Abstract

Thanks to recent advances in molecular biology, one's knowledge of microbial co-occurrence patterns, microbial biogeography and microbial biodiversity is expanding rapidly. This MiniReview explores microbial diversity–productivity relationships in the light of what is known from the general ecology literature. Analyses of microbial diversity–productivity relationships from 70 natural, experimental, and engineered aquatic ecosystems reveal patterns that are strikingly similar to those that have long been documented for communities of macroorganisms. Microbial ecology and the general science of ecology are thus continuing to converge.

Introduction

Although ecologists have not yet been able to state definitively how many species of organisms inhabit the Earth, remarkably consistent patterns have been observed in their diversity for more than 150 years (Rosenzweig, 1995). While debates are still ongoing about the processes that generate diversity patterns, and on the exact nature of patterns that may exist for different taxonomic groups, the existence of gradients and structure in the distributions of macroorganisms is clear (Fontaneto et al., 2006).

Regrettably, however, a communication gulf has long existed between general ecologists and microbial ecologists that is due in part to historical divisions between ecologists and microbiologists (Andrews, 1991; Atlas & Bartha, 1998; Curtiset al., 2002). However, this gap is beginning to close, especially in the areas of biodiversity and biogeography (Horner-;Devine et al., 2003a, b; Hughes Martinyet al., 2006), and it is increasingly clear that microbial systems offer valuable complementary approaches to field and laboratory studies of macroorganisms (Jessupet al., 2004). This paper is a result of a US National Center for Ecological Analysis and Synthesis (NCEAS) working group composed of scientists from both disciplines. Its goal is to explore microbial diversity–productivity relationships in the light of what is known about these relationships from the literature in general ecology.

Diversity–productivity relationships in macroorganisms: a brief overview

An extensive and rapidly expanding body of macroecological literature much too large to review here has revealed that the number of morphospecies or functional types of macroorganisms in a given habitat can be strongly influenced by local productivity (the rate of conversion of energy and abiotic resources into biomass per unit habitat area or volume, per unit time) (Waideet al., 1999). In particular, a hump-shaped response between diversity and productivity has frequently been observed (Rosenzweig, 1995). This relationship can be expressed as a well-delineated, unimodal curve (solid symbols in Fig. 1e), but it is also sometimes evidenced as a cluster of points having a statistically significant central maximum (solid plus open symbols in Fig. 1e). For some investigators, a unimodal response has been considered to be the canonical relationship between diversity and productivity for macroorganisms, and during the past several decades a wide variety of hypotheses have been proposed to explain this humped pattern (Wrightet al., 1993; Rosenzweig, 1995; Leibold, 1999; Waideet al., 1999; Dodsonet al., 2000).

1

Examples of potential diversity–productivity relationships. They may be (a) ‘random’, in which no detectable pattern is evident; (b) ‘positive’, in which diversity increases linearly (or sometimes curvilinearly) with productivity; data suggestive of a possible change in slope (designated by the open circles) may or may not be present; (c) ‘flat’, in which the magnitude of variation in diversity is restricted, but does not change in magnitude or sign across the productivity gradient; (d) ‘negative’, in which diversity decreases linearly (or sometimes curvilinearly) with productivity; data suggestive of a possible change in slope (designated by the open circles) may or may not be present; (e) ‘humped’, in which diversity exhibits a clear maximum at intermediate productivity levels; the ‘hump’ may be strongly curvilinear (solid circles), or may be filled in (open circles); (f) ‘hollow or U-shaped’, in which diversity exhibits a clear minimum at intermediate productivity levels; the local minimum may be strongly curvilinear (solid circles), or may be filled in (open circles).

