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Folia Geobotanica 38: 453–467, 2003 ON THE POSSIBLE ROLE OF LOCAL EFFECTS ON THE

Tamás Rédei1), Zoltán Botta-Dukát1), János Csiky2), András Kun1) & Tibor Tóth3)
1) Institute of Ecology and Botany of the Hungarian Academy of Sciences, H-2163 Vácrátót, Hungary; (Rédei), (Botta-Dukát), (Kun)2) Research Group for Biological Adaptation of the Hungarian Academy of Sciences, University of Pécs, Ifjúságu. 6., H-7601 Pécs, Hungary; e-mail moon@ttk.pte.hu3) Research Institute for Soil Science and Agricultural Chemistry of the Hungarian Academy of Sciences,Herman O. u. 15, H-1022 Budapest, Hungary; e-mail Abstract: EWALD (Folia Geobot. 38: 357–366, 2003, this issue) stated that in Central Europe the number of
calcifrequent species is higher than the number of acidofrequent species, while the range of acidofrequent
communities is larger than that of the calcifrequent ones. All the explanations considered in his paper are based
on an evolutionary spatial and temporal scale. In this paper we are trying to prove that local effects might also be
Five open rock grassland communities on different bedrocks, viz. rhyolite (acidic), andesite (slightly acidic), calcareous sandstone (slightly calcareous), limestone (calcareous) and dolomite (calcareous) were chosen for theanalysis. Two parameters of the species-area curve (i.e., local richness and the slope of log area-species richnessline) were estimated based on all species and on rock specialist species separately. With this method we couldsimultaneously study three attributes of diversity: local species number, the slope of log area-species richnessline, and species pool size.
We found that the size of the regional species pool is determined by local effects through local richness (slopes do not differ significantly). Consequently, in this case weathering is a more important characteristic forbedrocks than the Ca2+ content. The extremely high number of rock species on dolomite is also determined bylocal effects; the fine, continuously changing pattern of microhabitats makes the role of competition weaker.
The slope of log area-species richness line, calculated for the rock specialist species is unambiguously higher on the calcareous grasslands. The difference can be explained by the smaller species pool on acidic rockscaused by the lower speciation ability. This is supported by the fact that the endemic species of dry habitats areconcentrated on the calcareous ones. One possible explanation for the lower speciation ability could be thatadaptation to acidic habitats is more difficult than to calcareous ones.
The different behaviour of rock specialist species is the consequence of the limited permeability of the surrounding landsape. Hence, on calcareous habitats the arrival of all species from the larger species pool needsmore time.
Keywords: Dolomite, Regional scale, Rocky grasslands, Specialists, Species-area relationship, Species pool
Temperate and arctic plant communities of neutral soils tend to be more species-rich than those of acid soils (GRIME 1979, GRUBB 1987, PEET & CHRISTENSEN 1988, GOUGH et al.
2000). EWALD (2003, in this issue) suggested that this may be due to the so-called speciespool effect (ZOBEL et al. 1998), i.e., the number of species that are able to grow in acid soil is limited. He demonstrated the lower species pool of acid soils by the fact that in Central Europethe number of calcifrequent species (according to their Ellenberg indicator values) is higherthan the number of acidofrequent species, while the area of acidofrequent communities islarger than that of calcifrequent ones. However, such correlation between local richness andsize of species pool cannot be interpreted as evidence of the species pool effect (i.e., HERBEN2000, BARTHA & ITTZÉS 2001), because local effects can also generate such correlation(HERBEN 2000). In this paper we argue that local effects might also play an important role inthe differences in species richness of communities in calcareous and acidic soils.
Local species richness is determined by the size of the species pool (top-down effects) and local interactions (e.g. competition) (GRACE 2001). In the analysis of the relation betweenspecies pool size and local species richness, species pool is supposed to be constant and notinfluenced by local interactions on an ecological time scale (ZOBEL 1997). This is true ifspecies pool is determined by the fundamental niche (habitat requirement in monoculture) ofthe species. However, in most cases, species pools are determined based on field observations.
In such cases, the species pool is influenced by local interactions (bottom-up effect). The firsttype of species pool is called non-filtered (ZOBEL 1997) or potential (GRACE 2001) speciespool, while the second is called filtered (ZOBEL 1997) or observed (GRACE 2001) speciespool.
