Rafał Podlaski

The influence of chloride deicers on mineral nutrition and the health status of roadside trees in the city of Kielce, Poland

Application of chemical road deicers has a negative impact on roadside vegetation. Every year, the trees in cities suffer from direct and indirect effects of salt application for winter road maintenance. To elucidate this problem in the city of Kielce, the chemistry of snow, soil, tree bark, and leaf samples has been investigated together with an assessment of the health status of the trees. Twelve investigation sites were selected along the roads with different traffic intensity. Snow samples were collected twice during the winter and analyzed for pH, EC, Na + , Ca2 + , Mg2 + , and Cl − . In soil (collected from two depth intervals), tree bark, and leaf samples, the concentrations of B, Ca, Fe, K, Mg, Mn, N, Na, P, S, and Zn were determined. The contents of total organic carbon (TOC) in soils, as well as the pH of soil and tree bark samples were also measured. Negative symptoms revealed by roadside trees included the loss of assimilative apparatus and decreased vitality. The results of chemical analyses indicated that the snowmelt might be a substantial source of chloride ions and alkalizing substances that influenced higher pH of soils. The soil samples displayed elevated concentrations of S and Zn and lower than typical for soil contents of B, Mg, and TOC. The pH of alkaline soils favored greater bioavailability of B and reduced bioavailability of Na and Zn by the trees examined.

Diversity of patch structure in Central European forests: are tree diameter distributions in near-natural multilayered Abies–Fagus stands heterogeneous?

Near-natural multilayered Abiesalba Mill.–Fagus sylvatica L. forests form structural mosaics and consist of patches in different developmental stages and phases. Knowledge of the diversity of patch structure and adequate methods to describe the diameter structure is essential for modeling forest dynamics. The hypotheses tested in the study are that near-natural multilayered stands are structurally heterogeneous (i.e., tree diameter (DBH) distributions of these stands are heterogeneous) and, that in these forests the finite-mixture models are suitable for modeling the empirical DBH distributions. Diversity of patch structure was studied based on data collected from 33 sample plots. In multilayered stands, four groups of empirical DBH distributions were distinguished using hierarchical cluster analysis (HCA) and correspondence analysis (CA). Stands investigated are structurally heterogeneous; 27% multilayered stands showed the slightly rotated sigmoid (SRS) type of empirical DBH distribution, 34% the distinctly rotated sigmoid (DRS) type, 18% the bimodal M-shaped (BMS) type, and 21% the unimodal highly skewed (UHS) type. The gamma distribution, the two-component mixture gamma model, and the two-component mixture Weibull model were more flexible for the SRS type of DBH distributions. The average p-values (Chi-square test) for these theoretical distributions were 0.4712, 0.4718, and 0.4660, respectively. The two-component mixture gamma model and the two-component mixture Weibull model were a good choice for modeling the DRS, BMS, and UHS types of DBH distributions. The average p-values (Chi-square test) for these models ranged from 0.2684 to 0.4854. In near-natural multilayered Abies–Fagus forest patches of different DBH distributions occur together. The empirical DBH distributions in these stands are characterized by irregular and complicated shapes and therefore are best approximated by finite-mixture models.

Comparison of selected statistical distributions for modelling the diameter distributions in near-natural Abies–Fagus forests in the Świętokrzyski National Park (Poland)

The aim of the study is to compare selected theoretical distributions (normal, lognormal, Weibull, gamma, logistic, and exponential) in describing the tree diameter (DBH) distributions of mixed near-natural forests consisting of fir Abies alba Mill. and beech Fagus sylvatica L. growing in various vertical structures. Tree DBH data were collected between 1997 and 2008 from 51 sample plots established in the Świętokrzyski National Park in Poland. The empirical data represent differentiated DBH distributions, ranging from almost symmetric to extremely asymmetric ones. The chi-square test and the modified Kolmogorov–Smirnov test were chosen for the goodness-of-fit testing. In addition to the test statistics, the bias (B), the root mean square error (RMSE) and the graphical method (quantile–quantile plots) were used. In one-storied stands, the most suitable distributions were the normal and logistic distributions; in two-storied and multilayered stands, the Weibull and gamma distribution were the most suitable; and in selection stands, the exponential distribution was the most appropriate to describe the DBH distribution. The order of precision of the tested distributions (from the highest to the lowest) was Weibull, gamma, logistic, normal, exponential, and lognormal. The normal and exponential distribution should be applied only to one-storied and selection forests, respectively. The least suitable distribution for DBH distribution modelling was the lognormal one.

