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PubMed2000

Using traveling salesman problem algorithms for evolutionary tree construction.

MOTIVATION: The construction of evolutionary trees is one of the major problems in computational biology, mainly due to its complexity. RESULTS: We present a new tree construction method that constructs a tree with minimum score for a given set of sequences, where the score is the amount of evolution measured in PAM distances. To do this, the problem of tree construction is reduced to the Traveling Salesman Problem (TSP). The input for the TSP algorithm are the pairwise distances of the sequences and the output is a circular tour through the optimal, unknown tree plus the minimum score of the tree. The circular order and the score can be used to construct the topology of the optimal tree. Our method can be used for any scoring function that correlates to the amount of changes along the branches of an evolutionary tree, for instance it could also be used for parsimony scores, but it cannot be used for least squares fit of distances. A TSP solution reduces the space of all possible trees to 2n. Using this order, we can guarantee that we reconstruct a correct evolutionary tree if the absolute value of the error for each distance measurement is smaller than f2.gif" BORDER="0">, where f3.gif" BORDER="0">is the length of the shortest edge in the tree. For data sets with large errors, a dynamic programming approach is used to reconstruct the tree. Finally simulations and experiments with real data are shown.

Algorithms↗

PubMed2003

Phenology and density of balsam twig aphid, Mindarus abietinus Koch (Homoptera: Aphididae) in relation to bud break, shoot damage, and value of fir Christmas trees.

The balsam twig aphid, Mindarus abietinus Koch (Homoptera: Aphididae), is a major insect pest of balsam and Fraser fir grown for Christmas trees. Our objectives in this study were to 1) monitor the phenology of A. abietinus in fir plantations; 2) assess relationships among M. abietinus density, tree phenology, and damage to tree foliage; and 3) develop an esthetic injury level for M. abietinus on Christmas trees. We monitored phenology of M. abietinus and fir trees on three commercial Christmas tree plantations in central and northern Lower Michigan for 3 yr (1999-2001). Phenology of M. abietinus fundatrices and sexuparae was strongly correlated with accumulated degree-days (DD) base 10 degrees C. Fundatrices matured by approximately 83 DD(10 degrees C) and sexuparae were first observed at approximately 83-111 DD(10 degrees C). Trees that broke bud approximately 1 wk later than other trees in the same field escaped M. abietinus damage and shoot expansion rate in spring was generally positively correlated with M. abietinus damage. Retail customers surveyed at a choose-and-cut Christmas plantation in 2 yr did not consistently differentiate between similarly sized trees with no, light, and moderate M. abietinus damage, but heavy damage (>50% damaged shoots) did affect customer perception. Similarly, when wholesale grades were assigned, the high quality Grade 1 trees had up to 40% shoot damage, whereas Grade 2 trees had 32-62% shoot damage. Two trees ranked as unsaleable had sparse canopies and distorted needles on 42% to almost 100% of the shoots.

Abies↗

PubMed2004

3 using odor-baited trap trees as sentinels to monitor plum curculio (Coleoptera: Curculionidae) in apple orchards.

In commercial orchards in Massachusetts in 2003, we conducted experiments aimed at developing guidelines for use of perimeter-row trap trees baited with grandisoic acid plus benzaldehyde as sentinels in a practical approach to determining need and timing of insecticide applications against overwintered plum curculios, Conotrachelus nenuphar (Herbst). Evaluations were based on percentages of sampled fruit injured by plum curculio. Trap trees baited with grandisoic acid released at approximately 1 mg/d plus benzaldehyde released at approximately 40 mg/d performed as well as or better than trap trees baited with greater or lesser amounts of these attractants in combination. The distance over which a trap tree baited with such odor was effective in aggregating damage to fruit extended to at least 31-33 m (maximum evaluated) along a perimeter row. Trap trees at corners of orchard blocks were as effective as perimeter-row trap trees midway between corner trees. Within the canopy of a trap tree, damage did not tend significantly to be localized in the vicinity of the odor source but tended to be rather evenly distributed among various sectors of the canopy. Finally, among three candidate thresholds evaluated as a trigger for insecticide application, a threshold of one freshly injured fruit proved better than thresholds of two or four freshly injured fruit out of 50 fruit sampled on a trap tree in assuring that orchard-wide damage would remain below a preset economic injury level of 1%. Our findings lead us to suggest that after a whole-orchard application of insecticide to apple trees in Massachusetts orchards shortly after petal fall, subsequent applications of insecticide against plum curculio can be confined to peripheral-row trees and be driven by a provisional threshold of one freshly injured fruit out of 50 fruit sampled on a perimeter-row trap tree baited with the above-mentioned odor.

