ISSN 20790864, Biology Bulletin Reviews, 2012, Vol. 2, No. 3, pp. 197–210. © Pleiades Publishing, Ltd., 2012. Original Russian Text © Yu.G. Puzachenko, S.L. Kuzmin, R.B. Sandlerskiy, 2011, published in Zhurnal Obshchei Biologii, 2011, Vol. 72, No. 5, pp. 339–354.
Quantitative Estimation of Distribution Area Parameters: A Case Study of Members of the Genus Rana Yu. G. Puzachenko, S. L. Kuzmin, and R. B. Sandlerskiy Severtsov Institute of Ecology and Evolution, Russian Academy of Sciences, Leninskii pr. 33, Moscow, 119071 Russia email:
[email protected],
[email protected],
[email protected] Received January 19, 2011
Abstract—Quantitative analysis of “point” distribution areas of species is analyzed; this method interpolates species distribution to the whole territory based on its correlations with climatic and landscape variables. It is demonstrated that the application of standard statistical interpolation techniques is inappropriate. The new approach uses the interpolation of the speciesspecific relations with environmental variables determined at individual points to the whole territory. The basic method for solving this problem is factor analysis. This study analyzed methods for quantifying species relations to particular climate and relief variables. Efficiency of this analysis is demonstrated by a case study of three brown frog species: Rana temporaria, R. arvalis, and R. amurensis. DOI: 10.1134/S2079086412030048
Analysis of geographic determination of species distribution areas as a function of physicogeographi cal conditions (climate, relief, and location on the earth’s surface) is a traditional problem in biogeogra phy. This problem comprises determination of the ori gin of a distribution area with detection of its generic center, as well as the physical, climatic, edaphic, and biotic factors that regulate its boundaries, possible rates of expansion, and its limitations (Tolmachev, 1962). Currently, problems of prediction of potential species response to global climate change are associ ated with the analysis of distribution areas. The ecological aspect of analyzing a distribution area is connected with the concept of the Grinnellian ecological niche, i.e., the species relation to the terri tory and its properties. His seminal work, published in 1917 (Grinnell, 1991), involved logical comparative analysis of the distribution areas of three thrasher spe cies in their association with the climate of the area. According to the concept of a multidimensional eco logical niche by Hutchinson (1957), it is close to the concept of habitat as an environment appropriate in its spatial presentation for the individuals of a species. The difference between Grinnellian and Hutchinso nian niches reduces to the fact that Hutchinson regarded the niche as an attribute of species rather than something determined by environment, as in the Grinnell model. It is as if the Grinnell model specifies the niche in an a priori manner, while the Hutchinson model implies its association only with individual spe cies (Puzachenko et al., 2010). The advent of PCs provided for the transition from logical to quantitative analysis of distribution areas. Fine and mediumscale raster digital maps of climate
variables formed the background for this analysis. Using satellites, digital terrain models of the whole globe with resolution of 90 × 90 pixels have been con structed and biological production has been estimated based on the normalized differential vegetation index (NDVI). This made it possible to apply various statis tical methods for quantifying the correlations of distri bution areas with a multitude of environmental vari ables. For this purpose, specialized software tools have been elaborated that are directly associated with the GIS for areas and environmental characteristics, such as BioGeomancer (BioGeomancer Working, 2007), DIVA (DIVAGIS, 2009), DesktopGarp (Stockwell et al., 2006), Biomapper (Hirzel et al., 2002), Why Where (Stockwell, 2006; WhyWhere, 2009), and GEOLocate (Tulane University Museum …, 2009). Almost the entire toolkit of statistical methods is used in the current analysis: clustering methods, factor analysis, logistic regression, discriminant analysis, neural networks, and genetic algorithm. Each of these methods has its own advantages and shortcomings, and its efficiency is in many respects determined by the pattern of correlation between species and user defined external variables. Numerous direct compari sons of the similarity in results and efficiencies of dif ferent methods have been performed (Manel et al., 1999, 2001; Engelhard et al., 2003; McPherson et al., 2004; Peterson, 2006; etc.). For the adequate application of statistical methods, a distribution area must be represented by two subsets of points with the “presence” and “absence” of spe cies. Moreover, the latter should be confirmed by observations. Such analysis is natural for a traditional representation of a distribution area as a certain part of
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a territory with the assumed ubiquitous presence of a species, as opposed to the remaining total territory. However, statistical methods are inapplicable to point areas, which are widely used in biogeography (Tupik ova, 1996; Tupikova et al., 1998, 2000; Kucheruk, 1997; etc.). This representation lacks a formal alterna tive to presence and consequently lacks a probability space. In the first case, quantitative analysis makes it possible to refine the boundary based on the correla tion between distribution area and environmental conditions, whereas in the second case it is necessary to determine this boundary. It is evident that a territory with an almost zero speciesdetection probability almost always corresponds to the boundary region in a probability space. The goal of this work was to demonstrate the approach to quantitative analysis of point areas that eliminates the problem of documented species absence, by a case study of three brown frog species of the genus Rana. Of these frog species, the moor (R. arvalis) and common (R. temporaria) frogs have Eurasian distribution areas with the former spreading farther to the east (to central YakutiaSakha). As for the Siberian wood frog (R. amurensis), an Asian spe cies living predominantly in Siberia, as well as in northern Mongolia, Manchuria, and the Russian Far East. MATERIALS AND METHODS The analyzed point distribution area was obtained based on information from the database on amphibi ans of the USSR (®0229803415, State Register of Databases of the Russian Federation). The localities of findings were converted into GIS MapInfo data according to geographic coordinates. The mean values of the following climate variables for 1950–2000 from the database WORDCLIM (Wordclim …, 2009) with a resolution of 8 km were assigned to the finding points: daily mean temperature, mean daytime temperature, number of sunlight hours, number of days with mean negative temperature, total precipitation, number of days with precipitation, air humidity, and the NDVI for each month (GLCF, 2009). In addition, the fol lowing specialized variables recommended for solving such problems in the BIOCLIM program (BIOCLIM project, 2009) were involved in the analysis: mean annual temperature, temperature amplitude for each month, standard deviation of temperatures, maximum temperature of the warmest month, minimum tem perature of the coldest month, annual temperature amplitude, mean temperature of the most humid and driest quarters (seasons) of the year, the ratio of tem perature amplitude over month to that over year, annual total precipitation, total precipitation for the most humid and driest months, the variation coeffi cient for precipitation, and total precipitation in the humid and dry as well as the warm and cold quarters of the year.
