Hydrobiologia 138: 205-220, (1986). 205© Dr W. Junk Publishers, Dordrecht - Printed in the Netherlands.

Patterns of temporal variation in Lake Titicaca. A high altitude tropical lake.

I. Background, physical and chemical processes, and primary production

Peter J. Richerson', Patrick J. Neale l , Wayne Wurtsbaugh 2 , Ren6 Alfaro T.3 & Warwick Vincent4

'Institute of Ecology, University of California, Davis, CA 95616 USA2Department of Fisheries and Wildlife, Utah State Universuty, Logan, UT 84322 USA3Lake Titicaca Laboratory, Instituto del Mar del Peru, Apartado 292, Puno, Peru4 Taupo Research Laboratory, Division of Marine and Freshwater Studies, DSIR, PO. Box 415, Taupo,New Zealand

Keywords: seasonality, tropical lakes, time series, primary production, alpine lakes

Abstract

A statistical analysis is presented of patterns of variation in some physical, chemical, and biological varia-bles for a 6 year series of data from the tropical, high altitude Lake Titicaca (Peru-Bolivia). ANOVA tech-niques and autocorrelation analyses were used to partition the variance in Titicaca, and in some comparisontropical and temperate series, into components with repeatable annual cycles and components attributableto other kinds of patterns.

In Titicaca, insolation and stratification are highly seasonal in pattern of variation, although the amountof variance relative to means is small compared to temperate lakes. However, the seasonal pattern of physicalvariation is only weakly imposed on chemical and biological processes, to judge from analyses of sili-cate, oxygen, and primary production series. Comparable temperate series of primary production and chlo-rophyll a are much more seasonal.

Introduction

In this paper, we present a statistical analysis ofseveral time series of physical, chemical, and bio-logical variables from Lake Titicaca (Peru,Bolivia), ranging in length from three to six years,depending on the variable considered. The resultsfrom Titicaca are compared with several other se-ries available in the literature from temperate andother tropical lakes.

The objective is to determine the extent to whichseasonal patterns of climate and weather affect var-iations in lacustrine processes in Titicaca, com-pared to other sources of temporal variation. Forthe purposes of this paper, seasonal patterns are de-fined as those which have regular periodicities withthe same frequency as the regular patterns of cli-matic variation, and which are presumably causedby climatic seasonality. Seasonal effects in the tem-

perate zone lead to the observation of cycles witha period of 12 months, ultimately attributable todeterministic intra-annual variations in insolationcaused by the inclination of the earth's axis. Withinthe tropics, there is also a 6-month seasonal cyclecaused by the passage of the sun overhead twice peryear. Near the equator, the 6-month cycle of solarradiation is sometimes reflected in rainfall (Walter,1979). The amplitude of seasonal variations in tem-perature and solar radiation is small in the tropicscompared to the temperate zone (Sellers, 1965), al-though rainfall is very seasonal in many tropical cli-mates. Non-seasonal causes of variation, in bothtemperate and tropical climates, include the lessregularly cyclic inter- and intra-annual fluctuationsof weather and climate, as well as a large numberof other processes ranging from geological eventsto human impacts. Interactions among physical,chemical, and biological processes within a lake

206

could conceivably generate endogenous temporalvariation independently of climatic effects (Powell& Richerson, 1985), and these might be compara-tively or absolutely more important when seasonalvariation is weak.

All deep tropical lakes so far investigated exhibita monomictic pattern of thermal stratification,with isothermy, or near isothermy in the case of thevery deep meromictic lakes of the African Rift Val-leys, in the coolest and driest season (Talling, 1966,1969; Beadle, 1974; Lewis, 1973, 1983; Kittel &Richerson, 1978). Shallower lakes often show pro-nounced effects of a seasonal rainfall regime (Me-lack & Kilham, 1974). Thus, the degree of seasonal-ity in tropical lakes is likely to be smaller than athigher latitudes, but not necessarily absent.

As regards other kinds of temporal variation inthe tropics, two effects may be important. First,Lewis (1973, 1974) observed considerable short-term variation in depth of stratification and prima-ry production in response to weather events in LakeLanao, Philippines, and Lake Valencia, Venezuela(Lewis, 1984). Lewis (1978, and this symposium)also showed that phytoplankton succession is af-fected by such stratification events. Unlike temper-ate lakes where the successional sequence has aregular annual cycle (classically from diatoms inthe spring to blue-greens or dinoflagellates in latesummer: Reynolds, 1984), Lake Lanao and LakeValencia show a pattern of succession which variesbetween progression along the standard tempera-ture sequence during stratification episodes and apartial to complete re-setting of the sequence as aresult of mixing events of variable strength. Sec-ond, Kittel & Richerson (1978) hypothesized thatthe small seasonality of heat budgets in the tropicsmight lead to an enhanced sensitivity to within-and between-year variations in weather, becauseonly a relatively small change in heat content wouldbe necessary to make proportionately large changesin stratification. Thus, stratified tropical lakes maybe predicted to have a greater proportion of theirvariation in limnological variables explained by ir-regular variations within and between years, andless by regularly cyclical annual patterns, comparedto temperate lakes. This is the hypothesis to be test-ed in this paper.

Some comparative studies of patterns of tem-poral variation have been undertaken in the past,mostly with rather short series that did not permit

the partitioning of variance into effects with differ-ent time scales. Data from Lake George (Uganda),a shallow lake in a nearly aseasonal climate, havebeen compared with the shallow temperate LochLeven (Scotland) to show that seasonal fluctuationsof zooplankton and chlorophyll are very muchsmaller in Lake George (Burgis & Walker, 1972;Ganf, 1974). Melack (1979), using mostly annualrecords, showed that variation in primary produc-tion is a strong function of latitude, although thescatter about the trend line was substantial. Wil-liams & Goldman (1975), Richerson et al. (1977)and Lewis (1978) have reported estimates ofphytoplankton succession rates from tropical andtemperate lakes. Rates of change in species compo-sition appear to be smaller in the tropics and lessseasonally variable.

The hypothesis outlined above can be tested bycomparing time series now available from LakeTiticaca to other series from temperate and tropicallakes. Statistical analysis is used to estimate vari-ance at different time scales. If the hypothesis iscorrect, a relatively smaller proportion of the varia-tion in important limnological variables in strati-fied tropical lakes should be accounted for by regu-larly repeated annual patterns and more byirregular variations within and between years. TheTiticaca series also allows some insight into themechanisms which cause the patterns of variationobserved, because the series includes a measure ofclimatic variation (solar radiation) and measures ofthe limnological response to this variation, includ-ing a physical variable (temperature difference be-tween the epilimnion and hypolimnion), chemicalvariables (oxygen and silicate concentrations), andbiological variables (primary production, andphytoplankton biomass and species composition).This paper concentrates on analysis of variables forwhich the longest time series are available. A fullstatistical analysis of phytoplankton succession isreserved for further contributions in this series.Data on diatom biomass is included because of apotentially close relationship to silicate variation.

