‘Lassoing’ a phylogenetic tree I: basic properties, shellings, and covers

A classical result, fundamental to evolutionary biology, states that an edge-weighted tree T with leaf set X, positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the leaf-to-leaf distances between any two elements of X. In biology, X corresponds to a set of taxa (e.g. extant species), the tree T describes their phylogenetic relationships, the edges correspond to earlier species evolving for a time until splitting in two or more species by some speciation/bifurcation event, and their length corresponds to the genetic change accumulating over that time in such a species. In this paper, we investigate which subsets of ${\binom{X}{2}}$ suffice to determine (??lasso??) the tree T from the leaf-to-leaf distances induced by that tree. The question is particularly topical since reliable estimates of genetic distance??even (if not in particular) by modern mass-sequencing methods??are, in general, available only for certain combinations of taxa.     

Encoding phylogenetic trees in terms of weighted quartets

One of the main problems in phylogenetics is to develop systematic methods for constructing evolutionary or phylogenetic trees. For a set of species X, an edge-weighted phylogenetic X-tree or phylogenetic tree is a (graph theoretical) tree with leaf set X and no degree 2 vertices, together with a map assigning a non-negative length to each edge of the tree. Within phylogenetics, several methods have been proposed for constructing such trees that work by trying to piece together quartet trees on X, i.e. phylogenetic trees each having four leaves in X. Hence, it is of interest to characterise when a collection of quartet trees corresponds to a (unique) phylogenetic tree. Recently, Dress and Erdös provided such a characterisation for binary phylogenetic trees, that is, phylogenetic trees all of whose internal vertices have degree 3. Here we provide a new characterisation for arbitrary phylogenetic trees.     

Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZ _t = μ Z _t dt + σ Z _t dW _t , t ≥ 0, where the conditional law of Z _t+Δt ? Z _t given Z _t = z has mean and variance approximately z μΔt and z ² σ ²Δt when the time increment Δt is small. The long-term stochastic growth rate ${\lim_{t \to \infty} t^{-1}\log Z_t}$ for such a population equals ${\mu -\frac{\sigma^2}{2}}$ . Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model ${{\bf X}_t = (X_t^1, \ldots, X_t^n)}$ , t ≥ 0, for the population abundances in n patches: the conditional law of X _t+Δt given X _t = x is such that the conditional mean of ${X_{t+\Delta t}^i - X_t^i}$ is approximately ${[x^i \mu_i + \sum_j (x^j D_{ji} - x^i D_{ij})] \Delta t}$ where μ _i is the per capita growth rate in the ith patch and D _ij is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of ${X_{t+\Delta t}^i - X_t^i}$ and ${X_{t + \Delta t}^j - X_t^j}$ is approximately x ⁱ x ^j σ _ij Δt for some covariance matrix Σ = (σ _ij ). We show for such a spatially extended population that if ${S_t = X_t^1 + \cdots + X_t^n}$ denotes the total population abundance, then Y _t = X _t /S _t , the vector of patch proportions, converges in law to a random vector Y _∞ as ${t \to \infty}$ , and the stochastic growth rate ${\lim_{t \to \infty} t^{-1}\log S_t}$ equals the space-time average per-capita growth rate ${\sum_i \mu_i \mathbb{E}[Y_\infty^i]}$ experienced by the population minus half of the space-time average temporal variation ${\mathbb{E}[\sum_{i,j}\sigma_{ij}Y_\infty^i Y_\infty^j]}$ experienced by the population. Using this characterization of the stochastic growth rate, we derive an explicit expression for the stochastic growth rate for populations living in two patches, determine which choices of the dispersal matrix D produce the maximal stochastic growth rate for a freely dispersing population, derive an analytic approximation of the stochastic growth rate for dispersal limited populations, and use group theoretic techniques to approximate the stochastic growth rate for populations living in multi-scale landscapes (e.g. insects on plants in meadows on islands). Our results provide fundamental insights into “ideal free” movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology. For example, our analysis implies that even in the absence of density-dependent feedbacks, ideal-free dispersers occupy multiple patches in spatially heterogeneous environments provided environmental fluctuations are sufficiently strong and sufficiently weakly correlated across space. In contrast, for diffusively dispersing populations living in similar environments, intermediate dispersal rates maximize their stochastic growth rate.     

