal, and steeper VPD slopes indicate that Δ1′ and Δ2′ contain additional VPD-dependent PR signals. Thus, assuming that b3′ represents the common DR signal, the PR contributions to the Δ1′~VPD and Δ2′~VPD slopes are b1PR′ = b1′–b3′ and b2PR′ = b2′–b3′, respectively.Δer Figs. . In comp1′ and Δ2′. Bacterial glucose isomerase (EC 5.3.1.5) has substantial equilibrium and kinetic isotope effects at glucose C-1 and C-2 , according to previous authors18, who hypothesis that plant PGI should have similar effects, as it operates by the same reaction mechanism. Hence, shifts of the PGI reaction from irreversible to equilibrium conditions will be accompanied by correlated 13C shifts at C-1 and C-2 of the reaction product, G6P. Magnitudes of these 13C shifts are proportional to the differences between corresponding kinetic and equilibrium isotope effects, and 13C shifts at C-1 and C-2 of G6P are linearly related as (KIEC-1-EIEC-1)/(KIEC-2-EIEC-2) = 2.25. That is, a given shift at G6P C-2 will be accompanied by a 2.25-fold larger shift at C-1. This ratio should equal the ratio of the PR contributions to the Δ1′~VPD and Δ2′~VPD regression slopes, b1PR′/b2PR′. We found that b1PR′/b2PR′ = 2.74 , which is consistent with a PGI-related mechanism introducing a 13C signal in Δ1′ and Δ2′.Phosphoglucose isomerase  catalyses conversion of fructose-6-phosphate to glucose-6-phosphate (G6P), which is used in formation of starch or tree-ring cellulose. It is the only enzyme that simultaneously modifies C-1 and C-2 bonds of G6P and hence glucose units in tree-ring cellulose, and can therefore introduce isotope effects of substantial size at these positions (primary isotope effects). Hence, PGI is the most likely generator of the correlated PR signals in ΔPinus nigra, strong negative relationships between VPD and both stomatal conductance and intercellular [CO2] can be expected31. At high intercellular [CO2], plants photosynthesise at high rates, and stromal PGI is strongly displaced from equilibrium34. As intercellular [CO2] declines, plants photosynthesise at lower rates, and stromal PGI shifts towards equilibrium32. According to published isotope effects18, a shift towards equilibrium results in 13C enrichments at C-1 and C-2 of stromal G6P. From G6P, the signal is transmitted to transitory starch and the glucose units of tree-ring cellulose derived therefrom. Low intercellular [CO2], as induced by stomatal closure due to high VPD, is associated with 13C enrichment by the DR fractionation system. Consequently, DR and PR fractionation at C-1 and C-2 have synergistic effects, and lead to steeper Δ1′ ~ VPD and Δ2′ ~ VPD regression slopes. A regulated shift towards PGI equilibrium may putatively facilitate stabilisation of the Calvin-Benson cycle35, which is probably most important when intercellular [CO2] is low. Thus, a PGI-related mechanism can explain enhanced Δ1′ and Δ2′ fractionations and is ecophysiologically plausible.From an ecophysiological perspective, the occurrence of PGI-driven fractionation is plausible for the following reasons. In isohydric plants like 13C and δ18O of plant organic matter36. In its current form, however, application of such dual-isotope analysis depends on several assumptions, which impedes its widespread implementation37. One problem noted by the cited authors is that stomatal conductance and carbon assimilation are not the only processes that modulate isotope ratios. Our observation of PR fractionation, which the dual-isotope concept neglects, highlights this challenge.Analysis of intramolecular variation in isotope ratios is intended to resolve multiple ecophysiological signals using several information channels. In that sense, it is conceptually related to the so-called “dual-isotope approach”; the independent, but simultaneous, examination of stomatal conductance and carbon assimilation through combined analysis of whole-molecule δ13C fractionation system of plants and to derive ecophysiological and environmental information from Δ measurements. Generally, deconvolution of several signals with only one observable variable is not feasible. In contrast, resolution of six partly independent intramolecular 13C variables  is defined as the ratio between the rates of carbon assimilation and transpiration. It is a major determinant of plant performance at water-limited sitesi′ has greater descriptive and predictive capacities than the corresponding Δ model. This finding is especially noteworthy given the lower achievable accuracy of Δi′ measurements compared to Δ measurements . Currently, Δi′ measurements are time consuming and thus limited to small sample sets. We expect that Δi′ applications will improve markedly with anticipated analytical advancements and with the further elucidation of PR fractionation effects, which might allow more sophisticated mechanistic modelling.We found that a statistical model of VPD based on Δ13C abundances are functions of environmental and related physiological variables, studied here at annual resolution. The approach is generally suitable for analysis of samples covering much longer timeframes38, far exceeding the scope of manipulation experiments or direct observation. However, upscaling to these timeframes requires an assessment of the temporal robustness of 13C signals. In nature, wood cellulose often persists for long periods, and is datable with high accuracy. Several tree-ring chronologies with annual resolution and calendric exactness encompass the entire Holocene39. Subfossil wood samples date back to the last interglacial period, ≈130,000 to 115,000 BP41. Thus, intramolecular 13C distributions in wood are promising archives of information about physiological and environmental conditions in past decades, centuries, and millennia. Position-specific isotope abundances may be particularly valuable for acquiring information (which is difficult to acquire by any other available technology) about the capacity of different plant species to acclimatise and adapt to long-term environmental changes. This, in turn, might aid attempts to identify suitable plants, cultivars and genotypes for changing environments.Intramolecular 