Animals↗

PubMed1998

Tie trees generated by distance methods of phylogenetic reconstruction.

In examining genetic data in recent publications, Backeljau et al. showed cases in which two or more different trees (tie trees) were constructed from a single data set for the neighbor-joining (NJ) method and the unweighted pair group method with arithmetic mean (UPGMA). However, it is still unclear how often and under what conditions tie trees are generated. Therefore, I examined these problems by computer simulation. Examination of cases in which tie trees occur shows that tie trees can appear when no substitutions occur along some interior branch(es) on a tree. However, even when some substitutions occur along interior branches, tie trees can appear by chance if parallel or backward substitutions occur at some sites. The simulation results showed that tie trees occur relatively frequently for sequences with low divergence levels or with small numbers of sites. For such data, UPGMA sometimes produced tie trees quite frequently, whereas tie trees for the NJ method were generally rare. In the simulation, bootstrap values for clusters (tie clusters) that differed among tie trees were mostly low (< 60%). With a small probability, relatively high bootstrap values (at most 70%-80%) appeared for tie clusters. The bias of the bootstrap values caused by an input order of sequence can be avoided if one of the different paths in the cycles of making an NJ or UPGMA tree is chosen at random in each bootstrap replication.

Computer Simulation↗

PubMed1986

Estimating the reliability of evolutionary trees.

Six protein sequences from the same 11 mammalian taxa were used to estimate the accuracy and reliability of phylogenetic trees using real, rather than simulated, data. A tree comparison metric was used to measure the increase in similarity of minimal trees as larger, randomly selected subsets of nucleotide positions were taken. The ratio of the observed to the expected number of incompatibilities for each nucleotide position (character) is a good predictor of the number of changes required at that position on the minimal (most-parsimonious) tree. This allows a higher weighting of nucleotide positions that have changed more slowly and should result in the minimal length tree converging to the correct tree as more sequences are obtained. An estimate was made of the smallest subset of trees that need to be considered to include the actual historical tree for a given set of data. It was concluded that it is possible to give a reasonable estimate of the reliability of the final tree, at least when several sequences are combined. With the present data, resolving the rodent-primate-lagomorph (rabbit) trichotomy is the least certain aspect of the final tree, followed then by establishing the position of dog. In our opinion, it is unreasonable to publish an evolutionary tree derived from sequence data without giving an idea of the reliability of the tree.

Animals↗

PubMed1992

Root growth and carbohydrate responses in bearing citrus trees following partial canopy removal.

In August, eight 4-m tall citrus trees were pruned by removing the top third of their canopy. Eight unpruned trees served as controls. Root growth, which was examined nondestructively with minirhizotrons over a four-month period, tended to be less in the pruned than unpruned trees seven days after pruning and this difference was significant (P < 0.05) from 14 to 49 days after pruning. Total reducing and ketone sugars (includes free fructose, sucrose and fructans) in the fine roots were less in pruned than unpruned trees 20 days after pruning, but not thereafter. By 30 days after pruning, at least 20% of the roots of the pruned trees at a soil depth of 9 to 35 cm apparently died. By 63 days after pruning, root length density had recovered to that of the unpruned trees, although starch reserves were 18% less in the fine roots of pruned than unpruned trees at this time. Nine to eleven months after pruning (May to July), total biomass of leaves and fine roots to a depth of 1 m were similar in pruned and unpruned trees. However, fruit biomass harvested in April from pruned trees was only 24% of that in the unpruned trees. In May, nonstructural carbohydrates in the fine and coarse roots of pruned trees were generally greater than in unpruned trees, possibly reflecting previous differences in fruit production.

