LETTER Zooming in on size distribution patterns underlying species

coexistence in Baltic Sea phytoplankton

A. S. Downing,1,2* S. Hajdu,1 O.

Hjerne,1 S. A. Otto,2 T. Blenckner,2

U. Larsson1 and M. Winder1

1Department of Ecology

Environment and Plant Sciences

Stockholm University Frescati Backe,

10691, Stockholm, Sweden2Stockholm Resilience Centre

Stockholm University Kr€aftriket 2B,

10691, Stockholm, Sweden

*Correspondence: E-mail:

andrea.downing@su.se

Abstract

Scale is a key to determining which processes drive community structure. We analyse size distribu-tions of phytoplankton to determine time scales at which we can observe either fixed environmen-tal characteristics underlying communities structure or competition-driven size distributions.Using multiple statistical tests, we characterise size distributions of phytoplankton from 20-yeartime series in two sites of the Baltic Sea. At large temporal scales (5–20 years), size distributionsare unimodal, indicating that fundamental barriers to existence are here subtler than in other sys-tems. Frequency distributions of the average size of the species weighted by biovolume are multi-modal over large time scales, although this is the product of often unimodal short-term (<1 year)patterns. Our study represents a much-needed structured, high-resolution analysis of phytoplank-ton size distributions, revealing that short-term analyses are necessary to determine if, and how,competition shapes them. Our results provide a stepping-stone on which to further investigate theintricacies of competition and coexistence.

Keywords

Competition, discontinuities, diversity, multimodality, neutral, niche, paradox of the plankton,self-organised similarity, textural discontinuity hypothesis, time scales.

Ecology Letters (2014)

INTRODUCTION

In the continuing quest to understand how species coexist andform complex diverse communities, phytoplankton communi-ties represent the ultimate test. Indeed, theories presented toexplain the coexistence of species range from Hutchinson’sniche theory (Hutchinson 1957) which stipulates that all spe-cies are different enough with respect to one another and tothe way they experience their environment, that they do notout-compete each other. At the other end of the hypothesisspectrum is the neutral theory that stipulates all species areequal in the eyes of competition, and that observed diversityis the result of random migration, speciation and extinctionrates (Hubbell 2001). Phytoplankton communities, however,challenge both theories (Hutchinson 1961; Walker & Cyr2007) and often appear to hold more species (higher richness)than their environment is expected to support. Hutchinsoncalled this the paradox of the plankton (Hutchinson 1961),and research has since explored how a variety of other pro-cesses, such as predation, spatio-temporal heterogeneity orcomplex dynamics (Huisman & Weissing 1999; Roy &Chattopadhyay 2007) can explain the observed species rich-ness of phytoplankton communities. However, an importantdifficulty in detecting the mechanisms that shape coexistenceis that niche, neutral and ‘intermediate’ theories are difficultto distinguish in community data, and these data are mostoften analysed as species abundance distributions (SADs)(Chave et al. 2002). Indeed, noise intrinsic to empirical dataand the statistical power of tests used in comparisons ofSADs often make clear distinctions between niche, neutraland intermediate theories either difficult to attain or easy tocontend, and yield little consensus on the matter across

studies (Chave 2004; Adler et al. 2007; Walker & Cyr 2007;Vergnon et al. 2012; Barab�as et al. 2013).Interestingly, before the publication of Hubbell’s neutral

theory (2001), Holling (1992) made an observation thought tohold true across ecosystems and communities, and that wouldfurther spur the pursuit of a mechanism that could explaincoexistence, perhaps even in phytoplankton. Through theobservation and analysis of many terrestrial ecosystem com-munities, Holling came to the conclusion that community sizedistributions are fundamentally discontinuous (Holling 1992):in each community, there are aggregations of similar-sizedorganisms and gaps between aggregations that represent unin-habited size ranges. Holling presented the Textural Disconti-nuity Hypothesis (TDH) to explain these discontinuities,describing how lumpy size distributions reflect a discontinuoushierarchical environment. Following this hypothesis, processdynamics fluctuate at rates that are scaled to specific land-scape hierarchical crannies. Each organism size group liveswithin a cranny in the landscape that is scaled to the specificsize group and organisms of each group perceive the samelandscape differently, as a function of the process rates thatinfluence them. This landscape and process-rate discontinuitythus produces similar discontinuous organism size distribu-tions across communities (Holling 1992). The TDH provides aspecific characterisation of the fundamental niche, i.e. the abi-otic environment in which organisms can exist (Hutchinson1957).Based on similar observations of discontinuities, Scheffer &

van Nes (2006) proposed an alternative hypothesis, entitledSelf-Organised Similarity (SOS). In a simple modellingexperiment, the authors found that a lumpy size distributioncould be achieved through competition alone. They found

