A biosystematic basis for pelagic biodiversity

29 Pages·1994·2.1 MB·English

by  Van Der Spoel, S

Bijdragentot de Dierkunde,64 (1) 3-31 (1994)
SPB Academie Publishingbv, The Hague
A biosystematic basis for pelagic biodiversity
S. van der Spoel
Instituteof Systematics andPopulation Biology, University ofAmsterdam, P.O. Box94766, 1090GT
Amsterdam, TheNetherlands
Keywords: Biodiversity, diversity calculation, ecology, pelagic, phylogeny
Abstract diagrammeservirapourunecomparaisonentrelavariabilité de
ladiversitédans la natureetles changementsdeladiversitépro-
Biodiversitycanbeconsidered tobeahumanappreciationofthe voquéspar la société humaine. Les fluctuations dela diversité
danslepélagialdiffèrent des fluctuations dans labiomasse,mais
biologicalentity diversity. Diversity canbe expressed numeri-
callyonthebasis oftaxa found,but it canalso beexpressed as les fluctuations dans labiomasse ontaussi uneinfluence surles
fluctuations deladiversité. Du pointde vuescientifiqueet dela
the contribution ofaspecimentothe diversity,forwhich afor-
préservationde l’environnement,des étudesspéciales devraient
mula is proposed. Diversity is the sum of the taxonomic or
numerical diversity,andtheecological,genetical,historical,and être dévouées auxeauxocéaniquesetnéritiquesindo-malaises,
phylogeneticdiversity. Moreover,each group, orlargertaxon, ainsi qu’auxeauxnéritiques tempérées et subtropicales, aux
has itsowncharacteristic diversity.These types ofdiversityare eauxtropicalesengénéral,etspécialementauxeauxcentrales de
l’Atlantiqueetdu Pacifique.
considered separately.One formula is tentativelyproposed to
calculate the overall diversity. Diversity in nature is variable,
whichisdemonstrated inadiagramforcomparisonwithsociety-
induced diversity changes. Diversity in the pelagic fluctuates Introduction
differentlyfrom biomass fluctuations,but biomassfluctuations
also influence diversityfluctuations. From a scientific and an
environmental preservationpointofview,specialstudiesshould Diversityis such abasicconcept thatinspeakingof
bedevoted tothe Indo-Malayanneritic and oceanicwaters, the pelagic diversity,onemustalsomakesomegeneral
neritic temperate and subtropical waters, the tropical waters remarks. The organisms living in the open ocean
in general,and especiallytothe Atlantic and Pacific Central consist of plankton and nekton, floating with the
waters.
currents over enormous distances and dispersed
over depths averaging 3500 m. Despite the large
dimensions of the ocean which covers more than
Résumé
70% oftheearthsurface, its biological diversity in
general is small:only atmost40®7oofallknownspe-
La biodiversité peut être considérée commeuneappréciation
ciesareliving intheocean (Pierrot-Bults& Van der
humaine de l’entité biologique“diversité”. La diversité peut
êtreexpriméesurlabasedu nombre detaxatrouvés,mais aussi Spoel, 1979). Oceanlifeis ontheonehandvery sen-
commemesuredans laquelleunexemplairecontribue àla diver- sitiveto climaticchanges, as shown duringgeologi-
sité: pour ceci une formule est proposée. La diversité est la cal history. On the other handit is ocean life that
sommede la diversité taxonomique(numérique),écologique, largely determinesatmospheric conditionsthrough
génétique, historique et phylogénétique. En outre, chaque
its influenceon the atmospheric gases. By the year
groupe ou taxon assez grand a sa propre diversité caracté-
2000, 60% of the humanworldpopulation will be
ristique. Ces types de diversité ont étéconsidérés séparément.
Uneformule estproposéepourcalculer ladiversité globale.Un living inordepending onthecoastalzone(Lasserre,
* Paperpresentedat the SCOR WG93 workshop on PelagicBiogeography,Amsterdam,30 Aug.-l Sept. 1993.
