According to the studies of Hörandl et al. (2005), the section Batrachium comprises a clade of approximately 30 species that are part of yellow-flowered terrestrial and semi-aquatic Ranunculus species. Therefore, Batrachium is not considered here as a subgenus, but as a section within the genus Ranunculus. All species of the section Batrachium are characterized by a strong phenotypic variability depending on environmental factors and seasonal conditions. The species are generally fertile. Sterility and incomplete development of pedicels, petals and fruits indicate hybridization, but can also be caused by unfavourable environmental conditions. Hybridization and introgression are widespread, especially among the most common species R. peltatus, R. fluitans or R. trichophyllus hybridization is apparently frequent. Primary hybrids are often difficult to distinguish from their parental species due to the great morphological variability of the latter. Sterile clones can survive alongside fertile forms. Apomicts have not yet been documented in Batrachium, although Cook (1966) discussed this possibility. In addition to phenotypic variability and hybridization, the temporary persistence of epimutations, caused by changing selection pressure due to changing anthropogenic influences on the waters, might also play a role.

The species concept applied here is taxonomically conservative and aims at morphologically definable units. These are indispensable for practical purposes (nature conservation, water protection). These "morphospecies" can be genetically heterogeneous and form special regional morphotypes. Similarly, minor deviations in DNA content or the absence of individual chromosomes (aneuploidy) are of little importance as long as the phenotype does not deviate greatly. The species delimitation used here is based in particular on the work of Cook (1966, 1986) and Pizarro (1995). With a few exceptions (R. penicillatus, R. trichophyllus and R. peltatus), Cook (1966, 1986) eliminated all subspecific ranks, especially the varieties and forms that had been described in the course of the 19th and early 20th centuries. This concept has largely become established in Europe, except in Scandinavia (see Hong 1991, Dahlgren & Jonsell 2001). Current treatments in neighboring countries (Switzerland: Desfayes 2016; Austria: Englmaier 2016; Czech Republic: Koutečky et al. 2021) correspond to this approach.

Wiegleb et al. 2017 applied Cook's concept worldwide, whereby all subspecific ranks were either raised to species-level or eliminated, depending on whether they are morphologically distinct or not. Some non-European species that had been united with European species by Cook (1966) were split again due to their obvious morphological distinctness. This standardization was necessary because divergent concepts had developed, particularly in China (Wang & Tamura 2001) and North America (Whittemore 1997). The use of Russian work (Tsvelev 1998; Luferov 2002) was particularly helpful here. The work of Prančl et al. (2018; Czech Republic) follows a slightly different delimitation of species. There, "cryptic" species or lineages are distinguished within the traditional species.

While the description of hybrids has a long tradition in Great Britain and France (see Lansdown 2007, 2015), they have only been occasionally recognized in Germany since around 1970 (Vollrath & Kohler 1972, Wiegleb & Herr 1983). Here, mainly hybrids whose identification is possible without genetic or cytological data are listed. The occurrence of rare hybrids such as R. trichophyllus × R. rionii, R. baudotii × R. aquatilis = R. ×lamberti A. Félix, R. baudotii × R. peltatus and R. baudotii × R. trichophyllus = R. ×segretii A. Félix is likely, but unconfirmed. The taxonomic and nomenclatural treatment of the hybrids is not yet consistent in the current identification keys (Wiegleb et al. 2017, Wiegleb 2020, 2021), since binary name for some hybrids are lacking or their description is insufficient or the hybrid origin is questionable.

In the treatment used here the hybridogenic species R. penicillatus also includes the primary hybrids of R. fluitans × R. peltatus because a morphological differentiation is impossible. The hybrid or introgression swarm of R. peltatus × R. penicillatus also formally belongs to this group. This form is common and also rather easily to determine. (Nomenclatural note: The correct name for this species is probably R. pseudofluitans (Syme) Newbould, as Webster (1988) incorrectly assigned type specimens).

In the present circumscription the hybridogenic species R. pseudofluitans also includes the primary hybrids of R. fluitans × R. circinatus because morphological differentiation is also not possible. (Nomenclatural note: This species probably has no valid name, although it was accurately described by Vollrath & Kohler (1972)).