A total of 108 climate variables and 12 NDVI values were used in the analysis. The relief characteristics comprised altitude, illumination from the south and west, slope, gradient, laplacian, and profile curvature of the surface for four hierarchical relief levels obtained by spectral analysis of the eastern European terrain (Kotlov and Puzachenko, 2006). ANALYSIS AND INTERPOLATION METHODS Let us assume that there are generalized indepen dent variables reflecting the spatial variation of all cli mate and relief variables for the entire territory, in this case, the territory of the former USSR. The regions described by these variables are definable as a multidi mensional environmental space or an ecological space. The points where a species is present corre spond to a certain subregion of this total space; this subregion can be defined as speciesspecific. It is evi dent that this subregion is close in meaning to the eco logical niche given in observations. Consequently, it is necessary to represent this subregion by external vari ables and approximate it for the entire territory, thereby defining the spatial boundaries for the ecolo gical niche of the species. As a result, the initial space will be transformed into one that corresponds to the “perception” of the environment by the considered species. Each “specific” variable thus defined has regions within which the species occurs with a proba bility close to unity and to zero. Since the representa tion of how the species perceives the varying environ ment is regarded as continuous, it is admissible that there is a function correlating the variable values with the probability of finding the species in question. Assuming that the function is uniform from the maxi mal to minimal values of a specific variable, we obtain the projection of the fundamental ecological niche on this variable. A multidimensional fundamental niche corresponds to the intersection of all of these projec tions, that is, to their product. The projection of a fun damental ecological niche may be regarded as a poten tial distribution area of the species. Assuming that the representation function for a specific variable follows a normal distribution with a zero mathematical expec tation and mean square deviation covering the entire amplitude of the domain of species existence, the mul tidimensional niche is described by the speciesdetec tion probability with the parameters of a normal distri bution. The projection of this multidimensional space onto the territory will give the potential distribution area with its internal structure, where a speciesdetec tion probability is assigned to each point of the earth’s surface. If we accept this scheme for solving the prob lem, it is necessary to undertake the following actions: (1) To reduce the dimensionality of the space of external variables; (2) To determine the parameters of species location in the space of external variables with reduced dimen sionality and to calculate their values; BIOLOGY BULLETIN REVIEWS
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(3) To calculate the values of speciesspecific vari ables for the entire space using the multiple regression method; (4) Using the accepted model, to calculate the dis tribution of speciesdetection probability according to each of the variables and their product for the overall multidimensional space; and (5) For elaboration of the effects of climate and relief variables, to find the leading and mutually inde pendent initial variables using statistical criteria insen sitive to nonlinearity and to determine the pattern of their correlation with speciesdetection probability. RESULTS AND DISCUSSION Reducing the Dimensionality of the Space of External Variables In our case, the external variables are the character istics of climate and relief. Because of the different expected patterns of the effect of climate and relief on species distribution, the dimensionality is reduced for them separately. The methods for reducing dimension ality or determining the rank parameters in the context of a particular problem are described in several papers (Puzachenko, 2004; Krenke and Puzachenko, 2008). In this case, the most efficient is the principal compo nent method with space dimensionality determined based on the scree test with subsequent rotation of the obtained components (generalized variables). The first four principal components describe 81% of the varia tion of 104 climate and 14 NDVI variables. The first parameter determines 25.8% (Fig. 1a) of the variation of all climatic variables, and its positive region is first and foremost induced by variation in air humidity, number of days with precipitation, amplitudes of day temperatures for a month, and number of sunlight hours. In this figure, the light tone denotes the territo ries with high humidity, large number of days with pre cipitation, small number of sunny days, and relatively low monthly and interseasonal amplitudes of day tem peratures. Presumably, this generalized variable reflects a continentality of the climate, mainly in winter; the lower the continentality, the higher the variable. The second climatic parameter describes 23.2% of the variation in all variables (Fig. 1b). In this figure, the light tone denotes the territories with relatively high annual mean temperatures; mean temperatures; and number of days with negative temperatures and precipitation in the fall, winter, and spring (October through March). The third climatic parameter (14.8%) is induced by monthly sums of precipitation in May–September (Fig. 1c) and the NDVI for the same months. The light tone here corresponds to the territory with the highest precipitation. Finally, the fourth parameter (16.9%) mainly reflects the mean temperatures of the summer months (Fig. 1d). Thus, the four climate parameters in general reflect the vari ation in humidity and temperature over two seasons of BIOLOGY BULLETIN REVIEWS
