Abstract

Phytoplankton biovolume can be measured or calculated through the calculation of similar geometric models. A set of geometric models is suggested for calculating cell biovolume and surface area for 284 phytoplankton genera in China Sea waters. Thirty-one geometric shapes have been assigned to estimate the biovolume and surface area of phytoplankton cells. Reductions of error and microscopic effort are also discussed. The model has been verified by its application in the China Seas regions. The software to make these calculations is available at http://www.ouc.edu.cn/csmxy/sunjun/biovolume.htm

INTRODUCTION

The biovolume of marine phytoplankton cells is important to the study of phytoplankton ecology. The related parameters, such as cell size and conversion of carbon content from biovolume, and physiology functions are also important for marine ecosystem studies (Malone, 1980; Sournia, 1981; Chisholm, 1992).

Phytoplankton cell size varies greatly among different genera or even between different individuals. Sizes range from a few micrometres (or even less than 1 μm) to a few millimetres. Hence, there is a wide range of nine orders in magnitude for cell biovolume of phytoplankton. Several automated and semi-automatic methods for biovolume estimation have been described in the literature, such as the Coulter Counter (Hasting et al., 1962; Maloney et al., 1962; Boyd and Johnson, 1995), the micrographic image analysis system (Gordon, 1974; Krambeck et al., 1981; Estep et al., 1986; Verity and Sieracki, 1993; Sieracki et al., 1998), flow cytometry (Olson et al., 1985; Wood et al., 1985; Steen, 1990; Cunningham and Buonnacorsi, 1992) and holographic scanning technology (Brown et al., 1989). However, the general method for calculating phytoplankton cell biovolume is based on geometric assignation (Kovala and Larrance, 1966; Willén, 1976; Sicko-Goad et al., 1977; Smayda, 1978; Edler, 1979; Rott, 1981; Kononen et al., 1984; Vilicic, 1985; Hillebrand et al., 1999). The methods mentioned above have advantages and/or disadvantages. Microscopic observation is a direct, convenient way to obtain species level information on phytoplankton taxa, whereas biovolume calculation based on geometric models of phytoplankton cells and their related conversion biomass are popular in phytoplankton ecology studies (Kuuppo, 1994; Snoeijs, 1994; Sommer, 1994, 1995; Tang, 1995; Hillebrand, 1997; Young and Ziveri, 2000). Some references (Smayda, 1978; Baltic Marine Environmental Protection Commission–Helsinki Commission, 1988; Hansen, 1992; Kramer et al., 1992) list the biovolume calculations and their conversion biomasses as a routine method when studying phytoplankton.

Phytoplankton cell geometric models for biovolume calculation have been discussed in the literature (Kovala and Larrance, 1966; Willén, 1976; Edler, 1979; Rott, 1981; Kononen et al., 1984; Hansen, 1992; Hillebrand et al., 1999; Sun et al., 2000a; Young and Ziveri, 2000). The method applies the principle of geometric models or shapes that are most similar to the real shape of the organism. Often there is the dilemma of whether to assign a phytoplankton cell shape to a complex but similar geometric model or to a simple, conveniently measurable, but inadequate model or shape. Most of the above studies pay attention to special regions or microalgae classes. Although different geometric equations used in the literature were dependent on dominance of the respective species in the local plankton communities, routine phytoplankton analysis would benefit from a series of standardized geometric models.

Hillebrand et al. recommend a standard set of 20 geometric shapes for over 850 genera and provide equations to be used for accurate estimates of cell volume and surface area for phytoplankton and microbenthic algae from linear dimensions measured microscopically (Hillebrand et al., 1999). Its extensive listing of cell shapes will be a valuable resource for experimental and literature-based studies of relationships between cell size, surface area and biovolume for a wide variety of physiological characteristics. This comprehensive study will help set consistent parameters for evaluating the dynamics of phytoplankton standing stocks in terms of biovolume for ecological studies, and will be evaluated as a primary research reference in this field for studies of phytoplankton by physiologists and ecologists (Wheeler, 1999). Although it is comprehensive and extensive, its applicability is in need of expansion.

In the present study, based on earlier work of Hillebrand et al. (Hillebrand et al., 1999), and focusing on phytoplankton species in the China Sea, a set of 31 geometric shapes is proposed for routine analysis of marine phytoplankton in China Sea waters. After consultation with the literature on phytoplankton studies in China’s seas, we found that nearly 2000 taxa were recorded, belonging to 10 diverse groups and 284 genera (due to the volume of references, they cannot all be cited in this paper). Although the old nomenclature system is still in use in China, the checklist was modified according to Tomas (Tomas, 1997) (Table I). In order to improve the applicability of Hillebrand’s geometric models, we reduced the number of microscopically measured line parameters, improving the previous shapes and updating the models. Furthermore, considering the fact that identifications of phytoplankton taxa need expert knowledge, we used the linear dimensions for length, width and height instead of apical axis, transapical axis and pervalvar axis. For example, when phytoplankton samples were observed under the light microscope, in most circumstances, the length (may be the pervalvar axis in some diatoms, e.g. Leptocylindrus spp.) and width were measured, then the cell volume and surface area were calculated from the geometric models discussed in this paper. The models were checked with a set of phytoplankton counter data and a Visual Basic for Applications (VBA) program was written in Microsoft Excel for calculations.

Table I:

Shape codes of phytoplankton genera found in China Sea waters according to the geometric models in Table II