Methods

Data series

Routine, approximately bi-weekly, limnological

207

measurements were carried out at Lake Titicaca in1973, and at approximately monthly intervalsthereafter until August 1976. Two stations wereused, one near-shore for biological measurements,and one seven km offshore for chemical and physi-cal measurements (see Fig. 1). The station locationwas chosen because the 100 m contour is quiteclose to shore so that essentially open water condi-tions could be sampled from small boats withoutundue risks. This program yielded reliable profilesof temperature, silicate concentration, oxygen con-centration, primary production, and phytoplank-ton biomass. None of the measurements is com-plete for the whole period except insolation, but thetemperature and oxygen data are nearly so. Thephytoplankton data exist only for 1973, silicatemeasurements until August 1975, and primaryproduction until March 1975.

Temperature profiles were measured with a ther-mistor (a water-bottle thermometer on a few occa-sions in 1973) to an accuracy of +0.1 C. Tempera-ture difference between 10 m (i.e. epilimnion belowthe diurnal thermocline: Powell et al., 1984) and150 m was used to estimate epilimnetic-hypolimnetic temperature difference, a measure ofstratification. Temperature gradients below 150 mare always very small. Oxygen was determined byWinkler titration (+0.2 mg 1- 1) and silicatecolorimetrically by the heteropoly blue method(+0.05 mg Si 1-1). The depth of the mixed layerwas estimated as the depth of the maximum tem-

0 20 40km

Fig. 1. Map of Lake Titicaca showing the sampling stationsused in 1973-6 and 1981-2. Chemical and physical measure-ments in the earlier period were made at a station near the1981-2 location.

perature gradient in the seasonal thermocline, andmean epilimnetic and hypolimnetic concentrationswere determined using rectangular integration overthe appropriate depth interval. All chemical deter-minations were made with commerical water test-ing kit (Hach Chemical Company, Loveland, Colo.USA). Estimates of phosphate and nitrate were alsomade, but the sensitivity of the kit was too low toproduce acceptable data.

Insolation measurements from a Belfortpyranometer at Puno were furnished courtesy ofthe Servicio Nacional de Meteorologia y Hidrolo-gia. Primary production was estimated using in situincubations at 9 depths in 125 ml Pyrex bottleswith 2.2 ItCi of 14C-Na 2CO 3 for 4 h around mid-day. The samples were filtered onto 0.45 stm mem-brane filters and sent to Davis for activity determi-nation using a thin-window G-M counter. Theactivity of the counter was periodically estimatedby measuring the absolute activity of wet combust-ed sample filters in gas phase and the routinecounting of samples of known activity. Daily esti-mates were made by assuming that photosynthesisbefore and after the incubation periods is propor-tional to light availability. Diurnal experimentsshowed that this procedure is usually a slight un-derestimate (Neale, 1984).

Phytoplankton was enumerated using theglutaraldehyde-cleared filter technique of Dozierand Richerson (1975). Settled, Lugol preservedsamples and living material were used for floristicanalysis. Cells larger than 0.5 tzm in largest dimen-sion were enumerated (at 1 250x, with phase con-trast). No taxa encountered in the living and settledmaterial were absent in the filtered preparations,but quantitative comparison of the methods wasnot undertaken. Biomass was estimated using geo-metrical approximations to estimate volume andthe equation of Mullin et al. (1966) to estimate cellcarbon.

From December 1980 until December 1982 weconducted an intensive study of limnologicalprocesses at Titicaca which included all the meas-urements of the 1973-76 period at 14-day inter-vals. Methods were similar to 1973-76, but withsome improvements. The location of the samplingstation was further offshore than in 1973 (seeFig. 1). Temperature profiles were measured with abetter thermistor and calibrated routinely withreversing thermometer measurements at selected

ii

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depths. Silicate was measured on water filteredthrough acid washed glass-fiber filters, using thesilicomolybdate method described in Strickland &Parsons (1968). Nitrogen and phosphorus measure-ments were made in this period and are reported inVincent et al. (1984). 14C activity was estimated byliquid scintillation using Aquasol cocktail.

Methods for statistical comparisons

Four sets of comparison data were obtained fromthe literature. Series with two or more years ofphytoplankton biomass or primary productiondata taken at monthly or shorter intervals wereselected for analysis. At least two years of data arenecessary to estimate the year to year repeatabilityof patterns and to estimate between-years differ-ences in means. Series from tropical Lake George(Ganf, 1974) and the temperate Lakes Washington,Tahoe, and Loch Leven (Edmondson, 1972; Gold-man, 1981; Bindloss, 1974) met these criteria. Thedata were generally presented as graphs, which weredigitized using enlarged photocopies as necessary.The accuracy of this procedure is limited mainly bythe original figures, especially in the case of datapresented on logarithmic scales. When available,accompanying physical and chemical data werealso digitized and analyzed.

Each series was converted to monthly averages tofacilitate comparisons. Few of the series containedmore than one or two samples per month, andnone included a means to estimate error variancesindependently of within-month effects, so no at-tempt was made to estimate them.

Two-way analysis of variance was used to parti-tion the variance in each series into fractions due tofixed monthly effects and to between-year effects.When series contained missing values (an un-balanced design) monthly effects were calculatedfirst, followed by between years effects. Thus, asmuch variance as possible was attributed to the sea-sonal (monthly) effect before considering other(between year) sources of variation. We also calcu-lated autocorrelation functions for each series as anexplicit search for a twelve-month period in thedata. If a seasonal cycle exists, monthly effects willbe a significant contribution to the ANOVA, andthe autocorrelation function will show significantnegative peaks at lags of six months and positiveones at twelve months, or perhaps at other lags if

the 6-month tropical cycle is also important. Allstatistical analyses were implemented using theMinitab II statistical package run on an LSI 11/23minicomputer.

Results

Lake Titicaca: Limnological background

Lake Titicaca is situated at 16 °S latitude in theAltiplano region of Southern Peru/WesternBolivia. The lake is high (3 808 m asl), cool (epilim-netic temperatures 11-15 C) and fairly large(8 167 km 2, 107 m mean depth, volume 919 km 2).The climate is strongly seasonal in terms of rainfall(90% of total annual precipitation usually fallsfrom the beginning of November to the end ofApril), but the amplitude of the seasonal variationsof insolation and temperature is small. Depth tothe thermocline is usually about 30 m from Oc-tober to April, after which time it graduallydescends. A brief period of isothermy or near-isothermy occurs during the dry season in August(Fig. 2), but complete entrainment of the hypolimi-on does not occur in every year.