4 S. van derSpoel - Biosystematic basis forpelagic diversity
1992), wherea major foodsupply will come from this chaos by determining the principles underlay-
the pelagic. Last but not least, ocean pollution ing this chaos.
usually has dramaticeffects over greaterareas than Therearethustwo approaches to diversity possi-
terrestrial pollution. ble,onestartingwiththehumanbeing fulloffickle-
Thus, evidently pelagic diversity needsspecial at- ness andone dealing withthevery variablebiologi-
tention, focusing on the existing diversity that cal specimens.
needs to be maintainedand the reduced diversity Inthis paperthehumanconcern about diversity
thatneedstoberestored. Attentionshouldbegiven andtheneeds for diversity will be consideredfirst;
to studies of the natural fluctuationsin diversity, thediversity crisis can show thevalueof diversity.
which must be understoodbefore society-induced Secondly, the biological value for diversity is de-
changes can be detected. Here the time scale be- rived, first by considering thehigher taxaand later
comes important, e.g., the question of how long by considering the species. The relation of abun-
does it take to restore the environment and over danceand biomassto diversityis consideredbefore
what period should preservation measures be trying to calculatethe diversitybasedonindividual
taken. specimens of species. To this numerical diversity
First wehave todefinewhatthediversity is from the genetic, phylogenetic, historical,and ecological
ahumanpointof viewand from abiological point diversity is added to arrive at one formulatoex-
of view. Can we formulate diversity exactly, and press diversity.
how can we measure it? As diversityislinkedwithanarea, thegeographic
distributionof diversity is considered.Finally, the
taxon is briefly discussedas a diversity carrier, be-
What is biodiversity? fore making some remarks on more or less endan-
gered areas in the open ocean.
Ascientifictermshould haveadefinition. Apoliti-
cal term is valid already when ithas a long list of
synonyms although no definition.Who coinedthe A human concept
termbiodiversity? Apolitician I am afraid, though
manyscientists have advocatedtheuse oftheterm Human concern about diversity is not a recent
biodiversity (Wilson, 1992). Combining "bio" phenomenon. Thebibletellsusofthe Arkof Noah,
frombiology, thestudy of life,with "diversity" - the first global protection of diversity. The prin-
oneof the most typical characters of life - seems ciple is well described:
overdone, since without life there is no diversity
and without diversity, no life. Humans need a "Andofeverylivingthingofall flesh,two ofeverysort shalt
healthy, living anddiverse world and like to name thou bringinto theark, tokeep them alivewith thee;theyshall
thislifeinanattemptto havepowerover it. On the be male and female" (Gen. 6-19).
other hand, humans are afraid of the delicate "Ofeveryclean beast thoushalttaketothee bysevens, themale
wonder of the living world and look for euphe- and his female: and ofbeasts that arenotclean two,the male
and his female" (Gen. 7-2).
misms like biodiversity to indicate this wonder.
"Offowls also ofthe airby sevens the maleand his female;to
Diversity has also a purebiological content (we keep seed alive upon the face ofall the earth" (Gen.7-3).
willnot use further theterm biodiversity). Itis the "AndtheywentinuntoNoah into theark, two and two ofall
always variablepresentation, intimeand space,of flesh, wherein isthe breath oflife" (Gen. 7-15).
thephenomenon "life".Thescienceofsystematics
is entirely devoted to the study of the forms in Thus populations of all species, theirreproductive
whichlife is present andto thecreationoforderin ability, and incase thespecies are useful also their
the seemingly chaotic biota. Systematics is the variability, shouldbe protected to preserve diver-
sciencethatcan describeandhandlethediversityof sity on earthandto beusedby society. Clearly we
Bijdragen tot deDierkunde, 64 (1) - 1994 5
shouldnot only takecareoftheuseful species; also Forcertain, itis dangerous to manipulate diversity,
those seemingly unimportant to society shouldbe butitmay bemore dangerous to liveinapoisonous
preserved. Diversity seemsalso toindicateharmony atmosphere or underabioticconditions.Theremay
oforganisms in equilibrium with each other. Cer- comea moment when we havethe choiceonly be-
tainly this early environmentalwisdom ofthebible tween two such equally bad possibilities!