13C measurements will complement whole-molecule stable isotope measurements and multi-isotope approaches in several applications. These include: prediction of 13C abundances of CO2 formed by different respiratory pathways; characterisation of the C metabolism of soil microbial communities; analyses of soil carbon turnover; elucidation of plants’ physiological responses to environmental changes and their long-term acclimatisation ; and reconstructions of plant physiological and environmental traits based on mechanistic models .We anticipate that intramolecular Additional information is provided under Supporting Information.Pinus nigra Arnold trees (two cores per tree) from the Bierhäuselberg site , which has shallow, very dry soil. Both the site and samples have been previously described in detail42. In addition, we used dated tree-ring samples, pooling 5–10 annual rings of 11 angiosperm and gymnosperm species from ecologically different sites with global coverage  using a binocular microscope and a scalpel, and combined rings in annual pools. Thus, our data represent properties of the tree species at the site rather than individual trees. Pooled samples were ground  and their glucose contents were converted into 1,2-O-isopropylidene-α-D-glucofuranose following a published protocol43. Samples of 11 additional angiosperm and gymnosperm species were processed in the same way, but in a final step their glucose contents were converted into 3,6-anhydro-1,2-O-isopropylidene-α-D-glucofuranose43. Checks by 1H NMR showed that sample purity was ≥99.9%.We carefully separated dated 13CVPDB measurements of the glucose derivative were acquired for Pinus nigra samples. Quantitative 1D 13C NMR spectra were collected44 using a Bruker 400 MHz AVANCE III instrument equipped with a 5 mm BBFO SmartProbeTM . We recorded and processed 30 spectra per Pinus nigra sample and eight spectra per sample of the additional species using TopSpinTM 3.1 . We excluded Pinus nigra samples from 1977, 1978, 1981, and 1982 because they were too small.Conventional δ13C NMR spectra resulted in average signal integrals, Si, of specific carbon positions of the glucose derivatives, i = {C-1,…, C-6, C-q, C-Me1, C-Me2}. Each carbon is directly bound to one or two neighbouring carbons. Calculation of 13C molar equivalents, Si(c), considered corresponding signal satellites45. Removal of 13C variation related to TPC followed methods described below, eq. ′. Calculation of positional 13C/12C ratios, expressed as δ13Cpi and δ13Cpi′ followed published procedures46. Calculation of positional discrimination, Δi, and the TPC-free positional discrimination, Δi′, followed eqs. (13CO2 (=δ13Ca) for the northern hemisphere47. As the open canopy at our site presumably allows rapid mixing of biogenic and atmospheric CO2, errors in Δi and Δi′ due to the contribution of isotopically distinct biogenic CO2 should be minimal. Positional 13C deviations from the molecular average were calculated as Δδ13Ci = (Si(c)/(ΣSi(c)/n)−1)*103 with i = {C-1, …, C-6}.Integration of low, eq. , and res13C differences between these symmetry-related positions are partially levelled out by TPC. In the following text, we derive equations to back-calculate the intramolecular 13C distribution before TPC. Please note that the resulting TPC-free distribution does not represent the 13C distribution of any naturally occurring hexose. This is because both parts of sucrose, i.e. glucose and fructose, are used for cellulose synthesis, but differ with respect to their 13C distributions8.When cellulose is synthesized, translocated sucrose is first broken down to hexoses, which are converted to UDP-glucose. During these reactions, 40 to 50% of the hexose phosphates generated are further broken down to triose phosphates, before use in cellulose synthesis. This is known as triose phosphate cycling (TPC). Triose phosphate isomerase equilibrates glyceraldehyde 3-phosphate (G3P) with dihydroxyacetone phosphate (DHAP), respectively derived from C4–6 and C1–3 portions of hexoses. Their equilibration causes carbon exchange between C1–3 and C4–6 portions of hexoses. Thus, in comparison to the hexose units of sucrose, approximately 20 to 25% of carbons in the UDP-glucose pool have been effectively redistributed between symmetry-related carbon positions, i.e. between C-1 and C-6, C-2 and C-5, C-3 and C-4. This implies that intramolecular 13C abundance at a specific hexose carbon position, Ci, is given by:13C abundance of the symmetry-related carbon position, Cs, is given by:13Ci′ and 13Cs′ denote TPC-free 13C abundances. Solving eqs . Δi and Δi′ were then calculated as described above.Reported estimates of proportions of carbon redistributed by TPC include 20–25% in 13C abundances at symmetry-related hexose positions, it should lead to correlation between symmetry-related Δi values, and these correlations should be removed by the calculation of TPC-free Δi′ values. As expected for 13C abundances affected by TPC, Δi time series of symmetry-related glucose carbon positions correlate significantly ..13C abun Δi Fig. . General Δ6 Fig. .Table 1C51. We acquired monthly means of soil moisture from a global grid dataset  for 16°15′ E, 48°15′ N. Both the climate station and the selected grid point are no more than a horizontal distance of 15 km from the sampling site with a negligible vertical offset. Thus, all data should represent site conditions well. In conifers, tracheids form over several months52. Thus, we calculated climate averages and sums of the growing season, which we estimated to extend from March to November . Deficits in air vapour pressure, VPD [Pa], were calculated following published procedures1′ + Δ2′ + Δ3′ + Δ4′ + Δ5′ + Δ6′. We arrived at the minimal adequate model by stepwise model simplification based on Akaike’s information criterion using the step function of the Stats package with default settings. To test the predictive abilities of the simple linear regression model, VPD~Δ, and the minimal adequate model from multiple linear regression modelling, VPD~Δ1′ + Δ3′ + Δ5′, we performed 10-fold cross-validation using cv.lm(m = 10) and CVlm(m = 10) functions of the DAAG package. We performed Hierarchical Cluster Analysis on z-scores of Δi′ using Euclidean distances and Ward’s fusion criterion for cluster formation53.Statistical analyses were performed in R 1.0.143. We compared regression slopes by ANCOVA using two categories and type II sum of squares. For statistical description of VPD, we first fitted the maximal model, VPD~ΔThe datasets generated and analysed during the current study are available from the corresponding authors on reasonable request.Supporting Information