The hybrids of R. fluitans × R. trichophyllus representing a similar hybrid swarm, are not treated as a species complex. There is great morphological overlap with the two aforementioned species preventing unambiguous delimitation. (Nomenclatural note: The correct name for this species is probably R. calcareus Butcher, but this has also been used for R. pseudofluitans. The sometimes used name R. ×bachii Wirtgen probably refers to R. fluitans × R. baudotii and is also used for the hybrid R. fluitans × R. aquatilis (see Wiegleb 2020). For this reason, the hybrids between R. fluitans, R. trichophyllus, R. baudotii and R. aquatilis are summarized here as "R. fluitans hybrids" until clarification is provided).

R. baudotii and R. aquatilis are also hybridogenic complex species in which R. fluitans, R. trichophyllus and R. peltatus are primarily involved. The morphological separation of common hybrids such as R. peltatus × R. trichophyllus or R. peltatus × R. aquatilis is ambigous.

A total of 30 species have been distinguished worldwide within section Batrachium (Wiegleb et al. 2017). Species number is probably underestimated, as other clearly defined species (R. fucoides, R. lutarius, R. pachycaulon) were still insufficiently known at the time of publication. Both the South American and New Zealand forms represent previously undescribed species. Further taxa can be suspected in Ethiopia, Tibet and Northeast Asia.

The most widespread species is R. trichophyllus, which is distributed almost worldwide (subcosmopolitan), but is divided into insufficiently separated morpho- and karyotypes. Other species such as R. ashibetsuensis, R. bungei, R. confervoides, R. flavidus, R. kadzusensis, R. lobbii, R. nipponicus, R. porteri, R. schmalhausenii, R. tripartitus and R. vertumnus only occur in a limited area. Western Europe is the focus of species diversity with 18 species. High numbers of species are found in Eastern Europe (11), North Africa (10) and Western (9) and Central Asia (8). Similarly high species numbers are recorded from northern China, the Pacific coast of Russia and the west coast of North America. High species diversity is typical for oceanic and sub-oceanic climate regions. In Germany, 12 species have been recorded with certainty. Europe and the Mediterranean region comprise 22 species.

The evaluation of previous phylogenetic studies suggests (Wiegleb et al. 2017) that the section Batrachium consists of three clades (Zalewska-Gałocz et al. 2015, Wiegleb et al. 2017, Koutečky et al. 2021):
Clade 1 consists of small amphibious species that often do not form submerged leaves but floating leaves only. In the area, these include R. hederaceus and R. ololeucos.
Clade 2 comprises both floating-leaved and submerged species and represents the majority of species in the area: R. peltatus, R. fluitans, R. baudotii, R. saniculifolius, R. penicillatus, R. pseudofluitans, R. trichophyllus and R. aquatilis.
Clade 3 consists of species without floating leaves with short, mostly squarrose spreading leaves. In the area these include R. circinatus and R. rionii.

The chromosome base number is 2n = 16 in all clades (R. hederaceus, R. fluitans, R. saniculifolius, R. circinatus, R. rionii). The species of clades 1 and 3 are less frequently involved in hybridizations. Especially in clade 2 polyploid complexes have arisen due to auto- and allopolypoidization. These have chromosome numbers of 2n = 32 or 48 (R. peltatus, R. baudotii, R. penicillatus, R. pseudofluitans, R. trichophyllus, R. aquatilis). Crossing barriers between these species are only weakly developed. Chromosome numbers of 2n = 24 or 40 are usually an indication of hybridization, thus the differentiation of subgroups within clade 2 has been avoided. In R. fluitans, triploid forms (2n = 24) have been reliably detected in addition to diploid 2n = 16 (see Wiegleb et al. 2017).

In the auxiliary tables (Wiegleb 2018), morphological species groups that are directly recognizable in the field are used instead of the abovementioned clades. Group 1: Small amphibious species (usually only with flat leaves); Group 2: Large species of flowing waters, often without floating leaves; Group 3: Predominantly medium-sized species with regularly formed floating leaves; Group 4: Predominantly small to medium-sized species without floating leaves.

As typical for aquatic plants, the occurrence of Batrachium species is influenced by a variety of environmental factors. The most important factors are light and inorganic carbon. Nitrogen and phosphorus (trophic level) play a lesser role, especially in flowing waters. Other factors include salinity (chloride or sulphate content), mechanical stress from currents or waves and temperature. Remarkably, species are separated by the availability of hydrogen carbonate (hard water and soft water; Table 1). This corresponds to the ecophysiology of the species, which can either assimilate hydrogen carbonate (e.g. R. trichophyllus) or not. Possibly, these species have special adaptations that enable them to survive without floating leaves at low bicarbonate concentrations.