Ellenberg indicator values were determined by field observations, not by monoculture experiments, thus they indicate the realized niche of a species. Consequently, species pool ofacido- or calcifrequent species is observed species pool (sensu GRACE 2001), whose size maybe influenced by local interactions (LEPŠ 2001).
Based on the above-mentioned reasons, we deem it more appropriate to refer to species of low R indicator value as acidofrequent instead of acidophilous species, since no measurementor observation supports that these species prefer acidic habitats (this would be indicated by the-philous suffix), existing data only show that these species are frequently present in suchhabitats (this is indicated by the -frequent suffix). For the same reason, we will use the termcalcifrequent instead of calciphilous in this paper (JUHÁSZ-NAGY 1984, 1986).
In this paper species-area curves are used as a framework, because earlier studies showed that they are solid theoretical bases to consider the relationship between local species richnessand size of the species pool (cf. BARTHA & ITTZÉS 2001).
The criteria of habitat selection were(a) long and well-known acidity gradients within a geographical region,(b) no substantial influence of human activities,(c) the presence of species that live only in this habitat.
The second criterion was necessary because human activities may influence the ratio of acido- and calcifrequent species. The third criterion allows us to demonstrate that resultsstrongly depend on whether all species or only the specialist of the habitat are considered.
Based on the mentioned criteria, we chose five open rock grassland communities in northernHungary, which are dominated by Festuca species and have developed on different bedrock:rhyolite (acidic), andesite (slightly acidic), calcareous sandstone (slightly calcareous),limestone (calcareous) and dolomite (calcareous). These communities have supposedly beenstable for a long time; they have not been heavily influenced by human activities. Their soil is Local effects and the number of acidofrequent species shallow, thus soil acidity is mainly determined by the compound of the substrate (otherprocesses, e.g. leaching, are unimportant). There are many species that occur only in thishabitat. In this paper these species will be called “rock specialist species”.
The relationship between species number and area is most often characterized by either the power function suggested by ARRHENIUS (1921) or by the logarithmic function suggested byGLEASON (1922). Neither relationship can be considered generally valid unambiguouslybased on their fitting to real data (CONNOR & MCCOY 1979), nor based on their relationshipto theoretical distributions (FISHER et al. 1943, PRESTON 1948, 1960, 1962, WILLIAMS 1944,1947). Fortunately, from the viewpoint of our investigations, both functions give qualitativelythe same results. We use the logarithmic function (S = C + z ln A, where S = the speciesnumber, A = the observed area, C and z are parameters) because parameter C can beinterpreted better in this case (i.e., it is the local species richness).
The values in the equations belonging to acidofrequent species are subscripted by a, and the values belonging to calcifrequent species by c. The paradox reviewed by EWALD (2003, inthis issue) concerning the species-area relationship can be written as follows: Cc + zc ln > Ca + za ln Aa From a mathematical point of view, the two inequalities contradict each other if and only if Cc £ Ca and Zc £ Za. That is, the two inequalities can be valid at the same time only if at leastone parameter in the equation relating to calcifrequent species is greater than thecorresponding parameter relating to acidofrequent species.
The relevés for all five investigated communities were taken in northern Hungary, on different substrates in the Pannonian Range, on an area that measures roughly 200 km in theeast-west direction and 100 km in the north-south. The climate of the area is relativelyuniform; towards the western part it is submediterranean and towards the east the continentalcharacteristics begin to dominate. The maximum distance between the relevés for eachsubstrate is 15–25 km. All communities are open rock grasslands dominated by xerofrequentperennial grasses and all have a southern exposure. The main data of relevés are summarizedin Table 1.
The bedrocks
Triassic dolomite weathers slowly chemically and intensively physically. Due to the fast formation of small debris, dolomite mountains have steep slopes. Open rock surfaces are Table 1. The main data of relevés: bedrock, name of association, location, number of relevés, plot size,author/source. Plot size = 4 m ´ 4 m.
Limestone Campanulo-Festucetum pallentis Bükk Mts.
Sandstone Cleistogeni-Festucetum pallentis Nógrád-Heves- pseudodalmaticae(MIKYŠKA 1933) KLIKA 1938 pseudodalmaticae(MIKYŠKA 1933) KLIKA 1938 frequent. This favours the formation of rocky grasslands (GAMS 1930, ZÓLYOMI 1942). Thesoil pH of the rock grasslands is 7.2 on average (in water extract, KOVÁCSNÉ LÁNG 1966).