Although previous studies have shown that individuals with depressive tendencies have deficits in forgetting negative material, the detailed underlying neural mechanisms have not been elucidated. This study examined the intentional forgetting of negative and neutral material in individuals with depressive tendencies in two phases. In the study phase, the participants performed a directed forgetting task, where a total of 320 words were presented to them, each followed by an instructive cue to forget or remember the previously presented word. Subsequently, in the memory recognition test phase, the participants completed the “old or new discrimination task”. The results indicated that individuals with depressive tendencies had difficulties suppressing the memory encoding of negative words, while the suppression of memory encoding of neutral words was relatively intact. Moreover, individuals with depressive tendencies displayed enhanced word-evoked P2 and late positive potential for negative items, as well as enhanced cue-evoked P1 and N2 for the negative items that were required to be forgotten, as compared to individuals without depressive tendencies. Based on these results, we propose two mechanisms that may contribute to the failure of forgetting negative material in mild depression: (1) inefficient memory suppression and early selective attention, and (2) excessive preliminary processing. This negative bias plays a critical role in the etiology as well as the maintenance of depressive symptoms (e.g. the ruminative thinking style)6. The majority of previous studies focused on the biased processing of emotional information in the aspects of perception, attention, memory and interpretation, neglecting the functions of inhibition and cognitive control in the depressed population7. Recent studies have demonstrated that depressed individuals are less successful in excluding unwanted thoughts and memories from awareness due to inhibitory deficits in the cognitive control system10. This impaired inhibitory function may consequently hinder recovery from depressive symptoms, and induce a vicious circle of a mood-congruent state and a persistent low mood11. Therefore, it is important to investigate the intentional forgetting and the associated neural mechanisms in the depressed population, which may broaden our understanding of the pathology of this disorder and aid in the development of more efficient treatments.According to Beck’s cognitive model of depression, depressed individuals exhibit excessive negative biases in many aspects of cognitive processes, such as attention and memory, as compared to healthy controls12, memory inhibition or suppression may occur during the stages of memory encoding and memory retrieval. The intentional forgetting at the stage of memory encoding can efficiently limit and disrupt the consolidation and further reflection of unwanted memories, which is the focus of this study. Memory inhibition during encoding is usually investigated using the directed forgetting (DF) paradigm13, which consists of two phases. In the study phase, participants are presented with a series of items, some of which are “to be remembered” (TBR) and others that are “to be forgotten” (TBF). When the “remember” cue is given, participants are required to remember or consolidate the previously presented item. On the contrary, when the “forget” cue is given, they should try their best to forget the previously presented item. In the memory recognition test phase, participants complete the “old or new discrimination task”, where the previously studied words are mixed with new words. The DF effect is defined as a higher recognition rate for TBR than for TBF items in the phase of memory recognition test12. There are two methods to perform the DF task: the item-method, and the list-method14. In the item-method, the “remember/forget” cue is presented after each item, whereas in the list-method, the cue is presented after a list of items. Both methods involve activation of the frontal regions, but their cognitive and neural mechanisms are quite different12. This study employed the item-method paradigm, since it provides an insight into how individuals with depressive tendencies control new, incoming information.As reviewed by Anderson & Hanslmayr18. In particular, intentional forgetting recruits more executive control resources at the frontal lobe than incidental forgetting18. Furthermore, some studies demonstrated a negative correlation between activity in the dorsolateral prefrontal cortex and the hippocampus during successful forgetting17. Thus, the psychological mechanism of the DF task has been proposed as follows: items are tentatively kept in the working memory until the “remember/forget” instruction requires participants to selectively rehearse and elaborately encode the TBR items or to disrupt the encoding and suppress the consolidation of the TBF items using the inhibitory control mechanism24. In addition to selective rehearsal and inhibition, another three mechanisms have been proposed for the item-method DF, namely, set segregation (TBR and TBF items are organized into two groups so that the processing of the items of each group does not interfere with the other25), attentional withdrawal (attention is withdrawn from the task-irrelevant TBF items so that their representations are removed from the working memory26), and cognitive load .Previous DF studies have shown that, while the medial-temporal lobe, and especially the hippocampus, is significantly activated by the “remember” instruction, the prefrontal and parietal