Factors affecting the production of zooplankton in lakes - Harkness

Factors affecting the production of zooplankton in lakes - Harkness

359 Factors affecting the production of zooplankton in lakes1 B.J. Shuter and K.K. Ing Abstract: Multiple regression analysis and analysis of covari...

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359

Factors affecting the production of zooplankton in lakes1 B.J. Shuter and K.K. Ing

Abstract: Multiple regression analysis and analysis of covariance were used to assess the degree to which observed variation in rates of production among 108 lake zooplankton populations could be accounted for by variation in physical and biological factors. Seventy-six percent of the observed variation in growing season weight-specific production rates could be accounted for by differences in temperature, length of growing season, and taxonomic group (Rotifera, Chydoroidea, Cyclopoida, Calanoida, ordered from highest rate to lowest). Within taxonomic groups, effects of population biomass density, individual body size, and food availability were not detected. Fifty-eight percent of the observed variation in growing season population biomass density could be accounted for by differences in individual body size, mean chlorophyll concentration, and lake mean depth. Twentyfour percent of the observed variation in growing season length could be accounted for by differences in mean chlorophyll concentration and taxonomic group. Our findings suggest a simple model of the seasonal production cycle for limnetic zooplankton in which weight-specific rates of biomass production are largely set by temperature, and levels of biomass accumulation are largely set by food resource availability and individual body size. We briefly discuss the implications of this model for predicting the effects of climate change on lake productivity. Résumé : L’analyse de régression multiple et l’analyse de covariance ont été utilisées pour évaluer dans quelle mesure la variation observée dans les taux de production de 108 populations de zooplancton de lac pouvait s’expliquer par la variation de facteurs physiques et biologiques. Soixante-seize pour cent de la variation observée dans les taux de production spécifiques du poids au cours de la saison de végétation pouvait s’expliquer par des différences touchant la température, la longueur de la sa ison de végétation et le groupe taxinomique (rotifères, chydoroïdés, cyclopoïdés, calanoïdés, par ordre décroissant du taux de production). Au sein des groupes taxinomiques, on n’a pas décelé d’effets liés à la densité de biomasse de la population, à la taille corporelle individuelle ni à la disponibilité des aliments. Cinquante-huit pour cent de la variation observée dans la densité d e biomasse de la population au cours de la saison de végétation pouvait s’expliquer par des différences touchant la taille corporelle individuelle, la concentration moyenne de chlorophylle et la profondeur moyenne des lacs. Vingt-quatre pour cent de la variation observée dans la longueur de la saison de végétation pouvait s’expliquer par les différences touchant la concentration moyenne de chlorophylle et le groupe taxinomique. Nos constatations révèlent un modèle simple du cycle de production saisonnier pour le zooplancton limnétique, dans lequel les taux de production de biomasse spécifiques du poids sont en grande partie déterminés par la température, alors que les concentrations de biomasse sont en grande partie déterminées par la disponibilité des aliments et la taille corporelle individuelle. Nous discutons brièvement des implications de ce modèle pour la prévision des effets des changements climatiques sur la productivité des lacs. [Traduit par la Rédaction]

Introduction Empirical studies have demonstrated that biomass production in natural animal populations varies systematically with population biomass, body size, and broad taxonomic group (Humphreys 1979, 1981; Banse and Mosher 1980; Dickie et al. 1987). A series of recent studies on aquatic invertebrates

Received June 21, 1995. Accepted August 9, 1996. J12967 B.J. Shuter and K.K. Ing. Harkness Laboratory of Fisheries Research and Aquatic Ecosystem Science Section, Ontario Ministry of Natural Resources, Box 5000, Maple, ON L6A 1S9, Canada. 1

Contribution No. 95-07, Aquatic Ecosystem Science Section, Ontario Ministry of Natural Resources.