Genera Shape code 
1. Cyanobacteria  
Anabaena Bory de St.-Vincent 
Aphanothece Näegeli 
Arthrospira Stizenbberger 28 
Borzia Cohn 28 
Calothrix Agardh 28 
Camptylonemopsis Desikachary 28 
Chlorogloea Wille 
Chroococcus Näegeli 
Chroothece Hansgirg 28 
Dichothrix Zanardini 28 
Enthophysalis Kützing 
Gardnerula de Toni 28 
Gomphosphaeria Kützing 
Homoeothrix (Thuret) Kirchner 28 
Hormathonema Ercegovic 
Hydrocoleum Kützing 28 
Hyella Bornet & Flahault 28 
Isactis Thuret 28 
Johannesbaptista de Toni 
Kyrtuthrix Ercegovic 28 
Lyngbya Agardh 28 
Merismopedia Meyen 10 
Microchaete Thuret 28 
Microcoleus Desmazières 28 
Microcystis Kützing 
Nodularia Mertens 28 
Oscillatoria Vaucher 28 
Phormidium Kützing 28 
Pleurocapsa Thuret ex Hauck 28 
Richelia Schmidt 28 
Rivularia (Roth) Agardh 28 
Schizothrix Kützing 28 
Sirocoleum Kützing 28 
Scytonema Agardh 28 
Spirulina Turpin 28 
Symploca Kützing 28 
Synechococcus Näegeli 
Synechocystis Sauvageau 
Tolypothrix Kützing 28 
Trichodesmium Ehrenberg 28 
Campylosira Grunow ex Van Heurck 14 
Cerataulina Peragallo 28 
Cerataulus Ehrenberg 28 
Chaetoceros Ehrenberg 29 
Chrysanthemodiscus Mann 
Cistula Cleve 11 
Climacodium Grunow 23 
Climacosphenia Ehrenberg 31 
Cocconeis Ehrenberg 11 
Corethron Castracane 
Coscinodiscus Ehrenberg emend. Hasle & Sims 
Cyclotella Kützing ex de Brébisson 
Cymatodiscus Hendey 
Cymatoneis Cleve 13 
Cymatosira Grunow 29 
Cymatotheca Hendey 17 
Cymbella Agardh 17 
Dactyliosolen Castracane 28 
Delphineis Andrews 11 
Denticula Kützing 11 
Detonula Schütt 28 
Diatoma Bory de St.-Vincent 29 
Dictyoneis Cleve 12 
Dimeregramma Ralfs 29 
Diploneis Ehrenberg ex Cleve 12 
Ditylum Bailey ex Bailey 30 
Endictya Ehrenberg 
Entomoneis Ehrenberg 12 
Ethmodiscus Castracane 
Eucampia Ehrenberg 29 
Eunotia Ehrenberg 15 
Eunotogramma Weisse 14 
Eupodiscus Bailey 
Fallacia Stickle & Mann 11 
Fragilaria Lyngbye 29 
Fragilariopsis Hustedt emend. Hasle 29 
Frustulia Rabenhorst 11 
Gephyria Arnott 11 
Gomphonema Agardh 21 
Gomphonitzschia Grunow 21 
Gossleriella Schütt 
Plagiogrammopsis Hasle, von Stosch & Syvertsen 29 
Plagiotropis Pfitzer 11 
Planktoniella Schütt 
Pleurosigma Smith 13 
Pleurosira Trevison 28 
Podocystis Bailey 11 
Podosira Ehrenberg 
Proboscia Sundström 28 
Psammodictyon Mann 12 
Psammodiscus Round & Mann 
Pseudoeunotia Grunow 
Pseudo-nitzschia Peragallo 13 
Pseudosolenia Sundström 28 
Pseudostaurosira (Grunow) Williams & Round 20 
Pyxidicula Ehrenberg 11 
Rhabdonema Kützing 10 
Rhaphoneis Ehrenberg 13 
Rhizosolenia Brightwell 28 
Rhoicosphenia Grunow 21 
Rhopalodia Müller 17 
Rocella Hanna 
Roperia Grunow ex Pelletan 11 
Rossia Voigt 11 
Schroederella Pavillard 28 
Scoliopleura Grunow 11 
Sellaphora Mereschkowsky 10 
Skeletonema Greville 
Stauroneis Ehrenberg 29 
Stauropsis Meunier 29 
Staurosira (Ehrenberg) Williams & Round 29 
Stellarima Hasle & Sims 
Stenopterobia de Brébisson ex Van Heurck 13 
Stephanodiscus Ehrenberg 
Stephanopyxis (Ehrenberg) Ehrenberg 
Stictodiscus Greville 
Striatella Agardh 29 
Surirella Turpin 11 
Synedra Ehrenberg 10 
Synedrosphenia (Peragallo) Azpeitia 21 
Tabellaria Ehrenberg 20 
Cladopyxis Stein 
Dinophysis Ehrenberg 
Diplopelta Stein ex Jörgensen 
Diplopsalis Bergh 
Dissodinium Pascher 
Gambierdiscus Adachi & Fukuyo 
Gloeodinium Klebs 
Goniodoma Stein 
Gonyaulax Diesing 
Gymnodinium Stein 
Gyrodinium Kofoid & Swezy 
Heteraulacus Diesing 
Heterodinium Kofoid 
Histioneis Stein 
Karenia Daugbjerg, Hansen, Larsen, Moestrup 
Kofoidinium Pavillard 
Lingulodinium Dodge 
Noctiluca Suriray 
Ornithocercus Stein 26 
Ostreopsis Schmidt 
Oxytoxum Stein 
Peridiniopsis Lemmermann 
Peridinium Ehrenberg 
Phalacroma Stein 
Podolampas Stein 
Polykrikos Bütschli 
Preperidiunium Mangin 
Prorocentrum Ehrenberg 
Protoperidinium Bergh 
Xenococcus Thuret 
2. Chrysophyceae  
Chromulina Cienkowski 
Dictyocha Ehrenberg 
Dinobryon Ehrenberg 
Mallonmonas Perty 
Ochromonas Wyssotski 
Synura Ehrenberg 
3. Bacillariophyceae  
Acanthoceras Honigmann 29 
Achnanthes Bory de St.-Vincent 12 
Achnanthidium Kützing 11 
Actinocyclus Ehrenberg 
Actinoptychus Ehrenberg 
Amphipleura Kützing 11 
Amphiprora Ehrenberg 11 
Amphora Ehrenberg ex Kützing 17 
Aneumastus Mann & Stickle 11 
Anomoeoneis Pfitzer 11 
Anorthoneis Grunow 11 
Arachnoidiscus Deane ex Pritchard 
Arcocellulus Hasle, von Stosch & Syertsen 29 
Ardissonea De Notaris 10 
Asterionella Hassall 10 
Asterionellopsis Round 10 
Asterolampra Ehrenberg 
Asteromphalus Ehrenberg 
Aulacodiscus Ehrenberg 
Auliscus Ehrenberg 11 
Auricula Castracane 17 
Azpeitia Peragallo 
Bacillaria Gmelin 10 
Bacteriastrum Shadbolt 28 
Bellerochea Van Heurck emend. von Stosch 30 
Biddulphia Gray 29 
Bleakeleya Round 10 
Caloneis Cleve 11 
Campylodiscus Ehrenberg ex Kützing 11 
Campyloneis Grunow 11 
Grammatophora Ehrenberg 10 
Guinardia Peragallo 28 
Gyrosigma Hassall 13 
Hantzschia Grunow 10 