The oxygen and silicate data reflect the annualcycle of stratification, although the patterns arerather less regular. The silicate and oxygen data aresummarized in Fig. 2. Chemical gradients are weakor absent during the annual period of isothermy,and relatively strong during stratification. There is,however, relatively great variation within years andsubstantial differences between years. Conspicuousexamples of the latter include the high epilimneticsilicate concentrations in 1974 and the differencesin hypolimnetic oxygen depletion between 1981 and1982. The oxygen depletion in 1981 produced athick layer of anoxic water in the hypolimnion anda considerable loss of fixed nitrogen due todenitrification (Vincent et al., 1985).

In many respects Titicaca behaves physically likea low-altitude stratified tropical lake, despite itshigh elevation and lower temperatures. For exam-ple, differences between epilimnetic and hypolim-netic temperatures are modest (approx. 3 C), andthe mixing pattern is monomictic. This similarity isexpected because the seasonal variation of climatedoes not change appreciably as a function of eleva-tion even though mean insolation rises and temper-

209

LAKE TITICACA

75III I II I I II .I I I III

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Fig. 2. Monthly averaged data series from Lake Titicaca. A temp. is the difference between the temperature at 10 m and deep hypolim-netic temperatures at 150 m.

ature falls. However, many intra-lacustrine process-es are functions of temperature, so Titicaca mayrespond differently than otherwise similar low-elevation lakes. For example, the low partial pres-sure of oxygen at Titicaca slows re-oxygenationduring isothermy, encouraging the development ofhypolimnetic oxygen deficits and high rates ofdenitrification (Vincent et al., 1985).

Mean annual primary production averages about1.13 g C m - 2 d-' (Fig. 2 and Table 2) and chlo-rophyll a concentration is about 1.5 mg m -3 .Production is nitrogen-limited (Vincent et al., 1984;Carney, 1985; Wurtsbaugh et al., 1985). The annualnitrogen cycle of the main lake is described by Vin-cent et al. (1984). Further information on the gener-al limnology of the lake can be found in Richerson

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Table 1. The major planktonic algal species identified from Lake Titicaca in 1973, with notes on their relative abundance in this andother years. Previous reports of occurrence in the Titicaca plankton are also given. The notations 'dominant' and 'co-dominant' indicatespecies that were the most abundant and second or third most abundant respectively, in terms of estimated carbon biomass. 'Common'indicates species abundant enough to be enumerated in most samples, but seldom or never exceeding 10% of carbon biomass; 'rare'indicates species present in less than half the samples and never exceeding 10% of biomass.

Species Abundance Other occurrences

Cyanophyceae1. Anabaena spiroides Klebahn

2. Anabaena affinis Lemm.

3. Nodularia Harveyana (Thw.)Thuret

4. Gloeothece incerta Skuja

1973: Co-dominant Jan.-Feb.;Dominant Nov.-Dec.

1981: Common Jan.-Feb.;1982: Common to subdominant Jan.-June

1973: Rare1981: Rare1982: Common to subdominant Jan.-May,

Dec.

1973: Common Jan.-Mar., Nov.-Dec.1981: Common, Dec.1982: Common Jan.-May; Dec.

1973: Common

Lazzaro (1981): A. sphaerica, A. spiroides,A. flos aquae in L. Pequefio.

Thomasson (1966): Anabaena sp. in PunoBay.

Tutin (1940): fairly frequent.

None reported.

5. Gloeocapsa punctata Naegeli 1973: Common None reported.1981: Rare1982: Rare

Chlorophyceae1. Planctonema lauterbornii

Schmidle

2. Elakatothrix lacustris Kors.

3. Gloeotilopsis planctonicaIyengar & Philip.

4. Schroederia setigera(Schroed.) Lemm.

5. Pediastrum duplex Meyen

1973: Dominant, Sept.-Nov.1981: Subdominant, Jan.-Sept.

Dominant, Oct.-Dec.1982: Subdominant, Jan. Otherwise

common-rare.

1973: Common.1981: Common1982: Common

1973: Dominant or co-dominant.1981: Co-dominant, rarely dominant1982: Dominant or co-dominant

1973: Common1981: Rare1982: Common

1973: Common1981: Rare1982: Rare

None reported.

None reported.

Tutin (1940): Ulothrix subtilissima Raben-horst. CommonLazzaro (1981): U. subtilissima L.PequefoNone.

Thomasson (1956): Co-dominant in PunoBay.

6. Pediastrum Boryanum (Turpin)Meneghini

7. Coelastrum microporumNaegeli

1973: Rare1981: Rare1982: Rare

Tutin (1940): Present.Thomasson (1956): in Puno Bay.Lazzaro (1981): in L. Pequeho.

Tutin (1940): rare.1973: Common1981: Common1982: Common

211

Table 1. (Continued).

Species Abundance Other occurrences

1973: Common to subdominant

1981: Common to subdominant

1982: Common to subdominant

9. Closteriopsis longissimavar. tropica W. and G. S. West

1973: Rare1981: Rare1982: Rare

Tutin (1940): 0. gigas Archer var. BorgeiLemmerman.Thomasson (1956): 0. borgei, 0. crassa,in Puno Bay.Lazzaro (1981): 0. borgei in L. Pequefo.

Tutin (1940): Ankistrodesmus longissima(Lemm.) Wille (Synonym).

10. Monoraphidium capricornutus(Printz) Nygaard

11. Mougeotia sp.

12. Closterium acutum(Lyngb.) Br6b.

13. Staurastrum manfeldtii Delp.

14. Botryococcus Braunii Kuetz.

Cryptophyceae1. Cryptomonas ovata Ehr.

Bacillariophyceae1. Cyclotella striata

(Kuetz.) Grunn.

2. Cyclotella stelligeraCI. & Grun.

3. Cyclotella andina Theriot et al.

Dinophyceae1. Hypnodinium sp.

1973: Common1981: Common1982: Common

1973: Common to co-dominant1981: Rare1982: Common

1973: Common1981: Common1982: Common

1973: Common1981: Common to subdominant1982: Common

1973: 1981 - 82: Very rare

1973: Common1981: Common to subdominant1982: Common

1973: Common, May-June1981: Common1982:

1973: Common, May-June1981: Rare1982: Common

1973: Common to dominant, Mar.-Sept.1981: Common, dominant Sept.-Oct.1982: Common to subdominant all year;

dominant July-Sept.

1973: Common1981: Rare1982: Common

Lazzaro (1981): Monoraphidium sp. in L.Pequefno.

Tutin (1940): Mougeotia sp.Lazzaro (1981): Mougeotia sp. in L.Pequefo.

Tutin (1940): C. acerosum (Shrank)Ehrenb. from wetted mud.Thomasson (1956): 3 species in Puno Bay.Lazzaro (1981): 2 species in L. Pequefio.