1

Examples of potential diversity–productivity relationships. They may be (a) ‘random’, in which no detectable pattern is evident; (b) ‘positive’, in which diversity increases linearly (or sometimes curvilinearly) with productivity; data suggestive of a possible change in slope (designated by the open circles) may or may not be present; (c) ‘flat’, in which the magnitude of variation in diversity is restricted, but does not change in magnitude or sign across the productivity gradient; (d) ‘negative’, in which diversity decreases linearly (or sometimes curvilinearly) with productivity; data suggestive of a possible change in slope (designated by the open circles) may or may not be present; (e) ‘humped’, in which diversity exhibits a clear maximum at intermediate productivity levels; the ‘hump’ may be strongly curvilinear (solid circles), or may be filled in (open circles); (f) ‘hollow or U-shaped’, in which diversity exhibits a clear minimum at intermediate productivity levels; the local minimum may be strongly curvilinear (solid circles), or may be filled in (open circles).

However, many other responses of diversity to productivity gradients can also be found in the ecological literature (Abrams, 1995; Mittelbachet al., 2001; Scheiner & Willig, 2005): viewed progressively, they may be ‘random’, in which no detectable pattern is evident (Fig. 1a); ‘positive’, in which diversity increases linearly (or sometimes curvilinearly) with productivity (Fig. 1b); ‘flat’, in which the absolute variability in diversity is relatively restricted, and does not change in magnitude across the productivity gradient (Fig. 1c); or ‘negative’, in which diversity decreases linearly (or sometimes curvilinearly) with productivity (Fig. 1d). ‘Hollow U-shaped’ relationships have also sometimes been found, but these are typically rare (Fig. 1f).

The relationship between diversity and productivity can be altered, however, by changes in geographic and ecological scale (Wrightet al., 1993; Waideet al., 1999; Dodsonet al., 2000; Chase & Leibold, 2002), and by differences in community assembly history (Fukami & Morin, 2003). The shape of this relationship may also be sensitive to the measure of biological diversity that is being analyzed (e.g. morphospecies richness, functional diversity, or synthetic numerical indices such as Shannon–Weaver diversity or Simpson's index), and sensitive to the reported measure of productivity (e.g. direct estimates of photosynthesis vs. indirect or surrogate productivity measures such as biomass or resource availability).

Diversity–productivity relationships in aquatic microbial communities

A critically important question in microbial ecology is the degree to which the ecological behavior of microorganisms conforms to the rules that have been discovered by general ecologists. For some investigators (Fenchel & Finlay, 2004), the answer to this question has been no: based on studies of ciliates, they concluded that the characteristics of biodiversity differ substantially between microorganisms and macroorganisms; they proposed that most organisms smaller than 1 mm are cosmopolitan, occurring worldwide wherever their habitat requirements are met. However, a large and expanding body of evidence indicates that free-living microbial taxa can indeed exhibit biogeographical patterns (Dolan, 2005; Hughes Martinyet al., 2006). In addition, the species–area relationship, considered to be the oldest documented diversity pattern in macroecology (Rosenzweig, 1995), has recently been confirmed for phytoplankton and benthic microalgae (Hillebrandet al., 2001; Smithet al., 2005), and for bacteria (Bellet al., 2005; Reche et al., 2005). Finally, as illustrated in Fig. 2 (Ogawa & Ichimura, 1984), humped diversity–productivity patterns have been reported in natural phytoplankton assemblages (Leibold, 1999; Dodson et al., 2000), as well as in experimental microbial communities (Kassen et al., 2000; Horner-;Devine as well as in experimental microbial communities, 2003a, b).

2

Example of a humped relationship between microbial diversity and productivity in 23 Japanese lakes (Ogawa & Ichimura, 1984). The fitted curve was obtained using statistical LOWESS techniques.

2

Example of a humped relationship between microbial diversity and productivity in 23 Japanese lakes (Ogawa & Ichimura, 1984). The fitted curve was obtained using statistical LOWESS techniques.