Helicotheca Ricard 29 
Hemiaulus Ehrenberg 29 
Hemidiscus Wallich 17 
Hyalodiscus Ehrenberg 
Hydrosera Wallich 18 
Isthmia Agardh 29 
Lauderia Cleve 28 
Leptocylindrus Cleve 28 
Leudugeria Tempère ex Van Heurck 17 
Licmophora Agardh 16 
Lioloma Hasle 10 
Liradiscus Greville 
Lithodesmium Ehrenberg 30 
Luticola Mann 11 
Lyrella Karajeva 11 
Martyana Round 11 
Mastogloia Thwaites ex Smith 11 
Mastogonia Ehrenberg 11 
Melosira Agardh 28 
Meuniera Silva 29 
Minidiscus Hasle 
Minutocellus Hasle, von Stosch, & Syvertsen 11 
Navicula Bory de St.-Vincent 11 
Neidium Pfitzer 11 
Nitzschia Hassall 13 
Nitzschiella Rabenhorst 13 
Odontella Agardh 29 
Opephora Petit 29 
Östrupia Heiden ex Schmidt 11 
Palmeria Greville 17 
Paralia Heiberg 
Perissonoë Andrews & Stoelzel 10 
Petrodictyon Mann 29 
Phaeodactylum Bohlin 14 
Pinnularia Ehrenberg 10 
Plagiodiscus Grunow & Eulenstein 14 
Plagiogramma Greville 11 
Tabularia (Kützing) Williams & Round 10 
Tetracyclus Ralfs 20 
Thalassionema Grunow 10 
Thalassiosira Cleve emend. Hasle 
Thalassiothrix Cleve & Grunow 10 
Toxarium Bailey 24 
Trachyneis Cleve 11 
Triceratium Ehrenberg 18 
Trigonium Cleve 18 
Trinacria Heiberg 18 
Tropidoneis Cleve 11 
Tryblioptychus Hendey 11 
Xanthiopyxis (Ehrenberg) Ehrenberg 11 
4. Raphidophyceae  
Heterosigma Hada 
Chattonella Biecheler 
5. Prymnesiophyceae  
Acanthoica Lohmann emend. Schiller and 
Kleijne  
Calyptrolithia Heimdal 
Emiliana Hay & Mohler 
Gephyrocapsa Kamptner 
Hayaster Bukry 
Prymnesium Massart ex Conrad 
Syracosphaera Lohmann 
6. Cryptophyceae  
Chroomonas Hansgirg 
Cryptomonas Ehrenberg 
7. Dinophyceae  
Alexandrium Halim 
Amphidinium Claparède et Lachmann 
Amphisolenia Stein 
Balechina Loeblich J & Loeblich III 
Blepharocysta Ehrenberg 
Ptychodiscus Stein 
Pyrocystis Murray ex Haeckel 
Pyrophacus Stein 
Scrippsiella Balech ex Loeblich III 
Schuettiella Balech 
Spiraulax Kofoid 
Symbiodinium Freudenthal 
Triposolenia Kofoid 27 
Centrodinium Kofoid 
Ceratium Schrank 25 
Ceratocorys Stein 26 
8. Euglenophyceae  
Euglena Ehrenberg 22 
Eutreptia Perty 22 
9. Prasinophyceae  
Halosphaera Schmitz 
Mantoniella Desikachary 
Micromonas Manton & Parke 
Nephroselmis Stein 
Pyramimonas Schmarda 
10. Chlorophyceae  
Actinastrum Lagerheim 
Ankistrodesmus Cord 16 
Brachiomonas Bohlin 
Carteria Diesing 
Chlamydomonas Ehrenberg 
Dunaliella Teodoresco 
Pediastrum Meyen 11 
Scenedesmus Meyen 
Tetraëdron Kützing 10 
Genera Shape code 
1. Cyanobacteria  
Anabaena Bory de St.-Vincent 
Aphanothece Näegeli 
Arthrospira Stizenbberger 28 
Borzia Cohn 28 
Calothrix Agardh 28 
Camptylonemopsis Desikachary 28 
Chlorogloea Wille 
Chroococcus Näegeli 
Chroothece Hansgirg 28 
Dichothrix Zanardini 28 
Enthophysalis Kützing 
Gardnerula de Toni 28 
Gomphosphaeria Kützing 
Homoeothrix (Thuret) Kirchner 28 
Hormathonema Ercegovic 
Hydrocoleum Kützing 28 
Hyella Bornet & Flahault 28 
Isactis Thuret 28 
Johannesbaptista de Toni 
Kyrtuthrix Ercegovic 28 
Lyngbya Agardh 28 
Merismopedia Meyen 10 
Microchaete Thuret 28 
Microcoleus Desmazières 28 
Microcystis Kützing 
Nodularia Mertens 28 
Oscillatoria Vaucher 28 
Phormidium Kützing 28 
Pleurocapsa Thuret ex Hauck 28 
Richelia Schmidt 28 
Rivularia (Roth) Agardh 28 
Schizothrix Kützing 28 
Sirocoleum Kützing 28 
Scytonema Agardh 28 
Spirulina Turpin 28 
Symploca Kützing 28 
Synechococcus Näegeli 
Synechocystis Sauvageau 
Tolypothrix Kützing 28 
Trichodesmium Ehrenberg 28 
Campylosira Grunow ex Van Heurck 14 
Cerataulina Peragallo 28 
Cerataulus Ehrenberg 28 
Chaetoceros Ehrenberg 29 
Chrysanthemodiscus Mann 
Cistula Cleve 11 
Climacodium Grunow 23 
Climacosphenia Ehrenberg 31 
Cocconeis Ehrenberg 11 
Corethron Castracane 
Coscinodiscus Ehrenberg emend. Hasle & Sims 
Cyclotella Kützing ex de Brébisson 
Cymatodiscus Hendey 
Cymatoneis Cleve 13 
Cymatosira Grunow 29 
Cymatotheca Hendey 17 
Cymbella Agardh 17 
Dactyliosolen Castracane 28 
Delphineis Andrews 11 
Denticula Kützing 11 
Detonula Schütt 28 
Diatoma Bory de St.-Vincent 29 
Dictyoneis Cleve 12 
Dimeregramma Ralfs 29 
Diploneis Ehrenberg ex Cleve 12 
Ditylum Bailey ex Bailey 30 
Endictya Ehrenberg 
Entomoneis Ehrenberg 12 
Ethmodiscus Castracane 
Eucampia Ehrenberg 29 
Eunotia Ehrenberg 15 
Eunotogramma Weisse 14 
Eupodiscus Bailey 
Fallacia Stickle & Mann 11 
Fragilaria Lyngbye 29 
Fragilariopsis Hustedt emend. Hasle 29 
Frustulia Rabenhorst 11 
Gephyria Arnott 11 
Gomphonema Agardh 21 
Gomphonitzschia Grunow 21 
Gossleriella Schütt 
Plagiogrammopsis Hasle, von Stosch & Syvertsen 29 
Plagiotropis Pfitzer 11 
Planktoniella Schütt 
Pleurosigma Smith 13 
Pleurosira Trevison 28 
Podocystis Bailey 11 
Podosira Ehrenberg 
Proboscia Sundström 28 
Psammodictyon Mann 12 
Psammodiscus Round & Mann 
Pseudoeunotia Grunow 
Pseudo-nitzschia Peragallo 13 
Pseudosolenia Sundström 28 
Pseudostaurosira (Grunow) Williams & Round 20 
