Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Summary Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time‐varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi‐Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi‐Markovian manner. The underlying semi‐Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi‐Markov chain represent—in the corresponding growth phase—both the influence of time‐varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi‐Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation–maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.     

Identifying ontogenetic, environmental and individual components of forest tree growth

Background and Aims

This study aimed to identify and characterize the ontogenetic, environmental and individual components of forest tree growth. In the proposed approach, the tree growth data typically correspond to the retrospective measurement of annual shoot characteristics (e.g. length) along the trunk.

Methods

Dedicated statistical models (semi-Markov switching linear mixed models) were applied to data sets of Corsican pine and sessile oak. In the semi-Markov switching linear mixed models estimated from these data sets, the underlying semi-Markov chain represents both the succession of growth phases and their lengths, while the linear mixed models represent both the influence of climatic factors and the inter-individual heterogeneity within each growth phase.

Key Results

On the basis of these integrative statistical models, it is shown that growth phases are not only defined by average growth level but also by growth fluctuation amplitudes in response to climatic factors and inter-individual heterogeneity and that the individual tree status within the population may change between phases. Species plasticity affected the response to climatic factors while tree origin, sampling strategy and silvicultural interventions impacted inter-individual heterogeneity.

Conclusions

The transposition of the proposed integrative statistical modelling approach to cambial growth in relation to climatic factors and the study of the relationship between apical growth and cambial growth constitute the next steps in this research.     

Temporal Pattern of Ovarian Activity in a Major Carp Catla catla and its Possible Environmental Correlate in an Annual Cycle

Histophysiological studies of the ovary in a hitherto unconsidered major carp Catla catla, included in this investigative treatise, have allowed the present investigators to demonstrate the pattern of annual events in ovarian functions, as well as the inter-relationship between changes in the ovary and environmental conditions. Month-wise studies of cytological features along with various biochemical features of ovarian functions in free-living Catla revealed the existence of precise annual cyclic changes. On the basis of the studies made on gonads, the annual breeding cycle of this fish has been divided into four different phases, namely (a) the preparatory phase (January-March), (b) the pre-spawning phase (April-June), (c) the spawning phase (July-August), and (d) the post-spawning phase (September-December). A detailed analysis of the data employing various exploratory data-analytic techniques was aimed at drawing a possible relationship between the indices of different reproductive events (oogenesis and oocyte maturation, vitellogenesis, steroidogenesis) in mature free-living female Catla and the different components of the environment in an annual cycle. The results of the study indicate that annual variations in photoperiod, alone or in association with water temperature, may be the major environmental component which plays a significant role in the regulation of seasonal maturation of ovary in Catla. These observations provided a basis for further experimental studies on the specific role of photoperiods in the regulation of ovarian activities in the currently considered most economically important species of Indian major carp.     

Deciphering the developmental plasticity of walnut saplings in relation to climatic factors and light environment

Developmental plasticity, the acclimation of plants to their local environment, is known to be crucial for the fitness of perennial organisms such as trees. However, deciphering the many possible developmental and environmental influences involved in such plasticity in natural conditions requires dedicated statistical models integrating developmental phases, environmental factors, and interindividual heterogeneity. These models should be able to analyse retrospective data (number of leaves or length of annual shoots along the main stem in the present case). In this study Markov switching linear mixed models were applied to the analysis of the developmental plasticity of walnut saplings during the establishment phase in a mixed Mediterranean forest. In the Markov switching linear mixed models estimated from walnut data sets, the underlying Markov chain represents both the succession and lengths of growth phases, while the linear mixed models represent both the influence of climatic factors and interindividual heterogeneity within each growth phase. On the basis of these integrative statistical models, it is shown that walnut saplings have an opportunistic mode of development that is primarily driven by the changing light environment. In particular, light availability explains the ability of a tree to reach a phase of strong growth where the first branches can appear. It is also shown that growth fluctuation amplitudes in response to climatic factors increased while interindividual heterogeneity decreased during tree development.     