concerns diversity, protected to form a continuous For the long term, the care of diversity is a
source of foodand health. management problem. For the short term, it is a
preservation problem. This portrays a conflicting
situationas preservation introducesastaticsystem
Whatkind ofdiversity do we need? and managementa dynamic system. As society is
usually more involved in short time profit than in
Itis probably easierto detect whatkindof diversity long term profits, very possibly society willcreate,
is not needed, viz. the diversity thatisnolonger use- in the future, an insurmountableproblem: a large
ful, neitherfor nature nor for society. Too strong scale diversity crisis due to irreversible fixationof
a protection could freeze the existing diversity so present-day diversity dueto preservation activities.
that thecontinuousprocess ofnaturaldiversifica- Irreversible fixationin thepelagic realm is not ex-
tionandevolutionwouldbestopped. Suchafrozen pected tobepossible atpresent,butinotherrealms
diversity is useless, and a protection that prevents it may become a real problem.
society frommaking useoftheorganisms thatcon-
tributeto the diversity has no valueeither. Inthe
pelagic realm, no examples can be found of this Whatis a diversity crisis?
"freezing", but animalstocks inzoos and the ter-
restrial communities inwild preservation areas are A diversity crisis is causedby accumulationofir-
examples offrozen diversity that haveno potential reversiblechanges inourenvironment— afrighten-
for furtherdevelopment as longas the managed sit- ing phenomenon as itcauses "the accelerating rate
uationendures. ofextinctionofspecies" (Nelson &Ladiges, 1990).
What do weneed to live andto provide ouroff- The dramatic shift in species composition of the
spring with a world that is healthy, living and Mediterranean(Kouwenberg & Razouls, 1990)and
diverse, thusevolving and diversifying? The mini- the mass mortalities (Weinberg, 1992) are indica-
mum diversity required intheocean is thediversity tions ofa crisis inthisenclosed basin. Inotheriso-
of the organisms that keep the atmosphere and lated basins, diversity crises are also reported. In
hydrosphere in an equilibrium (e.g., 02 produc- theNorthSea,Balticandinvariousestuarineareas,
tion; C02, Caand nutrientabsorption, neutraliza- crises arereported to havebeencaused by fisheries
tionofriver output), provide biological stocks for activities, marineand river pollution, off-shore ac-
fisheries, and maintain anaesthetic environment. tivities, and transport accidents. Such crises, how-
Weknowthatchanges insolarradiation(forare- ever, are rare in the open ocean as the "irreversi-
cent modelsee: Caldeira&Kasting, 1992)and hu- ble" change is here more difficultto generate by
manactivities willchange thecomposition oftheat- humanactivities. The mass extinctions at the end
mosphere, biosphere, and hydrosphere, which ofthe Cretaceous, also a diversity crisis produced
form aninterconnectedsystem (Lovelock & Whit- by nature, however, showthat open ocean crisis is
field, 1982). So wemayeven thinkof increasing or indeed possible. Polluting the atmosphere on a
changing diversity to cope with problems of at- global scale, affecting ocean temperatureandinso-
mosphericchanges. Geneticmanipulation andspe- lation, maycause just such acomparable crisis.
cialprogrammesto generatespecies andecosystems Red tidesand El Ninoeffects can be considered
especially equipped to maintaintheatmosphere in crises, butthey are ecological crises fromwhich we
a good conditionmay be necessary in the future. recover after sometime, usually without changed
6 S. van derSpoel - Biosystematic basis forpelagic diversity
course, connect an "appreciation" ofits worth to
society as a derivedvalue.