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the year. Large values of the first variable correspond to relatively mild conditions with low continentality; the second variable corresponds to sufficient warmth and humidity in winter; the third, to the summer moisten ing regime; and the fourth, to summer temperature conditions. Four parameters account for 70% of the variation in 36 variables describing the relief. The first compo nent of relief (28.7% of the variation in all variables) reflects the structure of its exposure at all hierarchical levels (Fig. 2a). The light tone in this figure denotes the surfaces exposed to the southeast. The second compo nent (22.5%) mainly reflects the surface slope; the light tone shows the territories with relatively steep slopes. The third component (10.1%) is the alterna tion of upland and lowland territories. The fourth component (8.7%) reflects the surface shape, with the light tone corresponding to a convex form. Determining the Parameters of Species Location in the Space of External Variables and Calculating Them For the subset of points with the presence of a spe cies, the principal component method is applied to calculate the principal variables (components) for the independent variables of “environmental” space. Using a “rotation” procedure, we level the contribu tions of speciesspecific factors to the description of variation in all variables, thus bringing them to the maximum onetoone correspondence with the prin cipal environmental variables. Table 1 lists the values of the loads reflecting the maximum correlation of external principal variables with one of the coordinates of speciesspecific subspaces and the constants reflecting the center of projections of specific sub spaces on each of them. The “load” shows the value of the corresponding external variable in determining the position of the species distribution area, and the sign denotes the direction of the speciesspecific variable relative to the external one. The value for the constant is obtained using a regression equation for each exter nal variable on the speciesspecific one. The constant in these equations corresponds to the center of gravity of the projection of the multidimensional region of the distribution area onto the corresponding external vari able. Actually, this procedure determines the species optimum, while the parameters form the basis for a general comparison of the species relations to external variables. According to this estimation, R. amurensis occupies the most continental part of the distribution area, with R. temporaria the least continental part; note that the distribution areas of both species are directed toward the region with a lower continentality. The distribution area of R. arvalis occupies an inter mediate position but is oppositely oriented. The rela tion of these three species to winter conditions is quite evident, and R. amurensis occupies the coldest part of the territory. The requirements of these species in summer precipitation are similar in general, yet the
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(b)
(c)
(d)
Fig. 1. Representation of four generalized principal variables: (a) continentality (the lighter the tone, the lower the continental ity); (b) warmth and humidity in fall, winter, and spring (the lighter the tone, the warmer); (c) summer moistening regime (the lighter the tone, the higher the humidity); and (d) summer temperature (the lighter the tone, the warmer). BIOLOGY BULLETIN REVIEWS
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(a)
(b)
(c)
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Fig. 2. Representation of four generalized relief factors: (a) surface exposure (light tone denotes southeastern exposure); (b) sur face slope (light tone denotes steep slopes); (c) hierarchical relief structure (light tone denotes higher levels); and (d) surface shape (light tone denotes convex shape).
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Table 1. Parameters of the relation of speciesspecific subspaces to principal variables R. arvalis
R. temporaria
R. amurensis
Principal variables (factors) Continentality Heat availability in winter, spring, and fall Summer precipitation Temperature in summer months General exposure Slope Surface hierarchy Surface shape
load
constant
load
constant
load
constant
–0.800 –0.715 –0.557 0.655 0.576 0.728 0.625 0.597
0.808 0.352 0.602 0.412 0.201 –0.569 0.107 –0.025
0.706 –0.757 0.705 0.670 0.728 –0.735 –0.704 0.726
0.965 0.548 0.701 0.147 0.059 –0.634 0.174 –0.026
0.623 –0.850 –0.812 0.835 –0.731 –0.610 –0.732 0.711
–0.476 –0.348 0.888 0.089 0.000 –0.165 –0.352 –0.027
R. temporaria distribution area is directed toward the region of less precipitation. R. arvalis occupies the area with the highest summer temperatures, being more thermophilic according to this parameter, whereas R. amurensis is localized to the region with the lowest temperatures; note that their areas are directed toward the region of high temperature. As for the relief parameters, all species display an affinity for concave relief shapes with minimal slopes; only the R. arvalis distribution area is directed toward steeper slopes. Note that R. amurensis, unlike the other species, prefers wellpronounced lowlands, while the other two species have a propensity for plains and high lands. R. arvalis displays an affinity for southeastern slopes; the centers of the areas of two other species occupy a medium position but are differently oriented. Thus, according to our estimations, the most cold tolerant species is R. amurensis, and the least coldtol erant is R. temporaria. On the other hand, R. arvalis is the most thermophilic relative to summer temperatures. Calculating SpeciesSpecific Variables Table 2 lists the parameters of independent species specific variables for R. arvalis. The optimum for this species with the highest detection probability accord ing to each variable corresponds to the mean value of a parameter, which is by definition zero. The maxima and minima display the boundaries of projection esti mated according to the sample. In the case of a normal distribution, the speciesdetection probability in the boundary regions is close to zero. Under the hypothe sis of a normal distribution, the variation parameters make it possible to estimate the speciesdetection probability as a function of a variable. These species specific variables are unambiguously described using multidimensional regression with the help of environ mental parameters. Using a multidimensional regres sion equation, it is possible to calculate the values of speciesspecific variables for the entire territory. Fi gure 3 shows the distribution for one of the variables for the overall territory and the points of the distribu