Relationships among ontogenetic,static, and evolutionary allometry

The relationship between ontogenetic, static, and evolutionary levels of allometry is investigated. Extrapolation from relative size relationships in adults to relative growth in ontogeny depends on the variability of slopes and intercepts of ontogenetic vectors relative to variability in length of the vector. If variability in slopes and intercepts is low relative to variability in length, ontogenetic and static allometries will be similar. The similarity of ontogenetic and static allometries was tested by comparing the first principal component, or size vector, for correlations among 48 cranial traits in a cross-sectional ontogenetic sample of rhesus macaques from Cayo Santiago with a static sample from which all age- and sex-related variation had been removed. The vector correlation between the components is high but significantly less than one while two of three allometric patterns apparent in the ontogenetic component are not discernable in the static component. This indicates that there are important differences in size and shape relationships among adults and within ontogenies. Extrapolation from intra- or interspecific phenotypic allometry to evolutionary allometry is shown to depend on the similarity of genetic and phenotypic allometry patterns. Similarity of patterns was tested by comparing the first principal components of the phenotypic, genetic, and environmental correlation matrices calculated using standard quantitative genetic methods. The patterns of phenotypic, genetic, and environmental allometry are dissimilar; only the environmental allometries show ontogenetic allometric patterns. This indicates that phenotypic allometry may not be an accurate guide to patterns of evolutionary change in size and shape.     

A new theory on the origin and the nature of viruses

The hypothetical model presented herein concerns the origin and nature of viruses. It advances the possibility of the appearance and existence of an organism lacking a cohesive morphological structure, that is: its subsystems are not in structural continuity. An attempt to delimit the concepts of life and organism and to integrate the viruses into this framework is made. Viruses are presented as organisms which pass in their ontogenetic cycle through two distinctive phenotypic phases: (1) the vegetative phase and (2) the phase of viral particle or nucleic acid. In the vegetative phase, considered herein to be the ontogenetically mature phase of viruses, their component molecules are dispersed within the host cell. In this phase the virus shows the major physiological properties of other organisms: metabolism, growth, and reproduction. Therefore, life is an effective presence. It is shown also, that in this phase so called "DNA viruses" have both nucleic acids: RNA as well as DNA. The virions are considered to be "spores" or reproductive forms of the virus, possessing life only as a potential property.     

Effect of streaked shearwaterCalonectris leucomelas on species composition ofPersea thunbergii forest on Kanmurijima Island,Kyoto Prefecture,Japan

The effects of trampling and burrowing by streaked shearwaters were studied on thePersea thunbergii forest in Kanmurijima Is. The vegetation data were analysed using both the phytosociological tabulation method and principal component analysis (PCA). The vegetation ordination on the first axis reflected the environmental gradient from light to heavy disturbance by the streaked shearwater, and the vegetation ordination on the second axis represented the gradient from the latter phase of forest succession to retrogressive succession. The position of the three vegetation groups in the ordination diagram successfully explained the relation between the habitat and the species composition. The disturbance caused by activities of the streaked shearwater such as burrowing and trampling causes a decrease of species, especially character species of Camellietea japonicae, and also causes retrogressive succession: patches ofMallotus japonicus develop and many heliophytes occur.     

Seasonal patterns of root and shoot interactions in an alpine meadow on the Tibetan Plateau

Aims Numerous studies have showed that the balance between negative and positive plant–plant interactions shifted along environmental gradients. But little is known how the positive or negative plant–plant interactions varied with temporal fluctuating habitat conditions and plant ontogenetic phases.Methods In a 2-year experiment, the four perennial grasses (Kobresia humilis, Stipa aliena, Elymus nutans and Saussurea superba) were grown under four interaction treatments (no root or shoot interaction, only shoot interaction, only root interaction, root and shoot interaction). Intensity of above- and belowground interactions is proposed to vary with the fluctuation of seasonal climatic conditions and soil available nutrients. Here we report measurements of above- and belowground interactions during entire growing season. Correlation between plant interaction intensity and seasonal soil available N as well as habitat climate conditions was also performed.Important findings Our experiment found that root interactions had negative effect on plant growth for the four species during growing season. However, both negative and positive shoot interactions occurred among the four species. Despite there being shoot facilitative effect for E. nutans and S. superba, the full interaction was negative, suggested that root interaction take more important role on plant growth than that of shoot interaction. The interaction between root and shoot effect varied as a function of species identity and growth phases. The weak correlation of plant interaction intensity to habitat environmental factors suggested that plant ontogenetic characteristics may be primary factors causing temporal variation in plant interaction.     