A biological value
Diversity maybe viewed inthefirst instanceas an
expression ofthe biomassorofthe species compo-
sition.Withoutbiomass,thereis nodiversity, while
some biomass means some diversity. But does a
largebiomassindicatelarge diversity? Thebiomass
diversity is frequently studied. The Stommel's
modelasusedby Haury etal. (1977)shows thebio-
mass variability as a function of time and space
(Fig. 1A). The species composition or diversity can
bepresentedalso inaStommel'sdiagram(Fig. IB).
It is easily seen that large biomass variability is
linkedwithlow diversity fluctuationandvice versa,
whichfrom anecological point ofviewiscomplete-
ly logical. This probably also explains why Cohen
(1986) came to the conclusion "The latitude-
diversity-biomass relationship is not clear". Inthe
time/space areaofonecentimetreto one kilometre
andseconds to onemonth, thereisalarge variabili-
ty in diversity due to physical parameters such as
currents and waves, seasonal changes, diurnaland
seasonal migrations, and seasonal species succes-
sions. In theareaof 10years and 10 km there is a
Fig. 1.A,BiomassvariabilitysimplifiedaftertheStommel’s dia-
separatemaximumof variationin diversity dueto
gramby Haury etal.(1977).B, Diversity variabilityatthe spe-
physical variabilityofthetypegivingrise to ElNino
cies level. Diversity due to evolution takesplace atlargertime
scales and is added in thedotted area; space ony-axis,timeon andshiftsof major currentpatterns. Theserelative-
x-axis, variabilityonz-axis. ly "unstable" time/space areas are probably less
sensitiveto humaninfluencethantheareas without
variability.
diversity. The bloomings oftoxic algae due to hu-
Diversity has sofarbeen treatedinthis paperas
man-induced physicochemical changes in the en- arelativeandsomewhatsubjective concept. Purely
vironmentare ecological crises from which nature scientifically, without anthropocentric interpreta-
recovers, asthediversityis changed onlytemporari- tion, diversity can, however, also be given a value
ly. Though the diversity inthe environmenthas a as will be shown.
clear value for society, this value cannot be calcu- The diversity inthe oceanis smallwhenthespe-
lated directly. The value is also dependent on the cies level is considered, but when considering the
development of diversity in the future, which de- phylum or subphylum level, diversity is extremely
pends ontheabilityofthegenepool to generatethe high (cf. May, 1992:table2). Nearlyall(sub)phyla
coming diversity from itspresent diversity. For this are represented intheocean, and some 14 likethe
reason one can only "predict" a value for society Chaetognatha and Tunicata are endemic to it.
of biological diversity. For calculations one is de- Therefore one has to distinguish between: (a)
pendent on biological values, towhichonecan, of higher taxa diversityrelated tofamiliesand higher
Bijdragen tot deDierkunde, 64 (I) - 1994 7
taxa, (b) the species diversity, a combination of usually done?Shouldacompletely disjunct distri-
species andgeneraas genera canbe considerdtobe bution inthe north and south polar sea, or in the
based on the species diversity, and (c) the sub- tropical Atlantic and tropical Indian Ocean, be
specific diversity.The question: "Whynot consider considered a single species distribution, as is fre-
taxa in general as units, and embracethe fullmea- quently done? Itis easily seenthat it is impossible
sure ofbiodiversity?" by Nelson &Ladiges (1990) to answer both questions witheither yes or no. So
couldbeansweredpositively, butprobably thetaxa it is here proposed for thesake ofargumentto an-
at differentlevels are also of different nature, so swer thefirst question withyes andthesecond with
thatonemaybettertreatthemseparately in firstin- no. Thus one can no longer give great value to
stance. "potential" in the definition, but will haveto lay
stresson "naturalpopulations" and"which donot
reproduce with othersuch groups".