Pyxidicula Ehrenberg 11 
Rhabdonema Kützing 10 
Rhaphoneis Ehrenberg 13 
Rhizosolenia Brightwell 28 
Rhoicosphenia Grunow 21 
Rhopalodia Müller 17 
Rocella Hanna 
Roperia Grunow ex Pelletan 11 
Rossia Voigt 11 
Schroederella Pavillard 28 
Scoliopleura Grunow 11 
Sellaphora Mereschkowsky 10 
Skeletonema Greville 
Stauroneis Ehrenberg 29 
Stauropsis Meunier 29 
Staurosira (Ehrenberg) Williams & Round 29 
Stellarima Hasle & Sims 
Stenopterobia de Brébisson ex Van Heurck 13 
Stephanodiscus Ehrenberg 
Stephanopyxis (Ehrenberg) Ehrenberg 
Stictodiscus Greville 
Striatella Agardh 29 
Surirella Turpin 11 
Synedra Ehrenberg 10 
Synedrosphenia (Peragallo) Azpeitia 21 
Tabellaria Ehrenberg 20 
Cladopyxis Stein 
Dinophysis Ehrenberg 
Diplopelta Stein ex Jörgensen 
Diplopsalis Bergh 
Dissodinium Pascher 
Gambierdiscus Adachi & Fukuyo 
Gloeodinium Klebs 
Goniodoma Stein 
Gonyaulax Diesing 
Gymnodinium Stein 
Gyrodinium Kofoid & Swezy 
Heteraulacus Diesing 
Heterodinium Kofoid 
Histioneis Stein 
Karenia Daugbjerg, Hansen, Larsen, Moestrup 
Kofoidinium Pavillard 
Lingulodinium Dodge 
Noctiluca Suriray 
Ornithocercus Stein 26 
Ostreopsis Schmidt 
Oxytoxum Stein 
Peridiniopsis Lemmermann 
Peridinium Ehrenberg 
Phalacroma Stein 
Podolampas Stein 
Polykrikos Bütschli 
Preperidiunium Mangin 
Prorocentrum Ehrenberg 
Protoperidinium Bergh 
Xenococcus Thuret 
2. Chrysophyceae  
Chromulina Cienkowski 
Dictyocha Ehrenberg 
Dinobryon Ehrenberg 
Mallonmonas Perty 
Ochromonas Wyssotski 
Synura Ehrenberg 
3. Bacillariophyceae  
Acanthoceras Honigmann 29 
Achnanthes Bory de St.-Vincent 12 
Achnanthidium Kützing 11 
Actinocyclus Ehrenberg 
Actinoptychus Ehrenberg 
Amphipleura Kützing 11 
Amphiprora Ehrenberg 11 
Amphora Ehrenberg ex Kützing 17 
Aneumastus Mann & Stickle 11 
Anomoeoneis Pfitzer 11 
Anorthoneis Grunow 11 
Arachnoidiscus Deane ex Pritchard 
Arcocellulus Hasle, von Stosch & Syertsen 29 
Ardissonea De Notaris 10 
Asterionella Hassall 10 
Asterionellopsis Round 10 
Asterolampra Ehrenberg 
Asteromphalus Ehrenberg 
Aulacodiscus Ehrenberg 
Auliscus Ehrenberg 11 
Auricula Castracane 17 
Azpeitia Peragallo 
Bacillaria Gmelin 10 
Bacteriastrum Shadbolt 28 
Bellerochea Van Heurck emend. von Stosch 30 
Biddulphia Gray 29 
Bleakeleya Round 10 
Caloneis Cleve 11 
Campylodiscus Ehrenberg ex Kützing 11 
Campyloneis Grunow 11 
Grammatophora Ehrenberg 10 
Guinardia Peragallo 28 
Gyrosigma Hassall 13 
Hantzschia Grunow 10 
Helicotheca Ricard 29 
Hemiaulus Ehrenberg 29 
Hemidiscus Wallich 17 
Hyalodiscus Ehrenberg 
Hydrosera Wallich 18 
Isthmia Agardh 29 
Lauderia Cleve 28 
Leptocylindrus Cleve 28 
Leudugeria Tempère ex Van Heurck 17 
Licmophora Agardh 16 
Lioloma Hasle 10 
Liradiscus Greville 
Lithodesmium Ehrenberg 30 
Luticola Mann 11 
Lyrella Karajeva 11 
Martyana Round 11 
Mastogloia Thwaites ex Smith 11 
Mastogonia Ehrenberg 11 
Melosira Agardh 28 
Meuniera Silva 29 
Minidiscus Hasle 
Minutocellus Hasle, von Stosch, & Syvertsen 11 
Navicula Bory de St.-Vincent 11 
Neidium Pfitzer 11 
Nitzschia Hassall 13 
Nitzschiella Rabenhorst 13 
Odontella Agardh 29 
Opephora Petit 29 
Östrupia Heiden ex Schmidt 11 
Palmeria Greville 17 
Paralia Heiberg 
Perissonoë Andrews & Stoelzel 10 
Petrodictyon Mann 29 
Phaeodactylum Bohlin 14 
Pinnularia Ehrenberg 10 
Plagiodiscus Grunow & Eulenstein 14 
Plagiogramma Greville 11 
Tabularia (Kützing) Williams & Round 10 
Tetracyclus Ralfs 20 
Thalassionema Grunow 10 
Thalassiosira Cleve emend. Hasle 
Thalassiothrix Cleve & Grunow 10 
Toxarium Bailey 24 
Trachyneis Cleve 11 
Triceratium Ehrenberg 18 
Trigonium Cleve 18 
Trinacria Heiberg 18 
Tropidoneis Cleve 11 
Tryblioptychus Hendey 11 
Xanthiopyxis (Ehrenberg) Ehrenberg 11 
4. Raphidophyceae  
Heterosigma Hada 
Chattonella Biecheler 
5. Prymnesiophyceae  
Acanthoica Lohmann emend. Schiller and 
Kleijne  
Calyptrolithia Heimdal 
Emiliana Hay & Mohler 
Gephyrocapsa Kamptner 
Hayaster Bukry 
Prymnesium Massart ex Conrad 
Syracosphaera Lohmann 
6. Cryptophyceae  
Chroomonas Hansgirg 
Cryptomonas Ehrenberg 
7. Dinophyceae  
Alexandrium Halim 
Amphidinium Claparède et Lachmann 
Amphisolenia Stein 
Balechina Loeblich J & Loeblich III 
Blepharocysta Ehrenberg 
Ptychodiscus Stein 
Pyrocystis Murray ex Haeckel 
Pyrophacus Stein 
Scrippsiella Balech ex Loeblich III 
Schuettiella Balech 
Spiraulax Kofoid 
Symbiodinium Freudenthal 
Triposolenia Kofoid 27 
Centrodinium Kofoid 
Ceratium Schrank 25 
Ceratocorys Stein 26 
8. Euglenophyceae  
Euglena Ehrenberg 22 
Eutreptia Perty 22 
9. Prasinophyceae  
Halosphaera Schmitz 
Mantoniella Desikachary 
Micromonas Manton & Parke 
Nephroselmis Stein 
Pyramimonas Schmarda 
10. Chlorophyceae  
Actinastrum Lagerheim 
Ankistrodesmus Cord 16 
Brachiomonas Bohlin 
Carteria Diesing 
Chlamydomonas Ehrenberg 
Dunaliella Teodoresco 
Pediastrum Meyen 11 
Scenedesmus Meyen 
Tetraëdron Kützing 10 

