Sigmoid Relationships between Phosphorus, Algal Biomass, andAlgal Community Structure

Susan Watson and Edward McCauley

Ecology Division, Department of Biological Sciences, University of Calgary, Calgary, Alta. T2N 1N4, Canada

and John A. Downing

Department de sciences biologiques, University de Montreal, Montreal (Quebec) H3C 3}7, Canada

Watson, S E.. McCauley, and J. A. Downing. 1992. Sigmoid relationships between phosphorus, algal biomassand algal community structure. Can. J. Fish. Aquat. Sci. 49: 2605-2610. o.omass,

It has long been recognized that there is a positive relationship between total phytoplankton biomass and eutro-ph.cat.on. Recent independent studies demonstrated that algal biomass (chlorophyll) actually responds in a nonlinear, s.gmoidal fash.on w.th increasing phosphorus levels among lakes. Chlorophyll has been considered (bvsome authors) as an inconsistent estimate of algal biomass. Using a wide range of published data we first demonstrate that the s.gmoidal nature of the phosphorus-biomass relationship is quite robust, anc1 noUimply generated by a systematic variation in the relationship between algal chlorophyll to cell volume ratio and nutrientlevels We show that the s.gmoid relationship with total phosphorus persists whether algal biomass is meauredby chlorophyll or b.ovolume We hypothesize that this nonlinearity actually reflects an underlymg systeSvariation m one or more of the components of total phytoplankton biomass. In this paper, we examine twofunctional size groups and show that the large inedible fraction exhibits a strong, nonlinear response to increasingnutrient levels, while the small ed.be algae do not vary systematically with phosphorus. We hypothesize thatthis discontinuous shift in the ratio of edible to inedible phytoplankton should be accompanied by concomi anshifts in the structure of the herbivore community.

On sait depuis longtemps qu'il existe un rapport positif entre la biomasse phytoplanctonique totale et I'eutro-ph.sat.on. Des etudes independantes r<§centes confirmed que la biomasse algale (chlorophylle) re"aeit en faitselon une courbe non lin^aire sigmoVdale a ('augmentation du taux de phosphore dans les lacs. Certains auteurscons.derent la mesure de la chlorophylle comme etant une evaluation peu coherente de la biomasse alealeD apres un large eventail de donnas publiees, nous demontrons d'abord que la nature sigmoidale de la relationphosphore-b.omasse est tres marquee et n'est pas simplement le r&ultat d'une variation systematique dans lerapport entre la chlorophylle algale et le volume cellulaire ainsi que la teneur en elements nutritifs Nous demontrons que le rapport sigrnoTdal avec le phosphore total subsiste, que la biomasse algale ait ete mesuree d'apresla chlorophylle ou le volume des bio-elements. Notre hypothese est la suivante : cette relation non lineaire refleteen n§alite une variation systematique sous-jacente d'un ou de plusieurs elements de la biomasse phytonlanctonique totale. Dans le present rapport, nous etudions deux groupes de taille fonctionnels, et montrons aue lagrande fraction non comestible presente une forte reaction non lineaire a I'augmentation des taux d'ei^mentsnutr.t.fs, tand.s que la petite fraction d'algues comestibles ne varie pas de facon systematique par rapport auphosphore. Nous pensons que cette variation discontinue dans le rapport phytoplancton comestible - phyto-plancton non comestible doit etre accompagnee par des variations concomittantes dans la structure de la commu-naute herbivore.

Received January 30, 1992

Accepted June 25, 1992(JB390)

Recu le 30 Janvier 1992Accept le 25 juin 1992

The observation that phytoplankton biomass rises with

phosphorus concentrations in lake water has been a staple

component of limnological theory for three decades (e.g.

Sakamoto 1966; Dillon and Rigler 1974; Jones and Bachmann1976; Schindler 1977, 1978; Nicholls and Dillon 1978; Smith1982; Canfield 1983; McCauley et al. 1989). The theoretical

idea that algal growth is limited by phosphorus availability hasled to the belief that the relationship should be a power function

with constant exponent. When power functions of chlorophyllto total phosphorus are fitted for different geographical areas

or for different suites of data, exponents are not always equiv

alent (e.g. Nicholls and Dillon 1978; Janus and Vollenweider

1981; Straskraba 1986; McCauley et al. 1989; Prairie et al.