regions are activated by the “forget” instruction29 and individuals with depressive tendencies30 recognized more TBF words than nondepressed individuals, more specifically, they exhibit reduced forgetting of negative, compared to neutral, or positive TBF words32. However, to date, the neural mechanisms underlying the memory control deficits in the depressed population have only been explored in two empirical studies. In one study, Yang et al.9 found that depressed patients could not forget negative material and displayed stronger activation in their frontal and parietal regions (associated with inhibitory control function) when they attempted to forget negative TBF items. This abnormal activation indicated that even though more inhibitory control resources were recruited to terminate the rehearsal of negative TBF items, the intent failed due to excessive negative bias. Therefore, it was postulated that depressed patients are inefficient in forgetting negative material9. In the other study, Berman et al.8 demonstrated that patients with major depressive disorder have difficulty in forgetting negative words, using a DF procedure. They observed that when participants expelled negative information from their short-term memory, both major depressive patients and healthy controls robustly activated a network  that has been implicated in memory selection and interference resolution; there was no difference in the magnitude of activation of the two groups. However, while the control group displayed focal activation in the left inferior frontal gyrus, the major depressive patients exhibited more diffuse activation  in this region; this spatial variability was associated with the patients' greater behavioral variance in reaction times.Behavioral studies have revealed that individuals with high levels of depression exhibit deficits in directed forgetting; depressed patients9 demonstrated that depressed patients have abnormal brain activation when they attempt to forget negative material, the detailed neural mechanisms associated with their failure in the DF task is still unclear. As introduced above, there are two procedures in the study phase of the DF paradigm: the participants first preliminarily encode the presented item and then implement the “remember/forget” cue to remember or forget the encoded item. However, when using the fMRI technique, it is difficult to discriminate these two quick procedures due to its low temporal resolution. In this context, the authors of the present study considered that the event-related potential (ERP) is a more suitable tool to separately investigate the neural deficits in the two procedures. Moreover, another catalyst for the execution of this study was to shed light on the previous DF studies in healthy subjects, which presented contrasting results associated with the memories of emotional vs. neutral material34, that may be due to individual differences in these studies. To examine the impact of individual differences on the performance in the DF task, this study included measures of individual differences in depressive tendency, trait anxiety, ruminative tendency, and approach/avoidance motivational system. Subsequently, the relations between individual differences and behavioral/ERP indexes were explored.Although the two fMRI studies38. It has been established that the “forget” instructive cue evokes larger N2 amplitudes  than the “remember” cue34. In some DF studies, the N2 (approximately 200 to 300 ms after cue onset) was also referred to as “the frontal positivity”, since this negative-going component actually had positive amplitude34. The second component of interest is the parietal P3. This component usually displays larger amplitudes following the “remember” cue compared to the “forget” cue, reflecting selective rehearsal of the TBR items40. In addition to the cue-evoked N2 and P3, the word-evoked ERPs are also examined. Specifically, previous studies indicated that the late positive potential (LPP) displays larger amplitudes for negative items than for neutral items, indicating more elaborate processing of negative material in healthy individuals33. It should be noted that, both P3 and LPP refer to large and slow positive potentials, which peak at the parietal electrodes later than 300 ms post-stimulus. In this study, the term “P3” is used to refer to the relatively earlier positive component (about 300 ms) with a sharper peak, and the term “LPP” to refer to the slower positive wave (after 500 ms) with a blunter peak42. In addition to the three ERP components that have been often mentioned in the DF paradigm, the present study investigated early components such as the occipital P1 and the frontal P2, which are well-known attention-related components44, but have not been explored in previous DF studies. Although both P1 and P2 are usually used as indexes of selective attention, P1 is more sensitive to stimulus features (feature-based attention45) and arousal levels46, while the anterior P2 is often associated with the motivational salience of a stimulus as determined by either task-relevant features or novelty51.In accordance with previous DF studies in healthy subjects, the present work focused on three ERP components. The first one is the middle frontal N2, which reflects cognitive control and is usually observed in motor and memory inhibition tasks33, it was predicted that negative words may elicit larger word-evoked LPP in subjects with depressive tendencies than in nondepressed subjects. Furthermore, considering that the amplitude of cue-evoked P3 is associated with selective rehearsal40, it was predicted that negative TBR words may elicit larger cue-evoked P3 in subjects with depressive tendencies compared with nondepressed subjects. Moreover, since Yang et al.9 demonstrated that depressed patients presented stronger activations in the neutral networks associated with inhibitory control function, it was hypothesized that inhibitory control resources might be inefficiently recruited in subjects with depressive tendencies when they are required to forget negative words. Accordingly, it was expected that