Rapidly accumulating evidence from the microbial ecology literature thus suggests that microorganisms indeed obey the key principles of macroecology. If so, then it can be hypothesized that microbial communities of all kinds should exhibit diversity–productivity patterns that closely resemble those documented for macroorganisms (summarized in the reviews cited in ‘Diversity–productivity relationships in macroorganisms: a brief overview’), and illustrated here for phytoplankton in Fig. 2. This hypothesis was tested by creating and analyzing a database derived from the published literature on aquatic microbial diversity.

Data acquisition and analysis

The ecological literature was searched broadly in order to obtain published studies of aquatic microbial diversity–productivity relationships. The intent of this literature search was to provide examples having the widest possible geographical extent, and representing a broad range of aquatic habitats, including natural lakes, ponds, and oceans; these studies included experimental microcosms and mesocosms, as well as human-engineered systems such as wastewater treatment plants. Studies were included in the database if they provided a sample size ≥4, which allowed the quantitative assessment of relationships between investigator-provided measurements of microbial diversity and productivity, regardless of scale, taxon, or ecosystem.

In a number of these studies, investigator-provided measurements of microbial diversity were reported as morphospecies richness (phytoplankton and ciliates; the colony morphology of cultured microorganisms was also used to estimate microbial taxonomic richness in some cases). In a very few other studies, cytometric richness, genetic diversity, or functional diversity was measured. However, most investigators reported microbial diversity as operational taxonomic units (OTUs), which were derived using molecular approaches such as denaturing gradient gel electrophoresis (DGGE) or terminal restriction fragment length polymorphism (T-RFLP) analyses of PCR-amplified genes. Although some OTU definitions try to capture a species-like unit, it has been suggested that one can ask valid questions about biodiversity at any level, as long as the OTU definition is clear and consistent (Bohannan & Hughes, 2003).

Numerous measures of productivity were reported as well. Some investigators provided direct estimates of primary productivity or bacterial productivity, but more commonly, indirect or surrogate productivity measures such as total microbial biomass or resource availability were given.

The relationships between microbial diversity and productivity were classified into six general categories: (1) flat or random; (2) humped; (3) negative; (4) positive; (5) U-shaped; or (6) variable. In this analysis, microbial diversity patterns were included in the ‘variable’ category if the shapes of diversity–productivity patterns reported by the investigator were found to be dependent on other investigator-documented factors such as geographical region, ecosystem size, community assembly history, or food web structure. As in Waideet al (1999), these categorical classifications were based on original published analyses wherever possible. However, when the needed statistics were not available, the authors' raw data were typically analyzed using linear and quadratic regressions with a significance level of P≤0.10; nonlinear patterns thus included significant linear and quadratic regression terms. Because relatively few potential datasets for microbial diversity pattern detection could be found in the published literature, no effort was made to exclude human-perturbed natural ecosystems in order to maximize the breadth and scope of this analysis; artificial systems whose productivity was human-manipulated were explicitly coded in this analysis as ‘experimental’ and were also included in the database.

Aquatic microbial diversity–productivity patterns

The literature survey provided 70 published studies from which estimates of aquatic microbial diversity and ecosystem productivity could be obtained for inclusion in this analysis; 43 of these studies were from natural systems, and 27 were from experimental or engineered systems. As can be seen in the frequency distribution shown in Fig. 3, only one U-shaped relationship was found in the entire aquatic literature search; this experimentally obtained relationship for alphaproteobacterial richness (Horner–;Devine et al., 2003a, b) was, however, derived from only five data points (R2=0.91, P=0.09). Roughly equal numbers of the remaining diversity–productivity patterns were found among the datasets obtained from experimental or engineered systems; only 15% of these were classified as humped. In contrast, the diversity–productivity patterns from natural systems were predominantly either humped (23%), negative (35%), or positive (28%); only a very few (14%) of the natural systems exhibited either flat, random, or variable relationships.

3

(a) Frequency distributions of predominantly macrobial diversity–productivity relationships, using the five general categories analyzed in the study reported in Table 2 of the global analysis reported by Mittelbach et al (2001); (b) Frequency distributions of microbial diversity–productivity relationships in 70 natural (N) and experimental or engineered (E) systems, using the six general categories defined in this study.