1989). Recent studies have shown, however, that variation

Can. J. Fixh. Aquat. Sci., VoL 49, 1992

among lakes in chlorophyll a (Chi a) with total phosphorus (TP)

can be better described by a sigmoidal relationship than by simple linear models (McCauley et al. 1989; Prairie et al. 1989)This observation is significant in terms of lake management andmight account for discrepancies among the linear modelsderived from geographically discreet of relatively small datasets (e.g. Nicholls and Dillon 1978; Paloheimo and Zimmer

man 1983; Bierhuizen and Prepas 1985; Dillon et al. 1988).Furthermore, it suggests that explanations for the phosphorus-chlorophyll relationship may be incomplete.

Although the measurement of chlorophyll is one of the mostconvenient and widely applied methods used to estimate algalbiomass, there has been some debate concerning its validity asa measure of phytoplankton biomass (e.g. Tolstoy 1979; Can-

2605

field 1983; Lampou el al. 1982; White et al. 1988). In partic

ular, the relationship between Chi a and algal biovolume is

thought to be highly variable and generally unpredictable (e.g.

Saraceni et al. 1978; Dillon et al. 1988; Aleya and Amblard

1989). This has been attributed to species- or size-specific dif

ferences in cell chlorophyll content and/or to the influence of

environmental factors, such as light (e.g. SteeleandBaird 1965;

Ruggiu et al. 1979; Desortova 1981; White et al. 1988; Prid-

more el al. 1989) and nutrient levels (e.g. Steele and Baird

1965; Ahlgren 1970; Nicholls and Dillon 1978; Saraceni et al.

1978; White et al. 1988) on the ratio of chlorophyll to cell

volume.

The existence of a sigmoid relationship of chlorophyll with

TP raises two important possibilities: (1) the relationship

between phytoplankton biomass and phosphorus is really lin

ear, but chlorophyll is an inconsistent measure of plant bio

mass, or (2) chlorophyll is a good measure of plant biomass

but our theoretical explanation for the form of the relationship

between plant biomass and phosphorus in lakes is overly sim

plistic. We therefore begin this paper by presenting evidence to

show that the curviltnearity in the Chi a - TP relationship is

not an artefact of the lack of consistency in the chlorophyll to

biovolume ratio of cells. We do this by comparing the relation

ship between algal biovolume and TP among lakes with pre

vious results on the Chi a - TP relationship.

The sigmoidal nature of the algal-TP relationship suggests

that there are several important features of the nutrient-algal

relationship which have yet to be explained. For example, why

does the rate of change of algal biomass per change in total

phosphorus increase at very low nutrient levels and then decline

at very high nutrient levels? Many hypotheses could be

advanced to explain both of these features. One explanation

might be that the nonlinearities can be accounted for by sys

tematic variation in the biomass of functional algal groups.

Another possibility is that systematic variation in average

growth or loss rates of algae with TP might yield nonlinear

algal-nutrient relationships (McCauley et al. 1989). Much

emphasis has been placed recently on how properties of plank-

tonic food webs might influence algal biomass (e.g. Kerfool

and DcMott 1980; Carpenter et al. 1985, 1987; Kcrfoot et al.

1985; Dorazio et al. 1987; Kerfoot 1987; Vanni 1987;

McCauley et al. 1989; Vanni and Temte 1990; Elser and Gold

man 1991) either via direct or indirect interactions, and a fur

ther explanation for nonlinear plant biomass - phosphorus rela

tionships might be related to differential responses of algal

groups that are either susceptible or insusceptible to grazing by

planktonic herbivores. This study tests the hypothesis thai non-

linearities in the algal-phosphorus relationship are consistent

with changes in growth or loss rates of functional algal groups

mediated by shifts in the trophic structure of lakes of differing

fertility.