tion area. It is evident that the distribution of the vari able over the sample differs significantly from the nor mal one. Normal distribution with a mean square parameter in its righthand part does not include real data, which reflect the rare but actual events with a nonzero probability. All the points of the variable cal culated for the entire territory falling within the range of minimum–maximum values for the sample corre spond to the region where the species is present. Assigning the value of “unity” to this range (signal function) and “zero” to the region beyond it, we obtain the region of species detection (projection of principal niche) on the considered speciesspecific variable (Fig. 4). Since this region is determined according to the sample, there is no guarantee that any points located beyond its boundary do not exist. They are predictable based on the model of distribution for the sample. Unfortunately, these distributions can have the most diverse shapes that are indescribable by any known function. Thus, this uncertainty indicated the assump tion of a normal distribution. When a distribution has no considerable excess or asymmetry, the distribution range is well described by mean square deviation. Oth erwise, onesixth of the variation amplitude can be taken as a mean square value. Figure 4 shows the results of such transformation for the distributions in Fig. 3. Onesixth of the amplitude is taken as a variation parameter for a normal distribution. Despite this, the normal distribution at the boundary of the region of existence (signal function) near the maximum differs from zero by a negligible quantity and, on the contrary, predicts the presence of a species with a probability of 0.08 near the minimum. In this region, a normal dis tribution predicts the presence of a species with a non zero probability beyond the boundary determined by observation data. Undoubtedly, a normal distribution describes well the general patterns in the correlation between species presence and the corresponding external variable; BIOLOGY BULLETIN REVIEWS
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Table 2. Statistical parameters of variables of the R. arvalis subspace determined by the principal component method with rotation relative to the multidimensional space of climate and relief (sample volume, 3497 points of distribution area) Speciesspecific Mean value of parameter variables (factors) Variable 1 Variable 2 Variable 3 Variable 4 Variable 5 Variable 6 Variable 7 Variable 8
–0.000 0.000 0.000 0.000 0.000 –0.000 –0.000 –0.000
Boundaries of projection minimum
maximum
–9.148 –2.799 –3.002 –0.936 –4.176 –4.545 –3.423 –5.567
1.798 4.878 3.420 8.817 4.958 3.179 3.546 1.559
however, uncertainty inevitably exists in the boundary region with rare events. Multidimensional Representation of a Distribution Area Figures 5–7 show the projections of a fundamental niche: the distribution area based on the signal func tion “presence–absence” and the area with an inter nal structure based on the predicted speciesdetection probability. Thus, we obtain two variants for represent ing a distribution area. The areas constructed based on the signal function, including all the points of species detection, interpolate potential species distribution to a significantly larger territory with similar climate and
Variation parameters onesixth of amplitude mean square value 1.824 1.279 1.070 1.626 1.522 1.287 1.161 1.188
relief. The obtained representations can be referred to as a potential distribution area. The corresponding probabilistic models of distribution areas determine these outermost regions according to a very low spe ciesdetection probability and almost complete absence of species. There are also inverse correlations. In particular, the Russian Plain is outside of the suitable territory in the predicted R. amurensis distribution area. However, interpolation using the normal distribution demon strates that this territory is appropriate for the species in regard to a rather high probability. It is rather typical that empty regions determined by species preferences
9000
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8000 1 2
7000
350 300
6000 250 5000 200 4000 150
3000 2000
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50
Data frequency
Frequency of speciesspecific variable
1.041 1.010 1.001 1.006 1.005 1.012 0.978 0.948
0 0 –5.7521 –3.5029 –1.2536 0.9957 3.2449 5.4942 7.7435 0.9927 –4.6275 –2.3782 –0.1290 2.1203 4.3696 6.6188 8.8681
Speciesspecific variable, interpolation Fig. 3. An example of distribution of one of the variables for points of the distribution area: (1) data and (2) as a whole for the territory (interpolation); solid line denotes a normal distribution for the points. BIOLOGY BULLETIN REVIEWS
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Speciesspecific variable, data
5
1.0 0.9
4
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0
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–1
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–4 –6
Probability according to normal distribution and signal function
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0 –4
–2
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20
Speciesspecific variable, interpolation Fig. 4. Projections on a speciesspecific variable: (1) data; (2) normal distribution (realized ecological niche); and (3) signal func tion (fundamental ecological niche).