Can. J. Fish. Aquat. Sci. 54: 359–377 (1997)

(freshwater limnetic, Plante and Downing 1989; freshwater lotic, Morin and Bourassa 1992; marine benthic, Tumbiolo and Downing 1994; marine copepods, Huntley and Lopez 1992) has shown that much of the observed variation in annual production by natural populations of these organisms can be accounted for by variations in environmental temperature, population biomass density, and body size. Our objective in this paper is to examine the effects of these, and other variables, on the production of natural populations of limnetic zooplankton. Most empirical studies of production have focused on observed variation in annual rates. However, the literature on limnetic zooplankton contains considerable information on seasonal variation in daily production rates within a population, as well as information on variation in annual rates between populations. We wished to examine both types of data within a consistent theoretical framework. We used the recent findings of Huntley and Lopez (1992) to develop such a © 1997 NRC Canada

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Can. J. Fish. Aquat. Sci. Vol. 54, 1997

framework. These authors examined variation in daily weightspecific production rates of marine copepods, in both laboratory and field situations, and found that most of the observed variation was linked to variations in water temperature, according to a simple Van’t Hoff relationship. Let us assume that a similar relationship holds for freshwater zooplankton: (1)

[P/B]daily = a⋅eb⋅Tdaily

where [P/B]daily is the daily weight-specific rate of production and Tdaily is the daily water temperature. Given this, then annual production (Pannual) can be written as (2)

Pannual < [P/B]daily⋅Bgs⋅gs

where [P/B]daily is the average daily weight-specific rate of production over the growing season, Bgs is the average population biomass over the growing season, and gs is the length of the growing season. If the temperature covers less than a 15°C range over the growing season and b is about 0.045 (range of Huntley and Lopez (1992) estimates for b: 0.04–0.05), then it is easy to show numerically that the following equation holds: (3)

[P/B]daily < a⋅eb⋅Tgs

where Tgs is the average water temperature over the growing season. Substituting this into equation 2 yields (4)

Pannual < a⋅eb⋅Tgs⋅Bgs⋅gs

and we then rearrange terms to arrive at (5)

Pannual / Bgs < a⋅eb⋅Tgs⋅gs

The relationship between daily, weight-specific production rates and temperature can be recovered from information on annual production and growing season averages for both biomass and water temperature (eq. 5). Annual production is itself the product of three quite distinct variables (eq. 2): the average daily weight-specific production rate, the average biomass over the growing season, and the length of the growing season. We will analyze observed variation in each of these quantities for a wide variety of natural zooplankton populations. Our data set is derived from studies on 38 lakes that span the globe (Tables 1 and 2), from the High Arctic (74°N) through tropical Africa to New Zealand (44°S).

Methods Data acquisition and standardization As is common in comparative studies, many different workers were involved in generating the data for our analyses. In general, we have assumed that those workers had the experience and judgment necessary to collect useable data from their specific systems and to estimate population production from that data. Studies were checked in several ways to help buttress this assumption. (i) Studies were included only if they were published in the primary scientific literature and had, as a major objective, estimation of population production. (ii) Typically, these studies met the mesh size guidelines for sam-