Higher taxa diversity Aspecies as definedabovestill can be monotyp-
ic, polytypic, orpolymorphic. Does this variability
The higher taxa diversity is a measure of impor- contributeto diversity, and has it to be preserved?
tance mainly when considering large geographic This question is discussed later in the sections on
areas.Forexample, it is not interesting toknowthe genetic diversityandphylogenetic diversity; forthe
higher taxa diversity for a city park as the species moment the species will be treatedonly as a well
diversity is moreindicativeofsuch a place. Inthe limited, not variabletaxon.
ocean, differenthigher taxa diversities can be ex-
pected in differentlarge biotopes like the benthic, Abundanceof species and diversity — As we have
pelagic, oceanic, and neritic biotopes. In tropical seen that diversity fluctuations usually are differ-
andcoldwaters, differences canbe expected at the ent,andmostlyeven opposite,tobiomass(= abun-
family and order level (see Van der Spoel & Hey- dance) fluctuations, it is worth noticing that
man, 1983).Thesedifferencesbetweenthebiotopes (1) taxonomie groups tend to be represented by
in the ocean are still very small when I express abundant and rare species, (2) groups are com-
higher taxa diversity (D) as the sum ofthe number posed of diverse and less diverse subgroups,
offamilies(N{), orders(N0)and classes (Nc)divid- (3) withina taxon always occur a number of less
ed by the surface size ofthe biotope (Z?): related taxa and a numberof closely related taxa,
s
and(4) groupsarerepresented insomeareas by few
ZJhigher taxa diversity = (N{+7V0+Nc)/Bs and in other areas by many species. In diversity
studies, oneshould always mind thesefournatural
diversity phenomena.
Species diversity Taxonomie groups tend to be represented by
bothabundantandrare species, andthereseems to
Thespecies diversity is evidently dependent on the be arule determining theratio abundant/rarespe-
species concept used, and in discussing diversity of cies innature. Ineach group,manyrare species are
biogeographic areas, thegeographic componentin found, moderate numbers of common and very
the concept should be stressed. In the definition: commonspecies andlownumbersofveryabundant
"species are groupsof naturalpopulations which species. In Fig. 2 this distributionis given for spe-
actually orpotentially reproduce andwhich do not cies of Myctophidae and Hydromedusae in the
reproduce with other such groups" (Mayr, 1963), North Atlantic.This frequency distributionseems
theterms"naturalpopulations" and"potentially" tobe fractal in nature and can be describedwith a
should be given attention. For example, should a formulalike N(x) = ax~b.
population ofaPacificspecies livingintheAtlantic Groups are composed ofarangefrom diverseto
dueto transport by ships orto aquaculture be con- less diverse subgroups, andherealso a naturalrule
sideredan abnormal, not-naturalpopulation, as is seems to determine the diversity of groups in a
8 S. van der Spoel - Biosystematic basisforpelagic diversity
et al. (1991). A formula:N(x) = ax'b is proposed
by theseauthorsforcharacterizing the distribution
ofwithin-group diversity.Thevaluesofindexafor
pelagic molluscs, nemerteans,siphonophores, and
myctophids are 10,20, 30, and 10, respectively; for
the index b the values are 0.9, 1.5, 1.4, and0.7,
respectively. In Fig. 3 this N(x) function is repre-
sented by line "a". It is evident that these four
groupseachhavetheirowntypical diversity.Notice
thatthisformulawouldalso explain wellthe distri-
butionofrareand abundantspecies innature,as in
both cases the distribution is of the same fractal
Fig.2.Number ofspecimensforspeciesofMyctophidae(A)and
type.
Hydromedusae(B)in theNorthAtlanticOcean. Numberofspe-
ciesalongthe x-axis,numberclasses for specimensalong they- If the above statements are valid, a number of
axis in logarithmicscale. less closely related taxa and a number of closely
relatedtaxa occur inataxon always ina certainre-
taxon. InFig. 3 thenumberofspecies per genusis lation. Fig. 4 shows a cladogram based on 54
given in relationtothe generainpelagic molluscs, hypothetical species with7characterseachwithtwo
nemerteans, siphonophores, and myctophids. In character states distributedover the species at ran-
these groups many genera with few species are dom. In this randomized cladogram, one can dis-
found, moderatenumbersof generawith amoder- tinguish that above a certain level 70% of the
ate number of species, and low numbersof very groupsare composed offewspecies. This70%level
diversegenera.Thisphenomenon seems tobesimi- is indicated by line "x".
lar for all animals groups, as discussed by Minelli It is well known that each particular group (say
Fig.3. The number ofspecies pergenusin thepelagicmolluscs Pteropodaand Heteropoda(A), nemerteans(B), siphonophores(C),
and myctophids(D). Genera onx-axis,species per genusony-axisboth logarithmic,a = the line ofthe formula N(x) =ax-b after
Minelli et al.(1991).