© 2014 John Wiley & Sons Ltd/CNRS

Ecology Letters, (2014) doi: 10.1111/ele.12327

that species could coexist when they are similar enough toavoid competitive exclusion (mimicking intraspecificcompetition) or when they are different enough to avoidcompetition altogether. In gaps, or areas of intermediate sim-ilarity, competition was found to be too strong for survivalor invasion (Scheffer & van Nes 2006). The SOS hypothesiscan thus be related to Hutchinson’s ‘realised niche’, i.e. theenvironment species effectively live in, given biotic interac-tions (Hutchinson 1957). An important distinction betweenthe two hypotheses is that gaps in the TDH context areassumed to be a permanent environmental feature thatprecludes existence, whereas in the SOS gaps and lumps arespecific to the community and interactions that shape it.Furthermore, the TDH holds true for size distributions only,whereas the SOS relates to all niche axes representing traitsrelevant to competition. As omnipresent features ofcommunities, these discontinuous size distributions arethought to hold clues to the mystery of coexistence, andhave the potential to reveal nichiness more clearly thanspecies abundance distributions.The TDH and SOS have both received support in different

studies across terrestrial and aquatic ecosystems, includingphytoplankton communities. Havlicek & Carpenter (2001)found similar lumpy structures in phytoplankton, zooplanktonand fish size distributions across 11 lakes, indicating a regio-nal-scale pattern and thus supporting the TDH. Holling(1992) never studied discontinuities in aquatic systems, but heventured that similar processes, shaping seascape structureand then organism size distribution structures would also befound in aquatic systems, although process rates might differfrom terrestrial ones. Therefore, his hypothesis leads to expec-tations of fixed organism size gaps in aquatic systems,although perhaps not in the same size ranges as in terrestrialsystems. Havlicek & Carpenter’s (2001) analysis made theTDH bridge to aquatic systems, but their analysis could, how-ever, not reject alternative hypotheses. Vergnon et al. (2009)rejected Holling’s TDH on the premise that only permanentphytoplankton species appeared to have a lumpy structure,but temporary species occurred in gaps, and because theyfound competition patterns that stretched across lumps, notonly within them. Overall their study rejected all but the SOShypothesis. Segura et al. (2011, 2013) studied phytoplanktonsize distributions across multiple aquatic ecosystems, andfound that resource-competition-based processes shaped sizedistributions, consistently supporting the SOS hypothesis.Only Vergnon et al. (2009) confronted and rejected some ofthe different hypotheses although they measured not the sizedistribution of species per se, but that of abundant species,relating their study perhaps closer to niche-neutral perspec-tives than to the Textural Discontinuity Hypothesis presentedby Holling (1992).Unfortunately, these findings are very difficult to compare,

since the studies that produced them were carried out on dataspanning different temporal or spatial scales, including differ-ent taxonomic groups, using different techniques as well asmeasures of discontinuity in size distributions. Furthermore,these studies have received criticisms relating either to biasesof the methodologies or to the assumptions underlying theory(Manly 1996; Siemann & Brown 1999; Barab�as et al. 2013),

thus casting doubt on descriptions of discontinuous patternsas well as on interpretations of mechanisms underlying thesepatterns. There is therefore a great need to compare the per-formance of different analytical techniques.Allen et al. (2006) addressed these pitfalls and suggested

a conciliatory view on the two hypotheses, proposing thatboth abiotic (TDH) and biotic (SOS) processes drive discon-tinuous size distributions, albeit at different spatio-temporalscales: there are realised, competition-driven niches withinHolling’s fundamental niches (Allen et al. 2006). Scale istherefore an essential discriminant of the different theories.Indeed, Holling’s fundamental niche is expected to becomeapparent when all species that can establish in a system areaccounted for, illustrating a saturated landscape, whereunusual size differences between species reflect environmentalbarriers to existence (Holling 1992). The SOS realised niches,however, concern competing species, i.e. species thatcoexist in both space and time, and should thus becomeapparent when competition is at its peak (Scheffer & vanNes 2006).We used a multimethod and systematic approach to investi-

gate the temporal scales at which size discontinuities areobserved, the techniques that identify them best and theprocesses that explain patterns visible at different scales. Weused two consistent and high-resolution 20-year time series ofphytoplankton from the Baltic Sea, and aimed to characterisetheir size distribution and determine the scales at which dis-continuities in these distributions can be identified.