negative words may elicit larger cue-evoked N2 amplitudes for TBF items in subjects with depressive tendencies compared to nondepressed subjects. Furthermore, this study examined the potential influence of individual differences  on the performance of DF. According to previous studies using emotional material, the performance of DF might be affected by individual differences in depression30, rumination31, trait anxiety32, and the behavioral activation/inhibition system52. Consequently, this study included measures of individual differences in depression, ruminative tendencies, trait anxiety, and the activation/inhibition system (see detailed information in Methods).This study compared the behavioral and ERP data of individuals with and without depressive tendencies. It is hypothesized that individuals with depressive tendencies experience difficulty in forgetting negative material, which is due to deficits/dysfunctions in both procedures during the study phase of the DF task, i.e., the item encoding, and the implementation of the “remember/forget” cue. Accordingly, it is expected on the behavioral level that subjects with depressive tendencies will have a higher recognition rate for TBF negative words than nondepressed subjects. To examine the deficits during the encoding procedure, the word-evoked ERP components of occipital P1, frontal P2 and parietal LPP were investigated. While to examine the deficits in the implementation of the “remember/forget” cue, the cue-evoked ERP components of occipital P1, frontal N2 and parietal P3 were investigated. It was hypothesized that subjects with depressive tendencies would excessively encode and rehearse negative items compared with nondepressed subjects. Considering that the amplitude of word-evoked LPP is associated with elaborate encoding processing54, this study examined the impaired directed forgetting in individuals with depressive tendencies rather than in depressed patients. Furthermore, because previous studies have demonstrated a correlation between anxiety and deficits of directed forgetting56, this study only recruited participants with a moderate level of trait anxiety, i.e., the directed forgetting was compared between the individuals with and without depressive tendencies, and both the groups had a moderate level of anxiety.Considering that psychiatric medications may affect behavioral and/or ERP results57) and the Trait form of Spielberger's State-Trait Anxiety Inventory . In this sample, students with STAI-T scores within the middle 50% (from 25% to 75%) of the distribution were considered as subjects with a moderate level of trait anxiety61. Among the individuals with a moderate level of trait anxiety, students with BDI-II scores ≤ 13 were labeled as individuals without depressive tendencies, whereas students with BDI-II scores > 13 were labeled as individuals with depressive tendencies. According to Beck et al.57, a BDI-II score ≤ 13 indicates minimal depression, and a BDI-II score > 13 indicates mild (14–19), moderate (20–28), or severe depression (29–63). Among the students who met all these criteria, we randomly invited 60 individuals to participate the current study . As shown in Table In a mental health screening of Shenzhen University, all the freshman students (n = 6000) completed the Beck Depression Inventory Second Edition  seizure disorder; 3) history of head injury with possible neurological sequelae, and 4) substance abuse or dependence in the past six months.Exclusion criteria for both groups were 1) any Axis I and II disorders according to the Diagnostic and Statistical Manual (DSM-IV)Participants were told about the equipment used in the experiment and their tasks. Written informed consent was obtained prior to the experiment. The experimental protocol was approved by the Ethics Committee of Shenzhen University and this study was performed strictly in accordance with the approved guidelines.57. It consists of 21 items that assess the level of depressive symptoms in the past two weeks. The BDI-II scores from 0 to 63; a high score indicates a high level of depressive tendency.The BDI-II is a widely used self-reported measure of depressive symptoms59. It contains 20 items and scores from 20 to 80; a high score indicates a high level of trait anxiety.The STAI-T is developed to evaluate a relatively enduring tendency of anxiety65 is used to assess how participants tend to respond to sad feelings and symptoms of dysphoria. It contains 22 items and scores from 22 to 88; a high score indicates a high level of ruminative tendency.The Ruminative Response Scale (RRS)66. The BIS sub-scale contains 7 items (scores from 7 to 28) and the BAS contains 13 items (scores from 13 to 52). A high score on BIS or BAS indicates a larger tendency to regulate aversive or appetitive motives so as to move away from unpleasant, or to move toward desired, events and stimuli.The Behavioral Inhibition System and Behavioral Activation System Scale (BIS/BAS) is designed to assess individual differences in the sensitivity of two motivational systems, i.e., a behavioral approach system and a behavioral avoidance systemvs. forget) × two  × two (group: with depressive tendencies vs. without depressive tendencies) factors was used in this study.A design with two  = 10.0, p < 0.001), and the two categories differed significantly in valence  = −44.4, p < 0.001). No difference was found in the familiarity between negative and neutral words  = −0.17, p = 0.868).This study used 640 words  from Chinese Affective Words System13, the 640 words were randomly divided into two subsets, with equal number of words between neutral and negative conditions and between nouns and adjectives. One subset (320 words) was used in the study phase while the whole 640 words were used in the recognition test . The valence (negative: t(318) = −0.96, p = 0.336; neutral: t(318) = −0.85, p = 0.397), arousal (negative: t(318) = 0.39, p = 0.694; neutral: t(318) = 0.32, p = 0.748), and familiarity (negative: t(318) = 1.28, p = 0.201; neutral: t(318) = −0.20, p = 0.840) of negative and neutral words were counterbalanced between the two subsets. Furthermore, the