While taxonomic considerations are undeniably important

(e.g. Lampert 1981; Infante and Abella 1985). the general cate

gorization of the algal community into functional groups thai

span taxonomic boundaries is supported by extensive measure

ments of zooplankton feeding rates (e.g. Bums 1968; Gliwicz

1977; Porter 1977; McCauley and Downing 1985; Hawkins and

Lanipert 1989) and field manipulations of herbivorous zoo-

plankton (e.g. Porter 1972; Gliwicz 1975; Briand and McCauley

1978; McCauley and Briand 1979; Leibold 1989; Vanni and

Temte 1990). Nannoplanklon are typically consumed by her

bivorous zooplankton, and netphinkton are relatively insuscep

tible to grazing (e.g. Porter 1972; Gliwicz 1975; Briand and

McCauley 1978; McCauley and Briand 1979; McCauiey and

Downing 1985; Leibold 1989). These two groups have been

labelled "edible" and "inedible", respectively. They not only

display different short-term responses to manipulation of her

bivores, but they appear to respond differently to variation

among lakes in TP (Watson and McCauley 1988).

Ecological theory also predicts very different responses for

[he two groups with enrichment. Classical predator-prey theory

(e.g. Rosensweig 1972; Leibold 1989; McCauley et al. 1989)

predicts that if the edible group is regulated by herbivores, then

enrichment should lead only to an increase in herbivore biomass

which subsequently suppresses edible algal density to pre-

enriebment levels. Edible algal biomass should therefore be

invariant among lakes differing in enrichment. Other predic

tions are made by theory (Fretwell 1977; Oksanen et al. 1981)

that takes into account the potential effects of species at other

trophic levels (e.g. carnivorous zooplankton, planktivorous or

carnivorous fish). For example, Oksanenet al. (1981) predicted

that if productivity of algal prey increases with enrichment, then

prey biomass should vary as a step function with increasing lake

fertility (e.g. Leibold 1989, fig. 1). The discontinuities in the

predicted relationship are produced by the development of addi

tional trophic levels and their subsequent influence on the plant-

herbivore interaction.

In this paper, we examine differences in algal community

structure among lakes to test whether the sigmoidal pattern

observed in the biomass-TP relationship can be accounted for

by changes in the relative abundance of edible or inedible

phytoplankton.

Data and Analyses

We tested our hypotheses using a wide range of published

data on algal biomass, chlorophyll concentrations, and phos

phorus concentrations. Mean epilimnetic summer values were

used wherever possible, since the inclusion of spring and fall

data could affect the relationship beiwecn some algal size frac

tions and TP (e.g. Watson and McCauley 1988). These would

also represent values which were close to "equilibrium" val

ues, and eliminate some of the variation around temporal or

short-term fluxes. However, some individual observations were

also included (16%), although where these were reported over

one or more growing seasons for a particular lake, the mean

(summer) values were calculated. Where necessary, values were

converted to micrograms per litre. For algal biomass, we used

only estimates of wet weight or biovolume that had been arrived

at using the Utermohi technique (Vollenweider 1969). Where

biovolume was given, it was converted into micrograms wet

weight per litre (Vollenweider 1969). A total of 67 different

sources of data were used from 362 different lakes over one or

more stations or years.1 Nannoplankton or edible phytoplank

ton were defined as cells or colonies <35-5O |xm in maximum

linear dimension, while netplankton or inedible algae were

defined as cells or colonies >35-50 \L\n. The number of obser

vations used to test each hypothesis varied considerably

(Table I) because complete data for algal community structure

were not available from all studies.

Following the approach used by McCauley el al. (1989), the

shape of each of the curves was examined using two methods:

(3) multiple regression analysis (Draper and Smith 1981) with

variable selection by backward elimination (Mocking 1976) and

'A complete set oi tubular data is available at a nominal charge from

[he Depository of Unpublished Data, National Research Council of

Canada, Ottawa, Ont. K1A 0S2, Canada.