Tutin (1940): S. paradoxus Meyer.Thomasson (1956): Staurastrum sp. sub-dominant in Puno Bay.

Tutin (1940): Ueno (1967): Dominant.Thomasson (1956): in Puno Bay.

None reported.

Lazzaro (1981): Cyclotella sp. in L.Pequefno.

Frenquelli (1939)

Tutin (1940): Stephanodiscus astraea(Ehrenb.) Grun., rare plankter.Lazzaro (1981): Coscinodiscus sp. in L.Pequefio.Frenquelli (1939): Stephanodiscus astraeain Puno Bay.

None reported.

8. Oocystis spp.

212

et al. (1975, 1977), Widmer et al. (1975), Carmouzeet al. (1977), Boulang6 & Aquize (1981), Carmouze& Aquize (1981), and Lazzaro (1981).

General features of the phytoplankton

The planktonic flora of Lake Titicaca during1973 and 1981-2 was dominated by greens, blue-greens and diatoms. Cryptomonads were occasion-ally abundant, and dinoflagellates were occasional-ly fairly common. A list of the important speciesduring 1973 is given in Table 1. Table 1 also com-pares the data from 1973 with 1981-2 and withthat of other workers. The latter comparison is im-perfect, since collection methods are not compara-ble between studies, and species identifications bydifferent workers can only be roughly compared.For example, the collections of the Percy SladenTrust Expedition in June and July 1937 (Tutin,1940) were obtained with a rather coarse net (71meshes cm-').

Nevertheless, an impression of the similaritiesand differences over the years can be obtained.Some species, such as Nodularia Harveyana (Thw.)Thuret, and Gloeotilopsis planctonica Iyengar &Philip. (assumed to be the same as Ulothrix sub-tilissima Rabenh. in earlier collections), have beenidentified from most collections from the lake, in-cluding Puno Bay and Lago Pequefio. A longerlist of genera is common to most collections, in-cluding Anabaena, Pediastrum, Coelastrum,Oocystis, Mougeotia, Closterium, Staurastrum,and Cyclotella. The species identifications withinthese genera, when given, vary somewhat from col-lection to collection, probably reflecting both realdifferences and different evaluations of the sametaxa. A medium-sized centric diatom, identified asCoscinodiscus sp. or as Stephanodiscus astraea C1.& Grun. in most collections, is a new species,Cyclotella andina (Theriot et al., 1985).

Some conspicuous differences between collec-tions certainly represent real differences in the floraof the lake in different years. Botryococcus brauniiKitzing was reported to be an overwhelming domi-nant in the main lake by Tutin (1940) in 1937 andUeno (1967) in 1961. It also occurred in Puno Bayin 1954 (Thomasson, 1956). This species was ex-ceedingly rare in 1973 in the main lake and during1981-2 in both the main lake and Puno Bay. It wasnot reported as present in Lago Pequefio by Laz-

zaro (1981). On the other hand, Planctonema lau-terbornii Schmidle was a conspicuous dominantduring the dry season in 1973 and 1981-2, but isunreported in previous collections. Since this spe-cies is a relatively long and distinctive filament, itis unlikely to have been entirely missed if present.Thus, there appears to be an overall floristicsimilarity in Lake Titicaca from year to year andsub-basin to sub-basin, but large variation in rela-tive abundances of taxa. A complete floristic analy-sis of the 1981-2 collections is in preparation.

The pattern of succession of the more abundantspecies during 1973 is shown in Fig. 3. Thebluegreen Anabaena spiroides Klebahn was domi-nant during the most highly stratified season of theyear, and the new Cyclotella sp. during theperiod of the descent of the thermocline andisothermy. Two of the dominant green algae, G.planctonica and R lauterbornii, were most abun-dant late and early in the stratified season respec-tively. The distribution of the other importantgreen, Mougeotia sp., closely resembled that of Cy-clotella andina. Some of the subdominant speciesshowed patterns resembling those of dominants inthe same class (N. Harveyana similar to A.spiroides, the group of small Cyclotella speciessimilar to the larger species). Several of the sub-dominant greens fluctuated very little during thewhole year (Oocystis spp., Closterium acutum(Lyng.) Breb., and Staurastrum manfeldtii Delp.).The moderately common dinoflagellate, Hyp-nodinium sp., was most abundant late in the strati-fied period.

The pattern of seasonal succession in 1973 con-forms in some ways to the tropical version of theclassical pattern observed by Lewis (1978, and thissymposium), but differs in others. The order of ap-pearance of taxa, diatoms dominant during theperiod of deepest mixing, followed by chloro-phytes, blue-greens and finally a dinoflagellate, isgenerally followed in Lake Titicaca. Also, the dis-tribution of various chlorophytes throughout thesuccessional sequence compared to the narrowertemporal range for other higher taxa is consistentwith Lewis' observations. A similar pattern was ob-served by Talling (1966) in Lake Victoria. LakeTiticaca's pattern differs from those of Lakes La-nao and Valencia in having only one major succes-sional sequence, rather than several. In the last twolakes, the frequent partial to substantial resettings

213

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of the successional sequence are due to sharp in-creases in the depth of mixing followed by re-stratification at shallower depths (Lewis, 1973). Theheat budget of Lake Titicaca also shows more varia-tion within years than a typical temperate lake butless than Lake Valencia (Taylor & Aquize, 1984). Theclimate of the Titicaca basin lacks dramatic stormevents (Kirkish & Taylor, 1984), and the volume ofthe hypolimnion is very large compared to shallow-er lakes like Lanao and Valencia. Thus, the mainbasin of Titicaca is less frequently subject to sharpchanges in mixing depth, the minor descents of thethermocline that do occur entrain a smaller frac-tion of the hypolimnion, and effects of the nutrientconcentrations of the euphotic zone are small (Vin-cent et al., 1984; Wurtsbaugh et al., 1985). Only thedeep circulation during the dry season has the ef-

fect of starting a new successional sequence in themain lake.

