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1

Methods applied for measurement and visualization of changes in biodiversity

Łagód G., Chomczyńska M., Montusiewicz A., Malicki J., Stransky D.

Ecological Chemistry and Engineering. S

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2014

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Vol. 21, nr 4

593--604

EN

The article presents the possible methods for determining biological or statistically significant differences between taxocenoses compared with respect to biodiversity. To obtain a complete description of biological differences between the compared hypothetical communities, the following indices were calculated: S (taxon richness), H (the Shannon index), Hmax (the maximum value of the Shannon index for the richness of taxa represented by the same number of individuals), Vd (a percentage value of covering the structural capacity of community, “evenness deficiency”), E (the MacArthur index - a taxon number (S) in a community for which the observed value of H equals Hmax), and Ps (a taxon richness shortage in percents). Moreover, a graphic profile method (Дд, Tj, and Lj profiles) was used for comparing the diversity of the communities. To obtain information about statistically significant differences in biodiversity between the analysed communities, rarefaction curves were applied. The curves are based on the null models and the Monte Carlo method. The rarefaction method resulted in determination of the statistical significance of the differences between taxon richness and Shannon's index values for the compared communities. The Vd and Ps indices and the profile method allowed concluding about the significance of the biological differences between taxocenoses, even when their values of Shannon's H indices were numerically similar.

PL

W artykule przedstawiono metody określenia biologicznych i statystycznie istotnych różnic między taksocenozami porównywanymi pod względem bioróżnorodności. W celu pełnego opisu różnic biologicznych pomiędzy porównywanymi, hipotetycznymi zbiorowiskami obliczono wskaźniki: S (bogactwo taksonów), H’ (indeks Shannona), Hmax (maksymalna wartość indeksu Shannona dla danego bogactwa taksonów charakteryzujących się takimi samymi liczebnościami), Vd (wyrażona w procentach wartość wypełnienia strukturalnych możliwości zbiorowiska; niedostatek „równomierności”), E (indeks MacArthura, czyli liczba taksonów S w zbiorowisku, dla którego dany indeks H przyjąłby wartość maksymalną) oraz Ps (wyrażony w procentach niedostatek bogactwa taksonów). Dodatkowo, dla porównania bioróżnorodności zbiorowisk użyto graficznej metody profili Δb, Tj i Lj. W celu uzyskania informacji o statystycznie istotnych różnicach między analizowanymi zbiorowiskami pod względem bioróżnorodności wykreślono krzywe rarefakcji, bazujące na modelach numerycznych i metodzie Monte Carlo. Metoda rarefakcji umożliwiła określenie statystycznie istotnych różnic między wartościami bogactwa taksonów i indeksu Shannona obliczonych dla porównywanych zbiorowisk. Metoda profili oraz indeksy Vd i Ps pozwalają wnioskować o istotności różnic biologicznych nawet wtedy, kiedy wartości indeksów H’ Shannona są do siebie liczbowo zbliżone.

2

Methods for measurement and visualization of changes in biodiversity

Chomczyńska M., Łagód G., Montusiewicz A., Malicki J.

Proceedings of ECOpole

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2011

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Vol. 5, No. 1

29--34

EN

Biodiversity can be evaluated basing on the species numbers or numbers of chosen taxa (S). The biodiversity assessment is also enabled using the Shannon index (H) that includes numbers of taxa and their relative abundances (or relative biomass likely relative degrees of covering). The proper description of biological or statistically significant differences (or their absence) between the compared taxocenosis of identical or subjectively different values of S and H, is not possible by use of both methods mentioned. Thus, the aim of our work was to present the manners for solving these problems basing on the example of three hypothetical organism communities. Two of the communities mentioned were characterized by the same values of S (taxon richness) and different values of H (the Shannon index) and two ones had similar H values and different values of S. To obtain the complete description of biological differences between compared communities the following indices were calculated: Hmax (a maximum value of Shannon index for the richness of taxa represented by the same number of individuals), Vd (a percentage value of covering structural capacity of community, “evenness deficiency”), E (MacArthur index - a taxon number (S) in a community for which the observed value of H equals Hmax) and Ps (taxon richness shortage in percents). Moreover, graphical method of Δb, profiles was used for comparing community diversities. Instead, to obtain information about statistically significant differences in biodiversity between analyzed communities, the rarefaction curves were applied. The curves are based on the zero models and the Monte Carlo method.