Triassic limestone is a karstic rock that dissolves easily chemically. The soil is slightly alkaline with a pH of 7.3–7.6 (in water extract, KOVÁCSNÉ LÁNG 1966).
Oligocene calcareous sandstone weathers quickly, thus the grasslands of steep surfaces are open, and erosion is so rapid that soil formation and leaching cannot start. In the rockygrasslands of the soil pH is 7.2 on average (in water extract).
Miocene andesite is a neutral or slightly alkaline volcanic rock. Leaching can be strong on single standing rocks, leading to the formation of slightly acidic skeletal soils. In the openrock communities soil pH is 6.5 on average (in water extract, HORÁNSZKY 1964).
Miocene rhyolite is an acidic volcanic rock. The soils formed on it are strongly acidic. In the soil of rock grasslands pH is 5.1–5.5 (in water extract, SIMON 1977).
Statistical analysis
Acido/calcifrequent characters of species were described by their R-indicator values according to Ellenberg’s system (ELLENBERG et al. 1991) applied to the Hungarian flora byBORHIDI (1995). A low value means acidofrequent species, while a high value means acalcifrequent one.
We ordered the different communities according to their R-value spectrum in order to verify that the acidity gradient of the parent materials can really be observed in the vegetationdata. For ordination, concentration analysis was used (FEOLI & ORLÓCI 1979). PRÉCSÉNYI(1995) suggested applying this method to investigate the indicator values instead of themathematically incorrect averaging of ordinal data. In order to fulfil the conditions of themethod, R values 3 (acidofrequent species, mostly in acid soils) and 4 (moderatelyacidofrequent species), and values 8 (calcifrequent species) and 9 (specialists of basic soils) Local effects and the number of acidofrequent species were merged (c.f. BOTTA-DUKÁT &RUPRECHT RUPRECHT 1999). (For more detailsabout this analysis see Appendix 1).
parameter C means the species numberin a unit area, and z means the log area-species number slope. In our study,the increase in area was replaced by Fig. 1. Ordination of grassland communities and R indicator combining the species list of relevés; the value categories by concentration analysis according to PRÉCSÉNYI (1995). Importance of axes was tested by randomization (BOTTA-DUKÁT & RUPRECHT 1999, seedetails in Appendix 1). Only the first axis proved to be because the plot size was constant. In this case parameter z shows the difference of Concentration analysis produces parallel ordination of rock grassland communities and species groups based on R Thus the size of the species pool depends indicator values; these are plotted in two different rows.
on local species richness and thedifference in species composition on the different locations. The disadvantage of the method used for increasing the area is that thespecies numbers belonging to different relevés are not independent of each other, thereforethe maximum likelihood estimation of slope by least squares method cannot be applied. Thuslinear regression cannot be carried out, because it overestimates the slope. Therefore thespecies richness of relevés was used for estimating parameter C and Dahl alpha for parameterz (DAHL 1960; cf. Appendix 2). In the first case the communities were compared using aKruskal-Wallis test with subsequent Dunn post hoc test (ZAR 1999), while in the latter thejackknife method was used for the estimation and calculation of the 95% confidence interval(EFRON 1982). The calculations were carried out for all species and also for rock specialistspecies only.
Only the first axis of the ordination carried out on the R indicator value spectra proved to be significant (based on the randomization test only the first canonical correlation wassignificantly higher than the one expected in the random case). The R-values are located onthis axis in increasing order. It means that low values on the axis indicate acidic character,while high values indicate basic character. Relevés from dolomite were most basifrequent,this was followed by limestone mildly basifrequent and sandstone slightly basifrequentspecies pool. The species pool of andesite is slightly, while that of rhyolite is moreacidofrequent (Fig. 1).
Among the investigated relevés the slightly acidic andesite grasslands were significantly the richest in species (Fig. 2a). These were followed by dolomite and sandstone grasslands, each other significantly. The poorest inspecies are rhyolite and limestone relevés, but these differences cannot be species is lowest on andesite grasslands,and highest on dolomite. The other three communities, that is acidic rhyolite, the Fig. 2. Local species richness in 4 ´ 4 plots (median, of inter-quartile range, range) in the five rock grassland communities: (a) all species, (b) rock specialist species only.
significantly (slope = -0.17, t = 1.94, Communities were compared using Kruskal-Wallis test, n.s.) with an increase in species number.