The shallower sub-basins of Lake Titicaca, PunoBay and Lago Pequeflo, are predominantly poly-mictic, although a small part of Lago Pequefio isdeep enough to be monomictic. Lazzaro (1981)studied the limnology of this system and reportspatterns of seasonal succession from Feb. 1979 toJan. 1980 at one monomictic and one polymicticstation. Despite many resemblances between LagoPequefio and the main lake in terms of speciescomposition, the pattern of seasonal successionwas quite different. Dinoflagellates were relativelymore abundant, especially at the shallower station,and diatoms and blue-greens were relatively unim-portant at either station in any season. The mainsuccessional events involved changes in the abun-dances of various chlorophyte species. Concentra-tions of dissolved nitrogen and phosphorus were al-ways very low in the euphotic zone at themonomictic station, even during the period of en-trainment of the hypolimnion. Periphyton andmacrophytes are very important because the systemis shallow and transparent. They may play a role inkeeping nutrient concentrations low and relativelyconstant, and thus restricting the range of seasonalsuccession. The low importance of N-fixing blue-greens in Lago Pequefio is puzzling since dissolvedN:P ratios are very low, often 1:1 or less by weight.In the main lake, nitrogen fixation can sometimesbe shown to be limited by phosphate and iron(Wurtsbaugh et al., 1985). Thus, Lago Pequefioappears to be in a perennially arrested late succes-sional state of a somewhat unusual type (compareto the perennial dominance of N-fixing blue-greensat Lake George: Ganf, 1974).

Results of statistical analyses

Lake Titicaca appears to be quite seasonal in thesense that primary physical variables, insolationand the index of stratification, exhibit strong nega-tive autocorrelations at 6 months lag, and strongpositive ones at 12 months (Fig. 4). A large fractionof the total variance in the ANOVAs appears in themonths effect, and a small to negligible fraction inthe years effect. The main difference betweenTiticaca and temperate lakes in physical processesis not in its patterns of variation but in its smallertotal variance, as should be expected. For example,

Anobaena spiroides

- Gloeotilopsis planctonica

Planctonema louterborni

- Mougeotia cf. viridis

Cyclotello ondina

Oocystis sp.

H pnodinim Sp.

Closterium sp.--

Nodularia Harveyana

Staurostrum manfeldtii

Cyclotella stelligero + striate

Gloeocopsa punctatai _---~-

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214

the coefficient of variation of monthly means ofradiation is 10% for Titicaca, but 56% for LakeWashington (Table 2).

Seasonality affects dissolved oxygen and silicatemuch less than physical variables. The amount ofvariance explained by monthly effects is only8 - 31% and most of these values are not significantor are only barely so. Peaks in the autocorrelationfunctions for Titicaca are weak for these variables,but a hint of seasonal cycles can be seen in thehypolimnetic data for silicate (Fig. 4). In themonthly averaged data analyzed by ANOVA, onlyhypolimnetic oxygen shows significant (p<0.05)seasonality (Table 2).

Primary production per unit area in Titicaca isnearly aseasonal; the months effect in the ANOVAis small and not significant. The autocorrelationfunction for this parameter also suggests anaseasonal pattern (Fig. 4), although there is a slightsuggestion of an approximately 6-month cycle.There is also a small amount of autocorrelation atone month lag. The years effect in the ANOVA islarger (29%) and highly significant.

The contrast with the temperate lakes is sharp.Loch Leven and Lake Washington have more than50% of their variation in primary production ex-plained by months effects in ANOVA models, andhave distinct 6-month minima and 12-month peaksin autocorrelation functions. The years effect intemperate ANOVAs is proportionately lower, butabsolutely higher, than in Titicaca (in Table 2, com-pare the relative magnitudes of the percentages ofvariance explained by years effects with the coeffi-cients of variation of yearly means).

The pattern of variation in Lake Tahoe differsfrom those in the other two temperate lakes. Themonths effect in the ANOVA is a relatively smallpart of the total, but because the total variance ac-counted for by the model is fairly high, it is quitesignificant. The autocorrelation function shows at-tenuated peaks compared to Loch Leven and LakeWashington, indicating modest seasonality. Theyears effect in the ANOVA is quite strong as a resultof a monotonic trend of increasing primaryproduction attributable to cultural eutrophication.Lake Tahoe's lower latitude and drier, sunnier

Table 2. Results of analysis of variance of series from Titicaca and some comparison temperate and tropical lakes. One asterisk indi-cates a treatment effect significant at the .05 level, two asterisks at the 0.01 level. k/X is the coefficient of variation of treatment means..

Lake Latitude N df Variance k/X Grand mean

Months Years %o year % months Total Years Months

George 0°

1) Chlorophyll a 36 11 3 14 40 9581 0.09 0.15 411.5 mg Chla m 2

Titicaca 16 ° S1) Radiation 41 11 3 13** 76** 1101 0.05 0.10 251.8 watts m 22) Temperature difference 62 11 5 3 92** 0.131 0.11 0.67 1.55 °C3) Epilimnetic silicate 54 11 4 39** 8 45.8 0.43 0.20 9.69 g-at 1'4) Hypolimnetic silicate 54 11 4 31** 19 78.9 0.27 0.21 18.14 pg-at 1- '5) Epilimnetic oxygen 60 11 5 39** 13 0.300 0.06 0.03 6.38 mg 1-'6) Hypolimnetic oxygen 60 11 5 26** 31* 0.97 0.11 0.12 4.62 mg 1- '7) Primary production 49 11 5 29** 26 0.182 0.20 0.19 1.13 g C m 2 d-'8) Diatom biomass 25 11 2 17* 49* 0.101 0.41 0.82 0.256 ml m 3

Tahoe 39 °N1) Primary production 116 11 9 49** 22** 0.0046 0.24 0.16 0.196 g C m-2 d- 1

Washington 48 N1) Radiation 102 11 8 4 73** 7057 0.11 0.56 128 watts m-2

2) Chlorophyll a 102 11 8 23** 47** 109.5 0.41 0.59 12.2 pig 1'3) Primary production 102 11 8 18** 63** 2.77 0.34 0.64 2.07 g C m-2 d- 1

Leven 56 °N1) Primary production 43 11 3 9* 66** 13.48 0.28 0.76 4.82 g 02 m-

2

L. TiticocoAT

L. TiticocaHypolimnetic Silicate

1.0

0.5

0

-0.5

-1.0

1.0

0.5

0

-0.5

I I ' I I I I I a -1.0

6 12MONTHS LAG

Loch LevenPrimary Production

L. TahoePrimary Production

L. GeorgeChlorophyll o

: - - - - - - - - - - - - - -

I . . I Il

66I I I l I

I12

Fig. 4. Autocorrelation functions for data series from Titicaca and some comparison tropical and temperate lakes. The vertical axisgives the value of the autocorrelation (r) as a function of months of lag on the horizontal axis. The near-horizontal dashed lines delimitthe envelope in which 95% of the autocorrelations from a random series of the length of each data series should fall.

1.0

0.5

r 0

-0.5

-I

215

-I . -

. A

I.0

0.5

r 0

-0.5

-I n

I .U

0.5

r 0

-0.5

-I I .J

L. TiticocoPrimary Production

--------------------------

r ______-----------------

I .

-

-

. I-

r , ,

216

winters compared to the other temperate lakes inour sample contributes to its lesser seasonality. (SeeGoldman, 1981 for a detailed presentation of the Ta-hoe series.)