3

(a) Frequency distributions of predominantly macrobial diversity–productivity relationships, using the five general categories analyzed in the study reported in Table 2 of the global analysis reported by Mittelbach et al (2001); (b) Frequency distributions of microbial diversity–productivity relationships in 70 natural (N) and experimental or engineered (E) systems, using the six general categories defined in this study.

Conclusions

When compared with broad, inclusive analyses previously reported in the general ecology literature (Waide et al., 1999; Mittelbach et al., 2001), the data summarized in Fig. 3 suggest that diversity–productivity patterns are remarkably similar for macroorganisms and microorganisms. These conclusions are consistent with the results of other recent comparative analyses: Hillebrand et al (2001) found that differences between the relative local species richness of unicellular organisms and metazoans were not categorical; they also observed a broad overlap between the slopes of species–area relationships for micro- and macroorganisms, and demonstrated decreasing similarity in species composition with increasing geographical distance both for unicellular and for multicellular organisms. Similarly, field studies of natural unicellular eukaryotes have suggested that the most influential factors structuring communities of unicellular and multicellular organisms within a region may be rather similar, even if they are not identical, and that regional patterns (e.g. community gradients, nestedness, and co-occurrence) resulting from species' regional occupancy do not appear to differ appreciably between unicellular and multicellular organisms (Heino & Soininen, 2006).

As noted in Scheiner & Willig (2005), a large number of empirical and manipulative tests have now been conducted to confirm biodiversity patterns among macroorganisms, and to infer the causal mechanisms that underlie the diversity–productivity curves that have been reported. Lavers & Field (2006) have recently observed that diversity–productivity theories are now legion, but suggested that none has yet proven sufficiently intuitive to gain broad acceptance.

If the canonical relationship between productivity and species richness is indeed humped, then one might expect that the relationships most commonly reported in empirical studies of biodiversity in natural landscapes should predominantly be either positive or negative in shape. A very wide range (often two orders of magnitude or more) of productivities is often required in order to reveal clear and statistically convincing evidence of the entirety of a humped diversity–productivity curve (see e.g. Fig. 2), and it is more likely that an investigator will be able to capture data from one side of the hump or the other, and not from the entire range of potential productivity values (Waide et al., 1999; Mittelbach et al., 2001). Alternatively, a hump-shaped species richness gradient could be produced by chance alone: if the fundamental niche of each species with respect to an underlying environmental gradient is characterized by a randomly determined median and range along that gradient, then the number of species able to occupy the central portion of an empirical gradient should be high and should decrease monotonically toward the terminus of the gradient in either direction, producing a hump-shaped pattern (Scheiner & Willig, 2005).

In the absence of environmental noise due to confounding factors other than pure productivity (Fig. 4), obtaining flat or random relationships would be expected primarily by chance alone, if the investigator (1) sampled habitats that were only of intermediate productivity or (2) sampled a set of habitats having a relatively narrow range of productivities. Like many other ecological studies, relatively few of the studies analyzed here spanned two to three or more orders of magnitude in productivity. Apart from Scheiner & Willig (2005), no theory has been proposed to account for U-shaped productivity–diversity curves.

4

Many physical, biological, and chemical factors interact to generate and maintain local biological diversity. Influx of individuals or propagules comprising variable numbers of taxa from the regional species pool can occur at very different individual rates, and local factors can act as sorting agents or environmental sieves to produce the observed local biodiversity.

4

Many physical, biological, and chemical factors interact to generate and maintain local biological diversity. Influx of individuals or propagules comprising variable numbers of taxa from the regional species pool can occur at very different individual rates, and local factors can act as sorting agents or environmental sieves to produce the observed local biodiversity.