26G6 Can..!. Fish. Aquat. Sri., Vol. 49. 1992

(2) robust locally weighted sequential smoothing (LOWESS:

Cleveland 1979). Logarithmic transformations were used to sta

bilize residual variability. The multiple regression analysis was

used to examine whether relationships were linear or nonlinear

by assessing the pattern of residuals and the significance of

higher-order terms of the independent variable (i.e. TP).

LOWESS is a nonparametric smoothing technique that yields

an unbiased estimate of the form of the relationship between

two variables, which is not constrained by assumptions about

the form of the relationship (Cleveland 198S). It is an especially

powerful tool for studying the dependence of y on x when

'*.. .the signal is embedded in noise'' (Cleveland 1985). Because

LOWESS fitting is "model free", it has the flexibility to

describe many patterns including those with discontinuous

derivatives. LOWESS also includes a robust fitting procedure

that "guards against deviant points distorting the smooth

points" (Cleveland 1979). Because fitted trends are locally

weighted, so-called "outliers" have negligible effects on

LOWESS fits. All LOWESS analyses were performed with

delta = 0 (the smoothing function considers every single data

point), n - steps = 2 (number of iterations), and / = 0.5

(weighting factor). The values of «-steps and / were chosen

based on the recommendations of Cleveland (1985).

Results and Discussion

Total algal biomass varies nonlinearly with TP. The para

metric analysis and LOWESS fit yield comparable results,

showing a sigmoidal relationship between TP and total biomass

similar to that exhibited by Chi a (Fig. 1; Table 1). There are,

however, slight quantitative differences in the curves derived

from parametric and model-free methods. These differences

probably arise from constraints inherent in the parametric tech

nique (i.e. the use of polynomial equations to fit the data).

Below, we first discuss the LOWESS results and then compare

them with the parametric models.

In very oligotrophic systems (i.e. TP < 5 |xg/L), increases

in TP correspond to very little change in total biomass

(Fig. 1A); however, once TP exceeds this level, the rate of

increase of algal biomass accelerates dramatically with increas

ing TP. Over the range of TP from ~6 to 60 jxg/L, algal bio

mass appears to increase at a relatively constant rate, and this

rate decreases markedly once TP values surpass 65-75 |xg/L.

The polynomial fit yields a qualitatively similar pattern, but the

level of TP at which the rate of change of algal biomass begins

to decrease in eutrophic lakes differs substantially from that

described by the LOWESS results (Fig. 1 A). According to the

parametric model, the rate of change in algal biomass begins

to decline at ~300-500 jxg TP/L. In oligotrophic lakes, the

results are virtually identical for the two techniques.

It appears, therefore, that the sigmoid relationship between

TP and phytoplankton biomass (Chi a) found by McCauley

et al. 1989) and Prairie et al. (1989) is not an artefact of those

authors' use of chlorophyll to estimate algal biomass. This is

demonstrated by the fact that the relationship between algal bio

mass and TP is shown to be robustly sigmoid when either Chi a

or biovolume is used to measure total algal biomass. In fact,

the relationship between phytoplankton biovolume and TP is

more markedly sigmoidal than that between chlorophyll and TP

(Fig. IB). Over the range of TP where there are the most data

(3-1000 jig/L; Fig. 1A), both curves show a similar acceler

ation phase (Fig. IB). It is important to note that the nonlinear

relationship remains significant if the seeming "outliers" at the

extreme ends of the data range are removed and the data anal-

CD

Eo

m

"5*-<

o

eno

1.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

log10 Total Phosphorus

(01

lorophyllsz

o

olog1

2

2

1

1

0

.5

.0

.5

.0

.5

0.0

-0 5

1

'i

0.0 • 0.5

1 1 1—

i i t

1.0 1.5 2.0

login Total

—i 1

i i

2.5 3.0 3

Phosphorus

T

.5

—i—

4.0

B

-

-

-

-

4.