then Dunn post hoc test. The same letter above bars indicatesthat communities. The box encloses the middle 50% quartiles, while the median is indicated by the black square and range on the graph, where a decrease in species number entails an increase in rockspecialist species. Among them the andesite grasslands are characterized by a rather low proportion of rock specialist species andthe high species number; there is a significant, strongly negative correlation between them(slope = -0.89, t = 3.26, P < 1%). On sandstone, the low proportion of rock specialist speciesaccompanies a medium species number with significant negative correlation (slope = -0.35,t = 2.49, P < 5%). On limestone and rhyolite, the low species number is accompanied by ahigher proportion of rock specialist species, and correlation is significantly negative onlimestone (slope = -0.26, t = 2.27, P < 5%), while on rhyolite it is also slightly negative, butnot significant (slope = -0.09, t = 1.41, n.s.).
Local effects and the number of acidofrequent species Fig. 3. Relationship between the species richness and the differ significantly from each other.
proportion of rock specialist species.
whose alpha values are significantly higher than that of other communities, but do not differsignificantly from each other.
The estimated species pool (estimated number of species in 100 relevés) is much higher in andesite than in the other four communities, which do not differ considerably (Fig. 5a). Theestimated pool of rock species (Fig. 5b) increased with decreasing soil acidity from rhyolite tolimestone (andesite and sandstone do not differ considerably). The pool of rock species iseven higher in the dolomite grassland than in limestone, however these two communities donot differ considerably in soil pH.
Because different mechanisms can generate the same pattern, a hypothesized mechanism cannot be verified by observing the pattern that can be generated by this mechanism (HERBEN2000). Therefore, in discussing our results, we can only say that a certain mechanism ispossible (i.e., we can only point out the possible importance of local effects).
A hypothesized mechanism, however, can be falsified by observing patterns; i.e., if the observed pattern cannot be generated by this mechanism. In our opinion, the effects oflarge-scale mechanisms linked to soil acidity (and consequently the patterns generated bythem) should be the same within communities of either acidic or calcareous, or it shouldchange gradually. It allows us to falsify the hypothesis that the observed species richnesspatterns are generated by large-scale mechanisms linked to soil acidity.
In what respect are calcifrequent rock-grasslands more diverse?
We can say that based on our results summarized in Table 2, the species richness indicators obtained from different scales and set of species differ in their response to the acidic-basiccharacter of the substrate.
The species number in the relevés can be only partly explained by the number of specialists. Andesite grasslands were poorest in rock specialist species, while they were most Table 2. Comparison of the studied communities in parameters of soil and species richness. Rows that share thesame letter do not differ significantly at a = 0.05.
species-rich. Sandstone, which is also poor in rock specialist species, is also rather rich inspecies. The phenomenon is explained by the ratio of total species number and rock specialistspecies number. While on dolomite, limestone, and rhyolite this ratio is rather high and(except for limestone) does not correlate significantly with species number, on sandstone andandesite the relatively low ratio has a strong negative correlation with species number. Thisshows that the species richness of the two latter rocky-grasslands is not caused by the highnumber of their specialists (rock specialist species), but probably by the higherhabitat-diversity within sampling plots. The surface forms on these substrates do not favourformation of really connected rocky-grassland communities, but they make a mosaic withsteppe patches of deeper soil even inside the 4 m ´ 4 m plots . Therefore, the relevés are richin dry grassland generalists. Among the three highly rocky grasslands the dolomite has higherboth species number and ratio of rock specialist species. Several dolomite specialists areadded to the pool of calcifrequent rock specialist species, thus increasing the number of rockspecialist species. Species requiring deeper soil play a less important role. This results in theoutstanding ratio of rock specialist species.
Altogether it can be said that none of the two indicators of local species richness (total species number and rock specialist species number) can be explained definitely by the acidicor alkaline state of the substrate; i.e., neither they are homogeneous within acidic and withincalcareous communities, nor do they change gradually along the acidity gradient.
We experienced significant differences between the behaviour of the slope of species-area relationship calculated for all species and for rock specialist species only. Dolomite andlimestone grasslands have a higher slope of rock specialist species and thus they appear morediverse. It is important to note that significant flora-geographical differences cannot be shownwithin the different relevé groups. The differences among the rock specialist species weremasked by the homogeneity of the accompanying generalists when all the species wereinvolved. Thus, the slope of species-area relationship calculated for specialists is the onlyfeature that is clearly higher on the strongly calcareous habitats.