For all organisms, local diversity (Fig. 4) is almost certainly generated and maintained by a wide array of mechanisms (Chesson, 2000), and except under carefully controlled conditions it may prove difficult to observe humped diversity–productivity relationships in open, natural systems. As in macroorganisms (Hillebrand & Blenckner, 2002; Chase & Ryberg, 2004), connectivity with (and immigrant fluxes from) regional species pools may be a very important determinant of local microbial community composition and diversity (Lindström & Bergström, 2004). The local and regional disturbance regime may also be very important (Reynolds et al., 1993; Cardinale et al., 2005). Similarly, food web structure (Hillebrand, 2003; Irigoien et al., 2004) may have strong moderating influences on the response of local microbial diversity to changes in productivity.

Understanding the diversity of microbial communities is a high priority in ecology, but it is only within the last decade and a half that the development of key molecular tools has made it possible to address this question adequately (Ward, 2002). The graphical analyses of microbial data that are presented in Fig. 3 can be criticized (see Rahbek, 2005) because they are based on a wide range of data collected at different scales; they were generated from many different sampling and analytical techniques, and they reflect many heterogeneous measures of diversity and productivity. Such problems should diminish significantly in the future as a greater number of microbial investigators turn their attention to this important question, and as techniques arise and mature to allow estimates of microbial richness that are more reliable and general; have biologically meaningful SEs; and meet other fundamental statistical standards (Hong et al., 2006).

However, Fig. 3 represents the largest compilation of microbial diversity–productivity data that have yet been assembled. Like previous synthetic analyses that have been reported in the macroecological literature (Waide et al., 1999; Mittelbach et al., 2001), It is hoped very much that this initial study will help to stimulate further research into what appear to be universal patterns in biological diversity. It is also hoped that it will contribute to the ultimate development of a rich, consilient, and calibrated set of rules to describe and predict the behavior of the microbial world as a system (Battin et al., 2007; Curtis, 2007). Although methodological considerations will continue to pose significant challenges (Lindström et al., 2007; Reche et al., 2007), there is now a toolbox that is sufficiently large to allow us to begin to address difficult questions in microbial ecology, and new methods are being developed regularly (Fiereret al., 2007).

Acknowledgements

The author is deeply grateful to Prof. Ian Head for hosting this special SGM symposium, and for inviting this paper. The author also thanks two anonymous reviewers for their constructive reviews. This work was initiated while the author was a participant in the Patterns in Microbial Diversity Working Group supported by the National Center for Ecological Analysis and Synthesis, a center funded by the US National Science Foundation Grant DEB-9421535, the University of California, Santa Barbara, and the State of California. This research was supported in part by funding from NSF grant DMS – 0342239 to V.H.S. A data appendix for this paper, containing both summaries of and citations for the microbial studies analyzed here, is available upon request from the author.

References

Abrams
PA
(
1995
)
Monotonic or unimodal diversity–productivity gradients: what does competition theory predict?
Ecology
 
76
:
2019
2027
.
Andrews
J
(
1991
)
Comparative Ecology of Microorganisms and Macroorganisms
 .
Springer-Verlag
,
New York
.
Atlas
RM
Bartha
R
(
1998
)
Microbial Ecology: Fundamentals and Applications
 ,
4th edn
.
Benjamin/Cummings
,
New York
.
Battin
TJ
Sloan
WT
Kjelleberg
S
Daims
H
Head
IM
Curtis
TP
Eberl
L
(
2007
)
Microbial landscapes: new paths to biofilm research
.
Nature Rev Microbiol
 
5
:
76
81
.
Bell
T
Ager
D
Song
J-I
Newman
JA
Thompson
IP
Lilley
AK
Van Der Gast
CJ
(
2005
)
Larger islands house more bacterial taxa
.
Science
 
308
:
1884
.
Bohannan
BJB
Hughes
J
(
2003
)
New approaches to analyzing microbial biodiversity data
.
Curr Opin Microbiol
 