Table II:

Geometric shapes and equations for the calculation of biovolume and surface area

Shape code Simulated shape Volume (V) and surface area (A) model 
1-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a^{3}\\A\ =\ {\pi}{\cdot}a^{2}\end{array}\)
 
2-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}b^{2}{\cdot}a\\A\ =\ \frac{{\pi}{\cdot}b}{2}\left(b+\frac{a^{2}}{\sqrt{a^{2}{-}b^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{a^{2}{-}b^{2}}}{a}\right)\end{array}\)
 
3-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b+c\right){\cdot}\left[\left(\frac{b+c}{2}\right)+\frac{2a^{2}}{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}{2a}\right]\end{array}\)
 
4-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a^{2}{\cdot}c\\A\ =\ {\pi}{\cdot}a{\cdot}\left(\frac{a}{2}+c\right)\end{array}\)
 
5-H graphic 
\(\begin{array}{l}V\ =\ {\pi}{\cdot}b^{2}{\cdot}\left(\frac{a}{4}{-}\frac{b}{12}\right)\\A\ =\ {\pi}{\cdot}a{\cdot}b\end{array}\)
 
6-H graphic Suppose the height of cones is half of b:
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}\left(a{-}\frac{b}{3}\right)\\A\ =\ {\pi}{\cdot}b{\cdot}\left(a{-}\frac{4{-}\sqrt{3}}{4}b\right)\end{array}\)
 
7-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{4}{\cdot}b{\cdot}\left(b+\sqrt{4a^{2}+b^{2}}\right)\end{array}\)
 
8-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}\)
 
9-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b^{2}{\cdot}\left(b+\sqrt{\frac{2a^{2}{-}ab+b^{2}}{2}}\right)\end{array}\)
 
10-H graphic 
\(\begin{array}{l}V\ =\ a{\cdot}b{\cdot}c\\A\ =\ 2{\cdot}a{\cdot}b+2{\cdot}b{\cdot}c+2{\cdot}a{\cdot}c\end{array}\)
 
11-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
12-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
13-H graphic 
\(\begin{array}{l}V\ =\ \frac{1}{2}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ a{\cdot}b+\frac{\sqrt{a^{2}+b^{2}}}{4}{\cdot}c\end{array}\)
 
14-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}\)
 
15-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}\)
 
16-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{6}{\cdot}a{\cdot}b^{2}\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}\)
 
17-H graphic 
\(\begin{array}{l}V\ =\ \frac{2}{3}{\cdot}a{\cdot}c^{2}{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{b}{2c}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}a{\cdot}c+b{\cdot}\left[c+\frac{a^{2}}{2\sqrt{a^{2}{-}4c^{2}}}{\cdot}\mathrm{sin}^{{-}1}\left(\frac{\sqrt{a^{2}{-}4c^{2}}}{a}\right)\right]\end{array}\)
 
18-H graphic 
\(\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}c{\cdot}a^{2}\\A\ =\ 3a{\cdot}c+\frac{\sqrt{3}}{2}{\cdot}a^{2}\end{array}\)
 
19-H graphic 
\(\begin{array}{l}V\ =\ \frac{1}{6}{\cdot}a^{2}{\cdot}c\\A\ =\ \frac{1}{2}{\cdot}a^{2}+a{\cdot}\sqrt{a^{2}+8c^{2}}\end{array}\)
 
20-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
21-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{a{\cdot}b}{4}{\cdot}\left[a+\left(\frac{{\pi}}{4}{-}1\right){\cdot}b\right]{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)\\A\ {\approx}\ \frac{b}{2}{\cdot}\left(2a+{\pi}{\cdot}a{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)+\left(\frac{{\pi}}{2}{-}2\right){\cdot}b\right)\end{array}\)
 
22-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{3}{\cdot}\left(a_{1}+a_{2}\right){\cdot}b_{1}^{2}+\frac{{\pi}}{4}{\cdot}\left(a_{2}+b_{2}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}a_{2}{\cdot}b_{1}{\cdot}b_{2}\\A\ =\ {\pi}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}b_{1}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}{\cdot}\sqrt{\left(\frac{a_{1}}{b_{1}}\right)^{2}+\frac{1}{4}}{-}\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}\sqrt{\left(\frac{a_{1}{\cdot}b_{2}}{b_{1}}{-}a_{1}\right)^{2}+\frac{b_{1}^{2}}{4}}\end{array}\)
 
23-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{1}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{3}{\cdot}a_{2}{\cdot}b_{2}^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{2}{\cdot}a_{1}{\cdot}c_{1}+{\pi}{\cdot}b_{2}{\cdot}\left(\sqrt{4a_{2}^{2}+b_{2}^{2}}{-}b_{2}\right)\end{array}\)
 
24-SL graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
25-SL graphic 
\(\begin{array}{l}\mathrm{Suppose:}\ b_{2}=b_{3}=b_{4}\\V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}\left(a_{3}+a_{4}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{6}{\cdot}a_{1}{\cdot}b_{1}{\cdot}b_{2}\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\left[\frac{b_{1}+b_{2}}{2}+\frac{a_{1}^{2}}{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{\cdot}\mathrm{sin}^{{-}1}\frac{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{a_{1}}\right]+\frac{{\pi}}{2}{\cdot}b_{2}{\cdot}\left(2a_{2}+\sqrt{a_{3}^{2}+\frac{b_{2}^{2}}{4}}+\sqrt{a_{4}^{2}+\frac{b_{2}^{2}}{4}}{-}b_{2}\right)\end{array}\)
 
26-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a^{3}\\A\ =\ \frac{3{\pi}}{4}{\cdot}a^{2}\end{array}\)
 
27-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}a_{3}{\cdot}b_{3}^{2}+\frac{{\pi}}{12}{\cdot}a_{1}{\cdot}\left(b_{1}^{2}+b_{1}{\cdot}b_{2}+b_{2}^{2}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\sqrt{a_{1}^{2}+\left(\frac{b_{1}{-}b_{2}}{2}\right)^{2}}+\frac{{\pi}}{4}{\cdot}\left(b_{1}^{2}+b_{2}^{2}\right)+2{\pi}{\cdot}\left(a_{2}{\cdot}b_{2}+a_{3}{\cdot}b_{3}\right)\end{array}\)
 
28-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}a\\A\ =\ {\pi}{\cdot}b{\cdot}\left(\frac{b}{2}+a\right)\end{array}\)
 