Bijdragen tot deDierkunde, 64(1) - 1994 9
Fig.4. Ciadogramfor 54hypotheticalspecieswith 7 characters
distributedtotallyatrandom overthespeciestoshow thenatural
occurrence(e.g.,above the line x) oftaxa with many and with
few species. In the circles the areas are indicated where the
speciesAtoLarefoundtodemonstratethat eachareahasadif-
ferent phylogeneticdiversity.
Fig. 6. Maximum body size (mm)ofspeciesfor Gymnosomata
(A)andThecosomata(B) onx-axis,and number ofspecieswith
these sizes ony-axis (bothlogarithmic)(own data).
available.However,whenlengthinthethecosoma-
tous orgymnosomatouspelagicmolluscsistakenas
an indicationof body size, a distributionof this
value is found for thesegroups that is comparable
Fig. 5.Diagramoftherelation ofbiomass anddiversityfluctua- to the distributionof abundanceor of diversity.
tions with diversityin groups,species, and areas.For explana- Thus this also gives a distribution following the
tion seetext. N(x) = ax~b formulaofnon-linearcharacter given
by Minelliet al. (1991) (Fig. 6). Thevalueofafor
pelagic molluscs) shows areas with few species Thecosomata and Gymnosomata is 30 and 40,
(e.g., South Indian Ocean) and areas with many respectively, and for bit is for both 1.1.
species (e.g., NorthIndianOcean). Themorestable Abundant species will fluctuate with biomass,
biotopes tend to show higher diversities. thus innumbers,differently fromrare species, and
As we have shown that diversity and biomass sowillprobably also thelargerandsmallerspecies.
show an inversefluctuation (e.g., biomasstendsto The most abundant species are not always the
be lowin areas with high diversity),it is clearthat species ofthemost diversegenera, andtherare spe-
groups with abundant species, groups with less cies are not always the species of generawith few
diverse subgroups, groups with less related taxa, species. Limacinaretroversa(Fleminger, 1823)and
and areas with few representatives of a group Styliola subula Quoy & Gaimard, 1827 are very
should betreated differentlyfrom groupswith rare abundantover theirwholerange,but the first is a
species, groupswithdiversesubgroups, groupswith memberofadiverse genusandthelatterofamono-
closelyrelatedtaxa,andareas withmanyspecies of typic genus.Cliochaptali Gray, 1850andLaginiop-
a group.This is showninFig. 5, wheretherelation sis trilobataPruvot-Fol, 1922are both always rare
between these phenomena and variability in bio- butagain thefirstis amemberofavery diversege-
mass and in diversity is given. nus and thelatterofamonotypic genus.Theabun-
Thebody sizeof species is not consideredhere, danceand diversity fluctuationsare non-parallel or
asgood dataonbody sizeofspecies are usually not unrelatedprocesses. A further study ofthecharac-
10 S. van derSpoel - Biosystematic basisforpelagic diversity
Fig. 7. Euphausiiddistribution givenasnumbers ofspecies (inclasses of5) per 5° square(after Reid etal., 1976).
ters mentioned above for taxa in relationto bio- moreinformationonreal diversity.However,most
mass and diversity is highly recommended. calculations fail to indicate the contribution of
eachsingle species to thediversity. Inanattemptto
distinguish between more and less diverse water
Diversity calculation masses, a formulawas developed (Van derSpoel &
Bleeker, 1991)to calculatethecontributionofeach
The diversity can be expressed inthe most simple species to the diversity. This formulamay be of
way bygivingthenumbersof species ofataxon oc- value to evaluate diversity as well.