6
:
282
287
.
Cardinale
BJ
Palmer
MA
Ives
AR
Brooks
S
(
2005
)
The diversity–productivity relationship in streams varies as a function of the natural disturbance regime
.
Ecology
 
86
:
716
726
.
Chase
JM
Leibold
MA
(
2002
)
Spatial scale dictates the productivity–biodiversity relationship
.
Nature
 
416
:
427
430
.
Chase
JM
Ryberg
WA
(
2004
)
Connectivity, scale-dependence, and the productivity–diversity relationship
.
Ecol Lett
 
7
:
676
683
.
Chesson
P
(
2000
)
Mechanisms of maintenance of species diversity
.
Annu Rev Ecol Syst
 
31
:
343
366
.
Curtis
T
(
2007
)
Theory and the microbial world
.
Environ Microbiol
 
9
:
1
11
.
Curtis
TP
Sloan
WT
Scannell
JW
(
2002
)
Estimating prokaryotic diversity and its limits
.
Proc Natl Acad USA
 
99
:
10494
10499
.
Dodson
SI
Arnott
SE
Cottingham
KL
(
2000
)
The relationship in lake communities between primary productivity and species richness
.
Ecology
 
81
:
2662
2679
.
Dolan
JR
(
2005
)
Biogeography of aquatic microbes
.
Aquat Microb Ecol
 
41
:
39
48
.
Fenchel
T
Finlay
BJ
(
2004
)
The ubiquity of small species: patterns of local and global diversity
.
Bioscience
 
54
:
777
784
.
Fierer
N
Bradford
MA
Jackson
RB
(
2007
)
Toward an ecological classification of soil bacteria
.
Ecology
 
88
:
1354
1364
.
Fontaneto
D
Francesco Ficetola
G
Ambrosini
R
Ricci
C
(
2006
)
Patterns of diversity in microscopic animals: are they comparable to those in protists or in larger animals?
Global Ecol Biogeogr
 
15
:
153
162
.
Fukami
T
Morin
PJ
(
2003
)
Productivity–biodiversity relationships depend on the history of community assembly
.
Nature
 
424
:
423
426
.
Heino
J
Soininen
J
(
2006
)
Regional occupancy in unicellular eukaryotes: a reflection of niche breadth, habitat availability or size-related dispersal capacity?
Freshwater Biol
 
51
:
672
685
.
Hillebrand
H
(
2003
)
Opposing effects of grazing and nutrients on diversity
.
Oikos
 
100
:
592
600
.
Hillebrand
H
Blenckner
T
(
2002
)
Regional and local impact on species diversity – from pattern to process
.
Oecologia
 
132
:
479
491
.
Hillebrand
H
Watermann
F
Karez
R
Berninger
U-G
(
2001
)
Differences in species richness patterns between unicellular and multicellular organisms
.
Oecologia
 
126
:
114
124
.
Hong
S-H
Bunge
J
Jeon
S-O
Epstein
SS
(
2006
)
Predicting microbial species richness
.
Proc Natl Acad Sci USA
 
103
:
117
122
.
Horner-Devine
MC
Carney
KM
Bohannan
JMB
(
2003a
)
An ecological perspective on bacterial diversity
.
Proc Roy Soc Lond B
 
271
:
113
122
.
Horner-Devine
C
Leibold
M
Smith
V
Bohannon
B
(
2003b
)
Bacterial diversity patterns along a gradient of primary productivity
.
Ecol Lett
 
6
:
1
10
.
Hughes Martiny
JB
Bohannan
BJM
Brown
JH
et al
. (
2006
)
Microbial biogeography: putting microorganisms on the map
.
Nature Rev Microbiol
 
4
:
102
112
.
Irigoien
X
Huisman
J
Harris
RP
(
2004
)
Global biodiversity patterns of marine phytoplankton and zooplankton
.
Nature
 