METHODS

Sites and data

The data were collected from the coastal station B1 near Ask€o(58°48’ N, 17°38’ E, 40 m deep) and from the offshore stationBY31 at Landsort Deep (58°35.90’ N, 18°14.21’ E, 459 mdeep), in the NW Baltic Proper, the southern part of theBaltic Sea. In the area, the spring blooms start with diatoms,followed by dinoflagellates, and as nutrients are depleted andtemperatures increase, spring bloom species are replaced bycyanobacteria and flagellates that bloom in the summer(Hajdu 2002). The spring bloom is characterised by high phy-toplankton biomass, and the summer bloom by high speciesrichness. We here used data collected approximately fort-nightly and spanning 1992–2011 for station B1 and 1994–2011for station BY31.Samples were taken as integrated samples with a sampling

hose (inner diameter 19 mm) from 0 to 20 m and preservedwith acid Lugol’s solution (Will�en 1962). Phytoplankton(> 2 lm) were counted after sedimentation in 10- or 25-mLchambers using an inverted microscope with phase contrastand cells were measured and size classed according to themethods described in the HELCOM guidelines (2008).Species-specific, size-classed cell volumes were used to calcu-late the biovolume and the carbon content of each species(wet weight, mgL L�1, and biomass, pgC L�1) using the rec-ommendations by Olenina et al. (2006) and the related stan-dard volumes (http://www.ices.dk/marine-data/vocabularies/Documents/PEG_BVOL.zip).

© 2014 John Wiley & Sons Ltd/CNRS

2 A. S. Downing et al. Letter

Analyses

We assumed that time frames including the highest number oftaxa have the highest likelihood of divulging Holling’s funda-mental niches (Holling 1992), since when all possible taxa arepresent they cover a larger proportion of the habitable sizelandscape, and thus reveal permanent gaps more clearly.Therefore, we considered any time range longer or equal to1 year as having the potential to divulge permanent gaps, sincetaxa covering all seasons are present therein. Furthermore, toidentify whether these size distribution structures might havechanged over time, we divided the time series into successivelyshorter time frames: we first analysed the full 20 years as one,then divided the series into 2, and then 4 equal subseries andcarried out the analyses on these shorter series.To detect competition-driven size distribution patterns, we

focused on coexisting species and limited the time frames to3-month periods – the minimum time range we can analyse islimited by the number of taxa present: at too low diversity,the statistical methods used loose power and misestimate thenumber lumps and gaps in the distribution. We set the mini-mum analysable diversity to 15 taxa, as this is within the low-est diversity range reported within which lumps have beendetected (Havlicek & Carpenter 2001). To best capture com-munities of coexisting taxa, we thus analysed community sizedistributions in overlapping, consecutive 3-month periodsfrom January to December (i.e. January–March, February–April, etc.).To determine the data resolution within which niche pro-

cesses are detectable, we carried out all analyses at the specieslevel. We assumed that taxa that could not be identified to thespecies level would nonetheless represent groups with similarvariability to species, and would therefore make them compa-rable. For simplicity, we here forth refer to this species/taxaresolution as species level. Furthermore, for comparison, wecarried out analyses of size distributions using both units ofbiovolume (lm3) and biomass (carbon content, in pgC).For all time frames analysed, we produced two kinds of size