curring indifferentareas. InFig. 7 thenumbersof This formulais based on theassumption that a
euphausiids are given per5°squareafterReidetal. species has no value for diversity when it does not
(1976). This kind of presentation gives only infor- contributeto thelevelofdiversityofthe faunaand
mationon the biogeography of a group. So it is to the quality of diversity by showing a certain
clearfromFig. 7 that euphausiids mainly occur in abundance.Theimportance of aspecies ina fauna
Central waters and in the Indo-Malayan area, is thusgreater when its distance from thepoint of
whichis expected (cf. Van der Spoel et al., 1990). zero diversityand zeroabundanceis greater. This
Combining groups and dividing the ocean in is expressed in the formula:
"natural"subareas, likebasinsandcurrent systems
forpresenting the numbersof species, gives infor- B' = +C2)05
mationonspecies richness (Fig. 8).But this is again
mainly arepresentation ofbiogeography, though it Here B' is thediversity valueofthespecies for the
is less dependent on one group. faunaorsample in whichit is found, Cis thevalue
Thediversityofafaunaor inasample can be cal- thataspecies adds tothequalityofthefaunaby its
culated; e.g., the dominancevs. diversity formula abundance, andD is thevalueaspecies addsto the
(Dm/Dv, seebelow) is frequently used. This gives qualityofthefaunaby itscontributionto diversity.
11
Fig.8. Total number ofspecies ofPteropoda,Heteropoda,and Hydromedusaefound in the different oceanbasins (own data;scale
arbitrary).
ThevalueCofaspecies isdependent onthenum- A is thenumberof samples inwhich the species is
bersofspecimens relativeto theabundanceofthat found, and A is the maximumvalueof A for
max
species inothersamples andonthetotalnumberof the series ofsamples studied.
species in the sample relative to that number in Theconceptual advance is thatwiththeformula
other samples. Thus: B' = (D1+C2)0-5thecontributionofeach separate
species to thediversitybecomes visiblein asample
C = 100x (FxN' - UN')/ [(F x N'max - T.N') x F/Fmax] or fauna. This is not the case in the classical ap-
proaches of diversity as shown intheexamples be-
HereFis thenumberof species in the sample, N' low. As B' is usually high, it is represented as
is the logarithmofthenumberofspecimens + 1 of B' /100for comparison withotherindexes. Theac-
the species, Af' is the logarithm of the number tual influenceofthe numbersofspecimens is sup-
max
of specimens + 1 of themost abundantspecies in pressed by using log/V; the same formulacan also
the sample, and F is the number of species in beused withTV(the actualnumberofspecimens) by
max
the most species-rich sample. replacing \ogNwhentheinfluenceofthenumberof
The value of D of a species in a given sample specimens of each species should become better
is dependent on the number of specimens in the visible. WhenNinsteadoflogN is used, thediver-
sample, but relativeto the numberof the samples sity indexis calledBinsteadof B' (for anexample
in which the species is found and relative to the see TableI: line B/100, B'/100and the blocks B
numberof species found in other samples. Thus: and B').
The dominance/diversity formula is expressed
D2 = (1 +Amm-A)2 x (1+M-A) x N' as:
HereMisthetotalnumberofsamples inthestudy, Dm/Dv = %Nmax/S
12 S. van derSpoel - Biosystematic basisforpelagic diversity
TableI. Data setfor variable faunas (hypotheticalcollection of10 speciesand 12 samples).
