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Methods for comparison of biotic regionalizations: the case of
pteridophytes in the Iberian Peninsula
Ana L. Marquez, Raimundo Real and J. Mario Vargas
Marquez, A. L., Real, R. and Vargas, J. M. 2001. Methods for comparison of bioticregionalizations: the case of pteridophytes in the Iberian Peninsula. – Ecography 24:659–670.
We made several regionalizations of the Iberian Peninsula based on the distributionsof the pteridophyte flora to see whether the regionalization depended on the type andscale of lattice or the similarity index considered. We used five types of lattice inwhich the scale also varied: river basins, mountains and plains, natural regions,physiographic and geological regions, and administrative provinces; and two similar-ity indices: those of Jaccard and of Baroni-Urbani and Buser. The regionalizationsvaried according to the type of lattice, the grain size, and the similarity index used.To assess the different regionalizations we used four methods: 1) the coefficient of variation of the size of sites in each lattice, 2) the bestblock method, which considersas the best lattice that which maximizes the number of matches between presencesover all pairwise site comparisons, 3) the Mantel test, to assess the statisticalsignificance of the regionalizations obtained, and 4) mapability, which considers themost contiguous regionalization to be the best. The best regionalization according toour four criteria was that based on administrative provinces and Jaccard’s index. Thisyielded a small central region and three large regions: northern, western, and eastern.
A. L. Marquez ( [email protected] ) , R. Real and J . M . Vargas, Dept de BiologıaAnimal , Fac. de Ciencias, Uni 6. de Malaga, E -29071 Malaga, Spain.
A major objective of descriptive biogeography is to
simplify the complex patterns of contemporary species’
distributions by classifying areas based on their biotic
composition. That areas of the world can be character-
ized on the basis of the presence of certain taxa and the
absence of others has long been recognised by biogeo-graphers (Buffon 1761), and is a deeply entrenched
component of much contemporary biogeographical
thinking. In addition, classifying geographical areas
into groups with different species composition is valu-
able for nature conservation planning (Brown et al.
1993), so as to ensure that all groups are represented in
the selection of natural reserves (Margules 1986), and
to evaluate the biological resources of an area in a
regional and global context (Carey et al. 1995). How-
ever, currently administrators are often confused by the
number of different classifications of their country pro-
posed by ecologists and phytogeographers. In addition,
as Thaler and Plowright (1973) pointed out, phytogeo-
graphers have disagreed about whether floristic areas
represent real entities in nature or whether they are
simply convenient, subjective constructs that lack any
objective and unambiguous basis.
Operationally, it is possible to identify bioticboundaries when a group of areas with similar biota
shares fewer species than expected at random with
other group of areas with similar biota. Then the
Operational Geographic Units (OGUs; Crovello 1981)
of this territory can be grouped into biotic regions
(Real et al. 1992a, Myklestad and Birks 1993,
McLaughlin 1994). Clustering methods represent one
approach to this problem (Birks 1987, Legendre 1990),
but only when a probabilistic procedure allows the
researcher to distinguish between statistically significant
clusters and those indistinguishable from random ex-
pectation (Marquez et al. 1997). Area clusters may be
Table 1. Statistically significant boundaries between groups of OGUs formed by UPGMA using the Jaccard similarity index.DW\0 and significant GW indicate weak boundary between the groups; DS\0 and significant GS indicate a strong boundarybetween the groups. N.S.: p\0.05; *: pB0.05; **: pB0.01; ***: pB0.005.
Table 2. Statistical significant boundaries between groups of OGUs formed by UPGMA using the Baroni-Urbani and Buser
similarity index. DW\0 and significant GW indicate weak boundary between the groups; DS\0 and significant GS indicatea strong boundary between the groups. N.S.: p\0.05; *: pB0.05; **: pB0.01; ***: pB0.005.
Groups set up by Biotic boundaryUPGMA
StrongWeak
Group Group DW DW DW GW p DS GS pA B (A×A) (B×B)
River basins 3 –5 9 –8 0.116 0.116 0.116 6.98 ** −0.591 0 N.SMou ntains and p lain s 2 –4 1 –5 0.307 0.307 0.307 24.015 *** −0.400 0 N.SNatural regions 6 –14 5 –11 0.114 0.114 N.S.0.114 22.100 *** −0.593 0Physiographical regions 7 –14 4 –2 0.140 0.147 N.S.0.144 43.864 *** −0.551 0.007Administrative 16 –12 27 0.513 – 0.575 94.044 *** 0.089 28.972 N.S.
Table 3. Results of the application of the four criteria used to determine which is the best regionalization. CV: Coef ficient of variation of the OGUs’ size; TM: Total matches between presences in all pair-wise comparisons; SQ: Number of squares 50×50km necessary to join together each fragmented region.