valence (negative: t(158) = −1.36, p = 0.176; neutral: t(158) = −1.25, p = 0.213), arousal (negative: t(158) = 1.29, p = 0.199; neutral: t(158) = 1.14, p = 0.255), and familiarity (negative: t(158) = −0.56, p = 0.579; neutral: t(158) = −0.55, p = 0.580) of negative and neutral words were counterbalanced between the “to be remembered” and “to be forgotten” conditions. The allocation of the words to each experimental condition was not changed during the experiment, while the presentation order of words within one condition was randomized across subjects.Considering that the DF paradigm consisted of two phases (study and recognition test)Before the DF task, participants were required to complete the four questionnaires .In the study phase, the 320 words were sequentially presented and each word appeared only once. The phase was comprised of four blocks (80 words in each block), separated by self-paced rest periods. As shown in Fig. In the phase of memory recognition test, the old/new discrimination task was performed. The 320 studied words were mixed with another 320 new words. The words were sequentially presented and each word appeared only once. Participants were required to discriminate as quickly and as accurately as possible whether the word was presented in the study phase, irrespective of the “forget/remember” instructions. They responded by pressing the “F” or “J” button on a computer keyboard with their left or right index finger. The assignment of keys to old and new words was counterbalanced across participants. The inter-trial interval was 2000 ms. The phase was comprised of four blocks (160 words in each block), separated by self-paced rest periods.34).A task-irrelevant task  was filled between the study phase and the recognition phase . Electroencephalography (EEG) data were recorded during the study phase, with electrode impedances kept below 5 kΩ. Ocular artifacts were removed from EEGs using a regression procedure implemented in NeuroScan software (Scan 4.3). An on-line analogue filter (0.01–100 Hz) and a notch filter (50 Hz) continuously worked during the recording.The recorded EEG data were off-line filtered (0.01–30 Hz) and segmented beginning 200 ms prior to the onset of stimulus and lasting for 1200 ms. Trials contaminated with large artifacts (peak-to-peak deflection exceeded ±200 μV) were excluded from further analyses. As a result, 74 ± 6.3 trials (mean ± std), 76 ± 4.9 trials, 75 ± 5.0 trials, and 74 ± 6.1 trials per subject were left in the group without depressive tendencies for the “remember-negative”, “remember-neutral”, “forget-negative”, and “forget-neutral” conditions. Meanwhile, 74 ± 7.1 trials, 73 ± 7.6 trials, 74 ± 6.2 trials, and 75 ± 5.8 trials per subject were left in the group with depressive tendencies for the four conditions . All epochs were baseline-corrected with respect to the mean voltage over the 200 ms preceding the onset of stimulus, followed by averaging in association with experimental conditions.This study focused on the ERPs elicited by words and instructive cues. Although ERP data were recorded from all the 64 electrode sites, we analyzed only the sites at which the component of interest was large and the waveform showed a representative pattern. Time windows for mean amplitude calculation were centered at the peak latencies of ERP components in grand-mean waveforms, with a shorter window length for early components and a longer length for late components.For the word-evoked ERP, we analyzed average amplitudes of occipital P1, frontal P2 and parietal LPP components. The P1 amplitude was calculated as the average amplitude at the electrode sites of O1 and O2 between 80 to 120 ms after the onset of words. The P2 amplitude was calculated as the average amplitude at the electrode sites of F1, F2 and Fz between 220 to 270 ms post stimulus. The LPP amplitude was calculated as the average amplitude at the electrode sites of P1, P2 and Pz between 500 to 900 ms post stimulus.For the cue-evoked ERP, we analyzed average amplitudes of occipital P1, frontal N2 and parietal P3 components. In particular, the P1 amplitude was calculated as the average amplitude at the electrode sites of O1 and O2 between 115 to 155 ms after the onset of cues. The N2 amplitude was calculated as the average amplitude at the electrode sites of F1, F2 and Fz between 240 to 290 ms post stimulus. The P3 amplitude was calculated as the average amplitude at the electrode sites of CP1, CP2 and CPz between 260 to 460 ms post stimulus.It should be stated that the analysis of the word-evoked P1 and P2, and cue-evoked P1 was a post-hoc decision based on our data, because these components have not been reported in previous DF studies.Descriptive data were presented as mean ± standard error, unless otherwise mentioned. The significance level was set at 0.05.vs. forget) and the emotion category of words  as within-subject factors, and group  as the between-subject factor. Significant interactions were analyzed using simple effects model. Bonferroni correction was used for multiple comparisons.Repeated-measures ANOVA was performed on behavioral and ERP measurements, with instruction  = 22.6, p < 0.001, The main effect of instruction was significant  = 5.64, p = 0.021, The main effect of emotion was significant  = 6.38, p = 0.014, F = 5.48, p = 0.023). However, this group difference did not achieve significant level in any of the other conditions  < 1; individuals without depressive tendencies vs. with depressive tendencies: remember negative words = 83.6 ± 1.8 vs. 82.2 ± 1.8%, remember neutral words = 82.9 ± 2.2 vs. 83.5 ± 2.2%, forget neutral words = 74.8 ± 1.3 vs. 74.4 ± 1.3%).The interaction of instruction by emotion by group was significant  = 6.58, p = 0.013, F = 13.6, p = 0.001). However, this emotion effect did not achieve significant level in any of the other conditions  < 1.42, p > 0.238; negative vs. neutral: remember in subjects without depressive tendencies = 732 ± 17.1 vs. 735 ± 21.0 ms, forget in subjects without depressive tendencies = 720 ± 23.5 vs. 721 ± 26.4 ms, forget in subjects with depressive tendencies = 759 ± 