29-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
30-H graphic 
\(\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ 3a{\cdot}b+\frac{\sqrt{3}}{2}{\cdot}b^{2}\end{array}\)
 
31-SL graphic 
\(\begin{array}{l}V\ {\approx}\ c{\cdot}\left(a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}\right)\\A\ {\approx}\ c{\cdot}\left(2a_{1}+b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}+\frac{{\pi}}{2}{\cdot}b_{2}\right)+2a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}{\cdot}b_{2}\end{array}\)
 
Shape code Simulated shape Volume (V) and surface area (A) model 
1-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a^{3}\\A\ =\ {\pi}{\cdot}a^{2}\end{array}\)
 
2-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}b^{2}{\cdot}a\\A\ =\ \frac{{\pi}{\cdot}b}{2}\left(b+\frac{a^{2}}{\sqrt{a^{2}{-}b^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{a^{2}{-}b^{2}}}{a}\right)\end{array}\)
 
3-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{6}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b+c\right){\cdot}\left[\left(\frac{b+c}{2}\right)+\frac{2a^{2}}{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}\mathrm{sin}^{{-}1}\frac{\sqrt{4a^{2}{-}\left(b+c\right)^{2}}}{2a}\right]\end{array}\)
 
4-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a^{2}{\cdot}c\\A\ =\ {\pi}{\cdot}a{\cdot}\left(\frac{a}{2}+c\right)\end{array}\)
 
5-H graphic 
\(\begin{array}{l}V\ =\ {\pi}{\cdot}b^{2}{\cdot}\left(\frac{a}{4}{-}\frac{b}{12}\right)\\A\ =\ {\pi}{\cdot}a{\cdot}b\end{array}\)
 
6-H graphic Suppose the height of cones is half of b:
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}\left(a{-}\frac{b}{3}\right)\\A\ =\ {\pi}{\cdot}b{\cdot}\left(a{-}\frac{4{-}\sqrt{3}}{4}b\right)\end{array}\)
 
7-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{4}{\cdot}b{\cdot}\left(b+\sqrt{4a^{2}+b^{2}}\right)\end{array}\)
 
8-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}\)
 
9-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}b^{2}{\cdot}\left(b+\sqrt{\frac{2a^{2}{-}ab+b^{2}}{2}}\right)\end{array}\)
 
10-H graphic 
\(\begin{array}{l}V\ =\ a{\cdot}b{\cdot}c\\A\ =\ 2{\cdot}a{\cdot}b+2{\cdot}b{\cdot}c+2{\cdot}a{\cdot}c\end{array}\)
 
11-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
12-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
13-H graphic 
\(\begin{array}{l}V\ =\ \frac{1}{2}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ a{\cdot}b+\frac{\sqrt{a^{2}+b^{2}}}{4}{\cdot}c\end{array}\)
 
14-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}\)
 
15-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)+a{\cdot}c\end{array}\)
 
16-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{6}{\cdot}a{\cdot}b^{2}\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}b{\cdot}\sqrt{a^{2}+b^{2}}\end{array}\)
 
17-H graphic 
\(\begin{array}{l}V\ =\ \frac{2}{3}{\cdot}a{\cdot}c^{2}{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{b}{2c}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}a{\cdot}c+b{\cdot}\left[c+\frac{a^{2}}{2\sqrt{a^{2}{-}4c^{2}}}{\cdot}\mathrm{sin}^{{-}1}\left(\frac{\sqrt{a^{2}{-}4c^{2}}}{a}\right)\right]\end{array}\)
 
18-H graphic 
\(\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}c{\cdot}a^{2}\\A\ =\ 3a{\cdot}c+\frac{\sqrt{3}}{2}{\cdot}a^{2}\end{array}\)
 
19-H graphic 
\(\begin{array}{l}V\ =\ \frac{1}{6}{\cdot}a^{2}{\cdot}c\\A\ =\ \frac{1}{2}{\cdot}a^{2}+a{\cdot}\sqrt{a^{2}+8c^{2}}\end{array}\)
 
20-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
21-H graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{a{\cdot}b}{4}{\cdot}\left[a+\left(\frac{{\pi}}{4}{-}1\right){\cdot}b\right]{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)\\A\ {\approx}\ \frac{b}{2}{\cdot}\left(2a+{\pi}{\cdot}a{\cdot}\mathrm{a}\mathrm{sin}\left(\frac{c}{2a}\right)+\left(\frac{{\pi}}{2}{-}2\right){\cdot}b\right)\end{array}\)
 
22-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{3}{\cdot}\left(a_{1}+a_{2}\right){\cdot}b_{1}^{2}+\frac{{\pi}}{4}{\cdot}\left(a_{2}+b_{2}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}a_{2}{\cdot}b_{1}{\cdot}b_{2}\\A\ =\ {\pi}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}b_{1}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}b_{2}^{2}{\cdot}\sqrt{\left(\frac{a_{1}}{b_{1}}\right)^{2}+\frac{1}{4}}{-}\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}\sqrt{\left(\frac{a_{1}{\cdot}b_{2}}{b_{1}}{-}a_{1}\right)^{2}+\frac{b_{1}^{2}}{4}}\end{array}\)
 
23-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{1}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{3}{\cdot}a_{2}{\cdot}b_{2}^{2}\\A\ =\ \frac{{\pi}}{2}{\cdot}a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}b_{1}{\cdot}c_{1}+\frac{{\pi}}{2}{\cdot}a_{1}{\cdot}c_{1}+{\pi}{\cdot}b_{2}{\cdot}\left(\sqrt{4a_{2}^{2}+b_{2}^{2}}{-}b_{2}\right)\end{array}\)
 
24-SL graphic 
\(\begin{array}{l}V\ {\approx}\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ {\approx}\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
25-SL graphic 
\(\begin{array}{l}\mathrm{Suppose:}\ b_{2}=b_{3}=b_{4}\\V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{12}{\cdot}\left(a_{3}+a_{4}\right){\cdot}b_{2}^{2}+\frac{{\pi}}{6}{\cdot}a_{1}{\cdot}b_{1}{\cdot}b_{2}\\A\ {\approx}\ \frac{{\pi}}{4}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\left[\frac{b_{1}+b_{2}}{2}+\frac{a_{1}^{2}}{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{\cdot}\mathrm{sin}^{{-}1}\frac{\sqrt{a_{1}^{2}{-}\left(\frac{b_{1}+b_{2}}{2}\right)^{2}}}{a_{1}}\right]+\frac{{\pi}}{2}{\cdot}b_{2}{\cdot}\left(2a_{2}+\sqrt{a_{3}^{2}+\frac{b_{2}^{2}}{4}}+\sqrt{a_{4}^{2}+\frac{b_{2}^{2}}{4}}{-}b_{2}\right)\end{array}\)
 