Cytogenetic,cross-mating and molecular evidence of four cytological races of Anopheles crawfordi (Diptera: Culicidae) in Thailand and Cambodia

Twenty-nine isolines of Anopheles crawfordi were established from wild-caught females collected from cow-baited traps in Thailand and Cambodia. Three types of X (X₁, X₂, X₃) and four types of Y (Y₁, Y₂, Y₃, and Y₄) chromosomes were identified, according to differing amounts of extra heterochromatin. These sex chromosomes represent four metaphase karyotypes, i.e., Forms A (X₁, X₂, X₃, Y₁), B (X₁, X₂, X₃, Y₂), C (X₂, Y₃) and D (X₂, Y₄). Forms C and D are novel metaphase karyotypes confined to Thailand, whereas forms A and B appear to be common in both Thailand and Cambodia. Cross-mating experiments between the four karyotypic forms indicated genetic compatibility in yielding viable progenies and synaptic salivary gland polytene chromosomes. The results suggest that the forms are conspecific and A. crawfordi comprises four cytological races, which is further supported by very low intraspecific variation (mean genetic distance = 0.000–0.018) of the nucleotide sequences in ribosomal DNA (ITS2) and mitochondrial DNA sequences (COI, COII).     

On the page number of RNA secondary structures with pseudoknots

Let ${\mathcal {S}}$ denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. ${\{i, j\} \in \mathcal {S}}$ if there is a hydrogen bond between the ith and jth nucleotide. The page number of ${\mathcal {S}}$ , denoted ${\pi(\mathcal {S})}$ , is the minimum number k such that ${\mathcal {S}}$ can be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NP-complete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe an approximation algorithm from which it follows that ${\omega(\mathcal {S}) \leq \pi(\mathcal {S}) \leq \omega(\mathcal {S}) \cdot \log n}$ , where the clique number of ${\mathcal {S}, \omega(\mathcal {S})}$ , denotes the maximum number of base pairs that pairwise cross each other.     

Reconstructing a Phylogenetic Level-1 Network from Quartets

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on \(n\) taxa from the set of all quartets containing a certain fixed taxon, in \(O(n^3)\) time. We also present a more general method which can handle more diverse quartet data, but which takes \(O(n^6)\) time. Both methods proceed by solving a certain system of linear equations over the two-element field \(\mathrm{GF}(2)\) . For a general dense quartet set, i.e. a set containing at least one quartet on every four taxa, our \(O(n^6)\) algorithm constructs a phylogenetic level-1 network consistent with the quartet set if such a network exists and returns an \(O(n^2)\) -sized certificate of inconsistency otherwise. This answers a question raised by Gambette, Berry and Paul regarding the complexity of reconstructing a level-1 network from a dense quartet set, and more particularly regarding the complexity of constructing a cyclic ordering of taxa consistent with a dense quartet set.     

X-Y Exchange and the Coevolution of the X and Y Rdna Arrays in Drosophila melanogaster

The nucleolus organizers on the X and Y chromosomes of Drosophila melanogaster are the sites of 200-250 tandemly repeated genes for ribosomal RNA. As there is no meiotic crossing over in male Drosophila, the X and Y chromosomal rDNA arrays should be evolutionarily independent, and therefore divergent. The rRNAs produced by X and Y are, however, very similar, if not identical. Molecular, genetic and cytological analyses of a series of X chromosome rDNA deletions (bb alleles) showed that they arose by unequal exchange through the nucleolus organizers of the X and Y chromosomes. Three separate exchange events generated compound X·Y ^L chromosomes carrying mainly Y-specific rDNA. This led to the hypothesis that X-Y exchange is responsible for the coevolution of X and Y chromosomal rDNA. We have tested and confirmed several of the predictions of this hypothesis: First, X· Y^L chromosomes must be found in wild populations. We have found such a chromosome. Second, the X·Y^L chromosome must lose the Y^L arm, and/or be at a selective disadvantage to normal X⁺ chromosomes, to retain the normal morphology of the X chromosome. Six of seventeen sublines founded from homozygous X·Y^Lbb stocks have become fixed for chromosomes with spontaneous loss of part or all of the appended Y^L. Third, rDNA variants on the X chromosome are expected to be clustered within the X⁺ nucleolus organizer, recently donated (" Y") forms being proximal, and X-specific forms distal. We present evidence for clustering of rRNA genes containing Type 1 insertions. Consequently, X-Y exchange is probably responsible for the coevolution of X and Y rDNA arrays.     

Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons

We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength J, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As J is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an order parameter $\mathcal{O}$ . As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. The oscillator death leads to a transition from firing to non-firing states at the population level, which may be well described in terms of the time-averaged population spike rate $\overline{R}$ . In addition to the statistical-mechanical analysis using $\mathcal{O}$ and $\overline{R}$ , each population and individual state are also characterized by using the techniques of nonlinear dynamics such as the raster plot of neural spikes, the time series of the membrane potential, and the phase portrait. We note that population synchronization of noise-induced firings may lead to emergence of synchronous brain rhythms in a noisy environment, associated with diverse cognitive functions.     

Confidence intervals for demographic projections based on products of random matrices

This work is concerned with the growth of age-structured populations whose vital rates vary stochastically in time and with the provision of confidence intervals. In this paper a model Y_{t + 1}(ω) = X_{t + 1}(ω)Y_t(ω) is considered, where Y_t is the (column) vector of the numbers of individuals in each age class at time t, X is a matrix of vital rates, and ω refers to a particular realization of the process that produces the vital rates. It is assumed that {X_i} is a stationary sequence of random matrices with nonnegative elements and that there is an integer n₀ such that any product X_{j + n0} ··· X_{j + 1}X_j has all its elements positive with probability one. Then, under mild additional conditions, strong laws of large numbers and central limit results are obtained for the logarithms of the components of Y_t. Large-sample estimators of the parameters in these limit results are derived. From these, confidence intervals on population growth and growth rates can be constructed. Various finite-sample estimators are studied numerically. The estimators are then used to study the growth of the striped bass population breeding in the Potomac River of the eastern United States.     

茎瘤芥不同生长期植株营养特性及其与产量的关系

在涪陵区选取30个茎瘤芥种植农户,采用大田调查和室内化学分析方法,研究了茎瘤芥不同生长期（苗期、快速膨大期、采收期）叶片和茎瘤10种必需营养元素含量的变化特征及其与产量的关系。结果表明：茎瘤芥在整个生育期内,除K、S含量较高外,其余大、微量元素均在大多植物含量范围内;不同生育期茎瘤芥叶片、茎瘤中各养分含量变化具有明显的规律性,苗期叶片大量元素含量次序为N>K>Ca>P>S>Mg,快速膨大期和采收期叶片大量元素含量次序均为N>K>Ca>S>P>Mg,茎瘤中大量元素含量次序均为K>N>P>S>Ca>Mg,3个生长期叶片和茎瘤的微量元素含量,除快速膨大期茎瘤中略有不同（Fe>Zn>Mn>Cu）外,其余均为Fe>Mn>Zn>Cu;从苗期到快速膨大期再到采收期养分变化规律看,叶片中N、P、K、Fe、Cu和Zn含量呈降低趋势,而Ca、Mg、S和Mn则呈现先降低后升高的趋势,从快速膨大期到采收期茎瘤中除N、S、Fe和Cu元素呈降低趋势外,其余养分元素均呈上升趋势。从茎瘤芥不同器官养分含量高低看,快速膨大期和采收期叶片中N、P、K、Cu和Zn含量较茎瘤中低,而Ca、Fe和Mn含量的变化特点则相反,S和Mg差异较小,表明茎瘤芥不同部位对不同养分的敏感程度各异。相关分析表明,各生育期不同器官的Mg、Fe、Mn和Zn与产量呈显著或极显著的负相关关系,K、Cu与产量呈正的相关关系。通过逐步回归分析建立茎瘤芥各生育期植株营养元素与产量的回归预测模型,其中苗期叶片营养元素与产量的最优回归方程为Y= 36768 3583XK-6.328XFe-76.09XMn;快速膨大期叶片和茎瘤营养元素与产量的最优回归方程分别为Y=50458 21557XP 7925XCa-88092XMg-1145XCu和Y=32487 7294XK-116122XMg;采收期叶片和茎瘤营养元素与产量的最优回归方程分别为Y=36064 3413XK-30.15XFe和Y= 11791 7334XK-385XZn。因此,在茎瘤芥各生长期均应注意钾肥的合理施用,快速膨大期应重视磷肥的施用。而几种微量元素和镁素对茎瘤芥产量的负效应,则可通过增施充分腐熟的有机肥料加以调控。     