23.5 vs. 740 ± 26.4 ms).The interaction of instruction by emotion by group was significant  = 7.52, p = 0.008, The main effect of emotion was significant  = 5.08, p = 0.028, F = 5.14, p = 0.027). However, this group difference did not achieve significant level for neutral words  < 1; subjects without depressive tendencies = 3.92 ± 0.64 μV, subjects with depressive tendencies = 4.50 ± 0.64 μV).The interaction of emotion by group was significant  = 44.4, p < 0.001, The main effect of emotion was significant  = 4.61, p = 0.036, F = 4.16, p = 0.046). However, this group difference did not achieve significant level for neutral words  < 1; subjects without depressive tendencies = 1.31 ± 0.25 μV, subjects with depressive tendencies = 1.31 ± 0.25 μV).The interaction of emotion by group was significant  = 44.4, p < 0.001, The main effect of instruction was significant  = 11.5, p = 0.001, The main effect of emotion was significant  = 6.01, p = 0.017, F = 10.2, p = 0.002). However, this group difference did not achieve significant level in any of the other conditions  = 0.55 to 1.74, p = 0.192 to 0.461; individuals without vs. with depressive tendencies: remember previous negative words = 0.32 ± 0.26 vs. 0.80 ± 0.26 μV, remember previous neutral words = 0.12 ± 0.23 vs. 0.51 ± 0.23 μV, forget previous neutral words = 1.14 ± 0.23 vs. 0.89 ± 0.23 μV).The interaction of instruction by emotion by group was significant  = 43.8, p < 0.001, The main effect of instruction was significant  = 10.1, p = 0.002, The main effect of emotion was significant  = 4.44, p = 0.039, F = 15.4, p < 0.001). However, this group difference did not achieve significant level in any of the other conditions  < 1; individuals without vs. with depressive tendencies: remember previous negative words = 3.92 ± 0.29 vs. 3.66 ± 0.29 μV, remember previous neutral words = 3.92 ± 0.27 vs. 3.64 ± 0.27 μV, forget previous neutral words = 3.18 ± 0.30 vs. 2.91 ± 0.30 μV).The interaction of instruction by emotion by group was significant  = 198, p < 0.001, The main effect of instruction was significant  = 19.4, p < 0.001, The main effect of emotion was significant  and the six behavioral/ERP indices . In total, we performed 30 (5 × 6) correlations.r = 0.431, p < 0.001, corrected p = 0.016; Fig. r = 0.512, p < 0.001, corrected p < 0.001), and cue-evoked P3    Fig. . The BIS01) Fig.  .After controlling for the other four self-reported measures, only one significant correlation was detected. The BIS score was correlated with the amplitude of cue-evoked N2 .In addition, it was found that the three self-reported measures were pairwise correlated  and cue-evoked (P1 and N2) components for negative words in participants with depressive tendencies. In contrast to the hypothesis, negative words did not elicit larger cue-evoked P3 amplitudes for TBR items in subjects with depressive tendencies, compared to the control group. However, this result was consistent with the obtained recognition rate (subjects with depressive tendencies did not remember more negative words than nondepressed subjects), and other studiesBased on these results, we propose that two mechanisms may contribute to the failure of forgetting negative material in individuals with depressive tendencies.68. Accordingly, the “forget” cue evoked an obvious N2 while the “remember” cue did not. The data also revealed a main effect of emotion; larger N2 amplitudes were associated with negative words than with neutral words. This emotional effect is consistent with previous DF findings in healthy people, demonstrating that individuals usually recruit more inhibitory resources (indicated by larger N2 amplitudes) to suppress negative memories23 because forgetting negative stimuli is more laborious and less efficient69. In line with this interpretation, the N2 interaction of the current study suggests that subjects with depressive tendencies recruit even more inhibitory control resources to reduce the long-term memory of negative stimuli than nondepressed subjects, but this compensatory effort does not make up for their inefficiency in intentional forgetting. This is consistent with what was reported by Yang et al., who found that forgetting negative items, compared to neutral items, caused enhanced activation in the inferior and superior frontal gyrus in depressed patients9. Furthermore, the proposed association between the “compensatory effort” and the enhanced N2 was confirmed by the correlation between the BIS score and the N2 amplitude: a larger N2 in the forget-negative-word condition was associated with a larger motivation (or effort) to keep away from negative stimuli. This correlation was observed in both depressed and nondepressed individuals.The most important finding of this study was the N2 interactive effect; the “forget” instructive cue elicited larger N2 for negative words in subjects with, compared to subjects without, depressive tendencies. The frontal N2 is generally identified as an ERP marker of inhibitory control45 and it is sensitive to task demands70 and arousal levels46. The P1 result indicates that the “forget” cue following negative words attracted more early attention in individuals with depressive tendencies, compared to individuals without depressive tendencies. It is possible that the enhanced P1 in depressed individuals reflected a heightened unconscious amplification of the instruction of “forget the previous negative word” so as to facilitate the task72. Alternatively, the “forget-negative-word” cue evoked a higher level of arousal in subjects with depressive tendencies. Similar with this finding, previous studies demonstrated that depressed subjects have larger P1 amplitudes compared with nondepressed subjects, especially following the presentation of negative material77. However, since this is the first report of this P1 finding in the DF literature, further study is needed to verify the speculation.Another interesting finding was that the cue-evoked P1 displayed exactly the same pattern as the cue-evoked N2: the instruction of forgetting negative words evoked larger P1 amplitudes in subjects with depressive tendencies, than