Mantel testOGU Systems Coef ficient Best Mapabilityblockof variation
JaccardJaccard Baroni-Urbani Baroni-Urbaniand Buser and Buser
Fig. 2. Dendrograms andbiotic regions forpteridophytes in the IberianPeninsula using the Jaccardsimilarity index on eachlattice considered. Numbers of the units as in Fig. 1. W:weak boundary; S: strongboundary; *: pB0.05;**: pB0.01; ***: pB0.005.
those characteristics, which are inseparable from the
pattern obtained. This is especially true given the ex-
ploratory nature of current approaches to biotic re-
gionalization (Carey et al. 1995). However, the
biogeographic regions and boundaries are useful for
understanding the mechanisms underlying the distribu-tion of organisms, provided that each regionalization
reflects a distribution pattern that is statistically signifi-
cant and may be related to environmental conditions,
although detected through the filters of the OGUs, the
scale of grain, and the similarity index.
The indices of similarity
Oden et al. (1993) modified the method of Womble
(1951) to detect intervals of marked change in categori-
cal variables between contiguous sites. When the vari-
Fig. 3. Dendrograms and bioticregions for pteridophytes in theIberian Peninsula using theBaroni-Urbani and Busersimilarity index on each latticeconsidered. Numbers of theunits as in Fig. 1. W: weakboundary; S: strong boundary;*: pB0.05; **: pB0.01;***: pB0.005.
We used two criteria prior to the classification proce-
dure, and two criteria after the classification. The co-
ef ficient of variation (Sokal and Rohlf 1981) indicated
that the size of each OGU in the provinces is more
similar than in the other lattices and is thus to be
preferred independently of the distribution data. The
‘‘bestblock’’ method (Phipps 1975) showed that admin-
istrative provinces provide the best lattice for establish-ing the biotic boundaries of the Iberian Peninsula
according to its pteridoflora (Table 3), because the finer
scale of the partition produced more units, and because
the presences are more equitably distributed through
the OGUs, thus producing more matches of presences
in pairwise comparisons. The regionalization obtained
using provinces and the Jaccard index was one of five
regionalizations that were suitable according to both
the Mantel test and the mapability criterion, because it
had the highest statistical significance and was totally
mapable. Mantel and mapability tests were appliedto the final regionalization patterns, and showed
whether the patterns were in accordance with the origi-
nal similarities between OGUs and with the within-
region continuity recommendable for a biotic region,
respectively.
The higher number of units in the provinces lattice is
not the only cause of this partitioning being selected.
These four criteria are not biased towards partitionings
with a large number of units nor more isodiametrically-
shaped units. The coef ficient of variation selects a parti-
tioning of more equal-sized units, but not more circular
in shape, and irrespective of the number of units. The
Phipps algorithm not always chooses the partitioning
with the greatest number of units (see Phipps 1975).
Although the provinces lattice has more units it is notmore likely to produce statistically significant results
after using Mantel’s test, and, in fact, the partitioning
obtained using provinces has the same high significance
level than other partitionings. As regards the criterion
of mapability, a partitioning based on more units is
more likely to produce fragmented regions, although
this is not the case for provinces when using Jaccard’s
index.
Administrative provinces as operational geographicunits
In the Iberian Peninsula, provinces provide the latticethat yields the most appropriate regionalization accord-
ing to our four statistical criteria when using Jaccard’s
index, and is thus the regionalization to be preferred in
attempting to identify the biogeographical processes
affecting the distribution of pteridophytes. One reason
for this may be that provinces are administrative units
of ancient origin and are not completely arbitrary. This
is likely to be true elsewhere, at least in Europe, where
administrative units are partially based on natural par-
titions perceived by local people, as is the case, for
example, with vice-counties in the British Isles (Baroni-
Urbani and Collingwood 1976).
Different types of arbitrary areas within a study
region can be used, such as countries, counties,provinces, river basins, latitude/longitude blocks, or
equal size U.T.M. squares (Birks 1987). In the last
decade regular geographical units, like networks of
regular squares, have been commonly used (e.g. Mart ın
and Gurrea 1990, Lausini and Nimis 1991, Myklestad
and Birks 1993, Carey et al. 1995, Moreno-Saiz et al.
1998). However, regular squares have artificial borders
and, therefore, may include several fragments of differ-
ent geographic or environmental units, so hindering the
search for biogeographical processes that may only act
on natural units (Palomo and Antunez 1992). The
division in provinces is also arbitrary, but the adminis-
trative borders between provinces follow, in part, natu-
ral boundaries such as geographical ranges, so that theymay be more appropriate to assess the environmental
explanations for species distributions. In addition,
provinces may be a suitable type of OGU for analysing
human influence on natural distributions, because in
most countries human activities follow political-admin-
istrative borders.