Die Cytogenetik zweier norddeutscher Populationen von Nosopsyllus fasciatus Bosc (Aphaniptera)

Specimens of the populations Hamburg and Wilhelmshaven of the ratflea N. fasciatus exhibit variation of the chromosome number in the range of 2n=20–23 and 2n=20–27 respectively, resulting from individual differences in the number of supernumerary chromosomes beyond the basic chromosome complement of 2n=20. The supernumerary chromosomes are mostly euchromatic and partly or completely homologous to each other and to the 10. pair of the basic complement. The numerical variation in the population Wilhelmshaven is produced by recurrent mitotic non-disjunction of the supernumerary chromosomes in anaphase II of spermatogenesis. Constant mitotic non-disjunction and preferential segregation of the supernumerary chromosomes towards the pronucleus leads to their accumulation in the population.—A multiple sex-chromosome mechanism of the type X₁ X₂ Y₁ Y₂ (male): X₁ X₁ X₂ X₂ (female) has been demonstrated for the population Wilhelmshaven of N. fasciatus. The X₁ X₂ Y₁ Y₂-chain of four is restricted to the male meiosis, in oogenesis two sex bivalents (X₁ X₁ and X₂ X₂) are formed. — The cytogenetic data presented do not support the concept of a closer phylogenetic relationship between the Aphaniptera and Nematocera, but do not preclude the possibility of a kinship of Aphaniptera and Neomecoptera.     

PENDISC: A Simple Method for Constructing a Mathematical Model from Time-Series Data of Metabolite Concentrations

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC ( arameter stimation in a on- mensionalized -system with onstraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.     

NATURE OF THE ACTION CURRENT IN NITELLA : VI. SIMPLE AND COMPLEX ACTION PATTERNS

The experiments indicate that the protoplasm of Nitella consists of an aqueous layer W with an outer non-aqueous surface layer X and an inner non-aqueous surface layer Y. The potential at Y is measured by the magnitude of the action curve and the potential at X by the distance from the top of the action curve to the zero line. These potentials appear to be due chiefly to diffusion potentials caused by the activity gradients of KCl across the non-aqueous layers X and Y. The relative mobilities of K⁺ and Cl^- in X and in Y can be computed and an estimate of the activity of KCl in W can be made. In the complete resting state the mobilities of K⁺ and Cl^- in X are not very different from those in Y. The action curve is due to changes in Y which suddenly becomes very permeable, allowing potassium to move from the sap across Y into W, and thus losing its potential. A gradual loss may be due to changes in ionic mobility in Y. When recovery is incomplete and Y has not yet regained its normal potential a stimulus may cause a loss of the potential at Y giving an action curve of small magnitude. The magnitude may vary in successive action curves giving what is called a complex pattern in contrast to the simple pattern observed when recovery is complete and all the action curves are alike. Complex patterns occur chiefly in cells treated with reagents. Untreated cells usually give simple patterns. A variety of complex action patterns is discussed. It is evident that the cells of Nitella show much more variation than such highly specialized cells as muscle and nerve which give stereotyped responses. In some cases it may be doubtful whether the all-or-none law holds.     