that in subjects without depressive tendencies. The occipital P1 is an early ERP component associated with feature-based selective attentionAltogether, individuals with depressive tendencies, on the one hand, could not forget negative words successfully, and on the other hand, allocated more cognitive resources than nondepressed ones when suppressing negative material. Therefore, the present study proposes that the selective attention system (P1) and the inhibitory control system (N2) function in an inefficient way in individuals with depressive tendencies (or mild depression).9, this study also provided evidence for the excessive preliminary processing of negative words in individuals with depressive tendencies: during the encoding procedure, negative words elicited larger P2 and LPP in subjects with depressive tendencies, compared to subjects without depressive tendencies.Beyond what the previous studies reported on the abnormal neural activation in the implementation of the remember/forget cue82. The enhanced LPP for negative compared to neutral items suggests that negative items were processed more extensively than neutral items, which is consistent with previous DF studies34. In line with this interpretation, the even larger LPP for negative words in subjects with depressive tendencies indicates a more intensive encoding of negative material.The discovery of this LPP interactive effect is in accordance with the hypothesis of this study. The LPP has been widely considered to reflect sustained attentional allocation and continuous processing of emotional stimuli50. Many emotional studies found larger P2 amplitudes in response to negative than to neutral and positive stimuli87, indicating an attentional bias towards negative material. Furthermore, Bernat et al. proposed that the P2 plays a key role in determining which emotional stimuli become conscious ones, since the time window of 200 to 300 ms is on the boundary of nonconscious and conscious processing88. In this study, nondepressed subjects did not display differential P2 amplitudes between negative and neutral conditions, while subjects with depressive tendencies elicited larger P2 when viewing negative words. This result suggests that negative items may have more motivational significance to individuals with depressive tendencies, who exhibit excessive negative biases in many aspects of the cognitive processes2.An unexpected finding was that the frontal P2 was larger in response to negative than to neutral words in participants with depressive tendencies. According to previous literature, P2 is associated with the motivational salience of a stimulus and usually reflects motivation-related attentional allocation23. Although this excessive processing of negative words did not lead to higher recognition rate for negative TBR items in these individuals, a significantly shorter reaction time was observed in this group for negative compared to neutral TBR items.Taken together, the enhanced word-evoked P2 and LPP indicate an excessive preliminary processing of negative items in individuals with depressive tendencies, which may result in the subsequent failure of directed forgetting of negative materialThis study also found that, nondepressed participants could successfully forget both neutral and negative materials.69, while others argued that both neutral and negative material could be intentionally forgotten34. The inhomogeneity of experimental samples may be one of the reasons for the inconsistent results. After controlling for individual differences such as depression and trait anxiety, this study provided evidences which support the latter argument. Also, it was indicated that the BDI score was positively correlated with the recognition rate of negative TBF items. This result prompts the consideration of the level of depression as a variable when examining the emotional DF effect in a given population.Previous DF studies in healthy individuals resulted in conflicting conclusions on the issue of emotional bias. Some proposed that participants failed to forget negative materialTwo limitations should be considered for an appropriate interpretation of the current result. First, two possible mechanisms that may contribute to the failure of forgetting negative material in individuals with depressive tendencies were proposed. However, since the results indicated that the individuals with depressive tendencies also excessively processed negative material (reflected by enhanced word-evoked P2 and LPP), the recruitment of additional inhibitory resources in the implementation of the forget cue (reflected by enhanced cue-evoked N2) may be a compensation mechanism for this excessive processing, rather than due to the inefficiency of memory suppression of negative material. Thus, further studies using other paradigms are required to clarify this issue. Second, this study considered undergraduate students who scored > 13 in BDI-II as individuals with depressive tendencies. Thus the participants in the depressive tendency group were mildly depressed individuals. Further study is necessary to test the generalizability of the current conclusion to clinically depressed patients. Furthermore, because anxiety and depressive symptoms are highly comorbid, this study only selected participants with a moderate level of trait anxiety.The current study showed that individuals with depressive tendencies experienced difficulty in forgetting negative material. Individuals with depressive tendencies displayed enhanced word-evoked P2 and LPP for negative items and enhanced cue-evoked P1 and N2 for negative TBF items, compared to individuals without depressive tendencies. Consequently, we proposed two mechanisms during memory encoding that may contribute to the failure to forget negative material in mild depression. The two proposed mechanisms, which may influence the intentional forgetting in a negatively valenced context, are the inefficient early selective attention and memory suppression (reflected by cue-evoked P1 and N2) and the excessive preliminary processing (reflected by word-evoked P2 and LPP).Supplementary material