pling gear set out by De Bernardi (1984): 43% used mesh sizes #50 mm, while 49% used mesh sizes in the range >50–126 mm; larger mesh sizes were used for the larger species (i.e., daphnids and copepods); De Bernardi (1984) recommended 126 mm for larger zooplankton and 50 mm for the smaller species. (iii) Studies were included only if the method used to calculate production met the guidelines set by Rigler and Downing (1984): (a) production estimates derived by assuming equality of the turnover rates for population numbers and population biomass were accepted for organisms with simple life cycles (i.e., rotifers) without additional confirmation; for cladocerans, they were accepted when they could be checked against other data provided in the original paper; for copepods and cyclopoids, they were rejected; (b) production estimates based on reference values for the P/B ratio were rejected; (c) production estimates based on values for the durations of different life stages were used only if durations were estimated directly in the field, or were estimated from laboratory data, using observed field temperatures. (iv) Studies were included only if production values from all life stages, including egg production by adults, were part of the population production estimates. We began with the list of studies used by Plante and Downing (1989) and then extended it by systematically searching the more recent (1988–1994) literature for papers reporting production rates of limnetic zooplankton. The following data were extracted from these sources (Table 1): (i) daily estimates for biomass, production rate, and water temperature for at least one growing season (daily data set); (ii) annual estimates of total production, average biomass, and average water temperature (annual data set); (iii) within at least one annual cycle, estimates of growing season length, average biomass over the growing season, and average water temperature over the growing season (growing season data set); and (iv) measures of zooplankton food resource availability (dissolved phosphorus and chlorophyll concentrations), lake mean depth, pH, and other environmental variables. All production and abundance (numbers and biomass) estimates were standardized to a common spatial unit: 1 m2 of lake surface area. All production and biomass estimates were standardized to a common mass unit: grams dry weight. When unit conversion was required, appropriate conversion factors were taken from the original study whenever possible. If no conversion information was provided in the original study, the following standard values were used: dry weight = carbon/0.44 (Burgis 1971; Green 1976; Gophen 1978; Herzig et al. 1980; Andrew 1983; Mason and Abdul-Hussein 1991; Huntley and Lopez 1992) and species-specific and congener-specific conversions from calories to dry weight, as listed in Cummins and Wuycheck (1971). In studies of multiple years or stations, atypical years or stations, as indicated by the author(s), were excluded from our data base. Otherwise, averages for all years or stations were used. With the exception of two unusual populations from one lake (Lake Tjeukemeer), no attempts were made to recalculate production estimates from available data. In the two cyclopoid populations from Lake Tjeukemeer, weight-specific production values reported for nauplii far exceeded (by over 400%) values exhibited by the older life stages in these populations and by the other cyclopoid populations in our data base. Because of these anomalously high values, we recalculated population production for each population, assuming that the weight-specific production rate of naupliar stages was identical with that of the older life stages in the population. These adjusted values were used throughout our analyses.

Defining annual estimates and growing season estimates There are inconsistencies in the literature regarding definitions for annual estimates of production and biomass and growing season estimates of production and biomass (Edmondson 1974). Some authors equate growing season estimates with annual estimates, and some do © 1997 NRC Canada

Shuter and Ing

361

Table 1. Summary table of zooplankton populations by lake and species group. Continenta

Lake

1 1 1

Char Lake Clear Lake Lake Ontario

1 1 2

Mirror Lake Pyramid Lake Broa Reservoir

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Ardleigh Reservoir Eglwys Nyndd Reservoir Farmoor I Reservoir Lake Akulkino Lake Constance Lake Esrom Lake Krivoe Lake Krugloe Lake Kvernavatnet Lake Myvatn Lake Naroch Lake Ormajarvi Lake Port-Bielh Lake Taltowisko Lake Zelenetzkoye Lough Neagh Mikolajskie Lake Ovre Heimdalsvatn Queen Mary Reservoir Red Lake

3

Tjeukemeer

4 5 5

Lake Kasumigaura Lake Awasa Lake Chad

5

Speciesb

Data type

Reference(s)

5, 7 2, 5 3, 3, 3, 3, 6, 6 2, 4, 7 5 5

A, G D A, G

Rigler et al. 1974; MacCallum 1971 Schindler 1972 Borgmann et al. 1984

A, G A, G A, G

3, 3 6

A, D, G A, G

Makarewicz and Likens 1979 Herzig et al. 1980 Matsumura-Tundisi et al. 1989; Rocha and Matsumura-Tundisi 1984 Mason and Abdul-Hussein 1991 George 1976

3 1, 7, 7 3, 3 5, 7 2, 6, 7, 7, 4 2, 2, 4, 6, 7 3 3, 6, 7, 7, 7 2, 6 7, 7, 7, 7 3, 5 2, 5, 6, 7 1, 7, 7 7, 7, 7, 7, 7 2, 5, 6, 7 2, 3, 6 3 2, 2, 3, 3, 3, 5, 6, 6, 7 3, 3, 6, 6