distributions: ‘ordinary’ size distributions, which are frequencydistributions of the average size of species and are representedas presence of species along the size axis [as done in Holling(1992) and Havlicek & Carpenter (2001) for example]. In thiscase, lumps represent clusters of similar-sized species. We alsoproduced weighted size distributions, which are frequencydistributions of the average size of species, weighted by theirbiovolume (or biomass). Here, we looked at the averagespecies biomass (pgCL�1) or biovolume (lm3L�1) over thetime period analysed on the y-axis as a function of species size(x-axis) [c.f. studies of Vergnon et al. (2009) or Segura et al.(2011, 2013)]. In weighted distributions, lumps represent sizeranges where there is a high density of organisms. When aspecies is categorised only in one size class, we used the biovo-lume (lm3) or biomass (pgC) of that class. When species weredivided into multiple size classes, we computed an averagebiomass or biovolume for the taxon, based on the size of eachclass and the relative abundance of organisms in each class(sizes were obtained from the samples, not literature, see sitesand data section of methodology). All our analyses were runin R 2.15.3 (R Development Core Team, 2013).

For each time period studied, we applied five differentanalyses to the ordinary size distributions: (1) Kolmogorov–Smirnov test for non-uniformity, (2) Hartigan’s DIP test ofmultimodality (Hartigan & Hartigan 1985) (R package diptestversion 0.75-4), (3) kernel density estimate (KDE) (Silverman1981; Sheather 2004), (4) latent class analysis (LCA) (Gr€un &Leisch 2008) and (5) Holling’s Body Mass Difference Index(BMDI) to detect gaps in the distribution (Holling 1992). Wethen ran the Hartigan DIP test on weighted size distributions,this test is referred to here forth as the Standardised EffectSize – SES (Vergnon et al. 2009).The DIP test consists of first producing a unimodal distri-

bution that best fits the empirical distribution, and then deter-mining if the empirical distribution is a probable draw fromthe computed unimodal distribution. If the empirical size dis-tribution is not a likely draw from the unimodal (P < 0.05),the size distribution is considered multimodal. Put together,the results of the KS and DIP tests allowed us to determinewhether the distribution was uniform (P-value of KS andDIP > 0.05), unimodal (P-value of KS < 0.05, P-valueDIP > 0.05) or multimodal (P-value of KS and DIP < 0.05).The KDE and LCA allowed us to quantify lumps. In the

KDE, we used a Gaussian kernel, and determined the band-width using Silverman’s rule of thumb (Silverman 1981;Sheather 2004). We counted turning points in the density func-tion as a measure of multimodality. The KDE used in Havlicek& Carpenter (2001) differs in that the bandwidth is a functionof the SD in the size distribution of each species. We did nothere have sufficient species with multiple size classes to computeenough SDs for an unbiased KDE. The LCA determines howmany normal distributions characterise the size distributions(Gr€un & Leisch 2008). We used the FlexMix package (R, ver-sion 2.3-10), and tested models containing from 1 to 10 distribu-tions. We compared three different criteria used to determinethe best fitting model: the Bayesian Information Criterion(BIC), Akaike Information Criterion (AIC) and IntegratedCompleted Likelihood (ICL) criterion (Gr€un & Leisch 2008).To calculate gaps in the ordinary distribution, we used Hol-

ling’s Body-Mass Difference Index (Holling 1992), where foreach species one calculates an index based on the size of its twoneighbouring species. Computation of the BMDI requires adetrending value c. Using the two full time series, we estab-lished the optimal value of c = 1, producing BMDI distribu-tions that lied in between being right and left skewed (whichwould lead to an underestimation of gaps between larger andsmaller species respectively – we found gaps at either ends ofthe distribution), and then used this c = 1 for all analyses at allscales. We identified gaps in the same way as Holling (1992),where a gap is represented by an index that is higher than theaverage and SD of all indices, and is followed by two lowerindices. Given very variable results, the arbitrariness of theparameter c and criticisms of the method (Manly 1996), we alsomanually fine-combed the data. For this, we marked out thegaps detected in the large time frames, and then – cutting thedata set into 1-year periods (intermediate time scale), estab-lished whether species were found within marked-out gap areas.The SES method is used to detect departure from unimodality

in a weighted size distribution (weighted by the biovolume ofbiomass) (Mason et al. 2008; Vergnon et al. 2009). It represents

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Letter Baltic Sea phytoplankton size distributions 3

a scaled DIP test that is carried out in three steps. First, oneproduces a large number (here 10 000) of probability distribu-tions for the size distribution, where the probability of each sizeclass is scaled to its abundance. One then determines, for eachprobability distribution, whether it diverges from unimodalityusing Hartigan’s DIP test (as described above). Finally, if morethan 95% of the 10 000 probability distributions are signifi-cantly different from unimodal (P < 0.05), the weighted sizedistribution is considered multimodal.