Journal Article↗

PubMed1998

Quantitative estimates of uptake and internal cycling of (14)N-labeled fertilizer in mature walnut trees.

Uptake and internal cycling of nitrogen (N) in mature walnut trees was studied over a period of 6 years using (15)N-depleted fertilizer and full-canopied walnut (Juglans regia L. cv Hartley) trees. The magnitude of internal N cycling, i.e., the availability of N for new growth from internal N pools, was quantified using both the percent annual depletion (PAD) and the N balance budget approaches. There was good agreement between the two measures, and about 60% of annual N demand was derived from N redistribution from internal pools. The remaining 40% of annual tree N demand was met by an influx of N from the soil/fertilizer pool. Trees were excavated, processed and analyzed after 6 years to determine total tree N content and labeled N recovery. Trees recovered 29.4% of the labeled N applied and, based on previous evidence, we assumed that tree accumulation of labeled N occurred entirely in the first year. Labeled N in the fruits and leaves harvested in the first year represented 26% of the total labeled N accumulated, and the remaining 74% of the labeled N accumulated that year was stored and used to support development of annual organs in subsequent years. In the first year, the early maturing catkins did not accumulate labeled N, indicating their exclusive reliance on internal N. Using the atom% (14)N excess values of catkins and an exponential decline equation to determine turnover rate, the Mean Residence Time (MRT) of storage N in the tree was estimated to be 2.0 years. The size of the cycling pool of storage N in the tree was estimated to be about 50% of the total N content of perennial tree parts. Our data support the hypotheses that: (1) in any given year, mature walnut trees store the majority of soil and fertilizer N absorbed and within 2 years following uptake the N is remobilized and used for new growth, and (2) about half of the total N content of the perennial parts of mature walnut trees is present as nonstructural N and is available for recycling.

Journal Article↗

PubMed1998

A carbon balance model of peach tree growth and development for studying the pruning response.

We modeled tree responses to pruning on the basis of growth rules established on unpruned trees and a simple principle governing root-shoot interactions. The model, which integrates architectural and ecophysiological approaches, distinguishes four types of anatomical organs in a tree: rootstock, main axis, secondary axes and new roots. Tree structure is described by the position of secondary axes on the main axis. The main processes considered are plastochronal activity, branching, assimilate production, respiration and assimilate partitioning. Growth and development rules were based on measurements of two unpruned trees. The model was used to simulate growth of peach trees (Prunus persica (L.) Batsch) in their first growing season. Assuming that the equilibrium between roots and shoots tends to be restored after pruning, the response to removal of the main axis above the twentieth internode in mid-July was simulated and compared to the response measured in three pruned trees. The model fit the unpruned tree data reasonably well and predicted the main traits of tree behavior after pruning. Dry matter growth of the secondary axes of pruned trees was increased so that shoot seasonal carbon balance was hardly modified by pruning. Rhythmicity of growth was enhanced by pruning, and might result from variations induced in the root:shoot ratio. Variation in pruning severity had greater effects than variation in pruning date. A sensitivity analysis indicated that: (1) root-shoot partitioning was a critical process of the model; (2) tree growth was mainly dependent on assimilate availability; and (3) tree shape was highly dependent on the branching process.

Journal Article↗

PubMed1999

Water relations, stomatal response and transpiration of Quercus pubescens trees during summer in a Mediterranean carbon dioxide spring.