5.0

4.5

4.0

3.5

3.0

2.5

5

CO

Eo

S

Toat

Fig. I. Relationship between total phosphorus and total algal biomass

among lakes. (A) Algal biomass estimated from algal biovolume,

showing parametric (dotted curve) and LOWESS (solid curve) fits;

(B) LOWESS fits for algal biomass estimated from biovolume (solid

curve) and Chi a (dotted curve) (McCauley et al. 1989) versus total

phosphorus. All variables in |xg/L.

ysis is repeated. In addition, variation in the Chi a to biovolume

ratio does not account for observed nonlinearities in the rela

tionship between total algal abundance and TP. Inspection of

the relationship between the Chi a to biomass ratio and TP shows

that this ratio varies in a nonlinear but also nonsystematic fash

ion with phosphorus (Fig. 2). In fact, the general trend followed

by this curve is actually opposite to that which would be

expected if the relationship between TP and algal biomass were

primarily influenced by this ratio. Neither this, therefore, nor

the large amount of residual variation about the curve could

account for the sigmoidal nature of the phosphorus-biomass

curves. This nonsystematic variation of the Chi a to biovolume

ratio with TP may explain some of the discrepancies among

studies (e.g. Tolstoy 1979; Dillon et al. 1988) attempting to

find a consistent pattern in the relationship using smaller data-

sets covering a limited range of nutrient levels.

The two algal size categories, designated as edible and in

edible algae, respond very differently to variation in TP. Both

the parametric and LOWESS analyses show that over the range

of TP covered by available data, inedible algal biomass

increases nonlinearly with TP by more than 40-fold (Fig. 3;

Table 1). Edible algae, on the other hand, do not vary system

atically with TP. It appears that the overall shape of the curve

of total algal biomass is primarily influenced by changes in

Can. J. Fish. Aquat. Sci.. Vol. 49. 1992 2607

Table I. Partial regression coefficients for the effect of total phosphorus (TP) on log ,„ total, edible, and inedible algal biomass (estimated from

biovolume), found using least squares multiple regression analysis. The number of observations (/r). the coefficient of determination (r), and

the overall F-value are also given, together with the general shape of the corresponding curve obtained using locally weighted robust sequential

smoothing (LOWESS; Cleveland 1979) and the range of TP covered by each dataset. Previous results from a similar analysis of the relationship

between TP and total biomass estimated as chlorophyll a (Chi a) (McCauley et al. 1989) are included for comparison. TP, algal biomass

(biovolume), and Chi a measured in jig/L.

Parametric model

Variable

dog.o) LTP (LTP)2 (LTP)J Intercept «... Prob > F

LOWESS

model" TP range

Total biomass -0.92 1.24 -0.26 2.82 451 227 0.60 0.0001 *S 1-1300

Edible biomass -1.44 1.82 -0.54 2.92 101 9 0.22 0.0001 1-200

Inedible biomass NS 1.33 -0.46 1.85 101 39 0.44 0.0001 S 1-200

Total Chi a -0.83 0.34 -0.12 0.03 875 431 0.71 0.0001 *S 1-14093

(McCauley et al. 1979)

*S = sigmoidal, *S = strongly sigmoidal.

0.025

0.020 )v>v>CD

E

| 0-012

■>

"§■ 0.008o

s:

U 0.004

0.000

Fig. 2.

(jig/L)

0.5 1.0 1.5 2.0 2.5 3.0 3.5

log10 Total Phosphorus

LOWESS fit of the relationship between total phosphorus

and Chi a to biomass ratio.

large algae that cannot be ingested by zooplankton rather than

by edible phytoplankton.

Under very oligotrophic conditions (i.e. <5 |xg/L), both

inedible and edible algal biomasses are nearly constant or even

decline slightly with increasing TP (Fig. 4). From approxi

mately 5 to 30 fig TP/L, edible algal biomass appears to

increase slightly and then levels off, while inedible phytoplank

ton biomass increases rapidly. There is considerable variation

in edible or inedible biomass at a given level of TP, and assess

ing "significance" of patterns is somewhat problematic. How

ever, the LOWESS analysis shows a discontinuous change over

this TP range for both edible and inedible algal biomasses which

are measured independently, and the data density is high in the

region where most change occurs.