for certain relief are present within the R. arvalis distri bution area. The probabilistic model predicts a low occurrence for them. Evidently, the structure of the dis tribution area reflects the relief of the territory, thereby demonstrating its effect on both the species distribution and the probability of their detection. The Pattern of Effects of Physical Variables on Species Distribution Analysis of the main parameters of the niche made it possible to assess the differences in the species pref erences for environmental conditions. Having obtained the representation of distribution areas, we can strengthen this analytic component. It is possible to use the intersection of distribution areas estimated, for example, by the Spearman non parametric correlation (Table 3) as a general estimate for the relative position of species in an ecological space, since the Pearson parametric correlation, which does not take into account nonlinear relation ships between distribution areas, gives biased esti mates. It is evident that the distribution areas of Table 3. Intersection of the distribution areas based on the Spearman rank correlation Species R. arvalis R. temporaria R. amurensis
R. arvalis 1.000 0.752 0.538
R. temporaria R. amurensis 0.906 1.000 0.236
–0.002 –0.073 1.000
R. arvalis and R. temporaria are rather similar under any conditions. Similarity in the species relations to climate variables and relief characteristics can be esti mated based on the values of Fisher’s test calculated for each variable relative to discrete gradations of spe ciesdetection probability in a oneway ANOVA. As is evident from Table 4, the relations of all three species to the relief properties are rather similar. The sensitivities of the moor and common frogs to the cli matic variables are similar and differ significantly from that of the Siberian wood frog. Biological production (NDVI) in the summer months has the greatest effect on all three species. This variable corresponds to the third principal compo nent, which reflects the precipitation in summer. However, a direct correlation of the summer precipita tion with species occurrence is less statistically signifi cant, as compared with NDVI. In general, the consid ered species are associated with the territories display ing high NDVI values (Fig. 8). This correlation is especially pronounced for R. amurensis. The characteristic next in significance is the num ber of days with precipitation in November, which reflects the first component: climate continentality (Fig. 9). As is evident from Fig. 9, its effect on R. amu rensis is insignificant, whereas the two remaining spe cies prefer the conditions with precipitation, which is typical of a moderate continental climate. The condi tions of extreme marine and extreme continental cli mates are unfavorable for them. A high correlation of R. amurensis with annual tem perature amplitude is observed; this parameter is associ BIOLOGY BULLETIN REVIEWS
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(a)
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Probability
(b)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.0000 0.0001 0.0003 0.0005 0.0027 0.0133 0.0331 0.0587 0.0916 0.1304 0.1712 0.2171 0.2712 0.3336 0.4030 0.4825 0.5673 0.6602 0.7584 0.8633
Fig. 5. Representation of the R. arvalis distribution area according to (a) signal function and (b) normal distribution: (1) species presence; (2) species absence; and (3) detection points.
ated with the component determining heat availability in winter (Fig. 10). This species occupies the territories with small temperature amplitudes, whereas the other two species prefer medium amplitudes. Note that the boundary for the niches of these two species is very sharp in the region of low temperature amplitudes, ver sus the rather gradual boundary in the region of large amplitudes. The climate variables of the fourth compo nent display statistically significant but not high corre lations with the frog detection probability. The shown plots demonstrate that the relations of R. arvalis and R. temporaria to climate variables are similar within the considered territory, but the toler ance of the former species is higher in all cases. This is in agreement with the fact that the R. arvalis distribu tion area expands farther eastward than that of R. tem poraria. The details of the difference in relations to climate variables can be assessed by comparing their mean val ues for the region with a speciesdetection probability exceeding 0.8 (the optimum region). Figure 11 shows seasonal variation in temperature and precipitation for the optima of the three compared species. It is evident BIOLOGY BULLETIN REVIEWS
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that R. temporaria prefers a warmer winter than R. arvalis but a cooler summer with a large amount of precipitation in the autumn months. R. amurensis, being tolerant to very low winter temperatures, prefers the warmest and most humid summer (July and August). These correlations are rather evident and are shown as an illustration for this variant of analysis. The relief variables correlate with species occur rence in a statistically significant manner, but the sig nificance level in this case is considerably lower as compared with the climate variables. On the other Table 4. Similarity of the species relations to physical vari ables of the environment (Spearman’s coefficient); superdi agonal elements: climate variables; subdiagonal elements: relief variables Species
R. arvalis
R. arvalis R. temporaria R. amurensis
1.000 0.965 0.934
R. temporaria R. amurensis 0.877 1.000 0.904
0.276 0.092 1.000
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Probability 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
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0.0000 0.0001 0.0014 0.0115 0.0299 0.0532 0.0823 0.1184 0.1569 0.2009 0.2542 0.3176 0.3846 0.4610 0.5373 0.6195 0.7184 0.8265
Fig. 6. Representation of the R. temporaria distribution area according to (a) signal function and (b) normal distribution: (1) spe cies presence; (2) species absence; and (3) detection points.