(XXX − main occurrence, XX − occurrence with indifferent species, X − occasional occurrence)

Anthropogenic influences play a major role in the distribution of Batrachium species. The eutrophication of still waters and the associated algae growth have a negative impact. However, eutrophication plays only a minor role in running waters. In the lowlands, decoupling of rivers from groundwater inflow, deepening of the flood channel and terrain adjustments lead to changes in drainage and temperature regime. Thus, either potamalization or rhitralization can be observed (see Weyer 2017). Discharge of dissolved substances from the catchment area, especially iron ochre, leads to water turbidity. Whether these changes affect the occurrence of Batrachium species depends largely on their growth form. Increased shading usually has no influence on the species composition, but rather on the biomass. In the low mountain ranges, canalization or dam construction can even positively affect the occurrences of flowing water species due to the regulation of drainage and the avoidance of flood peaks. Pond and river management may also contribute to the spread of species. Optimal growing conditions for Batrachium species are not necessarily found in near-natural waters.

The section Batrachium includes aquatic or amphibious herbaceous plants with white or yellow-white flowers. As in general in aquatic plants, growth form represents an important character (see Weyer & Schmitt 2011), mirroring ecological conditions, as it directly influences gas exchange and nutrient uptake. Batrachium comprises three growth forms, the nymphaeid (floating leaves only), the batrachid (floating and submerged leaves) and the myriophyllid growth form (submerged leaves only) (Weyer & Schmidt 2011). Some species only develop one growth form only, others can be observed in all three growth forms (Table 2). The growth forms in combination with life form and plant size are suitable characters for pre-sorting the species into morphological groups. The present identification keys (Wiegleb et al. 2017, Wiegleb 2020, 2021) and auxiliary tables (Wiegleb 2018) largely follow this principle.

(XXX − main growth form, XX − frequent growth form, X − rarely developed growth form; (in brackets) − flat leaves, not floating
* probably only in the eastern Mediterranean distribution area, absent in Germany
** some forms have submerged leaves morphologically very similar to floating leaves

Some of the aquatic Batrachium species can also develop land forms with either flat and finely dissected leaves (R. aquatilis, R. peltatus) or finely dissected, often rigid leaves (R. circinatus, R. trichophyllus). In most cases these land forms cannot be identified, even if flowers and fruits are present. Flower characters can differ greatly from those of the aquatic forms. Only if aquatic forms grow in the immediate vicinity a reliable identification is possible.

Aquatic plants should be sampled according to the methods developed by K. van de Weyer (e.g. Weyer 2017), regardless of whether sampling is intended for floristic or ecological purposes. In shallow waters (up to 0.8 m), sampling can be carried out from the shore or by wading through the water. It is important to check whether populations are homogeneous and comprise several growth forms. Waters up to 4 m deep should be sampled with an extendable rake. Narrow flowing waters should be sampled from both sides, small still waters should be walked around. Larger shallow waters should be sampled by boat. Deeper waters (lakes, large flowing waters) should be sampled by diving. Collecting drifted parts of plants from the shore can only be regarded as a compromise, as these may exhibit an atypical morphology and their origin remains uncertain.

Herbarium specimens (size A3) of all plants collected are mandatory since data without vouchers remain generally questionable. The specimens must be prepared with all diagnostic characters are easily visible. Larger specimens should be folded inwards and, if necessary, divided and placed on several sheets. Locality, habitat, date o collection and collector’s name need to be noted. Characters that are difficult to preserve during drying, such as the structure of the submerged leaves, color of the stem, color and shape of the petals, should be noted in the field and documented photographically.

Only the middle and upper parts of fertile shoots, which bear typically developed submerged and floating leaves as well as flowers and ripe fruits, are suitable for identifying the species, especially with regard to flowing water forms. Sterile shoots occurring during the whole year usually have longer submerged leaves. Multiple collections over the course of the year or long-term observations of the same population are often necessary for a reliable determination. If observations are made several years apart, species composition might have been changed due to considerable colonization-extinction dynamics, particularly in small still waters and in fast-flowing sections of creeks and rivers. Cultivation in tanks is only helpful for small amphibian species. Forms from flowing waters grow badly in cultivation and develop atypical habit.