A, D, A, G A, G A, D, A, G A, G A, D, A, G A, D, A, D A, D, A, G A, G A, D, A, G A, G A, D, A, G

Jones et al. 1979 Winberg et al. 1973 Geller 1989; Sommer 1985; Trippel 1991 Bosselman 1975, 1979a, 1979b Alimov et al. 1972 Alimov et al. 1972 Borsheim et al. 1988 Adalsteinsson 1979 Babitskiy 1970, 1988 Cajander 1983 Rey and Capblancq 1975 Hillbricht-Ilkowska and Weglenska 1970 Winberg et al. 1973 Andrew and Fitzsimons 1992 Hillbricht-Ilkowska and Weglenska 1970 Larsson 1978 Andrew 1983 Andronikova et al. 1970

A, D, G A, G A, D, G

Lake George

2, 3, 3, 3 2, 6, 6 2, 2, 3, 3, 3, 3, 5, 6 6

5 5 5

Lake Kinneret Lake Naivasha Lake Nakuru

2, 4, 6 5, 6 5, 7, 7

A, D, G A, G A, G

6 6 6 6

Lake Lake Lake Lake

5 3, 3, 5 5 3, 5

A, A, A, A,

Hayes Okaro Ototoa Samsonvale

G

G

G G G

G

G

A, D, G

A, G

D, D, D, D,

G G G G

Vijverberg and Richter 1982a, 1982b; Vijverberg and Frank 1976 Hanazato and Yasuno 1985 Mengestou and Fernado 1991a, 1991b Lévêque and Saint-Jean 1983 Burgis and Walker 1972; Burgis 1971, 1974 Gophen 1978, 1988; Gophen et al. 1990 Mavuti 1990, 1994 Vareschi 1982; Vareschi and Jacobs 1984, 1985; Vareschi and Vareschi 1984 Burns 1979 Forsyth and James 1991 Green 1976 King and Greenwood 1992a, 1992b

Note: Types of data obtained from each population are also listed: A, annual production; D, daily production; G, growing season. a 1, North America; 2, South America; 3, Europe; 4, Asia; 5, Africa; 6, Australia. b 1, Crustacea; 2, Cladocera; 3, Chydoroidea; 4, Copepoda; 5, Calanoida; 6, Cyclopoida; 7, Rotifera.

not. Such inconsistencies can produce large and spurious differences in average biomass estimates, particularly for temperate zooplankton populations. Such populations typically have a short growing season, when biomass and production are at detectable levels, and a long period of dormancy, when biomass and production are often undetectable. Under these circumstances, annual production (P) and growing season production are essentially identical, but annual average

biomass (Bann) is effectively equal to the growing season average biomass (Bgs) multiplied by the fraction of the year taken up by the growing season. When the growing season is short, Bann will be low and will not reflect the average amount of biomass responsible for generating the production observed over the year. Plante and Downing (1989) based their analyses on annual averages for both population biomass and water temperature, and, for © 1997 NRC Canada

362 comparative purposes, we will use this approach on some of our data sets. However, we will focus our analyses around eq. 5 because it deals explicitly with the growing season effect. Only a minority of authors actually estimated growing season length (gs) and each used his own, often undefined, protocol. We wished to develop consistent estimates of growing season length for as many populations as possible. Because considerable variation existed among populations in the amount of data available for estimating gs, we developed three similar definitions (each with different data demands) to maximize the number of populations for which we could obtain roughly consistent estimates of gs. In order of preference, the three definitions are as follows: (i) that part of a year for which monthly biomass values exceeded 20% of the peak monthly biomass value for the year (54 of our 105 gs estimates were obtained using this protocol), (ii) that part of a year for which monthly production values exceeded 20% of the peak monthly production value for the year (5 of 105 estimates), and (iii) that part of the year identified by source authors as the “vegetative” or “growing” season (46 of 105 estimates). With the growing season defined, values for gs, Bgs, and Bann were readily determined. Because most production occurs during the growing season, we assumed a negligible difference between P and growing season production and equated the two.