Acknowledgements – We thank H. J. B. Birks, S. P. McLaugl-hin and P. L. Nimis for revisions of the manuscript and theirvaluable suggestions. We are also grateful to M. A. Rendon, J.C. Guerrero and J. Olivero for their help with the statisticalprocedures.
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Appendix 1. Calculation of parameters used to test theexistence of significant biotic boundaries.
For each dendrogram node we established a submatrix of significant similarities that only included the two groups of
OGUs separated by that node, which we named group A andgroup B, respectively. This submatrix was divided into threezones: zone A×A and zone B×B, which corresponded to thesignificant similarities between OGUs of group A and betweenOGUs of group B, respectively; and zone A×B, correspond-ing to the significant similarities between the two groups of OGUs.
We call Pp(A×A) the number of pluses within zone A×Adivided by the total number of pairwise OGU comparisons inzone A×A. So, Pp(A×A) is the proportion of pluses in zoneA×A. We call Psp(A×A) the number of OGUs in group Athat have at least one plus divided by the total number of OGUs in group A. We can then compute d1(A×A) asfollows: if the number of pluses in A×A is zero, then d1(A×A)=0; otherwise,
d1(A×A)=Pp(A×A)×Psp(A×A)
(Pp(A×A))2
+(Psp(A×A))2
The values of d1(A×A) range from 0 to 0.707, estimating towhat extent similarities higher than expected at random (+)predominate within zone A×A.
We define Pm(A×A) and Psm(A×A) as the proportion of minuses in zone A×A and the proportion of OGUs in groupA with at least one minus, respectively, and these are com-puted in the same way as Pp(A×A) and Psp(A×A), buttaking into account the minuses. We then define d2(A×A) inthe following way: if the number of minuses in zone A×A iszero, then d2(A×A)=0; otherwise,
d2(A×A)=Pm(A×A)×Psm(A×A)
(Pm(A×A))2+(Psm(A×A))2
The values of d2(A×A) range from 0 to 0.707, estimating to
what extent similarities lower than expected at random (−)predominate within zone A×A. We d efine Pp(A×B) andPsp(A×B) in a similar way to Pp(A×A) and Psp(A×A),but with reference to zone A×B. So, d3 is zero when thenumber of pluses in A×B is zero; otherwise,
The values of d3 range from 0 to 0.707, estimating to whatextent similarities higher than expected at random (+) pre-dominate within zone A×B.
The parameter DW(A×A) measures to what extent thesimilarities that are higher than expected (+) tend to be inzones A×A but not in A×B (see McCoy et al. 1986), whereDW(A×A)=d1(A×A)−d2(A×A)−d3.
Similarly, DW(B×B)=d1(B×B)−d2(B×B)−d3, whered1(B×B) and d2(B×B) are calculated as d1(A×A) andd2(A×A), but computing the pluses and minuses in zoneB×B. The average of DW(A×A) and DW(B×B), named
DW, measures to what extent similarities that are higher thanexpected (+) tend to be in either zones A×A o r B×B butnot in A×B.
We define d4 in the same way as d3, but compute theminuses in A×B. We then compute the parameter DS=d4−d3−d2(A×A)−d2(B×B), which gives a measure o f whether the similarities that are lower than expected (−) tendto be located in A×B, but not in A×A or B×B.
The statistical significance of a node was assessed using aG-test of independence (Sokal and Rohlf 1981, McCoy et al.1986) of the distribution of the signs ‘‘+’’, ‘‘−’’ and ‘‘0’’ inthe three zones of the submatrix, and so we obtained theparameters GW, for weak boundaries, and GS, for strongboundaries. If similarities higher than expected (+) tendsignificantly to be in zones A×A or B×B, but not in A×B,that is, if DW\0 and GW is statistically significant, thenthere is at least a weak biotic boundary between both groupsof OGUs. In this case, if DW(A×A)\0 then the group of OGUs A constitutes a biotic region, and the same applies forDW(B×B) and the group of OGUs B, because then a groupof OGUs with similar biota shares a number of species com-patible with random expectation with another group of OGUsthat also has a similar biota. If similarities significantly lower
than expected (−) tend to be located in A×B, but not inA×A or B×B, that is, if DS\0 and GS is significant, thena strong biotic boundary exists between the groups of OGUs.In this case a group of OGUs shares fewer species thanexpected at random with another group of OGUs. The areasdelimited by strong boundaries are biotic supraregions. Asupraregion can consist of several biotic regions separated byweak boundaries.