Quantifying interspecific spatial overlap in aquatic macrophyte communities

Levins’s asymmetrical α index quantifies between species overlap over resources more realistically than similar-purpose single-value indices. The associated community-wide \(\bar \alpha\) index expresses the degree of “species packing”. Both indices were formulated upon competing animal (i.e., mobile) organisms and are independent of population densities. However, overlap over resources for nonmobile organisms such as plants may have an impact even below carrying capacity. The proposed \(\hat \alpha\) index, based on Levins’s α index, quantifies spatial overlap for plants integrating information on species spatial distribution and crowding conditions. The \(\hat \alpha\) index is specifically designed for plant distribution data collected in discrete plots with density expressed as percent coverage (%cover) of substratum. We also propose a community-wide \({\hat \alpha_{\text{c}}}\) index, conceptually analogous to \(\bar \alpha\) , but furnished with a measure of dispersion (se \({\hat \alpha_{\text{c}}}\) ). Species importance within the community is inferred from comparisons of pairwise \(\hat \alpha\) ’s with \({\hat \alpha_{\text{c}}}\) . The \(\hat \alpha\) and \({\hat \alpha_{\text{c}}}\) indices correlate closely and exponentially with plant density, and correct apparent over- and underestimations of interaction intensity at low and very high crowding by Levins’s α and \(\bar \alpha\) , respectively. Index application to aquatic plant communities gave results consistent with within-community and general ecological patterns, suggesting a high potential of the proposed \(\hat \alpha\) and \({\hat \alpha_{\text{c}}}\) indices in basic and applied macrophyte ecological studies and management.     

Advantages of fungal enzyme production in solid state over liquid fermentation systems

The present paper attempts to explain why enzyme production in solid-state fermentation (SSF) is higher than in submerged fermentation (SmF). Recent work done in our laboratory [Biotechnol. Lett. 22 (2000) 1255; J. Ind. Microbiol. Biotechnol. 26 (5) (2001) 271; J. Ind. Microbiol. Biotechnol. 26 (5) (2001) 296] related to the production of invertase, pectinases and tannases, by Aspergillus niger grown by SSF and SmF is reviewed. To do such a comparative study, logistic and Luedeking–Piret equations are used in order to estimate the values of the following coefficients: maximal specific growth rate (μ_M), maximal biomass level (X_M), enzyme/biomass yield (Y_P/X) and secondary rate of production, or breakdown (k). It is shown that enzyme productivity is proportional to group, μ_MY_P/XX_M, corrected by a function of ν=k/Y_P/Xμ_M. In all three cases of enzyme production studied, productivity using a SSF system was higher than in SmF. Studies with invertase resulted in higher values of μ_MX_M. Studies with pectinases resulted in higher values of Y_P/XX_M. Studies with tannases resulted in higher Y_P/X and less negative values of k. Finally, a reaction–diffusion model is presented to try to explain such differences based on micrographic measurements of mycelial aggregates for each kind of fermentation system.     

Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one

In this paper, we investigate the chaotic behavior of a gene regulatory network modeled by four differential equations and seventeen parameters. This network, called \(\mathrm{V}\) -system, has been designed to couple in a simple way an oscillating system with one having a bistable switch. After having studied it analytically, we exhibit (by a constructive proof) the mechanism responsible of chaos for a general differential system presenting such a coupling. Namely, given a generic one-parameter family of smooth vector fields on \(\mathbb R ^n\) presenting a Hopf bifurcation, we prove that under an assumption on the Jacobian at the bifurcation point, we can create such a chaotic system by perturbing the parameter thanks to a hysteresis-type dynamics. Finally, we numerically show that the mechanism highlighted previously takes place in the \(\mathrm{V}\) -system, for a particular set of values of its parameters.     

Comparison of Energy and Growth Yields for Desulfitobacterium dehalogenans during Utilization of Chlorophenol and Various Traditional Electron Acceptors

Desulfitobacterium dehalogenans grew with formate as the electron donor and 3-chloro-4-hydroxyphenylacetate (3-Cl-4-OHPA) as the electron acceptor, yielding Y_X/formate, Y_X/2e⁻, and Y_X/ATP ranging from 3.2 to 11.3 g of biomass (dry weight)/mol, thus indicating that energy was conserved through reductive dechlorination. Pyruvate was utilized as the electron donor and acceptor, yielding stoichiometric amounts of acetate and lactate, respectively, and a Y_{X/reduced acceptor} of 13.0 g of biomass (dry weight)/mol. The supplementation of pyruvate-containing medium with additional electron acceptors, such as 3-Cl-4-OHPA, nitrate, fumarate, or sulfite, caused pyruvate to be replaced as the electron acceptor and nearly doubled the Y_X/ATP (Y_{X/acetate formed}). A comparison of the yields for 3-Cl-4-OHPA with those for other traditional electron acceptors indicates that the dehalogenation reaction led to the formation of similar amounts of energy equivalents. The various electron acceptors were used concomitantly with 3-Cl-4-OHPA in nonacclimated cultures, but the utilization rates and amounts utilized differed.     