RESULTS

Using biovolume or carbon content as size metrics did notinfluence the results much (Appendix S1). We therefore heredescribe results obtained using biovolumes.

Long-term analyses

Ordinary distributionsWe found no multimodality in the ordinary size distributionsat any long-term scale (20 years, 2 9 10 years, 4 9 5 years)in either site. The distributions significantly diverged from uni-formity in most analyses (Kolmogorov–Smirnov (KS) test,P < 0.05), but not from unimodality (Table 1). At the off-shore station (BY31), the Latent Class Analyses with AkaikeInformation Criterion (LCA-AIC) revealed that 2–3 normaldistributions best described the longest time series, althoughboth the Bayesian and Integrated Completed Likelihood crite-ria (BIC and ICL) only detected one normal distribution(Table 1). We found that the three proposed normal distribu-tions had a high overlap and after an additional visual inspec-tion of the distributions, we concluded that multimodality wasan artefact of too high sensitivity of the AIC (Fig. 2 andAppendix S2 for comparisons of outputs from different tests).

Weighted distributionsIn all long-term analyses, we found a significant deviationfrom unimodality in the weighted distributions (SES), indicat-ing that while the size of species follows a unimodal distribu-tion, it is not necessarily the modal-sized species that have thehighest abundances (Table 1).

Gap analysisResults from the BMDI analysis, aimed at revealing gaps inthe size distributions, were variable: we found between five

and two gaps in the different time scales. After manual sift-ing of the data at an intermediate time scale (1 year), wefound that no gap represented a permanently uninhabitedsize range.

Short-term analyses

Ordinary distributionsLooking at size distributions covering 3-month periods, testsrevealed very little convergence of results, indicating perhapsthat patterns lie on the border of detection of the differenttests. The KDE and LCA-AIC detected multimodality in upto 66% of years, during March–April–May or April–May–June periods (Fig. 1). The LCA-BIC, LCA-ICL did not revealthe same patterns of frequency of multimodality as the LCA-AIC (Fig. 1), although the LCA-BIC followed a similar quali-tative distribution of multimodality than the LCA-AIC, butwith much lower frequencies (Fig. 1 and Fig. 3). Hartigan’sDIP test only detected a significant difference from unimodali-ty on two occasions in station BY31 (Fig. 1). When differentfrom unimodal, results of the KDE were most often bimodal,although the multimodal pattern was not very distinct (Fig. 2and Appendix S2). Similarly, when the LCA-AIC detectedhigher than bimodality, the modes, or normal distributionswere often overlapping (Appendix S2 for comparison ofresults produced by the LCA-AIC and KDE). With these con-siderations, we conclude that the most consistent result acrosstests in the short-term analyses is that size distributions aremost often unimodal, and occasionally slightly bimodal.

Weighted distributionsAnalysis of weighted distributions yielded different results: theSES revealed a successional pattern across both sites, with ahigh peak in frequency of multimodality in the period centredaround April, a lesser peak in July, and a third smaller peakin October, following a declining trend in frequency of mul-timodality during the year. Peak months correspond tomonths of highest phytoplankton abundance: the spring, sum-mer and fall blooms. However, while the pattern appearedquite clear, it was not strong: most 3-month periods in mostyears revealed no multimodality (Fig 1). Considering the dif-ference in frequency of detection of multimodality betweenresults obtained from the DIP test and the SES, we concludethat weighted size distributions show clearer multimodalitythan ordinary size distributions.

Table 1 Size distributions in the long time scales for station B1 (coastal) and BY31 (offshore)

B1 KS-DIP KDE LCA SES BY31 KS-DIP KDE LCA SES

1992–2011 1994–2011 *

1992–2001 1994–2001 *

2002–2011 2002–2011 *

1992–1996 1994–1997

1997–2001 1998–2001

2002–2006 2002–2006

2007–2011 2007–2011

White represent a uniform distribution, light grey a unimodal distribution and dark grey a multimodal distribution. KS-DIP: Kolmogorov–Smirnov test for

uniformity with Hartigan DIP test for unimodality; KDE: Kernel Density Function; LCA: Latent Class Analysis; SES: Standardised Effect Size. The stars

indicate LCA tests where both Bayesian information criterion and integrated likelihood criterion determined a single mode, but the Akaike information cri-

terion determined more.