hand, characteristic preferences are distinguishable here. In particular, all the species at the level of very large relief forms (Fig. 12) prefer plain surfaces. R. amurensis and R. temporaria display an affinity for lowlands, whereas R. arvalis prefers somewhat higher altitudes but with minimal slopes. At the same level of relief hierarchy, the two other species prefer small alti tudes with steeper slopes, i.e., with a more pro nounced compartmentalization. Note in addition that R. arvalis prefers convex relief shapes in valleylike depressions with a linear size of about 400 km, whereas the two remaining species prefer plain surfaces at all levels of relief structure. Thus, relief contributes to a certain degree to the differentiation in species distri butions, providing the basis for separation of the R. arvalis and R. temporaria territories. They show a general affinity for uplands and valleys, respectively. The data on ecotopic distribution of the considered species agree in general with the data on the analysis of distribution area. In particular, R. temporaria starts its overwintering somewhat later and ends it and repro duces somewhat earlier than R. arvalis (the difference may reach one week or more), which fits the obtained relation to summer conditions. These data for emer
gence from overwintering and beginning of reproduc tion have been obtained for Belarus (Pikulik, 1985), Karelia (Kutenkov et al., 1990), and Moscow oblast (authors’ data). According to this parameter, R. arvalis is more thermophilic than R. temporaria relative to the conditions of the vegetation period. The latter prefers less acidified aquatic bodies for its reproduction, as compared with R. arvalis (Severtsov et al., 1998). The embryos and larvae of R. temporaria are more sensitive to high water acidity than those of R arvalis. Corre spondingly, the limiting factor for the former is a defi ciency in aquatic bodies in the regions with large swampy areas, such as Western Siberia and the Belarussian Poles’e; it is fewer in number in the regions with large river overflows (Kutenkov, 2009). This factor has not been explicitly reflected in the analysis of the factor nature of the distribution area. Adult R. arvalis are more droughttolerant than R. temporaria (Severtsov et al., 1998), which manifests itself in the relation of these two species to relief. In the south of the distribution area, R. temporaria prefers the most humid sites, in particular, the habitats with underground water outlets (Garanin, 1986; Bakiev and Faizulin, 2002; authors’ data). BIOLOGY BULLETIN REVIEWS
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(a)
1 2 3 @ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
(b)
0.0000 0.0001 0.0011 0.0059 0.0141 0.0256 0.0401 0.0567 0.0748 0.0951 0.1222 0.1587 0.2014 0.2499 0.3126 0.4079 0.5503 0.7201
Fig. 7. Representation of the R. amurensis distribution area according to (a) signal function and (b) normal distribution: (1) spe cies presence; (2) species absence; and (3) detection points.
0.14 0.12
Mean detection probability
0.10
1 2 3
0.08 0.06 0.04 0.02 0 –0.0709 0.0698 0.2105 0.3512 0.4919 0.6325 0.7732 –0.0005 0.1402 0.2808 0.4215 0.5622 0.7029 Biological productivity (NDVI) in July
Fig. 8. Correlation of speciesdetection probability (model of normal distribution) with biological productivity (NDVI): (1) R. arvalis; (2) R. temporaria; and (3) R. amurensis (lines show the trends). BIOLOGY BULLETIN REVIEWS
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Number of days with precipitation in December
0.14 0.12
1 2 3
0.10 0.08 0.06 0.04 0.02 0 0 2.048
4.096 8.192 12.288 16.384 20.480 24.576 6.144 10.240 14.336 18.432 22.528
Mean detection probability Fig. 9. Correlation between speciesdetection probability (model of normal distribution) and the number of days with precipita tion: (1) R. arvalis; (2) R. temporaria; and (3) R. amurensis (lines show the trends).
0.14 1 2 3
Mean detection probability
0.12 0.10 0.08 0.06 0.04 0.02 0 17.40 13.05
26.10 21.75
43.50
34.80 30.45
39.15
52.20 60.90 69.60 47.85 56.55 60.90
Annual temperature amplitude Fig. 10. Correlation between speciesdetection probability (model of normal distribution) and annual temperature amplitude: (1) R. arvalis; (2) R. temporaria; and (3) R. amurensis (lines show the trends).
In the northeast of European Russia, R. temporaria also prefers the most humid types of forest (Anufriev and Bobretsov, 1996). In the Republic of Komi, R. temporaria is numerous in the Ural Mountains and
foothills (Anufriev and Bobretsov, 1996), unlike R. arvalis, which lives in the plain. In the southern part of the distribution area (central and eastern Europe), R. temporaria is more confined to mountain regions BIOLOGY BULLETIN REVIEWS
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100 80 60 40 20
2
3
4
5
6
7
Month
8
9 10 11
700 600 500 400 300 200 100 0 –100 –200 –300
0.012
1 2 3 4 5 6
0.010 0.008 0.006 0.004 0.002
1600
0
209
400
100
40
8
Slope, arbitrary units
120
1 2 3 4 5 6
Altitude, m
25 20 15 10 5 0 –5 –10 –15 –20 –25 –30
Precipitation, mm
Temperature, °C
QUANTITATIVE ESTIMATION OF DISTRIBUTION AREA PARAMETERS
0
Hierarchical levels in relief organization
Fig. 11. Seasonal temperature and precipitation variation for the optima of three compared species. Temperature: (1) R. amurensis; (2) R. temporaria; and (3) R. arvalis. Pre cipitation: (4) R. amurensis; (5) R. temporaria; and (6) R. arvalis.