Diatom biomass in Titicaca shows significantseasonal and between-years effects (Table 2). As inthe spring diatom maximum of temperate lakes,greatest diatom abundance is found during theperiod of deep mixing, entrainment of nutrient-enriched hypolimnetic waters, and sufficient sur-face insolation (Fig. 2). Thus, the diatoms clearlyreflect the seasonal monomixis of Titicaca. Thebetween-years effect is also pronounced. Mean andpeak diatom biomass differ by more than threefoldbetween the low biomass year of 1981 and the highbiomass years of 1973 and 1982. However, between-years variation of diatom biomass in Lake Titicacais within the range of between-years differencesreported in temperate Windermere (Lund, 1964).

The 4-year chlorophyll a series from Lake Georgeillustrates the well-known constancy of this system(Ganf & Viner, 1973). The seasonal effect in theANOVA is a moderately large proportion of the to-tal, but is not significant due to the very small totalvariance accounted for by either years or monthseffects. The coefficient of variation for primaryproduction in Lake Titicaca is 38%, while that forchlorophyll a in Lake George is only 24%. The au-tocorrelation function for Lake George indicatesonly a very weak 6-month cycle resembling the oneseen in primary production for Titicaca.

Discussion

Lake Titicaca is probably reasonably representa-tive of tropical lakes large enough not to be domi-nated by the seasonality of their inflows and deepenough to be seasonally stratified. If so, somegeneral conclusions can be drawn from our data se-ries with the caveat that similar series from a widervariety of tropical lakes must be accumulated be-fore any secure generalization is possible. Titicacahas one obvious special feature, its altitude andconsequent low mean temperature.

Seasonality

The statistical analysis suggests that seasonalvariations in insolation and stratification in the

tropics exert modest influence on some ecologicalprocesses, at least in the sense of causing them tovary with a regular seasonal pattern. The absolutemagnitudes of variations in most physical variablesare less in deep, stratified tropical lakes like LakeTiticaca than in morphometrically similar temper-ate lakes, although much of this small variation ishighly seasonal in pattern of fluctuation. In thecases of silicate and oxygen concentrations, andprimary production, intra-lacustrine processes ap-pear to mute the expression of seasonality. Within-year variation in these variables is also relativelysmall, and little of this variation is entrained in aregular seasonal cycle.

The low amplitude of the variation of insolationat Lake Titicaca may be the main cause of low sea-sonal variation in primary production. In both themain lake and in Puno Bay correlations between in-solation and primary production are low (r<0.10for Titicaca), in contrast to temperate Loch Levenwhere the correlation coefficient ranges from 0.51to 0.88, depending on the year (authors' unpub-lished analysis). Even in the lowest light periods atLake Titicaca, light availability is very high relativeto the temperate winter, so even though the patternof insolation is quite seasonal, primary productionis not. Stratification also has a very seasonal pat-tern, if not a high total variance, but, again, hasvariable influence on the seasonality ofphytoplankton, i.e. diatom biomass is seasonal butprimary productivity is not.

Presumably, these statistical patterns are the re-sult of effects mediated mainly by nutrient concen-trations. Periods of N-fixation occur when stratifi-cation is strongest, and often contribute to highprimary production (e.g. the maxima in December1973 when heterocystous blue-green algae were veryabundant, and in the early months of 1982 whensubstantial rates of N-fixation were measured).Otherwise, peaks of primary production can occurduring the period of hypolimnetic entrainment asin the August peak of 1973, and the broad May-September peak of 1981, a year in which we meas-ured very low N-fixation rates in the main lake.Minima of production often occur during stratifiedperiods, as during Sept.-Oct. 1973, Jan.-Feb. andNov.-Dec. 1981 and Sept.-Dec. 1982. Thus minimafrequently occur in the same months that exhibithigh production in other years when N-fixation isactive.

217

The net result seems to be that the events ofstratification, although they are related to patternsof primary production, produce somewhat differ-ent patterns of nutrient supply rates each year, andthe deterministic seasonal pattern of stratificationis weaker than other intra-lacustrine effects.

The response of the Lake Titicaca ecosystem toseasonal forcing is statistically characterized by au-tocorrelation functions for oxygen and silicate con-centrations, and primary production, that are posi-tive and fairly large at lags of one and two months,but lack the strong, significant 6- and 12-monthminima and maxima of temperate series. Also, inthe ANOVA analyses, the proportion of the vari-ance in primary production attributable (regardlessof significance) to months plus years effects issomewhat smaller than for temperate lakes (L.Titicaca, 55%; L. Tahoe, 71%; L. Washinton, 81%;L. Leven, 75%).

Thus, in Titicaca a large share (457o) of the totalvariance in primary production occurs at timescales of greater than 1 month up to slightly longerthan 1 year, i.e. short enough to contribute little tointerannual variation. These events, for examplehigh or low production persisting over a 1 to 4month period, contribute to patterns that appearroughly seasonal in any given 12-month sequence,but that are not repeated from year to year. If thispattern is typical of tropical lakes some cautionmust be exercised in defining and interpretingseasonality in them, especially from the short, mostoften one-year, data series usually available. Anysingle year's pattern of variation is likely to be relat-ed to seasonal patterns in physical variables, eventhough the patterns generated may be rather differ-ent from one year to another. By the definitionused here, such patterns are not seasonal. Melack(1979) included Titicaca in his type A lakes withseasonal fluctuations, but noted that with the ex-ception of Lake Chad, which is clearly seasonal inour sense (Lemoalle, 1973), records were too shortto test for repeatability of patterns. We suggest thatlakes of the Titicaca type are likely to be commonin the tropics, and that some special term be usedto distinguish them from lakes that are seasonal inthe sense of Chad's regular response to the wet-dryseason cycle or the regular annual patterns of tem-perate lakes. Perhaps 'quasi-seasonal' is appropri-ate, by analogy with 'quasi-cyclical' in the terminol-ogy of time series analysis.

Variance (or power) spectral analysis of lacus-trine time series would resolve these distinctions inseasonal patterns. Spectral analysis estimates theproportion of variance that occurs on a range oftime (or space) scales (Platt & Denman, 1975), butlong series of close and regularly spaced samplesare required. Such series are rare in limnologicalstudies, and thus we were unable to apply this tech-nique in the present analysis. The spectra of strictlyseasonal temperate lakes would be expected to con-trast significantly with the spectra of quasi-seasonal tropical lakes. A high, narrow variancepeak at 12 months would result from a temperateseries, while the variance spectra of a tropical-lakeseries would be broad and low, perhaps with peaksat 6 and 12 months.