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4 A. S. Downing et al. Letter

Long-term spring analysesTo see if we could strengthen the signal of the pattern, we car-ried out the analyses at long-term scales (5, 10 and 20 years),using only March–April–May communities. In ordinary distri-butions, this did not reveal stronger multimodality: 50%uniformity (KS), and artefactual bimodality (KDE, BY31,1994-1997, 1998–2001) and trimodality (LCA-AIC, B1 2002–2006). In weighted analyses, the multimodal pattern was againclearer: we obtained the same results as in the long-termfull-year analyses, the SES detected multimodality in all of thelong-term 3-month analyses (results not shown).Looking closer at the weighted size distributions during

March–April–May of multimodal and non-multimodal years,we found that there was no single ‘multimodal’ or ‘unimodal’configuration (Appendix S2). Distributions were very variablefrom year to year, as were the phytoplankton dynamics.

DISCUSSION

We used two 20-year phytoplankton time series to identifyscales at which different niche processes shape community size

distributions. Surprisingly, and in stark contrast to existingstudies we found that size distributions are not consistentlydiscontinuous or multimodal at any scale in the Baltic Seaphytoplankton communities analysed. We thus show that thebasic premise of this study – community size distributions arefundamentally discontinuous – cannot be expected to holdtrue for all communities.Of course, the absence of evidence for a significant multi-

modal pattern is no evidence of absence of such a pattern.However, we use a variety of techniques that have successfullyrevealed multimodality in size distributions (Holling 1992;Allen et al. 2006; Vergnon et al. 2009; Hirota et al. 2011;Segura et al. 2011), using high-quality long-term data sets anda thorough search pattern. We therefore conclude with confi-dence that discontinuities in the Baltic Sea phytoplankton sizedistributions here analysed occur only occasionally.We tested both ‘ordinary’ size distributions and weighted

size distributions. Ordinary distributions were primarily notsignificantly different from uniform or unimodal at all scales.Although we occasionally detected two or three modes (KDEand LCA-AIC tests), further analyses revealed that these pat-terns were weak, representing at most slight bimodality. Theseresults are quite strongly indicative that the permanent struc-turing forces hypothesised by Holling (Holling 1992) do notshape size distributions of the phytoplankton communitiesstudied, or if they do, they have a subtler effect than in com-munities previously analysed.In weighted distributions results diverged significantly from

unimodality in the long time scales (> 1 year), indicating thatsuccessful species – those that attain highest biovolumes (orbiomass) – are not all similar-sized. These results match thefindings of Vergnon et al.’s (2009) study of phytoplanktonfrom the Western English Channel. From our comparativeanalyses across long-term time scales, we found that patterns ofmultimodality varied from time frame to time frame – not fol-lowing any apparent trend – but further dismissing the notionof a permanent structuring force on the size distributions.Hypothesising that competition drives community structure,

we expected to find multimodal weighted distributions in theshort-term analyses, representing communities of coexisting –and thus directly competing – species. Specifically, weexpected that multimodality would be clearest during thesummer months, when diversity is at its peak. Interestingly,we found that weighted distributions were occasionallymultimodal, and that frequency of multimodality peaked inspring but decreased during the year. Although these resultsdiffer from our expectations, they do not allow us to rejectthe hypothesis that competition plays a role in communitysize distributions. Indeed, we probably should not expectcompetition to be a strong structuring force in winter monthswhen biomass and diversity is low. However, they compel usto refine this hypothesis in that – should competition be astructuring force – it is a varying one, and that environmentaland/or community conditions modulate its effects. Althoughit remains unclear why spring would present a higher likeli-hood of multimodality in size distributions, we find that thispattern correlates, be it weakly, with patterns of phytoplank-ton biomass and/or resource availability. In this way, wemight speculate that competition that is the product of an

Figure 1 Percent years where tests detected multimodality in stations B1

and BY31 during consecutive and overlapping 3-month periods. KS-DIP:

Kolmogorov–Smirnov test for uniformity with Hartigan DIP test for

unimodality; KDE: Kernel Density Function; LCA: Latent Class

Analysis; SES: Standardised Effect Size.