Fig. 12. The altitudes and slopes preferred by three frog species for five hierarchical levels of relief organization at a detection probability >0.8. Altitude: (1) R. amurensis; (2) R. temporaria; and (3) R. arvalis. Slope: (4) R. amuren sis; (5) R. temporaria; and (6) R. arvalis.
and lives exclusively in the mountains in the southern most part (Grossenbacher, 1997). In general, these facts comply with the preference of this species for sur faces with somewhat steeper slopes and correspond ingly more compartmentalized relief. Certainly, by no means should one expect that relations to environ mental conditions determined based on analysis of the overall distribution area will explain the distribution and abundance of a species at the habitat level. At this level, physiological, biochemical, and behavioral adaptations can significantly differ from the norm for the species as a whole.
statistical method, since the relation of the multidi mensional subspace of a characteristic to the entire multidimensional space of the environment is strictly determined, and the detection probability is intro duced based on a model of tabulated normal distribu tion. This specific feature of the method determines its limitations. For example, in order to avoid the estimate bias caused by the finiteness of the considered territory, it is optimal to analyze the whole potential distribution area or a considerable part of it. Otherwise, it is neces sary to strictly correlate the detected relations with a particular territory involved in the analysis. Naturally, it is desirable to have at least 10 documented points for the studied characteristic, keeping in mind that the envi ronmental conditions in the case of such a limited sam ple may be unique, and this uniqueness may have no physical meaning in the determination of characteristic distribution over the territory. Nevertheless, despite all of these limitations, we believe that the proposed method will be a useful tool in a capable researcher’s hands.
CONCLUSIONS The geography of many properties of animals and plants is presented or presentable in a form similar to point distribution areas. Biogeographic analysis makes it possible to find their correlation with environmental conditions. These correlations may be both functional and formal in nature, but biogeographic analysis is unable to prove which of the obtained correlations are determined by physical cause–effect relations. This analysis can only give certain grounds for formulating the corresponding hypotheses, the testing of which belongs to another field of research. Biogeographic analysis of a point distribution area, by reducing the uncertainty region for the inferences on relations of a studied characteristic with the environment, has tradi tionally been an important methodological technique in a wide range of studies. The proposed method allows the correlation between the presence of a char acteristic and the environment to be quantified and, on this basis, the distribution area of this characteristic to be interpolated to the territory as a whole. Although this method uses statistical analysis tools (principal component method), strictly speaking, this is not a BIOLOGY BULLETIN REVIEWS
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REFERENCES Anufriev, V.M. and Bobretsov, A.V., Fauna evropeiskogo severovostoka Rossii (The Fauna of the NorthEast European Russia), Vol. 4: Amfibii i reptilii (Amphibians and Reptiles), St. Petersburg: Nauka, 1996. Bakiev, A.G. and Faizulin, A.I., Zemnovodnye i presmykay ushchiesya Samarskoi oblasti (Amphibians and Reptiles of the Samara Oblast), Samara: IEVB RAN, 2002. Engelhard, G.H., Dieckmann, U., and Godo, O.R., Age at Maturation Predicted from Routine Scale Measure ments in Norwegian SpringSpawning Herring (Clupea harengus) using Discriminant and Neural Network Analyses, ICES J. Mar. Sci., 2003, no. 60, pp. 304–31. Garanin, V.I., Some Patterns of Ecological Differentiation of Amphibians and Reptiles of Eastern Europe, in
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PUZACHENKO et al.
Prirodnye resursy VolzhskoKamskogo kraya (Natural Resources of the VolgaKama Region), Kazan: Izd. Kazan. Univ., 1968, pp. 113–120. Grinnel, J., The NicheRelationships of the California Thrasher, Foundation of Ecology, Chicago: The Univ. of Chicago Press, 1991, pp. 118–125. Grossenbacher, K., Rana temporaria Linnaeus, 1758, in Atlas of Amphibians and Reptiles in Europe, Gasc, J.P., Cabela, A., CernobrnjaIsailovic, J., et al., Eds., Paris., 1997, pp. 158–159. Hirzel, A.H., Hausser, J., Chesser, D., and Perrin, N., Eco logicalNiche Factor Analysis: How to Compute Habi tatSuitability Maps without Absence Data?, Ecology, 2002, vol. 83, no. 7, pp. 2027–2036. Hutchinson, G.E., Concluding Remarks, Cold Spring Har bor Symposium on Quantitative Biology “Population Studies: Animal Ecology and