Variations in water relations and stomatal response of Quercus pubescens Willd. were analyzed under Mediterranean field conditions during two consecutive summers (1993 and 1994) at two locations characterized by different atmospheric CO(2) concentrations because of the presence at one of them of a CO(2) spring. Trees at the CO(2) spring site have been growing for generations in elevated atmospheric CO(2) concentrations. The heat-pulse velocity technique was used to estimate water use of trees during a 5-month period from June to November 1994. At the end of the sap flow measurements, the trees were harvested and foliage and sapwood area measured. At both sites, maximum leaf conductance was related to predawn shoot water potential. Effects of summer drought on plant water relations, including whole-plant transpiration, were severe, but leaf conductance and water potential recovered to predrought values after major rainfall in September. Leaf conductance, predawn water potential, and sometimes sap flow, decreased in parallel with increases in hydraulic resistance, reaching a minimum in midsummer. Hydraulic resistance was higher in trees at the control site than in trees at the CO(2) spring site. The effect of elevated CO(2) concentration on leaf conductance was less at high leaf-to-air water vapor pressure difference than at low leaf-to-air water vapor pressure difference. Mean and diurnal sap fluxes were consistently higher in trees at the control site than in trees at the CO(2) spring site. During the summer period, plant water use varied between the two sites. Trees at the control site had consistently higher sap flow at corresponding values of sapwood cross-sectional area than trees at the CO(2) spring site. Because trees at the CO(2) spring site supported a smaller foliage area for a corresponding sapwood cross-sectional area than trees at the control site, the overall mean sap flux/foliage area ratio did not differ between sites. The results are discussed in terms of effects of elevated CO(2) concentration on plant water use at the organ and whole-tree scale.

Journal Article↗

PubMed2001

Genome trees constructed using five different approaches suggest new major bacterial clades.

BACKGROUND: The availability of multiple complete genome sequences from diverse taxa prompts the development of new phylogenetic approaches, which attempt to incorporate information derived from comparative analysis of complete gene sets or large subsets thereof. Such attempts are particularly relevant because of the major role of horizontal gene transfer and lineage-specific gene loss, at least in the evolution of prokaryotes. RESULTS: Five largely independent approaches were employed to construct trees for completely sequenced bacterial and archaeal genomes: i) presence-absence of genomes in clusters of orthologous genes; ii) conservation of local gene order (gene pairs) among prokaryotic genomes; iii) parameters of identity distribution for probable orthologs; iv) analysis of concatenated alignments of ribosomal proteins; v) comparison of trees constructed for multiple protein families. All constructed trees support the separation of the two primary prokaryotic domains, bacteria and archaea, as well as some terminal bifurcations within the bacterial and archaeal domains. Beyond these obvious groupings, the trees made with different methods appeared to differ substantially in terms of the relative contributions of phylogenetic relationships and similarities in gene repertoires caused by similar life styles and horizontal gene transfer to the tree topology. The trees based on presence-absence of genomes in orthologous clusters and the trees based on conserved gene pairs appear to be strongly affected by gene loss and horizontal gene transfer. The trees based on identity distributions for orthologs and particularly the tree made of concatenated ribosomal protein sequences seemed to carry a stronger phylogenetic signal. The latter tree supported three potential high-level bacterial clades,: i) Chlamydia-Spirochetes, ii) Thermotogales-Aquificales (bacterial hyperthermophiles), and ii) Actinomycetes-Deinococcales-Cyanobacteria. The latter group also appeared to join the low-GC Gram-positive bacteria at a deeper tree node. These new groupings of bacteria were supported by the analysis of alternative topologies in the concatenated ribosomal protein tree using the Kishino-Hasegawa test and by a census of the topologies of 132 individual groups of orthologous proteins. Additionally, the results of this analysis put into question the sister-group relationship between the two major archaeal groups, Euryarchaeota and Crenarchaeota, and suggest instead that Euryarchaeota might be a paraphyletic group with respect to Crenarchaeota. CONCLUSIONS: We conclude that, the extensive horizontal gene flow and lineage-specific gene loss notwithstanding, extension of phylogenetic analysis to the genome scale has the potential of uncovering deep evolutionary relationships between prokaryotic lineages.

Bacteria↗

PubMed2006

Fast calculation of the quartet distance between trees of arbitrary degrees.