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Letter Baltic Sea phytoplankton size distributions 5

environment that is at first resource-rich but becomes limiting,as occurs when nitrogen becomes depleted in early to mid-spring in the Baltic, shapes community size distributions dif-ferently than competition that establishes itself between spe-

cies that settle in a limiting environment, such as the nitrogen-depleted ‘pre-summer’-Baltic. Alternatively, we might specu-late that multimodality is ‘grazed down’ by zooplankton thatusually appear shortly after the spring phytoplankton bloom.

Figure 2 Results from the Latent Class Analysis, with Bayesian Information Criterion. On the x-axis, the log biovolume of each species, and the histogram

represents the size distributions where the bandwidth is set at an arbitrary value of size range/39. Each line represents a normal distribution, where more

than one line characterises the distribution, it is said to be multimodal (e.g. years 1994, 1999, 2003, 2004 and 2005).

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6 A. S. Downing et al. Letter

There are of course many other potential explanations for theobserved patterns. Nonetheless, variability in size distributionsis a promising observation on which to base further researchinto intricacies of competition interactions and their role inspecies coexistence and size distributions.This study is a rigorous comparative analysis of size distri-

butions across scales and methods. In this respect, we findthat scale matters, complex patterns observed in aggregateddata do not necessarily scale down to the process level. Themultimodality (significant divergence from unimodality) inweighted distributions detected over the long time frames isthe product of very variable and often unimodal short-termdistributions and is thus perhaps not a reliable standaloneproof – should there ever be one – of the SOS hypothesis.We suggest that there is need for further research on knownmultimodal size distributions, at different temporal scales, inphytoplankton and other aquatic and terrestrial communities,to detect whether they are the product of many differentlyunimodal distributions or of ‘fundamental’ multimodality.Of all the tests of ordinary and weighted distributions at

different time scales that have been carried out here and inprevious research, we here find that most are not useful to dis-

tinguish the TDH from SOS hypothesis (Fig. 3). The TDHshould be rejected if uniformity or unimodality is detected inlong time frames, using ordinary size distributions, whereasthe SOS can be rejected if uniformity or unimodality isobtained in short time frame analyses of weighted distribu-tions (Fig. 3).In addition to comparisons of results across temporal

scales, we here demonstrate the importance of comparisonsacross methodologies. Indeed, each test has its own level ofsubjectivity, be it in the choice of a smoothing factor for theKDE, the detrending exponent of the BMDI (c), or thenumber of models with which to test the LCA, and ofcourse the number of random distributions with which tocompare the empirical distributions in the SES. Each ofthese tests, at any given scale, can potentially be adjusted toreveal multimodality (Allen et al. 2006). Nonetheless, the dis-tributions here are too variable for any consistently appliedadjustment to systematically reveal multimodality. Our multi-method approach also reveals that methods have very differ-ent sensitivities. We found the BMDI technique to be leastinformative, and the selection of c quite arbitrary. Overallour interpretation of results relied more heavily on the LCA,

Figure 3 Synthesis of analyses and results that can discriminate between the TDH (Textural Discontinuity Hypothesis) and SOS (Self Organised Similarity).

Question marks indicate no information can be gleaned, the tick mark indicates support for the hypothesis and the cross indicates rejection of the

hypothesis. Long term refers to time frames longer than 1 year, and short time frames refers to periods including coexisting and competing organisms, here

3 months. Shaded boxes refer to results obtained in this study.

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Letter Baltic Sea phytoplankton size distributions 7

KDE and SES tests, although always with a visual inspec-tion of the distributions and projected models. While theLCA-BIC, LCA-ICL and Hartigan’s DIP test were not verysensitive, they were perhaps more robust than the LCA-AIC.We emphasize the conclusion of Allen et al. (2006) that it isessential to use multiple methods when attempting todescribe size distributions.We could of course cast doubt on the applicability of the