Demography”, 1957, vol. 22, pp. 415–427. Kotlov, I.P., and Puzachenko, Yu.G., Struktura rel’efa Russkoi ravniny kak landshaftoobrazuyushchego faktora (The Structure of the Topography of the Russian Plain as a LandscapeForming Factor), in Landshaftnoe planirovanie. Obshchie osnovaniya. Metodologiya. Tekh nologiya (Landscape Planning. Common Ground. Methodology. Technology), Moscow: Izd. Mosk. Gos. Univ., 2006, pp. 166–172. Krenke, A.N. and Puzachenko, Yu.G., Building a Map of the Land Cover Based on Remote Sensing Data, Ekol. Planir. Upravl., 2008, no. 7, pp. 26–37. Kucheruk, V.V., General Patterns of the Distribution and Types of Ranges of Gerbils, in Ekologiya i meditsinskoe znachenie peschanok fauny SSSR (Ecology and Medical Significance of Gerbils of the USSR), Moscow: Vse soyuz. Teriol. Obshch. 1977, pp. 58–63. Kutenkov, A.P., Panarin, A.E., and Shklyarevich, F.N., Ecology of Breeding of Anurans in Karelia and the Kola Peninsula, in Nazemnye pozvonochnye zhivotnye v zapovednikakh severa evropeiskoi chasti RSFSR (Terres trial Vertebrate Animals in Nature Reserves of the North of the European Part of RSFSR), Moscow: TsNIL Glavokhota, 1990, pp. 54–70. Kutenkov, A.P., Ekologiya travyanoi lyagushki (Rana tempo raria L., 1758) na SeveroZapade Rossii (Ecology of the Grass Frog (Rana temporaria L., 1758) in Northwestern Russia), Petrozavodsk: Izd. Petrozav. Univ., 2009. Manel, S., Dias, J.M., and Ormerod, S.J., Comparing Dis criminant Analysis, Neural Networks and Logistic Regression for Predicting Species Distributions: A Case Study with a Himalayan River Bird, Ecol. Modell., 1999, vol. 120, nos. 2–3, pp. 337–347. Manel, S., Williams, H.C., and Ormerod, S.J., Evaluating PresenceAbsence Models in Ecology: The Need to Account for Prevalence, J. Applied Ecol., 2001, vol. 38, no. 5, pp. 921–931. McPherson, J.M., Jetz, W., and Rogers, D.J., The Effects of Species’ Range Sizes on the Accuracy of Distribution Models: Ecological Phenomenon or Statistical Arte fact?, J. Applied Ecol., 2004, vol. 41, no. 5, pp. 811– 823. Peterson, A.T., Ecologic Niche Modeling and Spatial Pat terns of Disease Transmission, Emerg. Infect. Dis., 2006, vol. 12, no. 12, pp. 1822–1826.
Pikulik, M.M., Zemnovodnye Belorussii (Amphibians of Belarus), Minsk: Nauka i tekhnika, 1985. Puzachenko, Yu.G., Matematicheskie metody v ekolog icheskikh i geograficheskikh issledovaniyakh (Mathe matical Methods in Ecological and Geographical Stu dies), Moscow: Academia, 2004. Puzachenko, Yu.G., Zheltukhin, A.S., and Sandlerskii, R.B., Analyzing SpatialTemporal Dynam ics of the Ecological Niche: A Marten (Martes martes) Population Case Study, Zh. Obshch. Biol., 2010, vol. 71, no. 6, pp. 467–487. Severtsov, A.S., Lyapkov, S.M., and Surova, G.S., The Cor relation of the Ecological Niches of the Common (Rana temporaria L.) and of the Moor (Rana arvalis Nilss.) Frogs (Anura, Amphibia), Zh. Obshch. Biol., 1998, vol. 59, no. 3, pp. 279–301. Stockwell, D.R.B., et al., The Use of the GARP Genetic Algorithm and Internet Grid Computing in the Lifemapper World Atlas of Species Biodiversity, Ecol. Modeling, 2006, vol. 195, issues 1–2, pp. 139–145. Tolmachev, A.I., Osnovy ucheniya ob arealakh (Fundamen tals of the Theory of Ranges), Leningrad: Izd. Len. Gos. Univ., 1962. Tupikova, N.V., Experience of Creation of the Map of the Population of Rodents (Rodentia) and Pikas (Ochotona) of the Territory in the Former USSR: The Content and Principles of Construction of the Legend, Usp. Sovrem. Biol., 1996, vol. 116, no. 2, pp. 243–254. Tupikova, N.V., Varshavskii, A.A., and Khlyap, L.A., Map and Geographic Information System: “The Population of Rodents and Pikas in the South of the Former USSR,” in Aridnye ekosistemy (Arid Ecosystems), Moscow, 1998, vol. 4, no. 8, pp. 74–84. Tupikova, N.V., Khlyap, L.A., and Varshavskii, A.A., Rodents of Fields of the Northeastern Palaearctic, Zool. Zh., 2000, vol. 79, no. 4, pp. 480–494. Zemnovodnye SSSR. ®0229803415. Gosudarstvennyi registr baz dannykh RF (Amphibians of the USSR. ®0229803415. State Register of Databases of RF), Compiled by Kuzmin, S.L.
INTERNET RESOURCES BIOCLIM project. 2009. http://www.andra.fr/bioclim/ BioGeomancer Working. 2007. http://classic.biogeo mancer.org/ DIVAGIS. 2009. http://www.divagis.org Georeferencing Software for Natural History Collections “GEOLocate”. 2009. http://www.museum.tulane.edu/ geolocate/ GLCF. Global Inventory Modeling and Mapping Studies. 2009. http://ftp.glcf.umd.edu/data/gimms/ Tulane University Museum of Natural History. GEO Locate. A Platform for Georeferencing Natural History Collections Data. 2009. http://www.museum.tulane.edu/ geolocate/default.html WhyWhere 2.0: The Portal of the new WhyWhere 2.0. http://landshape.org/enm/whywhere20server2/ Wordclim. Global Climate Data. 2009. www.worldclim. org/current BIOLOGY BULLETIN REVIEWS
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