BACKGROUND: A number of algorithms have been developed for calculating the quartet distance between two evolutionary trees on the same set of species. The quartet distance is the number of quartets - sub-trees induced by four leaves - that differs between the trees. Mostly, these algorithms are restricted to work on binary trees, but recently we have developed algorithms that work on trees of arbitrary degree. RESULTS: We present a fast algorithm for computing the quartet distance between trees of arbitrary degree. Given input trees T and T', the algorithm runs in time O(n + /V/./V'/ min{id, id'}) and space O(n + /V/./V'/), where n is the number of leaves in the two trees, V and V are the non-leaf nodes in T and T', respectively, and id and id' are the maximal number of non-leaf nodes adjacent to a non-leaf node in T and T', respectively. The fastest algorithms previously published for arbitrary degree trees run in O(n3) (independent of the degree of the tree) and O(/V/./V'/.id.id'), respectively. We experimentally compare the algorithm with existing algorithms for computing the quartet distance for general trees. CONCLUSION: We present a new algorithm for computing the quartet distance between two trees of arbitrary degree. The new algorithm improves the asymptotic running time for computing the quartet distance, compared to previous methods, and experimental results indicate that the new method also performs significantly better in practice.

Journal Article↗

PubMed2005

A Gibbs sampling approach to detection of tree motifs.

This paper introduces a method to detect tree patterns (tree motifs) in a database of rooted unordered labeled trees. The method can be viewed as an extension of the Gibbs sampling approach to detect sequence motifs. Basically, we enumerate tree topologies and for each topology we seek within the database for tree motifs with the given topology. A tree motif can be detected by matching the tree topology against the database of trees and then applying Gibbs sampling on the matching set. After completion of the process for a given tree topology, the process is restarted for the next enumerated tree topology. The method outputs for each topology the best tree motif found. We applied our method to an artificially created database of trees as well as to a database of carbohydrate (glycan) structures.

Algorithms↗

PubMed1999

Combining classification trees using MLE.

We propose a probability distribution for an equivalence class of classification trees (that is, those that ignore the value of the cutpoints but retain tree structure). This distribution is parameterized by a central tree structure representing the true model, and a precision or concentration coefficient representing the variability around the central tree. We use this distribution to model an observed set of classification trees exhibiting variability in tree structure. We propose the maximum likelihood estimate of the central tree as the best tree to represent the set. This MLE retains the interpretability of a single tree model and has excellent generalizability. We implement an ascent search for the MLE tree structure using a data set of 13 classification trees that predict the presence or absence of cancer based on immune system parameters.

Classification↗

PubMed2005

13C-isotopic fingerprint of Pinus pinaster Ait. and Pinus sylvestris L. wood related to the quality of standing tree mass in forests from NW Spain.

Pine forest plantations of Pinus pinaster Ait. and P. sylvestris L. located in Galicia, NW Spain, were selected to study the 13C/12C-isotopic fingerprint in wood core samples in order to find possible relationships between the delta(13)C at natural abundance levels and the quality of the standing tree mass. For each pine species, 24 forests growing on acidic soils were studied: half developed over granite and half over schists. Two dominant trees from each plot, corresponding to all possible combinations of forest stands with high or low site index and with adults or young trees, were drilled at the basal part of trunks using a Pressler drill to obtain tree ring samples. The C-isotopic compositions of the litter and the soil organic matter from different soil depths were also determined and statistically significant correlations between these values and the 13C content of the wood were observed. Despite internal variations due to the influence of site index, tree age and parent material, the isotopic fingerprint of P. pinaster wood (mean value delta13C=-26.2+/-0.8 per thousand) significantly differed (P<0.001) from that of P. sylvestris (mean value delta13C=-24.6+/-0.7 per thousand). Relationships between the quality of the stand and the C-isotopic composition of the wood were observed, high quality stands having trees more 13C-depleted than low quality ones. A high correlation between wood delta13C and site index values for P. pinaster stands (r=-0.667, P<0.001) was found, this correlation being even clearer when only P. pinaster growing over schists (r=-0.833, P<0.001) are considered. Again, the correlation between the site index and the wood delta13C of young P. pinaster trees is higher when plots over granite or schists are separately considered. A similar fact occurs for adult P. sylvestris trees from schists stands, high quality specimens being 13C-depleted compared with low quality ones. On the other hand, 13C natural abundance of wood from P. sylvestris trees seems to be also strongly influenced by the underlying parent material, young trees from granite stands having a statistically higher 13C-isotopic composition (P<0.05) than young trees from schists stands.

Biomass↗

PubMed2004

Dendroremediation of trinitrotoluene (TNT). Part 2: fate of radio-labelled TNT in trees.