Interannual variations

A fair proportion of the total variation in the pri-mary production record can be attributed tobetween-year variations, more than is the case inthe temperate zone. The hypothesis of Richerson etal. (1977) that Titicaca and other stratified tropicallakes would show more between-year variation butless seasonality thus appears to be supported. How-ever, in light of the data analyzed here, it must bequalified and modified. Although proportionatelymore variation in primary production is explainedby a years effect in Lake Titicaca, the coefficient ofvariation of annual means (k/X, Table 2) for thetemperate primary production series we have usedfor comparison are actually slightly higher than forTiticaca - although in Lakes Tahoe and Washing-ton, at least, much of this year-to-year variation isattributable to cultural effects. Still, interannualvariation may be much the same in tropical andtemperate lakes. There is also no evidence that thestratification regime at Lake Titicaca is as differentfrom year to year as Kittel & Richerson (1978) esti-mated it would be.

Conclusion

The moderate seasonality of tropical lakes thusappears from our analyses to be largely a result ofthe low magnitude of insolation variation. Themodest effect of the seasonal stratification regimeon several limnological processes is surprising, giv-

218

en the classical view of the role of the thermoclinein regulating primary production by controlling nu-trient chemistry. It is, however, consistent with theconclusion of Brylinsky & Mann (1973) that insola-tion has a greater effect than nutrient concentra-tion variables in explaining latitudinal variations inprimary production. Our present working hypothe-sis is that more subtle differences in the strength ofstratification, and in timing and extent of mixing,combined with the lack of strong seasonality in in-solation, encourage somewhat more unpredictableseason-to-season and perhaps year-to-year varia-tion than occurs in otherwise similar temperatelakes.

The interannual variation, whether it is greateror only comparable to that in temperate lakes, doesnot seem in Lake Titicaca to be a direct result offorcing by large interannual variations in physicalprocesses. These are quite regularly seasonal anddiffer little from year to year. Rather, interannualvariations may be the result of interaction betweenbiological and nutrient chemical processes that arenot entrained by the seasonality of physicalprocesses. Even though the physical forcing in thetropics is seasonal in pattern, the variance in thesepatterns is small compared to the temperate ones.One can imagine that endogenous, long period,natural oscillations in biological processes are morefreely expressed in tropical environments. Similarly,some endogenous ecosystemic processes may havequite slow return times to equilibrium. The relative-ly small interannual variations in environmentalvariables that do occur may excite biologicalresponses that persist for longer periods when sea-sonal effects are weak. Powell & Richerson (1985)have observed long-period intrinsic oscillations(> 1 yr) and very slow approaches to equilibria (ca.100 days) in theoretical models with coupledphytoplankton and nutrient dynamics.

Between-year variations of comparable magni-tude occur in our comparison temperate series ofprimary production and phytoplankton biomass,suggesting that such endogenous variation mayalso be important at other latitudes. If so, tropicallakes offer excellent systems for the study ofstratification-nutrient ion-phytoplankton interac-tions because the confounding correlation with theseasonal patterns of insolation and stratificationpresent in the temperate zone is much reduced. Inany case, the problems of describing patterns of

temporal variation in lakes, and determining thecause of these patterns, are worthy of considerableattention on their own merits. Much interestingwork remains on the problem of seasonality; evenin temperate lakes detailed time series of any lengthare few.

Acknowledgments

This work was supported by National ScienceFoundation grant DEB 7921933, by the Universityof California Agricultural Experiment Station, andby the Instituto del Mar del Peru. Carl Widmer andTim Kittel were responsible for the field programand much of the data analysis in 1973. PerttiEloranta helped immensely with algal identifica-tions, and Heath Carney with enumerations.Alejandro Ardiles, Hugo Treviiio, and EufracioBustamante collected the data in 1975 and 1976.Eufracio Bustamante was Chief of the PunoLaboratory of IMARPE during the 1981-2 proj-ect, and the work would not have been possible butfor his and his staffs substantial help and sincerecooperation. We also thank Jose Vera, Chief of theInland Waters Branch of IMARPE, and LuisGonzales-Mugaburu, then Executive Director ofIMARPE, and their staffs, for may kindnesses onbehalf of our project. Charles Brush helped withthe analysis of the data. Mike Kirkish and MarcusTaylor were instrumental in collecting the physicaldata used here and Dolores Dumont typed part ofthe manuscript.

References

Beadle, L. C., 1974. The inland waters of tropical Africa. Long-man, London, 365 pp.

Bindloss, M. E., 1974. Primary productivity of phytoplanktonin Loch Leven, Kinross. Proc. R. Soc. Edinburgh (B) 74:157-181.

Boulang, B. & E. Aquize Jr., 1981. Morphologie, hydrographieet climatologie du lac Titicaca et de son bassin versant. Rev.Hydrobiol. trop. 14: 269-287.

Brylinsky, M. & K. H. Mann, 1973. An analysis of factorsgoverning productivity in lakes and reservoirs. Limnol.Oceanogr. 18: 1-14.

Burgis, M. J. & A. E Walker, 1972. A preliminary comparisonof the zooplankton in a tropical and a temperate lake (LakeGeorge, Uganda, and Loch Leven, Scotland). Verh. int. Ver.Limnol. 18: 647-655.

219

Carmouze, J. P., C. Arce & J. Quintanilla, 1977. La regulationhydrique des lacs Titicaca et Poopo. Cah. O.R.S.T.O.M., ser.Hydrobiol. 11: 269-283.

Carmouze, J. P. & E. Aquize Jr. 1981. La regulation hydrique dulac Titicaca et I'hydrologie de ses tributaires. Rev. Hydrobiol.trop. 14: 311-328.

Carney, H. J., 1984. Productivity, population growth, and phys-iological responses to nutrient enrichments by phytoplanktonof Lake Titicaca, Peru-Boliva. Ver. int. Ver. Limnol. 22:1253- 1257.

Dozier, B. J. & P. J. Richerson, 1975. An improved membranefilter method for the enumeration of phytoplankton. Ver. int.Ver. Limnol. 19: 1524-1529.

Edmondson, W. T., 1972. The present condition of LakeWashington. Verh. int. Ver. Limnol. 18: 284-291.

Frenguelli, J., 1939. Diatomeas del Lago Titicaca. Notas delMuseo de la Plata 4: 175-196.

Ganf, G. G., 1974. Phytoplankton biomass and distribution ina shallow eutrophic lake (Lake George, Uganda). Oecologia(Berl.) 16: 9-29.

Ganf, G. G. & A. B. Viner, 1973. Ecological stability in a shal-low equatorial lake (Lake George, Uganda). Proc. R. Soc.Lond. B 184: 321-346.

Goldman, C. R., 1981. Lake Tahoe: Two decades of change in anitrogen deficient oligotrophic lake. Verh. int. Ver. Limnol.21: 45-70.