On rhyolite, the same few acidofrequent rock specialist species appear in all relevés. On andesite and sandstone, the low number of rock specialist species found is chosen randomlyfrom the slightly larger pool of primarily neutral or slightly acidofrequent or calcifrequentrock specialist species; this increases the difference between the relevés. The limestone Local effects and the number of acidofrequent species rhyolite andesite sandstonelimestone dolomite Fig. 4. Dahl alpha in the different rock grassland communities (estimated value and 95% confidence intervalcalculated by jack-knife method) calculated for all species (a) and rock specialist species only (b).
relevés, which contain rock specialist species in similar numbers to rhyolite, prove to be muchmore diverse in this respect, and thus have a much bigger pool of rock specialist species. Thehigh number of rock specialist species per relevé and the high diversity on dolomite mean anexceedingly large pool of rock specialist species.
The smaller species pool in strongly acidic habitats may be also due to physiological constraints. The low pH value influences nutrient uptake of plants in many ways (LUCAS &DAVIES 1960). Acidofrequent plants have developed several mechanisms for warding offthis effects, which point to strong, more time-demanding specialization, thus limiting thenumber of specialists.
Top-down or bottom-up effects?
Two types of causation can be considered between the shape of the species area curve and (1) bottom-up effect: the shape of the species-area curve is determined by local effects and the size of species-pool depends on this; (2) top-down effect: the size of the species-pool is determined by global effects (e.g.
vegetation history) and it influences the shape of the species-area curve.
Most often both effects may take place, but their importance varies. If all species are considered, species-pool – which in this case is mainly made up of xerofrequent, generalistspecies that can be found in other habitats – is significantly higher than local species number.
Thus, in our opinion, it does not limit the species richness of communities. The observeddifferences between the studied communities suggest that the species number is primarilydetermined by the weathering characteristics of the substrate that is not simply related to thecalcium content of bedrock. This local effect, however, probably has an influence bychanging the size of the (filtered) species pool (bottom up effect), i.e., many xerofrequentgeneralists can establish on andesite and sandstone, where habitat conditions are not tooextreme, and shallow and deep soil patches pattern up at a scale that is finer than the size of arelevé.
There is no difference between calcareous and acidic rock grasslands in the local number of rock specialist species; however, the number is exceedingly high on dolomite. Due to the Fig. 5. The species-area curves based on the estimated parameters (C and z) for all species (a) and rock specialist species pool of this heavily stressed,but weakly competitive habitat, is rather large; this is partly explained by the high persistence (survival of relic species), andpartly by the high speciation (formation of endemisms) rate (ZÓLYOMI 1942, 1950, 1958).
Thus the high species pool on dolomite is a consequence of a long-term cumulative localeffect (low competition). Dolomite is locally very rich in rock specialist species partly due tothe larger species pool, and partly directly due to the low competitive intensity.
Significant differences can be found in the slope of species-area relationship (the z value) calculated for rock specialist species in favour of the calcareous habitats. Mathematically, thespecies pool size is determined by the local species number and slope together. From abiological viewpoint, however, the interplay among the three measures is not so simple. Forexample, local species richness may be restricted by low species pool size, but the observedspecies pool is the sum of species in local assemblages. Dependent or independent variablesare therefore hard to define. The difference in slopes of species-area relationships could beexplained by the difference in the ratio of local species richness and species pool size or by thedifferent heterogeneity of habitats at a macro scale (e.g. mineralogical heterogeneity).
However, we have not found any proof for the heterogeneity of calcareous habitats being Local effects and the number of acidofrequent species larger at a macro scale. The lower slopes of rock specialist species in silicate-rock grasslandsis caused by the low species pool.
The different behaviour of rock specialists is explained by the fact that the surrounding area, which is more or less permeable for generalists, has an isolating effect for rockspecialists. This results in a lower settlement rate (MACARTHUR & WILSON 1967). In the caseof large species pools, characteristic of calcareous communities, the low settlement rateincreases the difference between relevés significantly, while the limited species pool ofsilicate- and sandstone-rock grasslands arrive much earlier even at the same colonization rate.
EWALD (2003, in this issue) studied the role of evolutionary space and time-scale processes in the formation of species pools. In our article we wanted to draw attention to the fact that therole of local effects cannot be excluded. Our investigations have shown that the obtainedresults heavily depend on whether all species or just a selected set of species (i.e., specialistsof the habitat) are investigated, and that habitats formed on calcareous and acidic substratecannot be handled as separate but uniform groups, and that there can be significant differenceswithin the groups.