BACKGROUND, AIM AND SCOPE: Problems of long-term existence of the environmental contaminant 2,4,6-trinitrotoluene (TNT) and necessities for the use of trees ('dendroremediation') in sustainable phytoremediation strategies for TNT are described in the first part of this paper. Aims of the second part are estimation of [14C]-TNT uptake, localisation of TNT-derived radioactivity in mature tree tissues, and the determination of the degree of TNT-degradation during dendroremediation processes. METHODS: Four-year-old trees of hybrid willow (Salix spec., clone EW-20) and of Norway spruce (Picea abies) were cultivated in sand or ammunition plant soil (AP-soil) in wick supplied growth vessels. Trees were exposed to a single pulse application with water solved [U-14C]-TNT reaching a calculated initial concentration of 5.2 mg TNT per kg dry soil. Two months after application overall radioactivity and extractability of 14C were determined in sand/soil, roots, stem-wood, stem-bark, branches, leaves, needles, and Picea May sprouts. Root extracts were analysed by radio TLC. RESULTS: 60 days after [14C]-TNT application, recovered 14C is accumulated in roots (70% for sand variants, 34% for AP-soil variant). 15-28% of 14C remained in sand and 61% in AP-soil. 3.3 to 14.4% of 14C were located in aboveground tree portions. Above-ground distribution of 14C differed considerably between the angiosperm Salix and the gymnosperm Picea. In Salix, nearly half of above-ground-14C was detected in bark-free wood, whereas in Picea older needles contained most of the above-ground-14C (54-69%). TNT was readily transformed in tree tissue. Approximately 80% of 14C was non-extractably bound in roots, stems, wood, and leaves or needles. Only quantitatively less important stem-bark of Salix and Picea and May shoots of Picea showed higher extraction yields (up to 56%). DISCUSSION: Pulse application of [14C]-TNT provided evidence for the first time that after TNT-exposure, in tree root extracts, no TNT and none of the known metabolites, mono-amino-dinitrotoluenes (ADNT), diaminonitrotoluenes (DANT), trinitrobenzene (TNB) and no dinitrotoluenes (DNTs) were present. Extractable portions of 14C were small and contained at least three unknown metabolites (or groups) for Salix. In Picea, four extractable metabolites (or groups) were detected, where only one metabolite (or group) seemed to be identical for Salix and Picea. All unknown extractables were of a very polar nature. CONCLUSIONS: Results of complete TNT-transformation in trees explain some of our previous findings with 'cold analytics', where no TNT and no ADNT-metabolites could be found in tissues of TNT-exposed Salix and Populus clones. It is concluded that 'cold' tissue analysis of tree organs is not suited for quantitative success control of phytoremediation in situ. RECOMMENDATIONS AND OUTLOOK: Both short rotation Salicaceae trees and conifer forests possess a dendroremediation potential for TNT polluted soils. The degradation capacity and the large biomass of adult forest trees with their woody compartments of roots and stems may be utilized for detoxification of soil xenobiotics.

Biodegradation, Environmental↗

PubMed2001

Demographic analysis of tree colonization in a 20-year-old right-of-way.

Past tree colonization dynamics of a powerline-right-of-way (ROW) corridor in the Haut-Saint-Laurent region of Quebec was studied based on the present age distribution of its tree populations. This colonization study spans 20 years, from 1977 (ROW clearance) to 1996. The sampled quadrats were classified into six vegetation types. Tree colonization dynamics were interpreted in each type, and three distinct patterns were identified. (1) Communities adapted to acidic conditions were heavily colonized by Acer rubrum, at least for the last 12 years. (2) Communities adapted to mesic or to hydric conditions were more intensely colonized in the period 1985-1987 than in the following 9 years; this past success in tree colonization may have been caused by herbicide treatments, which could have facilitated tree establishment by damaging the herbaceous and shrub vegetation. (3) Cattail, vine-raspberry, and reed-dominated communities contained few tree individuals, with almost all trees establishing between 1979 and 1990; those three vegetation types appear as the most resistant to tree invasion in the ROW studied. This study supports the need for an integrated approach in ROW vegetation management, in which the selection of vegetation treatment methods would depend on the tree colonization dynamics in each vegetation type. Minimizing disturbances inflicted on ROW herbaceous and shrub covers should be the central strategy because disturbances jeopardize natural resistance to future tree invasion, except in communities adapted to acidic conditions where the existing vegetation does not prevent invasion by A. rubrum. Many trees are surviving the successive cutting operations by producing new sprouts each time, particularly in communities adapted to mesic and hydric conditions. In these cases, mechanical cutting should be replaced by a one-time stump-killing operation, to avoid repeated and unsuccessful treatments of the same individuals over time.