Vegetation changes along a precipitation gradient in Central Argentina

Changes in vegetation along a precipitation gradient in Central Argentina were studied. Floristic samples were taken along an east-west transect of about 300 km. Correlation analysis between precipitation and ordination axes was used to provide an environmental interpretation of vegetation variability.Floristic analysis produced an ordination of plant communities from evergreen forests (precipitation >500 mm) to desert shrublands and therophyte communities (precipitation <200 mm). Results showed a trend of floristic and structural impoverishment towards the west. There is a replacement of species along the transect and a shift in dominant growth forms. The first ordination axis is significantly, negatively correlated with annual precipitation.     

Ontogenetic plasticity of anatomical and ecophysiological traits and their correlations in Iris pumila plants grown in contrasting light conditions

To better understand what directs and limits the evolution of phenotype, constraints in the realization of the optimal phenotype need to be addressed. That includes estimations of variability of adaptively important traits as well as their correlation structures, but also evaluation of how they are affected by relevant environmental conditions and development phases. The aims of this study were to analyze phenotypic plasticity, genetic variability and correlation structures of important Iris pumila leaf traits in different light environments and ontogenetic phases, and estimate its evolutionary potential. Stomatal density, specific leaf area, total chlorophyll concentration and chlorophyll a/b ratio were analyzed on I. pumila full‐sib families in the seedling phase and on the same plants after 3 years of growth in contrasting light conditions typical for ontogenetic stage in question. There was a significant phenotypic plasticity in both ontogenetic stages, but significant genetic variability was detected only for chlorophyll concentrations. Correlations of the same trait between different stages were weak due to changes in environmental conditions and difference in ontogenetic reaction norms of different genotypes. Ontogenetic variability of correlation structures was detected, where correlations and integration were higher in seedlings compared with adult plants 3 years later. Correlations were affected by environmental conditions, with integration being higher in the lower light conditions, but correlations between phases being stronger in the higher light treatment. These findings demonstrated that the analyzed traits can be selected and can mostly evolve independently in different environments and ontogenetic stages, with low genetic variability as a potentially main constraint.     

Genetic and environmental factors in the longitudinal growth of rats: I. Body weight and overall craniofacial size

By means of roentgenographic cephalometry and quantitative genetic analysis, the relative contribution of the genetic and environmental components to total variance of body weight and overall craniofacial size was shown to vary with age. The genetic component of variance significantly increased until 80 days of age. Inversely, the maternal component of variance showed a high value during the early stage of postnatal growth and gradually decreased thereafter to a very small amount by day 80. Thus it appeared that the genetic effect became larger with age of the rat and the maternal effects diminished. The environmental component of variance did not change much over the course of the experiment. We thus conclude that genetic effect contributed the change of ontogenetic variation of craniofacial complex through all experimental periods and that maternal effect contributed to it at early growth stage of the craniofacial complex.     

Analysing branching pattern in plantations of young red oak trees (Quercus rubra L., Fagaceae)

Branching patterns of the growth units of monocyclic or bicyclic annual shoots on the main axis of 5-year-old red oaks were studied in a plantation in south-western France. For each growth unit, the production of axillary structures associated with each node was described in the form of a sequence. For a given category of growth units, homogeneous zones (i.e. zones in which composition in terms of type of axillary production does not change substantially) were identified on such sequences using a dedicated statistical model called a hidden semi-Markov chain. For instance, on the first growth unit of bicyclic annual shoots, a zone with 1-year-delayed branches was found systematically below a zone with buds and one-cycle-delayed branches. Branching patterns shown by the growth unit of monocyclic annual shoots and on the second growth unit of bicyclic annual shoots were very similar. Branches with a 1-year delay in development tended to be polycyclic at the top of the growth unit and monocyclic lower down. The number of nodes shown by the branched zone of the growth unit of monocyclic annual shoots was stable, irrespective of the total number of nodes of the growth unit. In contrast, the second growth unit of bicyclic annual shoots exhibited a correlation between the number of nodes in the branching zone and the total number of nodes. The contribution made by this method to understanding plant functioning is discussed.     