The markedly different responses to increased nutrient levels

exhibited by the two algal size fractions seem to be related to

their susceptibility to grazing by herbivores. This indicates that

the nonlinearity of the total biomass curve may be attributable

to factor(s) other than differential responses to nutrient levels.

The discontinuities and shifts in community structure are per

haps best illustrated by Fig. 5. Below levels of —8-10 (xg

TP/L, total biomass is dominated by edible algae. Above this

range, there is a transition zone where both the edible and ine

dible biomasses are similar in relative abundance, but the ine

dible fraction exhibits a much more pronounced rate of change

(Fig. 4). With increasing concentrations of TP (i.e. TP >

—30 (xg/L) the inedible algae rapidly become more dominant,

Eo

3

p

0.5 1.0 1.5 2.0

log10 Total Phosphorus

2.5

0.0 0.5 1.0 1.5 2.0

loglo Total Phosphorus

2.5

Fig. 3. Relationship between total phosphorus and algal size fractions

(biomass; estimated from biovolume), showing parametric (dotted

curve) and LOWESS (solid curve) fits. (A) Edible algal biomass;

(B) inedible algal biomass. All units in |Ag/L.

until at TP > —50 |xg/L the phytoplankton biomass consists

almost entirely of this larger size fraction (Fig. 5).

If the discontinuous change in edible-inedible community

structure results from mechanisms proposed by Oksanen et al.

(1982), then we should see concomitant changes in the rela

tionship between average herbivore biomass and TP. Specifi

cally, herbivore biomass should increase with TP among lakes

with TP < 5 ng/L. and in the region of 5 < TP < 30 |xg/L,

there should be a discontinuous change in herbivore biomass

among lakes. Alternatively, the rate of change of zooplankton

2608 Can. J. Fish. Aquat. Set., Vol. 49. 1992

0.5 1.0 1.5 2.0 2.5

log1o Total Phosphorus

3.0 3.5

to(0a

Eo

3

75

o

log10 Total Phosphorus

Fig. 4. Relationship between total phosphorus and total (solid curve),

edible (broken curve), and inedible (dotted curve) algal biomass. (A)

Parametric fits; (B) LOWESS fits. All units in |Ag/L. Note that the

calculated intercept for the edible fraction is higher than that of the

total biomass simply because the lakes represented in each dataset

differ among fractions.

100

V)«CD

Eg

in

o

0.0 0.5 1.0 1.5 2.0

log10 Total Phosphorus

Fig. 5. Relationship between total phosphorus and the relative pro

portions of edible (solid curve) and inedible (dotted curve) algal bio

mass. While the curves are obviously mirror images, both have been

presented to facilitate interpretation.

biomass could remain the same, and systematic changes in zoo-plankton community structure could occur. The discontinuouschange in edible algae would occur if the herbivorous zooplank-ton shifted to species with lower attack rates over this range ofTP, thereby yielding a higher "equilibrium" concentration ofprey (McCauley et al. 1989). Unfortunately, existing studies ofamong-lake variation in zooplankton biomass (McCauley andKalff 1981; Hanson and Peters 1984; Pace 1984) have not'looked for patterns at this scale of comparison, nor have observations been analysed using model-independent techniques suchas LOWESS. We are currently investigating these possibilities.We recognize that the division of the phytoplankton com

munity into only two functional size groups may limit thepotential interpretation of the phosphorus-biomass curve.Analyses based on size and those based on taxonomic divisions

may not be mutually exclusive: some of the major taxonomicgroups comprise primarily smaller individuals (e.g. Chryso-

phyta, Cryptophyceae) and others larger algae (e.g. Cyano-

phyta). Furthermore, as we noted previously, the response ofthe grazer community to certain dominant taxonomic algalgroups could in tum influence the overall shape of the phos

phorus-biomass curve. In a subsequent paper, we examine the

relationships between major taxonomic groups and phosphorusenrichment and compare them with those of the major sizegroups that we have described here.

Acknowledgements

We thank Sophie Lalonde and Chris Briggs for technical help. Thisresearch was supported by NSERC operating grants to E.M. and J. A.D.

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