a b c d e f g h i j k 1 samples
species A
Data
I 5 5 5 5 5 5 0 4 8 0 1 1 10
II 5 4 3 2 0 20 6 5 10 0 1 1 10
III 1 2 3 4 2 0 5 7 14 0 1 1 10
IV O 6 7 8 6 3 3 4 8 3 3 1 11
V 0 0 5 1 7 2 25 3 8 4 4 1 10
VI O 0 0 20 0 0 10 1 6 1 1 1 7
VII 0 0 0 0 0 0 0 7 14 1 1 1 5
VIII 0 0 0 0 0 0 0 8 16 1 1 1 5
IX 0 0 0 0 0 0 0 12 24 2 2 1 5
X 0 0 0 0 0 0 0 19 18 23 23 2 5
F 3 4 5 6 4 4 5 10 10 7 10 10 11
LN 11 17 23 40 20 30 49 70 126 35 38 11
Miiax 5.0 6.0 7.0 20.0 7.0 20.0 25.0 19.0 24.0 23.0 23.0 2.0
/•max 10 Amax 11 M 12
Bvalues
B 31.0 18.8 11.4 10.8 7.7 11.1 0.0 25.9 41.5 0.0 15.0 11.6
B 31.0 9.0 33.9 21.6 0.0 42.9 15.1 18.4 25.3 0.0 15.0 11.6
B 60.1 51.7 33.9 13.9 60.2 0.0 17.6 9.2 17.9 0.0 15.0 11.6
B 0.0 40.1 50.1 7.2 20.3 14.6 22.5 25.2 40.5 8.2 4.8 11.2
B 0.0 0.0 11.4 25.7 41.0 18.3 52.9 33.9 41.5 7.9 7.0 11.6
B 0.0 0.0 0.0 81.2 0.0 0.0 38.7 51.5 65.2 19.8 19.0 16.5
B 0.0 0.0 0.0 0.0 0.0 0.0 0.0 52.4 75.1 25.2 24.6 22.7
B 0.0 0.0 0.0 0.0 0.0 0.0 0.0 56.6 84.6 25.2 24.6 22.7
B 0.0 0.0 0.0 0.0 0.0 0.0 0.0 80.3 139.3 30.3 29.5 22.7
B 0.0 0.0 0.0 0.0 0.0 0.0 0.0 132.1 96.4 118.0 137.9 103.8
B' values
B' 30.2 21.8 13.7 3.9 7.8 3.3 0.0 26.8 49.5 0.0 22.2 11.3
B' 30.2 2.9 38.4 29.5 0.0 40.2 10.0 10.4 20.3 0.0 22.2 11.3
B' 60.0 61.4 38.4 6.6 72.0 0.0 16.8 16.7 25.6 0.0 22.2 11.3
B' 0.0 40.0 50.0 21.1 24.8 14.7 34.9 26.6 49.4 2.2 12.0 11.1
B' 0.0 0.0 13.7 48.1 40.1 24.2 50.2 47.1 49.5 10.8 23.1 11.3
B' 0.0 0.0 0.0 61.6 0.0 0.0 16.6 110.5 86.8 25.3 23.1 13.0
B' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24.9 33.2 26.7 24.6 15.5
B' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 33.3 48.8 26.7 24.6 15.5
B' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 64.2 102.7 16.4 13.8 15.5
B' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 102.5 63.9 73.8 102.7 100.9
Indexes
ß/100 1.2 1.2 1.4 1.6 1.3 0.9 1.5 4.9 6.3 2.3 2.9 2.5
BW100 1.2 1.3 1.5 1.7 1.4 0.8 1.3 4.6 5.3 1.8 2.9 2.2
m/v/10 1.5 0.9 0.6 0.8 0.9 1.7 1.0 0.3 0.2 0.9 0.6 0.2
D 0.8 1.1 1.3 1.4 1.0 0.9 1.0 2.1 1.9 1.7 2.5 3.8
X 0.6 0.7 0.8 0.7 0.7 0.5 0.7 0.9 0.9 0.5 0.6 0.9
H 1.0 1.6 1.9 1.8 1.6 1.2 1.7 3.5 3.4 3.6 3.7 2.3
H' 3.5 4.1 4.5 5.3 4.3 4.9 5.6 3.0 3.2 5.1 2.1 3.3
J' 0.0 0.2 0.4 0.4 0.2 0.1 0.4 1.6 1.6 1.2 1.7 1.1