Although Germany`s Batrachium diversity consists of only 12 species and 10-12 hybrids, it is generally hardly possible to rely exclusively on dichotomous key for identification. Rarely, All of the important characteristics are rarely present on one plant, and the character states are largely overlapping. Single characters should not be emphasized too strongly. In combined sets of characters some traits fit and others may not, thus, characters need to be weighted according to rules. Therefore, in addition to the main identification keys (Wiegleb et al. 2017, Wiegleb 2020, 2021), tables were created (Wiegleb 2018) that contain unique characters for a species (occurring in one or two species only) as well as typical characters of a species, even if they may also occur in other not closely related species. Additionally, characters were evaluated with regard to whether a deviation impacts the morphological species concept or not. It is important to consider the developmental state of an individual plant. Did the plants germinate from seeds, or did they grow from last year's shoots from the ground, or from floating fragments? How were the weather conditions? Were there dry periods or a strong increase in water levels? Were there any mechanical disturbances?

For determining hybrids, it is important to consider the occurrence of potential parental species, their frequency in the water system and their flowering times. Are there ecotones at the site in which species with different habitat requirements can co-occur? Note, that Batrachium hybrids are not intermediate (due to dominance, backcrossing or F2 splitting). They often show reduced vigor and fertility, but no heterosis effects, as postulated by Prančl et al. (2018). Since hybrid swarms are common, hybrids are usually at least partially fertile. Sporadically developed fruits are often only found on one fifth or sixth of the pedicels. Attention should also be paid to abnormal developments of organs, such as atypical branching, axillary short shoots with atypical submerged leaves, sometimes fused with the pedicel, weakly developed pedicels or closed flowers with abortive sepals and petals.

For a comprehensive characterization of the species, a large number of traits must be taken into account (Wiegleb et al. 2017, Wiegleb 2018, Wiegleb 2020, 2021). The characters are not all equally important but for a deeper understanding careful observation is necessary to consider correlations between the characters. The distinction between the character states follows Pizarro (1995) and Wiegleb et al. (2017), unless otherwise noted. Important characteristics are:

Habit

Life form − lifespan: annual, biennial, perennial. Seasonality: wintergreen, deciduous. Adaptation to aquatic habitat: amphiphyte, hydrophyte.

Growth form of the aquatic form − nymphaeid, batrachid, myriophyllid. Aquatic form: erect, erect-spreading, prostrate. Land form: prostrate to sod-forming, caespitose.

Leaves and Stems

Floating leaves (flat leaves) − present or absent. Arrangement: alternate, opposite. Size (blade without petiole): Length, width, in mm. Shape: reniform, cordate, orbicular, semi-orbircular. Number of primary lobes: 3, 5, 7. Depth of incisions: incised up to 1/3, 1/2, 2/3 or more than 2/3 of the blade. Shape of primary lobes (in case of deep incisions): with narrow base, parallel, cuneate (with broad base). Total number of secondary lobes. Margin: entire, undulate, serrate (acute or obtuse), dentate. Angle of basal sinus, in °. Pubescence: hairy, glabrous. Petiole: length, in cm, in relation to blade.

Transitional leaves − present or absent. Shape: 'aquatilis-type': broad with basal capillary segments (Cook, 1966: 72, fig. 3b; Webster, 1998: 9, fig. c); 'ashibetsuensis-type': narrow widened segments with both basal and terminal capillary segments (Bobrov et al., 2014: 133, fig. 5); 'baudotii-type': rounded segments with parallel margins, sometimes with basal capillary segments, often fleshy (Cook, 1966: 72, fig. 3a; Webster, 1998: 9, fig. b); 'bungei-type': with up to 12 palmately spread acute segments with parallel margins; 'peltatus-type': broad with terminal capillary segments (Cook, 1966: 72, fig. 3c; Webster, 1998: 9, fig. d); 'tripartitus-type': radially symmetrical with 3(-5) acute lobes (Webster, 1998: 9, fig. a).

Submerged leaves (capillary leaves) − present or absent. arrangement: alternate, (pseudo-)opposite. Length (of petiole and capillary-divided part), in cm; or divided into classes as small (< 30 mm long), medium (30-60 mm long), large (> 60 mm long). Leaf shape (spatial dimension): 2-dimensional (in plane): orbicular, semiorbicular; 3-dimensional: spherical, hemispherical, conical, cone-shaped, or elongated cone-shaped. Color: light green, dark green, yellowish, brownish, blackish (when fresh); changes on drying. Pubescence: hairy, glabrous. Divided part of leaf: structure of capillary segments: fleshy, more or less rigid, brushing. Brushing segments may be filiform, sometimes only terminal. Orientation of segments: spreading, subparallel, parallel, collapsing. Length of central part: shorter than lateral parts. Distance between first and second bifurcation of the divided part. Number of bifurcations: 3, 4, 5, 6 or more. Resulting number of terminal segments: between 10 and 900. Length of petiole (including stipules) in mm, or divided into classes as short (< 10 mm), long (> 10 mm).