Conservation of Natural Resources↗

PubMed1994

Optimization by trees on simple adaptive landscapes.

We evaluate the optimizing ability (rate of adaptation) of trees on simple adaptive landscapes. At points away from a peak, there is a strong negative relationship between rate of adaptation and tree precision P, a relationship that is independent of the size of the tree. P measures the variability among trial solutions generated by the tree: high precision trees have low variability, low precision trees have high variability. Near a peak, the situation reverses, with high precision trees showing higher rates of adaptation than low precision trees; however, for all trees, the absolute rate of adaptation is uniformly low. On multiple-peak landscapes, the probability of crossing an adaptive valley from a lower peak to a higher peak is also negatively correlated with tree precision. These results suggest that under a wide range of conditions, trees with low precision are, on average, the best optimizers.

Adaptation, Biological↗

PubMed2001

Time-series analysis of delta13C from tree rings. I. Time trends and autocorrelation.

Univariate time-series analyses were conducted on stable carbon isotope ratios obtained from tree-ring cellulose. We looked for the presence and structure of autocorrelation. Significant autocorrelation violates the statistical independence assumption and biases hypothesis tests. Its presence would indicate the existence of lagged physiological effects that persist for longer than the current year. We analyzed data from 28 trees (60-85 years old; mean = 73 years) of western white pine (Pinus monticola Dougl.), ponderosa pine (Pinus ponderosa Laws.), and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca) growing in northern Idaho. Material was obtained by the stem analysis method from rings laid down in the upper portion of the crown throughout each tree's life. The sampling protocol minimized variation caused by changing light regimes within each tree. Autoregressive moving average (ARMA) models were used to describe the autocorrelation structure over time. Three time series were analyzed for each tree: the stable carbon isotope ratio (delta(13)C); discrimination (delta); and the difference between ambient and internal CO(2) concentrations (c(a) - c(i)). The effect of converting from ring cellulose to whole-leaf tissue did not affect the analysis because it was almost completely removed by the detrending that precedes time-series analysis. A simple linear or quadratic model adequately described the time trend. The residuals from the trend had a constant mean and variance, thus ensuring stationarity, a requirement for autocorrelation analysis. The trend over time for c(a) - c(i) was particularly strong (R(2) = 0.29-0.84). Autoregressive moving average analyses of the residuals from these trends indicated that two-thirds of the individual tree series contained significant autocorrelation, whereas the remaining third were random (white noise) over time. We were unable to distinguish between individuals with and without significant autocorrelation beforehand. Significant ARMA models were all of low order, with either first- or second-order (i.e., lagged 1 or 2 years, respectively) models performing well. A simple autoregressive (AR(1)), model was the most common. The most useful generalization was that the same ARMA model holds for each of the three series (delta(13)C, delta, c(a) - c(i)) for an individual tree, if the time trend has been properly removed for each series. The mean series for the two pine species were described by first-order ARMA models (1-year lags), whereas the Douglas-fir mean series were described by second-order models (2-year lags) with negligible first-order effects. Apparently, the process of constructing a mean time series for a species preserves an underlying signal related to delta(13)C while canceling some of the random individual tree variation. Furthermore, the best model for the overall mean series (e.g., for a species) cannot be inferred from a consensus of the individual tree model forms, nor can its parameters be estimated reliably from the mean of the individual tree parameters. Because two-thirds of the individual tree time series contained significant autocorrelation, the normal assumption of a random structure over time is unwarranted, even after accounting for the time trend. The residuals of an appropriate ARMA model satisfy the independence assumption, and can be used to make hypothesis tests.

Carbon Isotopes↗