Ontogenetic trends in the morphological features of main stem annual shoots of Pinus pinaster (Pinaceae)

Phase change refers to the transition between juvenile and adult vegetative phases. The study of trees throughout their entire life span requires retrospective analyses and validates the use of a chronosequence by sequencing observations at different and successive stages. The main axis growth pattern of 62 maritime pines (Pinus pinaster) selected in a chronosequence of three stands consisting of 8-, 22-, and 48-yr-old trees was analyzed retrospectively. Comparison of measured features (length, number of axillary products, reproductive organs) at common ages from the three stands supported the validity of using these data to form a continuous chronosequence. Endogenous trends in tree development are revealed free from variability due to annual growth conditions. Two main phases of development corresponding respectively to the juvenile vegetative and adult reproductive stages were identified, and the transition between both occurred in 9-yr-old trees. The relevance of these two phases and more generally the notion of phase changes are discussed in light of observed trends in the values of studied growth and branching parameters that may either show gradual variations (such as length of annual shoot) or a distinctive expression in one or the other phase (such as presence of female cones).     

Insights into succession processes using temporally repeated habitat models: results from a long‐term study in a post‐mining landscape

Questions: The early phases of primary succession are governed by chance events and dispersal‐related processes in an environment that is largely free of competition. Thus, the predictability of vegetation patterns using environmental site factors can be expected to be low and spatial autocorrelation to be high. We asked whether the match between vegetation and environment becomes better in the course of succession, and whether vegetation types shift their realized niche with time. Location: Lignite mining region in Central Germany, the post‐mining landscape “Goitzsche” (Saxony‐Anhalt). Methods: Vegetation types were mapped in a 10‐m grid (total area 4.8 ha), starting in 1995, at 3‐year intervals until 2007. We used a temporal comparison of habitat models. We applied: GLS regression to partition the variation in coverage of vegetation types into environmental (soil pH) and spatial components; logistic regression to model the presence/absence of vegetation types along a soil acidity gradient; and autologistic regression allowing for soil acidity and neighbourhood effects. Results: For most vegetation types, the proportion of variation explained by space was high but declined during succession. The outcome of autologistic models suggests that soil acidity often plays a minor role compared to neighbourhood effects in the earlier phase of succession than 12 years later. For four vegetation types, the pH range in which the type was expected to be dominant clearly became smaller with time. These trends support the view that the role of processes related to chance and dispersal decrease with time, while those related to environmental filtering mediated by biotic interactions increase. Conclusions: We conclude that temporal comparisons of spatially explicit habitat models provide insights into changing biotic community processes and their effects on habitat specificity of species or their communities. Thus, this approach may be particularly important for analysis of ecological systems that are not in equilibrium with their environmental drivers.     

The ontogeny of sexual dimorphism in the cranium of Bornean orang-utans (Pongo pygmaeus pygmaeus) as detected by principal-components analysis