26-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{12}{\cdot}a^{3}\\A\ =\ \frac{3{\pi}}{4}{\cdot}a^{2}\end{array}\)
 
27-SL graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}^{2}+\frac{{\pi}}{2}{\cdot}a_{3}{\cdot}b_{3}^{2}+\frac{{\pi}}{12}{\cdot}a_{1}{\cdot}\left(b_{1}^{2}+b_{1}{\cdot}b_{2}+b_{2}^{2}\right)\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(b_{1}+b_{2}\right){\cdot}\sqrt{a_{1}^{2}+\left(\frac{b_{1}{-}b_{2}}{2}\right)^{2}}+\frac{{\pi}}{4}{\cdot}\left(b_{1}^{2}+b_{2}^{2}\right)+2{\pi}{\cdot}\left(a_{2}{\cdot}b_{2}+a_{3}{\cdot}b_{3}\right)\end{array}\)
 
28-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}b^{2}{\cdot}a\\A\ =\ {\pi}{\cdot}b{\cdot}\left(\frac{b}{2}+a\right)\end{array}\)
 
29-H graphic 
\(\begin{array}{l}V\ =\ \frac{{\pi}}{4}{\cdot}a{\cdot}b{\cdot}c\\A\ =\ \frac{{\pi}}{2}{\cdot}\left(a{\cdot}b+b{\cdot}c+a{\cdot}c\right)\end{array}\)
 
30-H graphic 
\(\begin{array}{l}V\ =\ \frac{\sqrt{3}}{4}{\cdot}a{\cdot}b^{2}\\A\ =\ 3a{\cdot}b+\frac{\sqrt{3}}{2}{\cdot}b^{2}\end{array}\)
 
31-SL graphic 
\(\begin{array}{l}V\ {\approx}\ c{\cdot}\left(a_{1}{\cdot}b_{1}+\frac{{\pi}}{4}{\cdot}a_{2}{\cdot}b_{2}\right)\\A\ {\approx}\ c{\cdot}\left(2a_{1}+b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}+\frac{{\pi}}{2}{\cdot}b_{2}\right)+2a_{1}{\cdot}b_{1}+\frac{{\pi}}{2}{\cdot}a_{2}{\cdot}b_{2}\end{array}\)
 

Simulated shapes were given by a three-dimensional image with a cross-section view or a transapical section view. In the shape code column, H = models from Hillebrand et al. (Hillebrand et al., 1999), amended by ourselves; SL = models from Sun & Liu in this paper; V = volume; A = surface area; a = length; b = width; c = height. Other symbols are marked in the table.

METHOD

Phytoplankton samples from sample sites covering most of China’s seas (with samples collected from the first comprehensive investigation in 1958 up to now) were selected and analysed using a light microscope. Net samples were collected with a standard net III (76 μm mesh size, simple conical tow net, which is a standard phytoplankton tool used in China) and a vertical haul was made from just off the bottom to the surface. These samples were preserved in 2 or 5% neutral formaldehyde (final concentration) in glass or polyethylene bottles. Samples were observed with an Olympus BH-2 microscope at × 200, × 400 or × 1000 magnification in a phytoplankton counting chamber (a standard tool used in China fabricated in our laboratory, 0.25 ml, similar to a Palmer–Maloney chamber) and identified to species level (Yamaji, 1991; Tomas, 1997). Water samples were preserved initially in 250 ml polyethylene bottles containing 1% Lugol’s iodine solution and ultimately the samples were preserved in 1% neutral formaldehyde (final concentration). Twenty-five millilitres of preserved sample were left for >24 h in settling chambers and then analysed with an American Optical Ltd inverted microscope at × 200, × 200 or × 640 magnification (Utermöhl, 1958) to identify phytoplankton to species level (Yamaji, 1991; Tomas, 1997). The scale bar for the microscopic ocular was calibrated using a standard scale bar (S22-StageMic; Graticules Ltd, UK) mounted on the microscopic objective.

Linear dimensions were measured according to Table II or by obtaining taxonomic information and searching the shape code in Table I. In most cases, it was possible to determine the length and width of the target cell. As the cell settles on the base plate on the posture of synthetic effect of several forces, such as gravitation and buoyancy, the length may not always be the apical axis. The individual analysing the sample need not consider the morphological information when using this set of models, thus the applicability will be improved in the models. The height of the target cell can be measured after rolling the cell by gently touching the coverslip with a pin-like object under routine examination by light microscope.

Twenty or more individual cells should be measured to avoid biasing results (Sournia, 1978; Hillebrand et al., 1999). The information on taxa and linear dimensions were then input into a Microsoft Excel worksheet; cell and community biovolume and surface areas were calculated by a VBA program which compiled data according to the shape code in Table I and the equation in Table II. History samples from which the cell abundance and community information to species level have been derived can also be converted from cell counts to biovolume and surface area. When linear dimensions of 20 typical cells in the sample were measured, individual cells of chain-forming species were measured and calculated. Software enabling these calculations is available from the first author, or at http://www.ouc.edu.cn/csmxy/sunjun/biovolume.htm.

RESULTS AND DISCUSSION

Measurement of phytoplankton cell height

Measuring the height of phytoplankton cells under the microscope can be difficult for some species. The algal cell usually keeps a definite position on the slide when the centre of gravity is low, making it difficult to measure the cell height. In most instances, an algal species will keep a fixed position, but on rare occasions the side view of the cell is visible, providing the opportunity to measure the height. If the cell is rotated, it will increase the chances of getting a side view. Using a pin-like object to tip the coverslip, algal cells will roll with the movement of the surrounding medium.

Usually it is not possible to rotate the cell using a pin in order to measure the cell height, either when the sample is examined by the Utermöhl method or when special counting slides such as Sedgwick–Rafter or Palmer–Maloney slides are used. There are two ways to solve the problem: one is to concentrate the sample after observation and follow up with a standard compound microscope; the other is to estimate the height from the width of the cell, because the height of small algal cells is usually approximately equal to the width. Verity et al. also pointed out that there is little variation between the depth and width of nanoplankton cells (Verity et al., 1992). However, as Hillebrand et al. (Hillebrand et al., 1999) suggest, the height of large cells should be measured.

Error sources in the models

For each genus, the error sources within these models come from the choice of geometric shapes assigned to the algal cell, in addition to the accuracy of measurement and consequent estimation of biovolume.

The selection of geometric shapes in this model was similar to Hillebrand’s model (Hillebrand et al., 1999). It was based on an assumption of similar shapes within each genus. In general, this principle applies, but there are some exceptions within genera, as pointed out by Hillebrand et al. (Hillebrand et al., 1999). The main distinguishing feature between these two models is that some geometric shapes were divided into two similar models for convenience of measurement, each one being the side view of the opposite one, such as ‘prism on elliptic base’ and ‘prism on elliptic base girdle view’ (cf. Table II). Meanwhile, six additional geometric shapes were assigned to additional morphologically complex genera.