Tree diameter structural diversity in Central European forests with Abies alba and Fagus sylvatica: managed versus unmanaged forest stands

Abstract The biodiversity of forest stands should be analysed from the point of view of not only compositional elements but also structural diversity. The main objective of this study was to compare tree diameter structural diversity of the mixed managed and unmanaged stands with Abies alba and Fagus sylvatica. There were 62 study plots established in the Carpathians (Southern Poland) and in the Świętokrzyskie Mountains (Central Poland) in managed and unmanaged stands. The comparison of the studied stands involved the identification and modelling of size structures, the use of the Gini coefficient and the relative distribution method (including entropy and polarisation). Six structural types were distinguished: three unimodals of a different width of diameter at breast height (DBH) range (mainly for the managed stands), reverse-J, rotated-sigmoid and bimodal (for unmanaged stands). Modelling of the distinguished structural types by means of theoretical distributions has shown that the best results of approximation for unimodal skewed and reverse-J DBH distributions were obtained with the single Weibull and gamma distribution, while in the case of rotated-sigmoid and bimodal DBH distributions the best results were obtained with mixture models. The comparisons have shown that tree diameter structural diversity was more complex in unmanaged forests compared to managed stands. For managed stands the Gini coefficient assumed values from 0.31 to 0.48, while in the case of the unmanaged forests, from 0.33 to 0.73. One should aim to increase tree diameter structural diversity in managed forests, adopting the close-to-nature silviculture concept which consists of imitating natural processes.

Modelling diameter distributions of two-cohort forest stands with various proportions of dominant species: A two-component mixture model approach

In recent years finite-mixture models have been employed to approximate and model empirical diameter at breast height (DBH) distributions. We used two-component mixtures of either the Weibull distribution or the gamma distribution for describing the DBH distributions of mixed-species, two-cohort forest stands, to analyse the relationships between the DBH components, age cohorts and dominant species, and to assess the significance of differences between the mixture distributions and the kernel density estimates. The data consisted of plots from the Świętokrzyski National Park (Central Poland) and areas close to and including the North Carolina section of the Great Smoky Mountains National Park (USA; southern Appalachians). The fit of the mixture Weibull model to empirical DBH distributions had a precision similar to that of the mixture gamma model, slightly less accurate estimate was obtained with the kernel density estimator. Generally, in the two-cohort, two-storied, multi-species stands in the southern Appalachians, the two-component DBH structure was associated with age cohort and dominant species. The 1st DBH component of the mixture model was associated with the 1st dominant species sp1 occurred in young age cohort (e.g., sweetgum, eastern hemlock); and to a lesser degree, the 2nd DBH component was associated with the 2nd dominant species sp2 occurred in old age cohort (e.g., loblolly pine, red maple). In two-cohort, partly multilayered, stands in the Świętokrzyski National Park, the DBH structure was usually associated with only age cohorts (two dominant species often occurred in both young and old age cohorts). When empirical DBH distributions representing stands of complex structure are approximated using mixture models, the convergence of the estimation process is often significantly dependent on the starting strategies. Depending on the number of DBHs measured, three methods for choosing the initial values are recommended: min.k/max.k, 0.5/1.5/mean, and multistart. For large samples (number of DBHs measured ≥ 80) the multistage method is proposed--for the two-component mixture Weibull or gamma model select initial values using the min.k/max.k (for k=1,5,10) and 0.5/1.5/mean methods, run the numerical procedure for each method, and when no two solutions are the same, apply the multistart method also.

Forest modelling: the gamma shape mixture model and simulation of tree diameter distributions

Abstract• Key messageNew types of distribution functions are needed to model the dynamics of stands where important age classes are represented by few trees. In this study the gamma shape mixture model and two simulation methods were used for generating tree diameter data.• ContextTo analyse forest dynamics, it is necessary to know distribution of the characteristics (mainly tree diameters) of trees forming particular developmental phases. In many forest inventories, the measurement of large diameter at breast height (DBH) samples is practically impossible. In this case, DBH distributions can be generated using theoretical models.• AimsThe aim of this study was to assess the precision of the approximation of empirical DBH data using the gamma shape mixture (GSM) model and kernel density estimation. The strengths and weaknesses of the two simulation methods were presented and discussed.• MethodsThe GSM model was adopted to approximate empirical DBH data collected in 20 near-natural stands. Two simulation methods were used: (a) the procedure based on a multimodal distribution and gamma random numbers (MDGR procedure) and (b) MCMC techniques with Metropolis–Hastings sampling (MH method).• ResultsThe GSM model precisely fitted the investigated DBH distributions. The MDGR procedure was slightly more precise than the MH method, especially in the case of the samples of 250 DBHs. The level of homogeneity within the drawn DBH sets was similar for all samples.• ConclusionThe GSM model is very flexible. The DBH random variates, generated with the use of analysed procedures, represented all tree generations being significant from a biological point of view.