The ontogeny of cranial sexual dimorphism in the Bornean orang-utan (Pongo pygmaeus pygmaeus) is examined by means of principal-components analysis (PCA). Normalized first components are called allometry vectors or vectors of relative growth and show that sexual dimorphism is present at all stages of growth. Two patterns of sexual dimorphism are present: (1) sexual differences at age groups 2 and 3 are the result primarily of differences in principal component II scores, reflecting mainly shape-related differences, and (2) age groups 5, 6, and 7 show a trend of stronger size-related shape differences with increasing age in the allometry vector along with decreasing differences in principal component II scores, reflecting an increase in size-related shape differences between the sexes. Age group 4 shows a combination of both patterns. Our results support Shea's hypothesis (1985a) that when using multigroup PCAs in closely related taxa, the allometry vector will generally estimate the shape variation resulting from the extension of common growth allometry patterns (ontogenetic scaling). The second and subsequent components summarize shape variation from slope and intercept differences between the groups, provided that ontogenetic scaling is not solely responsible for all the shape differences present. Subanalyses of those dimensions previously found to show ontogenetic scaling and acceleration follow this pattern well. The total sample provides a pattern whereby ontogenetically scaled dimensions possess a stronger influence over accelerated dimensions but still generally follow Shea's hypothesis. Finally, variously derived coefficients provided several interesting findings: (1) strong evidence was found against multivariate isometry for both the pooled and the separate samples, (2) multivariate allometric coefficients for both sexes follow the general growth pattern of negative scaling in neurocranial dimensions and positive scaling in the viscerocranium, and (3) multivariate slopes have a very high correlation with bivariate slopes relative to the same independent X variable, thereby lending further support to Jolicoeur's (1963a, b) allometry generalization.     

Deciphering the ontogeny of a sympodial tree

This paper addresses the identification and characterization of developmental patterns in the whole structure of a sympodial species, the apple tree. Dedicated stochastic models (hidden variable-order Markov chains) were used to (i) categorise growth units (GUs) on the basis of their morphological characteristics (number of nodes and presence/absence of flowering) and position along axes, (ii) analyse dependencies between successive GUs and (iii) identify repeated patterns in GU sequences. Two successive phases, referred to as “adolescent” and “adult”, were identified in two apple tree cultivars. In the adolescent phase, “very” long monocyclic GUs were followed by long polycyclic GUs, whereas in the adult phase medium GUs were preferentially followed by short GUs. Flowering GUs constituted a preferential pathway between vegetative GUs of decreasing vigour (long, medium and short) and generated patterns that were interpreted with respect to fruiting regularity. The proposed modelling gave a global and quantitative picture of the two-scale structuring of apple tree ontogeny: a coarse scale corresponding to the succession of the previously mentioned phases and a fine scale corresponding to the alternation between flowering and vegetative GUs. This led us to propose a synthetic scheme of apple tree ontogeny that combines growth phases, polycyclism and flowering, and which could be transposed to other sympodial trees.     

Densitometry from digitized images of X-radiographs: Methodology for measurement of coral skeletal density

Skeletons of massive coral colonies contain annual density bands that are revealed by X-radiography of slices cut along growth axes. These bands allow measurement of skeletal growth parameters such as annual extension rate and annual calcification rate. Such measurements have been important in understanding coral growth, in assessing environmental impacts and in recovering proxy environmental information. Measurements of coral calcification rate from annual density banding require measurements of skeletal density along tracks across skeletal slices and, until now, such density measurements have depended upon specialized and expensive equipment. Here, we describe a straightforward, inexpensive and accurate technique for measuring skeletal density from digitized images of X-radiographs of coral skeletal slices. An aragonitic step-wedge was included in each X-radiograph of a coral slice together with two aluminium bars positioned along the anode-cathode axis. Optical density was measured along tracks across the X-ray images of these different objects. The aragonite step-wedge provided a standard for converting optical density to skeletal density. The aluminium bars were used to correct for the heel effect—a variation in the intensity of the X-ray beam along the anode-cathode axis that would, otherwise, introduce large errors into measurements of skeletal density. Exposure was found to vary from X-radiographs to X-radiograph, necessitating the inclusion of the calibration standards in each X-radiograph of a coral slice. Results obtained using this technique compared well with results obtained by direct gamma densitometry of skeletal slices.     