Kirkish, M. & M. J. Taylor, 1984. Micrometeorological measure-ments at Lake Titicaca (Peru-Bolivia). Verh. int. Verh. Lim-nol. 22: 1232-1236.

Kittel, T. & P. J. Richerson, 1978. The heat budget of a largetropical lake, Lake Titicaca (Peru-Bolivia). Verh. int. Ver.Limnol. 20: 1203-1209.

Lazzaro, X., 1981. Biomasses, peuplement phytoplanctoniqueset production primaire du lac Titicaca. Rev. Hydrobiol. trop.14: 349-380.

Lemoalle, J., 1973. L'activit6 photosynth6tique du phytoplanc-ton en relation avec le niveau des eaux du lac Tchad (Afrique).Verh. int. Ver. Limnol. 19: 1398-1403.

Lewis, W. M., Jr., 1973. The thermal regime of Lake Lanao(Philippines) and its theoretical implications for tropicallakes. Limnol. Oceanogr. 18: 200-217.

Lewis, W. M., Jr., 1974. Primary production in the planktoncommunity of a tropical lake. Ecol. Monogr. 44: 377-409.

Lewis, W. M., Jr., 1978. Analysis of succession in a tropicalphytoplankton community and a new measure of successionrate. Am. Nat. 112: 401-414.

Lewis, W. M., Jr., 1983. Temperature, heat, and mixing in lakeValencia, Venezuela. Limnol. Oceanogr. 28: 273-286.

Lewis, W. M. Jr., 1984. A five-year record of temperature, mix-ing, and stability for a tropical lake (Lake Valencia, Venezue-la). Arch. Hydrobiol. 99: 340-346.

Lewis, W. M. Jr., 1986. Phytoplankton succession in LakeValencia, Venezuela. In: M. Munawar & J. E Talling, (eds),Seasonality of freshwater phytoplankton: a global perspec-tive. Developments in Hydrobiology 138, 189-203. Junk.

Lund, J. W. G., 1964. Periodicity and primary production ofphytoplankton. Verh. int. Ver. Limnol. 15: 37-56.

Melack, J. M., 1979. Temporal variability of phytoplankton intropical lakes. Oecologia (Berl.) 44: 1-7.

Melack, J. M. & P. Kilham, 1974. Photosynthetic rates ofphytoplankton in East African alkaline, saline lakes. Limnol.

Oceanogr. 19: 743-755.Mullin, M. M., P. R. Sloan & R. W. Eppley, 1966. Relationship

between carbon content, cell volume and area in phytoplank-ton. Limnol. Oceanogr. 11: 307-311.

Neale, P. J., 1984. Photoinhibition and the diurnal variation ofphytoplankton photosynthesis in tropical, alpine Lake Titica-ca (Peru-Bolivia). Ph.D. Thesis, University of California, Da-vis, 164 pp.

Platt, T. & K. L. Denman, 1975. Spectral analysis in ecology.Ann. Rev. Ecol. Syst. 6: 189-210.

Powell, T. M., M. H. Kirkish, P. J. Neale & P. J. RichersJn,1984. The diurnal cycle of stratification in Lake Titicaca:eddy diffusion. Verh. int. Ver. Limnol. 22: 1237-1243.

Powell, T. M. & P. J. Richerson, 1985. Temporal variation, spa-tial heterogeneity and competition for resources in planktonsystems: a theoretical model. Am. Nat. 125: 431-464.

Reynolds, C. S., 1984. Phytoplankton periodicity: the interac-tions of form, function and environmental variability. Fresh-wat. Biol. 14: 111-142.

Richerson, P. J., C. Widmer & T. Kittel, 1977. The limnology ofLake Titicaca (Peru-Bolivia), a large, high altitude tropicallake. University of California, Davis, Institute of EcologyPublication No. 14, 78 pp.

Richerson, P. J., C. Widmer, T. Kittel & A. Landa C., 1975. Asurvey of the physical and chemical limnology of Lake Titica-ca. Verh. int. Ver. Limnol. 19: 1498-1503.

Sellers, W. D., 1965. Physical climatology. University of ChicagoPress, Chicago, Ill., 212 pp.

Strickland, J. D. H. & T. J. Parsons, 1968. A practical hand-book of seawater analysis. Bull. Fish. Res. Bd. Canada 167,311 pp.

Telling, J. F., 1966. The annual cycle of stratification andphytoplankton growth in Lake Victoria (East Africa). Int.Rev. ges. Hydrobiol. 51: 545-621.

Talling, J. E, 1969. The incidence of vertical mixing and some bi-ological and chemical consequences in tropical African lakes.Verh. int. Ver. Limnol. 17: 998-1012.

Taylor, M. & E. Aquize, 1984. A climatological energy budget ofLake Titicaca (Peru-Bolivia). Verh. int. Ver. Limnol. 22:1246 -1251.

Theriot, E., H. J. Carney & P. J. Rioherson, 1985. Morphology,ecology, and systematics of Cyclotella andina sp. nov. (Bacil-larophyceae) from Lake Titicaca, Peru-Bolivia. Phycologia, inpress.

Thomasson, K., 1956. Reflections on arctic and alpine lakes. Oi-kos 7: 117-143.

Tutin, T. G., 1940. The algae. Report No. XI. In H. C. Gilson(ed.), Reports of the Percy Sladen Trust Expedition. Trans.Linn. Soc. Lond. 1 (Ser. 3): 191-202.

Ueno, M., 1967. Zooplankton of Lake Titicaca on the Bolivianside. Hydrobiologia 29: 547-568.

Vincent, W., W. Wurtsbaugh, C. L. Vincent & P. J. Richerson,1984. Seasonal dynamics of nutrient limitation in a tropicalhigh-altitude lake (Lake Titicaca, Peru-Bolivia): applicationof physiological bioassays. Limnol. Oceanogr. 29: 540-552.

Vincent, W. F., C. L. Vincent, M. T. Downes & P. J. Richerson,1985. Nitrate cycling in Lake Titicaca (Peru-Bolivia): the ef-fects of high altitude and tropicality. Freshwat. Biol. 15:31-42.

Walter, H., 1979. Vegetation of the earth. Springer-Verlag, N.Y.,274 pp.

220

Widmer, C., T. Kittel & P. J. Richerson, 1975. A survey of thebiological limnology of Lake Titicaca. Verh. int. Ver. Limnol.19: 1504-1510.

Williams, N. J. & C. R. Goldman, 1975. Succession rates in lakephytoplankton communities. Verh. int. Ver. Limnol. 19:

808-811.Wurtsbaugh, W. A., W. F. Vincent, R. Alfaro, C., C. L. Vincent

& P. J. Richerson, 1985. Nutrient limitation of algal growthand nitrogen fixation in a tropical alpine lake, Lake Titicaca(Peru-Bolivia). Freshwat. Biol. 15: in press.