429
:
863
867
.
Jessup
CM
Kassen
R
Forde
SE
Kerr
B
Buckling
A
Rainey
PB
Bohannan
BJM
(
2004
)
Big questions, small worlds: microbial model systems in ecology
.
Trends Ecol Evol
 
19
:
189
197
.
Kassen
RA
Buckling
A
Bell
G
Rainey
PB
(
2000
)
Diversity peaks at intermediate productivity in a laboratory microcosm
.
Nature
 
406
:
508
512
.
Lavers
C
Field
R
(
2006
)
A resource-based conceptual model of plant diversity that reassesses causality in the productivity–diversity relationship
.
Global Ecol Biogeogr
 
15
:
213
224
.
Leibold
MA
(
1999
)
Biodiversity and nutrient enrichment in pond plankton communities
.
Evol Ecol Res
 
1
:
73
95
.
Lindström
ES
Bergström
A-K
(
2004
)
Influence of inlet bacteria on bacterioplankton assemblage composition in lakes of different hydraulic retention time
.
Limnol Oceanogr
 
49
:
125
136
.
Lindström
ES
Eiler
A
Langenhede
S
Bertilsson
S
Drakare
S
Ragnarsson
H
Tranvik
LJ
(
2007
)
Does ecosystem size determine aquatic bacterial richness? Comment
.
Ecology
 
88
:
252
253
.
Mittelbach
GG
Steiner
CF
Scheiner
SM
Gross
KL
Reynolds
HL
Waide
RB
Willig
MR
Dodson
SI
Gough
L
(
2001
)
What is the observed relationship between species richness and productivity?
Ecology
 
82
:
2381
2396
.
Ogawa
Y
Ichimura
S-E
(
1984
)
Phytoplankton diversity in inland waters of different trophic status
.
Jap J Limnol
 
45
:
173
177
.
Rahbek
C
(
2005
)
The role of spatial scale and the perception of large-scale species-richness patterns
.
Ecol Lett
 
8
:
224
239
.
Reche
I
Pulido-Villena
E
Morales-Baquero
R
Casamayor
EO
(
2005
)
Does ecosystem size determine aquatic bacterial richness?
Ecology
 
86
:
1715
1722
.
Reche
I
Pulido-Villena
E
Morales-Baquero
R
Casamayor
EO
(
2007
)
Does ecosystem size determine aquatic bacterial richness?
Ecology
 
88
:
253
255
. Reply.
Reynolds
CS
Padisak
J
Sommer
U
(
1993
)
Intermediate disturbance in the ecology of phytoplankton and the maintenance of species-diversity – a synthesis
.
Hydrobiologia
 
249
:
183
188
.
Rosenzweig
ML
(
1995
)
Species Diversity in Space and Time
 .
Cambridge University Press
,
New York
.
Scheiner
SM
Willig
WR
(
2005
)
Developing unified theories in ecology as exemplified with diversity gradients
.
Am Nat
 
16
:
458
469
.
Smith
VH
Foster
BL
Grover
JP
Holt
RD
Leibold
MA
DeNoyelles
F
Jr
(
2005
)
Phytoplankton species richness scales consistently from laboratory microcosms to the world's oceans
.
Proc Natl Acad Sci USA
 
102
:
4393
4396
.
Waide
RB
Willig
MR
Steiner
CF
Mittelbach
G
Gough
L
Dodson
SI
Juday
GP
Permenter
R
(
1999
)
The relationship between productivity and species richness
.
Annu Rev Ecol Syst
 
30
:
257
300
.
Ward
BB
(
2002
)
How many species of prokaryotes are there?
Proc Natl Acad Sci USA
 
99
:
10234
10236
.
Wright
DH
Currie
DJ
Maurer
BA
(
1993
)
Energy supply and patterns of species richness on local and regional scales
.
Species Diversity in Ecological Communities
  (
Ricklefs
RE
Schluter
D
, eds), pp.
66
74
.
University of Chicago Press
,
Chicago
.

Author notes

Editor: Ian Head