Stipules − adnate to the petiole: percentage of adnate part in relation to total length of stipule. Shape of the free part: acute, semiorbicular, rounded, cuneate, attenuate (Cook, 1966: 69; Webster, 1998: 54). Pubescence: hairy, glabrous.

Stem − hoot dimorphism in perennial species: vegetative, generative. Total stem length (from base): in cm, or divided into three classes; small (< 30(−50) cm long), medium (50−150 cm long), long (> 200 cm long). Branching pattern: dichotomous branching, branching from leaf axils. Diameter in mm. Pubescence: hairy, glabrous. Color: whitish, light green, dark green, yellowish, brownish, reddish (due to specific hairs), blackish (when fresh); changes on drying. Length of internodes in relation to neighboring structures (leaves, petioles or pedicels). Rooting: primary root still present; adventitious root formation: only in the lower part of the shoot, at each node.

Flower and fruit

Pedicel − length at fruit maturity. Position in relation to different leaf types. Length in relation to the size of the opposing leaf. Elongation at fruit maturity. Shape at fruit maturity: straight, reflexed, coiled. Pubescense: hairy, glabrous. Diameter in mm; uniform, narrowed towards flower.

Sepals − number. Size: length, width in mm. Shape: oblong-ovate, ovate, elliptic, lanceolate. Color: green, greenish, whitish, yellow-green, purple, blue, blue-tipped, with dark tip. Orientation: spreading, prostrate. Persistence: deciduous, persistent.

Petals − number. Size: length, width in mm. Flower size: small (petals < 5 mm long), medium (petals 5-10 mm long) or large (petals > 10 mm long). Length in relation to the sepals. Shape: oblong-ovate, ovate, elliptic, lanceolate, spatulate. Color: white, white with yellow base (the yellow base can be either very small or normal in size). Margin: entire, undulate, lobed or toothed. Overlapping at flowering: overlapping, non-overlapping.

Nectaries − number per petal. Shape: crescent-shaped, cup-shaped, orbicular, elongated, pear-shaped, horseshoe-shaped, irregular (see Dahlgren, 1992; Cook, 1966: 76; Pizarro, 1995: 45; Webster, 1998: 55).

Stamens − number. Length: longer than the stigma, shorter than the stigma.

Carpels − number.

Fruit − size of the ripe fruit: Length in mm, or classified into small (< 1.2 mm long), medium (1.2-2.0 mm long) or large (> 2.0 mm long); width. Shape: elongated-ovate, ovoid, elliptical, hemispherical, globous. Pubescence when mature (pubescence may be restricted to the terminal part or lost in the course of development). Wings: present or absent (when dry); position of wings: dorsal, ventral, both. Position of style: lateral, subterminal, terminal. Length of style, in mm. Persistence of style: decidous, persistent.

Sterility − difficulties in development cause sterility: malformed pedicels, petals, malformed fruits; especially if no regular fruits are formed at the sixth pedicel.

Receptacle − spherical, hemispherical, elliptical, conical. Elongation at fruit maturity: not elongated, elongated. Shape at fruit maturity: same as at flowering, awl-shaped, pubescence: very densely hairy, hairy, sparsely hairy, glabrous.

An obstacle in naming the species is the insufficient typification. Only 13 of the 30 species listed by Wiegleb et al. (2017) are verified by an authentic specimen that has been considered as such since the first description. Of the German species, this only includes R. fluitans. In seven cases, a lectotype was designated due to a lack of unambiguous material (including R. aquatilis, R. hederaceus and R. pseudofluitans). However, this happened up to 210 years later than the description, implying a long period of uncertainty. Historical specimens of three species (including R. peltatus and R. trichophyllus), and historical illustrations of three other species (including R. circinatus and R. ololeucos) have been designated as neotypes. The type specimen of R. saniculifolius has been lost, a neotype has never been designated. The specimens of R. penicillatus and R. baudotii, respectively, which are considered as types may not represent the species understood today under these names (see note on R. fluitans hybrids; Jeanmonod & Naciri 2021: R. baudotii vs. R. saniculifolius). Other important taxa were overlooked, such as R. peucedanifolius All., which was published prior to R. trichophyllus Chaix.