Ontogenetic variations in leaf morphology of the tropical rain forest species Dipterocarpus alatus Roxb. ex G. Don

Under natural conditions ontogenetic development often coincides with changes in environmental factors. When explaining variations in leaf parameters, analyses based solely on environmental factors will lead to significant errors if the plant shows substantial ontogenetic variations in leaf properties. We evaluated intraspecific variations in eight morphological leaf traits of Dipterocarpus alatus over six architectural development stages under two different light conditions. An architectural analysis was conducted to distinguish precisely and objectively developmental stages of D. alatus. Leaves were collected on the most recent complete growth unit on the trunks of trees growing under two different light conditions. Eight leaf morphological traits were measured and calculated using ImageJ on greyscale images of leaf tracings. One-way ANOVA and Tukey tests were used to determine differences in leaf traits during ontogeny. The correlation coefficients were compared to determine whether leaf traits correlated more strongly with ontogenetic stage than with light intensity. D. alatus develops through a progressive transformation of its structure and architecture that adds one new axis category stage after stage. Specific leaf area, blade shape index and leaf dissection index decreased whereas blade area, perimeter, length, width and blade dry weight increased. Leaf traits correlated more strongly with ontogenetic stage than with light intensity. Our results demonstrated that studies on the responses of leaf traits to the environment may need to be corrected for an ontogeny effect. To strengthen this conclusion, future work should evaluate leaf variations during the ontogeny of different axis orders and/or axis categories.     

The ontogeny of plant indirect defenses

Plants frequently attract natural enemies of their herbivores, resulting in a reduction in tissue damage and often in enhanced plant fitness. While such indirect defenses can dramatically change as plants develop, only recently have ecologists begun to explore such changes and evaluate their role in mediating plant–herbivore–natural enemy interactions. Here we review the literature documenting ontogenetic patterns in plant rewards (i.e. extrafloral nectaries (EFNs), food bodies (FBs) and domatia) and volatile organic compounds (VOCs), and identify links between ontogenetic patterns in such traits and the attraction of natural enemies (ants). In the case of reward traits we concentrate in ant–plant studies, which are the most numerous. We report that all indirect defensive traits commonly vary with plant age but ontogenetic trajectories differ among them. Myrmecophytic species, which provide both food and shelter to their defenders, do not produce rewarding traits until a minimum size is reached. Then, a pronounced increase in the abundance of food rewards and domatia often occurs as plants develop, which explains the temporal succession or colony size increase of mutualistic ant species and, in some cases, leads to a reduction in herbivore damage and enhanced fitness as plants age. In contrast, ontogenetic patterns were less consistent in plant species that rely on VOC emissions to attract natural enemies or those that provide only food rewards (EFNs) but not nesting sites to their associated ants, showing an overall decline or lack of trend with plant development, respectively. Future research should focus on uncovering: (i) the costs and mechanisms underlying ontogenetic variation in indirect defenses, (ii) the relative importance of environmental and genetic components shaping these ontogenetic trajectories, and (iii) the consequences of these ontogenetic trajectories on plant fitness. Advances in this area will shed light on the context dependency of bottom-up and top-down controls of herbivore populations and on how natural selection actually shapes the ontogenetic trajectories of these traits.     

Ontogenetic succession in Amazonian ant trees

In the tropical rain forest of the Central Amazon, a small guild of specialized plant-ants nest exclusively inside the leaf domatia of Tachigali (Caesalpinaceae). Since normally each plant houses a single ant colony, the number of unoccupied plants in the environment is quite low and the number of potential colonizer queens is high, the conditions for intense intra and interspecific competion for nesting site are set. This study describes an intriguing ecological pattern that explains how this ant guild can coexist using exclusively Tachigali plants as nesting site. We found that each of the eight different ant species occurs in plants of different heights (Kruskal-Wallis test statistics=148.6, d.f.=7, P<0.001). This spatial pattern emerges due to interspecific ant colony replacements along the ontogeny of the tree. We discuss that this pattern can be seen as an ontogenetic succession since an organism's ontogeny is defining a non-seasonal, directional and continuous pattern of colonization and extinction of interacting populations. Ontogenetic succession can be classified at the same level of another class of succession that has been termed degradative succession. The ontogenetic succession view highlights chains of indirect interactions that are mediated by the focal organism and has the potential to produce unexpected outcomes in population interactions and community structure. We suggest that ontogenetic succession should be widespread in nature and that the concept can contribute to our understanding of the temporal and spatial organization of the world biodiversity .