analyses on phytoplankton communities sampled here: as anexample, our samples are integrated over 20–m depth – welack spatial vertical resolution. This methodological aspect is,however, common to previous studies that have detectedmultimodality in phytoplankton communities (Havlicek &Carpenter 2001; Vergnon et al. 2009; Segura et al. 2011,2013). Therefore, deviations from expected results obtainedthrough our comparative analyses across time scales andmethods ought also to spur a rethink of expectations of theTDH and SOS theories for phytoplankton communities.Indeed, difficulties in determining community saturation andborders as well as competition strategies for phytoplanktonmay be more obvious than for terrestrial communities. Withthis in mind, perhaps determining the role of competition ver-sus environment in driving species coexistence is better investi-gated looking at dynamics of the species: for example. in theirsynchrony (c.f. Vergnon et al. 2009) or in quantifying the roleof environment versus interactions in temporal dynamics.With their variability, our results deviate from our some-

what oversimplistic expectations, and leave us with the follow-ing dichotomy: on one hand, perhaps other processes thancompetition, such as predation, stochastic environmentalchanges or environmental heterogeneity, here overshadow theeffects of competition, and in this system play a more impor-tant role than competition in driving species coexistence. Onthe other hand, we might hypothesize that size is not alwaysthe dominant competition trait. Indeed, colour (Stomp et al.2007), element-specific assimilation efficiencies (Sommer 1986)and other traits that are not direct functions of size can alsoplay an important role in determining the outcome of compe-tition. The SOS theory is compatible with this hypothesis,since multimodality is expected to be expressed on niche axesthat correspond to traits determining competition outcomes(Scheffer & van Nes 2006). Therefore, to reject the SOS onewould need to investigate the distributions of different traitsalong their niche axes.The idea that there are multiple traits relevant to competi-

tion or that the dominant competition trait (species-fitness)might change over time can have other interesting implicationsfor our understanding of species coexistence. Sasaki (1997)proposed that biotic processes, such as competition, producediscontinuous size distributions in the presence of heteroge-neous environmental conditions. Huisman & Weissing (1999)demonstrated how species-specific competitive abilities withregard to different resources, in conjunction with an everchanging resource-base, could lead to chaotic dynamics, whichin turn allow for the coexistence of many species (Huisman &Weissing 1999, 2001). Similarly, Fox et al. (2010) demon-strated that fluctuation-based mechanisms, such as chaos,could explain the paradox of the plankton. However, theyargue that it is these dynamics that cause changes in species fit-

ness over time, and thus allow for co-existence (Fox et al.2010). In this sense, future research avenues might investigatewhether chaotic dynamics produce discontinuous size distribu-tions, and whether, in communities such as the ones here stud-ied, lumpiness is expressed successively on different niche axes.In short, we cannot here dismiss the idea that a simple

mechanism, such as competition, drives community structurein such a way that allows for the coexistence of many species.However, our findings emphasize the notion that, should sucha simple mechanism be at play, it might often have complexrealisations, as in cases where competition is a changing, mul-tivariate process that can be nudged by subtle changes in theenvironment.Our study leaves us perhaps as perplexed as Hutchinson

(1961), since we cannot generalize to the system studied herethose mechanisms suggested to allow for coexistence of manyspecies. However, we here provide a first exception to the‘fundamentally discontinuous nature of size distributions incommunities’ described by Holling (1992), and it is only withsuch exceptions that one can learn the rules that define thestructure of size distributions in communities.

ACKNOWLEDGEMENTS

We thank the staff at the Department of Ecology, Environ-ment and Plant Sciences (former Systems Ecology) that col-lected the samples and worked with the chemical analysisand Marika Tir�en for counting the phytoplankton samples.This study was partially supported by Stockholm University’sstrategic marine environmental research funds through theBaltic Ecosystem Adaptive Management (BEAM) program.The use of the data from the National Swedish MonitoringProgram, supported by the Swedish EPA, is gratefullyacknowledged. We are very grateful to Remi Vergnon forcodes and discussions and to Jennifer Griffiths for construc-tive comments.

AUTHORSHIP CONTRIBUTIONS

ASD designed the study, analysed the data and wrote themanuscript, SH and UL provided the data, SAO, OH, MWand TB contributed to the design and conduct of the studyand the writing of the manuscript. All authors contributedsignificantly to revisions.

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SUPPORTING INFORMATION

Additional Supporting Information may be downloaded viathe online version of this article at Wiley Online Library(www.ecologyletters.com).

Editor, James GroverManuscript received 10 February 2014First decision made 17 March 2014Second decision made 31 May 2014Manuscript accepted 17 June 2014

© 2014 John Wiley & Sons Ltd/CNRS

Letter Baltic Sea phytoplankton size distributions 9