The measurement procedure can potentially be the largest error source when estimating biovolume if the sampler does not follow the standard protocol accurately. The scale bar must be calibrated for each magnification. Light halos affect the measurement of small-sized cells (Montagne et al., 1994), but can be overcome by increasing the magnification of the microscope.

Between the initial field sampling and final interpretation of data, there are several potential sources of bias or variability. They include initial sampling methods, preservation (primary samples), subsampling (including concentration or dilution), counting use of tertiary subsamples, or random field selection, and statistical analyses. Some of these can be minimized or eliminated by following a strictly standardized procedure (Sournia, 1978; Hallegraeff et al., 1995).

It is not possible to measure every cell during routine analysis. Subsamples for line dimension measurement should consider phytoplankton assemblages. For each phytoplankton assemblage, at least 25 randomly selected cells of each species should be measured (Smayda, 1978), and the mean biovolume should be calculated from the mean value of these individual cell biovolumes. Hillebrand et al. propose that biovolume should be calculated from the mean of measured linear dimensions, not as a mean of a set of individually calculated biovolumes (Hillebrand et al., 1999). When the two methods for mean biovolume calculation were compared, we found that although the latter method usually underestimated the variability, its trend has better agreement with increased measurements (Figure 1). Thus, the mean measured linear dimension can be used to calculate biovolume in routine analysis. Although, under most circumstances, the standard error (SE) is <5% of the mean biovolume after the measurement of 10 cells (cf. Figure 1), we suggest that taking as many measurements as possible is better.

Fig. 1.

Comparison of the mean biovolume of four species calculated from the mean of the linear dimension (dashed line) or the mean of individual biovolumes (solid line).

Fig. 1.

Comparison of the mean biovolume of four species calculated from the mean of the linear dimension (dashed line) or the mean of individual biovolumes (solid line).

Comparison with other models

A comparison between this study and the other three models, Hansen (Hansen, 1992), HELCOM (Helsinki Commission, 2000) and BIOVOL (Kirschtel, 1992), is shown in Figure 2. Five typical species were assigned to five different geometric shapes with a length/width ratio from 1.2 to 25. Sample measurements were conducted under the microscope as described previously. Compared with these models, Hansen’s model underestimated the volume and the BIOVOL model overestimated the biovolume. The HELCOM model had similar results to our study. However, most results have a SE of not more than 30%. With the exception of Ceratium furca, the calculation equations of the other four species in this study were equal to the Hillebrand et al. model (Hillebrand et al., 1999). Hillebrand et al. (Hillebrand et al., 1999) also compared their results with Edler’s model (Edler, 1979), Rott’s model (Rott, 1981) and Kovala–Larrance’s model (Kovala and Larrance, 1966). They pointed out that there were some genera without a geometric model for calculating biovolume. In each model mentioned in this paper, including this study, none can give every phytoplankton species/genera a geometric model for calculating biovolume. Because of the diversity of phytoplankton morphology, it is impossible to calculate biovolume according to a set of geometric models, but all the models determine biovolume by simulation. It is important to focus on how to attain more accurate and available data when we choose appropriate models to calculate biovolume. Thus, for resolving a specific problem we can use different biovolume models. For example, Young and Ziveri use a cubic function, V = Ks × l3, to calculate coccolithophorids (Young and Ziveri, 2000). They assigned a specific shape constant, Ks, to a definite coccolithophorid species, thus they can get a more accurate value of biovolume for the species. If a phytoplankton assemblage is dominated by a microalga that has a more complex geometric shape, such as C. furca, it is important to produce a more complex geometric model or employ the models mentioned above to calculate this particular species.

Fig. 2.

Comparison of calculated biovolume by four models for five typical phytoplankton species.

Fig. 2.

Comparison of calculated biovolume by four models for five typical phytoplankton species.

Related ecological parameters

Biovolume and surface area calculations for phytoplankton cells are important for many related ecological parameters (Malone, 1980; Sournia, 1981; Chisholm, 1992), such as biomass, growth, photosynthesis, respiration, assimilation, sinking, grazing, etc. Most relationships between these parameters and biovolume follow the allometric theory, i.e. R = a × Vb, where R is a specific rate process or biomass, V is biovolume, and a and b are constants. So the biovolume and surface area of phytoplankton cells are used for conversion of cell counts into many related parameters. Although this procedure is complex and tedious, the conversion parameters provide the opportunity of differentiating between the contribution of different taxonomic groups which cannot be calculated accurately in ‘bulk measurement’.

In these biovolume-related parameters, carbon conversion is obviously important to phytoplankton studies, and is becoming a routine quantity derived from phytoplankton sample analyses. Several relationships between carbon and biovolume have been established in the literature (Mullin et al., 1966; Strathmann, 1967; Eppley et al., 1970; Taguchi, 1976; Rocha and Duncan, 1985; Verity et al., 1992; Montagne et al., 1994; Menden-Deuer and Lessard, 2000). The different phytoplankton assemblages have their own special carbon–biovolume relationship, but this measurement has not been carried out in the China Sea waters until now. Following the calculation of biovolume for 87 commonly found phytoplankton species in China Sea waters, Sun et al. (Sun et al., 2000a) compared four carbon–biovolume relationships (Mullin et al., 1966; Strathmann, 1967; Eppley et al., 1970; Taguchi, 1976) for carbon estimation of net phytoplankton, and proposed using Eppley’s method (Eppley et al., 1970) for carbon conversion in China Sea waters.

Model applications in China

There are few biovolume studies on phytoplankton in China (Sun et al., 2000a,b,c 1980). In these studies, Jiaozhou Bay was chosen as a case study area, and phytoplankton cell biovolume was calculated for each species by assigning one or several combinations of regular geometric shapes. This is not easily done as we required to consider each species’ morphological information. The new model, as described above, was established at the end of 1999. According to the convenient feature of inputting data in Microsoft Excel, we compiled a VBA program for this model. This model was tested using the conversion carbon estimates from elsewhere (Sun et al., 2001).

In conclusion, the geometric model for estimating phytoplankton cell biovolume is applicable in China and easier to use in routine phytoplankton analyses. It provides taxonomic information while calculating biovolume-related parameters. Its application should be extended to other regions, and should be attempted in many other related fields, such as historical data assimilations, studies on carbon flux at the species level, studies on biovolume and surface area relationship with related parameters, etc.

We are indebted to the National Natural Science Foundation of China (NFSC) which supported the work under contract No. 40206020, 2001CB409702 and the State Oceanic Administration of China (SOA). We thank the following colleagues for useful discussions: Dr Jennifer Martin (Fisheries & Oceans, Canada) and Dr Claus-Dieter Dürselen (Oldenburg University, Germany). The manuscript benefited from comments by Dr Ian Jenkinson, Professor Helmut Hillebrand and one anonymous reviewer.

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