In this respect, misidentifications were inevitable for a long time. Incorrect identifications in herbaria led to incorrect information in floras and incorrect entries in databases from which automatic distribution maps were generated (e.g. Euro+Med-Plantbase, GBIF, FloraWeb). In many German herbaria, often only the species R. aquatilis, R. circinatus, R. fluitans, R. hederaceus and R. trichophyllus described before 1800 were distinguished, sometimes a fascicle was created for R. peltatus after Cook's nomenclature was used for the first time in 1976 in the critical volume of Rothmaler Flora. While obsolete synonyms frequently used in the specialist literature at that time (R. radians for R. aquatilis, R. paucistamineus for R. trichophyllus, R. divaricatus for R. circinatus) came out of use, they continue to exist in some herbaria and thus also in databases. Until around 1980, vegetation studies often only distinguished between R. aquatilis, R. circinatus and R. fluitans although these species occur in Central Europe, have been described with sufficient morphological precision since 1874 (most recently R. penicillatus).

According to the herbarium revisions carried out between 2016 and 2018, R. peltatus is by far the most common species in Germany. R. circinatus and R. trichophyllus are also common. Considerably less frequent are R. aquatilis, R. fluitans, R. hederaceus and R. baudotii. All other species are rare or only regionally distributed (see Table 3).

(frequency classes: 5 - common, 4 - frequent, 3 - scattered, 2 - rare, 1- very rare) and misidentifications (very frequent confusions in bold).

The correct determinations are those that clearly refer to the type. For R. peltatus, for example, B. peltatum or R. peltatussect. subsp. are also "correct". Although the name 'R. floribundus' is a synonym of R. peltatus, it has not always been used as such outside Great Britain. Names such as 'R. aquatilis var. truncatus' or 'R. aquatilis β peltatus' always include other taxa in addition to R. peltatus. Most misidentifications concern R. aquatilis. For a long time this species was regarded as a collective species ('R. aquatilis s.l.', 'R. aquatilis agg.') and was not used correctly even after the publication of Cook's work (1966). More than 40-70% of R. aquatilis usually belong to R. peltatus, another 10-20% to R. trichophyllus. Conversely, many forms of R. trichophyllus have been mistaken for R. aquatilis, which almost balances each other out. In collections after 1970, identifications as R. penicillatus and R. pseudofluitans were frequently found, but these only represent special morphotypes of other species, especially R. peltatus. Hybrids have been rarely distinguished in collections. An exception are specimens of the plants described by Cook (1966) and Vollrath & Kohler (1972). This has some implications for the revision of the distribution maps on FloraWeb.de.

R. aquatilis s.l.: The map is not meaningful, as the delimitation from other species was handled differently.

R. aquatilis: The focal areas in Schleswig-Holstein, Mecklenburg-Western Pomerania, the Lower Rhine and Westphalia, the Havel-Spree region and northern Bavaria are realistic. Overall, however, the species is also rarer there than previously assumed and declining.

R. circinatus: The focal areas in the Rhine, Ems, Weser and Elbe valleys, on the northern German Young Drift, in northern Bavaria and the foothills of the Alps are realistic.

R. confervoides: The occurrences shown on the map belong to R. trichophyllus.

R. fluitans: The map is partially incomplete, e.g. in the Rhenish Massif, but otherwise realistic. The occurrences in the coastal area do not refer to this species but to R. baudotii or R. penicillatus.

R. hederaceus: The map is realistic.

R. ololeucos: The map is realistic.

R. baudotii (as subsp. of R. peltatus): The map is accurate in coastal areas, inland sites are more common.

R. peltatus (as subsp.): The map is largely correct. Due to the confusion with R. aquatilis, the particular abundance in the Saale glacial sandy areas and the acid-weathering low mountain ranges is underestimated.

R. penicillatus: The map contains R. penicillatus, R. pseudofluitans and other R. fluitans hybrids and lacks sufficient differentiation. The exact distribution of the these taxa is unknown due to the lack of specimens.

R. rionii: The distribution is incomplete, the recently discovered occurrences in western and central Germany from North Rhine-Westphalia and Hesse to Saxony are missing.

R. trichophyllus: The map is realistic. The frequent confusion with R. aquatilis does not affect the distribution pattern since both species have similar ecological requirements.

We would like to thank K. Wesche (Görlitz) and K. van de Weyer (Nettetal) for reviewing the manuscript; P. Gebauer (Görlitz, GLM) and C. Barilaro (Oldenburg, LMO) for their support in the herbarium work; all other curators of the herbaria who provided material or helped to clarify questions on typifications by sending digitized specimens; J. Zalewska-Galocz (KRA) for the discussions on taxonomic and nomenclatural questions.

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