Estimating stem infestation density of Pityokteines curvidens (Germ.) on windfalls: a statistical approach

The objective of this study was to elaborate a statistical method for estimating the total average density of infestation of silver fir (Abies alba Mill.) windfalls by the bark beetle (Pityokteines curvidens Germ.) that allows calculation of estimation errors and does not require debarking of the whole stem. The study was conducted in near-natural forests with A. alba growing in the Świętokrzyski National Park in Central Poland. In total, 56 windfalls of this species were examined. Two main patterns (A and B) of spatial distribution of P. curvidens egg galleries on stems of A. alba were observed. In pattern A, egg galleries were present in the first 1-m length of stem (measured from the base), and the probability of infestation in the first, second, and third 1-m-long stem section was 100%; it then decreased as the distance from the tree base increased. In pattern B, egg galleries were absent from the first 1-m length, but the probability of infestation in successive 1-m lengths increased (from the second to the ninth sections); then it decreased (from the 10th to the 18th sections). The linear regression equations were calculated for trees with the infested (pattern A) and uninfested (pattern B) first 1-m-long stem section measuring from the tree base. The most significant correlation between the number of P. curvidens egg galleries in individual 1-m-long stem sections and the total infestation density in the case of pattern A was found for the sixth and seventh sections counting from the tree base (coefficients of determination were 0.8551 and 0.8516, respectively, while the mean relative errors of estimation did not exceed 28%), and in the case of pattern B for the tenth section (coefficient of determination was 0.7992, and the mean relative error of estimation was 39.7%). The method presented in this paper facilitated quick estimation of the density of infestation of A. alba stems by P. curvidens. Together with survey sampling, it allows estimation of the P. curvidens numbers in the area investigated, also in stands situated in zones under strict protection in nature reserves and national parks.

Validation of a small-area method for estimating the spatial distribution of the degree of tree damage

This article presents a validation of a method, proposed in Podlaski (2003), for estimating the degree of tree damage. This method belongs to a group of small-area methods. To estimate the degree of tree damage in individual P3 sub-blocks of the SINUS system of information on the natural environment, a classification based on the degree of defoliation was used. Spatial distribution of the degree of tree damage was estimated through unrestricted simple random sampling. The maximum total estimation error for proportions of fir and beech with a damage degree of zero, and also with second and third degrees jointly, reached a maximum of 35.6% for fir, and 33.8% for beech. P3 sub-blocks characterised by the highest proportion of the healthiest trees (at least 15% being undamaged trees) occurred in patches in the case of fir, and in larger, compact areas in the case of beech. Because spatial diversification in the health of fir, and to a smaller degree in the case of beech, occurs at small scales, small-area methods for estimating tree condition are necessary. An analogous scheme, combining small-area with large-area methods (utilising sub-blocks of the network of large-area systems in a small-area inventory, and establishing a common database), could be used on a wider scale; for example, by supplementing the program of estimating tree health carried out by the United Nations Economic Commission for Europe (Lorenz et al. 2002) with local inventories.

The gamma shape mixture model and influence of sample-unit size on estimation of tree diameter distributions: Forest modelling

Abstract The gamma shape mixture (GSM) model is based on a mixture of gamma distributions. A general Bayesian approach for estimating the unknown parameters of the GSM model was employed. Tree diameter at breast height (DBH) sets of complex and stratified forests are ideal data sources for testing the usefulness of theoretical distributions applied to modelling and simulating strongly differentiated data sets. The GSM model was useful in fitting these DBH structures. During the identification of homogenous forest patches of the similar DBH structures one should select sample plots of at least 0.15 ha in area, with a minimum of 30 trees. The use of GSM model has the potential to facilitate the presentation of not only DBH structures, but also other empirical distributions, describing e.g. various biological stages and processes. The GSM model can be employed especially for modelling multimodal, asymmetrical and heavy-tailed survey data.