Unique Reconstruction of Tree-Like Phylogenetic Networks from Distances Between Leaves

In this paper, a class of rooted acyclic directed graphs (called TOM-networks) is defined that generalizes rooted trees and allows for models including hybridization events. It is argued that the defining properties are biologically plausible. Each TOM-network has a distance defined between each pair of vertices. For a TOM-network N, suppose that the set X consisting of the leaves and the root is known, together with the distances between members of X. It is proved that N is uniquely determined from this information and can be reconstructed in polynomial time. Thus, given exact distance information on the leaves and root, the phylogenetic network can be uniquely recovered, provided that it is a TOM-network. An outgroup can be used instead of a true root.     

Retention of Dissolved Inorganic Nitrogen by Foliage and Twigs of Four Temperate Tree Species

Nitrogen (N) retention by tree canopies is believed to be an important process for tree nutrient uptake, and its quantification is a key issue in determining the impact of atmospheric N deposition on forest ecosystems. Due to dry deposition and retention by other canopy elements, the actual uptake and assimilation by the tree canopy is often obscured in throughfall studies. In this study, ¹⁵N-labeled solutions ( $ ^{15} {\text{NH}}_{4}^{ + } $ and $ ^{15} {\text{NO}}_{3}^{ - } $ ) were used to assess dissolved inorganic N retention by leaves/needles and twigs of European beech, pedunculate oak, silver birch, and Scots pine saplings. The effects of N form, tree species, leaf phenology, and applied $ {\text{NO}}_{3}^{ - } $ to $ {\text{NH}}_{4}^{ + } $ ratio on the N retention were assessed. Retention patterns were mainly determined by foliar uptake, except for Scots pine. In twigs, a small but significant ¹⁵N enrichment was detected for $ {\text{NH}}_{4}^{ + } $ , which was found to be mainly due to physicochemical adsorption to the woody plant surface. The mean $ {{^{15} {\text{NH}}_{4}^{ + } } \mathord{\left/ {\vphantom {{^{15} {\text{NH}}_{4}^{ + } } {^{15} {\text{NO}}_{3}^{ - } }}} \right. \kern-0em} {^{15} {\text{NO}}_{3}^{ - } }} $ retention ratio varied considerably among species and phenological stadia, which indicates that the use of a fixed ratio in the canopy budget model could lead to an over- or underestimation of the total N retention. In addition, throughfall water under each branch was collected and analyzed for $ ^{15} {\text{NH}}_{4}^{ + } $ , $ ^{15} {\text{NO}}_{3}^{ - } $ , and all major ions. Net throughfall of $ ^{15} {\text{NH}}_{4}^{ + } $ was, on average, 20 times higher than the actual retention of $ ^{15} {\text{NH}}_{4}^{ + } $ by the plant material. This difference in $ ^{15} {\text{NH}}_{4}^{ + } $ retention could not be attributed to pools and fluxes measured in this study. The retention of $ ^{15} {\text{NH}}_{4}^{ + } $ was correlated with the net throughfall of K⁺, Mg²⁺, Ca²⁺, and weak acids during leaf development and the fully leafed period, while no significant relationships were found for $ ^{15} {\text{NO}}_{3}^{ - } $ retention. This suggests that the main driving factors for $ {\text{NH}}_{4}^{ + } $ retention might be ion exchange processes during the start and middle of the growing season and passive diffusion at leaf senescence. Actual assimilation or abiotic uptake of N through leaves and twigs was small in this study, for example, 1–5% of the applied dissolved ¹⁵N, indicating that the impact of canopy N retention from wet deposition on forest productivity and carbon sequestration is likely limited.