PL

Bioróżnorodność można oceniać na podstawie liczby gatunków lub liczby dowolnie wybranych taksonów (S). Ocenę bioróżnorodności można również przeprowadzić za pomocą indeksu Shannona (H), do obliczeń którego wykorzystuje się liczbę taksonów oraz ich względne liczebności (lub względne biomasy ewentualnie relatywne stopnie pokrycia). Przy użyciu obu wymienionych metod nie można poprawnie określić statystycznie istotnych czy też biologicznych różnic (lub ich braku) pomiędzy porównywanymi taksocenozami o identycznych lub subiektywnie różnych wartościach S i H. Stąd celem prezentowanej pracy było przedstawienie sposobów rozwiązania tego problemu na przykładzie trzech hipotetycznych zbiorowisk żywych organizmów. Wśród tych taksocenoz dwie charakteryzowały się takimi samymi wartościami S (bogactwa taksonów) i różnymi wartościami H (indeksu Shannona), a dwie miały zbliżone wartości H, a różne wartości S. Dla pełnego określenia różnic biologicznych pomiędzy porównywanymi zbiorowiskami obliczono wskaźniki: Hmax (maksymalna wartość indeksu Shannona dla danego bogactwa taksonów charakteryzujących się takimi samymi liczebnościami), Vd (wyrażona w % wartość wypełnienia strukturalnych możliwości zbiorowiska; niedostatek „równomierności”), E (indeks MacArthura, czyli liczba taksonów S w zbiorowisku, dla którego dany indeks H przyjąłby wartość maksymalną) oraz Ps (wyrażony w % niedostatek bogactwa taksonów). Dodatkowo, dla porównania bioróżnorodności zbiorowisk użyto graficznej metody profili Δb. W celu uzyskania informacji o statystycznie istotnych różnicach między analizowanymi zbiorowiskami pod względem bioróżnorodności wykreślono krzywe rarefakcji, bazujące na modelach zerowych i metodzie Monte Carlo.

3

Metoda profili w budowie numerycznego modelu rzeźby terenu

Stateczny A., Kozak M.

Roczniki Geomatyki

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2005

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T. 3, z. 1

147-153

EN

A numerical model of topographic relief can be defined as a set of measurement points with an interpolation algorithm. It enables the visualisation of 3D spatial data; therefore, the scope of its application is very wide. On the one hand it is applied for simulating the development of phenomena, and on the other, for designing the location of facilities and buildings. With the growing number of DTC (Digital Topographic Chart) users, there also increase their requirements concerning data quality (accuracy, reliability, up-to-dateness) and the possibilities of analysis in real time. The article presents research on the DTC construction method, which stresses the organisation of data recording, limiting them to minimum, at the same time aiming at the possibility of analysis in real time, and the construction of the model with assumed accuracy. Modern measurement systems permit the automatic acquisition of very large data sets. Traditional construction methods of a numerical topographical relief model most frequently process the data sets to the shape of a regular GRID net. At nodal points, the height/depth of the terrain is calculated on the basis of an interpolation algorithm. A problem encountered while applying a GRID net for the construction of a DTC is its large size. Applying a GRID net for 1 sq. km with net size of 1m we will obtain 1 million points. For larger areas the number of points will be proportionately higher. Using such a number of data in real time is impossible; their very storage is a problem in itself. By additionally applying methods based on GRID net for areas with irregular shapes (e.g. a fairway) a rectangleshaped net is obtained as a result, with a large number of unnecessary and distorted data. The method of profiles used for the construction of a numerical model of topographical relief is dedicated for fairway-type areas. The purpose of this method is to restrict the number of data necessary for reproducing a 3D bottom model. The time of constructing the method is inessential, as the model will not be constructed on a vessel unit, and it will be changed only if new measurement data are acquired. The accuracy of the reconstructed surface is a very important criterion, assumed by the user in advance as the maximum error. The input data for the method are measurement points with the designated fairway axis. The data are divided into sections, and in the next stage the system of coordinates is turned around and shifted for each section, so that the width of the considered data fragment should be as small as possible. Next, cross-sections are built for all sections in equal distances. Based on interpolations between sections (maximum error), it is checked if the distances between sections are correct. If the value of maximum error is too large, a successive profile is added. If the value of maximum error is too small, it is checked if a profile is not an excess profile. The method of profiles restricts the number of data necessary for a 3D spatial visualisation; it does not contain excessive and distorted data, which occur in the case of GRID-net based methods. Adaptively selected cross-sections will be kept on the unit, and they will be visualised in real time. The method of profiles makes it possible to construct a numerical model of topographical relief with previously assumed accuracy.