From the viewpoint of local species richness determined based on the full species list, the differences between the rocky grasslands are at least partly caused by local effects. Therelative importance of this effect cannot be determined from the data included in this study,because most of the species appear not only in rocky grasslands but also in other communitiesas well. If the rock specialist species only are investigated, then the high local species numberof dolomite and its high species pool can both be connected to local processes (lowcompetition) as well. For the other four rocky grasslands it is rather the evolutionary orvegetation history that causes the difference in species pool, and this low species pool causesthe low local species number of acidic rocky grasslands. In Hungary the vegetation historiesof the two types of habitats were not so different as in Central Europe, because during theglaciations there was no ice cover in the Carpathian Basin. Thus the scenario described byEwald is not very likely here. In our opinion it is rather the much higher speciation rate that isresponsible for the high species pool of calcareous rock grasslands, which is supported by thehigh number of endemisms as well.
Acknowledgements: We thank Sándor Bartha, Miklós Kertész, Tibor Kalapos, János Podani, László Békei and
two anonymous reviewers for the comments on our manuscript. This study was supported by the Hungarian
National Science Foundation (OTKA F012873, F026458) and the Hungarian National Research and
Development Program (NKFP-3B/0008/2002).
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Received 14 February 2003, revision received 18 July 2003, accepted 11 August 2003Encl. Appendix pp. 466–467 APPENDIX 1
Analysis of indicator values by concentration analysis
Concentration analysis was developed by FEOLI & ORLÓCI (1979) for analyzing the relationship between the groups of species and the groups of relevés. PRÉCSÉNYI (1995) pointed out that if species are divided intogroups based on their indicator values, the pattern of indicator values can be analyzed by this method.
The main point of the method is the following: fjk is the total number of occurrences of species belonging to species-group j in relevés belonging to relevé-group k. The value of fjk depends on the sizes of species-group jand relevé-group k. Eliminating this effect the corrected values (Fjk) have to be used in the analysis (ORLÓCI &KENKEL 1985): m = number of relevé-groupspj = number of species belonging to group j qk = number of relevés belonging to group k.
In the analysis we regard F as a contingency table, although this matrix may contain fractions. First, the independence of species grouping and the grouping of relevés is statistically tested. If they are independent ofeach other F will not significantly differ from F0: This hypothesis can be tested by c2- (FEOLI & ORLÓCI 1979) or G2-test (PRÉCSÉNYI 1995). If F significantly differs from F0, the matrix F will be analyzed by correspondence analysis. The scores of species and relevégroups in the same min{m,n}-1 dimensional ordination space and the canonical correlation coefficientsbetween scores are obtained this way. The sum of canonical correlation coefficients are connected with the c2value computed earlier: R1 = canonical correlation between first scores of species-groups and first scores of relevé-groups, The c2 value can be taken to components. The values of canonical correlation coefficients show the importance of the axes. If the value of F R 2 is smaller than the appropriate critical value of c2 distribution with (m-1)(n-1) degree of freedom, the jth axis may be left out of consideration.
BOTTA-DUKÁT & RUPRECHT (1999) showed that decreasing the number of species groups increases efficiency of pattern recognition, because due to the decreasing number of groups the probability of fulfilling thepreliminary conditions of c2-test increase. They suggested that the significance level of canonical correlationshould be tested by randomization (by the so-called “random group size” method) instead of the comparison Local effects and the number of acidofrequent species critical values obtained from c2 distribution, because it results in correct significance levels, even if thepreliminary conditions of the use of c2 distribution are not fulfilled. During this randomization indicator valuesare assigned to the species randomly with the constraint that all indicator values have to be assigned at least onespecies.
Estimation of the slope of Gleason species-area relation by Dahl alpha
Dahl alpha (DAHL 1960) was originally introduced to estimate the a parameter of logarithmic distribution. It S = average species number of relevésSn = number of species in the pooled species list of n relevés.
Expected value of a is the z parameter of Gleason species-area relationship: E(a) = z.
(1) As a starting point for our proof we use the following identity: E(S ) − E(S ) (2) Let the size of all relevés be the same, and let us measure the area by the number of relevés, then A = 1 for single relevés and A = n for the pooled species list.
(3) By Gleason equation E(S ) = C + z ln 1 = C,(4) and E(S ) = C + z ln n.
C + z ln n C (5) By using relations (1), (3) and (4) it is easy to see that E( )




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