Other variables Estimates for annual (Tann) and growing season (Tgs) average water temperatures were derived from temperatures recorded in the upper isothermal layer of each lake. Arctic and tropical lakes were essentially isothermal from top to bottom throughout the year; hence, Tann and Tgs equated to whole-lake average temperatures. For temperatezone dimictic lakes, Tann and Tgs were derived from mixed-layer temperatures during the ice-free period and whole-lake temperatures during the ice-cover period (i.e., all lakes were essentially isothermal from top to bottom during the ice-cover period). In dimictic lakes, some zooplankton populations almost certainly spend time in both epilimnion and hypolimnion. Thus, our measure of temperature must be regarded as merely an index of the average temperature experienced by these populations. Although this introduces some unavoidable noise into our data set, we feel that its overall influence on our results will be minimal because (i) the only strict cold-water form in our data set (Limnocalanus macrurus) is from an essentially isothermal arctic lake, and therefore, our protocols will provide an accurate measure of its temperature exposure; (ii) in our data set, all species from dimictic lakes spend all or part of their time in the epilimnion; in one detailed study (Geller 1989), the time budgets of migratory and strictly epilimnetic species were examined and the difference in average temperature exposure between the two species was small (3–5°C) relative to the overall temperature range in the data set (about 28°C); and (iii) observations at the extremes of temperature exposure (arctic and tropical lakes) will be most influential in defining the character of whatever temperature effect exists in the data set; all of these estimates are from essentially isothermal lakes and therefore are not affected by the vertical migration problem. We used the following protocols for estimating water temperatures. When intraannual time series of lake water temperature estimates were available, mean annual water temperature and mean water temperature during the growing season were calculated from these estimates. Mean annual air temperature (air) for the lake was obtained from the source reference, or was estimated from a world climatic summary as needed (Wernstedt 1972). When direct estimates of lake water temperatures were not available, estimates for Tann were obtained from the mean annual air temperature and mean lake depth, using a multiple regression equation derived from those lakes with direct estimates of Tann, air, and mean lake depth (R2 = 0.97, N = 37, p < 0.001). This equation was used to derive Tann estimates for 12 of 108 populations (2 of 38 lakes). When direct estimates of growing season water temperatures were not available, estimates for Tgs were obtained from Tann and gs estimates, using a

Can. J. Fish. Aquat. Sci. Vol. 54, 1997 multiple regression equation derived from those populations with direct estimates of Tgs, Tann, and gs (R2 = 0.90, N = 77, p < 0.001). This equation was used to derive Tgs estimates for 23 of 87 populations (from 9 of 38 lakes). In addition to temperature, we examined the relative importance of the following variables in predicting annual production: (i) biotic variables: taxonomic group, average annual population biomass (Bann), average growing season population biomass (Bgs), adult body mass (Mad), and average individual mass in the population (Mav); (ii) climatic and morphometric variables: maximum solar radiation (mxsol) and lake mean depth (Z); and (iii) indices of zooplankton food resource availability: mean annual dissolved phosphorus concentration (phos) and mean chlorophyll concentration (chl) over the vegetative season (i.e., usually equivalent to the ice-free period). We used two criteria to select variables: first, previous recognition in the literature (e.g., Brylinsky 1980; Straskraba 1980; Plante and Downing 1989) that the variable was associated with invertebrate productivity, and second, availability of estimates for a substantial (>20) number of populations. Protocols for estimating variables are outlined below. We used two quite different measures of body size: Mad reflects the ultimate size attainable by individuals in a population, while Mav reflects the age and size structure of the population over the growing season. Estimates of adult individual size (Mad) were standardized to mean female adult mass (milligrams dry weight), because we found that estimates of mean female mass were more readily available in the original articles reporting production. When such direct estimates were not available, we derived indirect estimates using one of the following sources (in order of preference): (i) different source article describing the same population, (ii) species-specific size data provided in summary publications (Edmondson 1959; Clegg 1963; Balcer et al. 1984; McCauley 1984; Culver et al. 1985; Pennak 1989; Thorp and Covich 1991), (iii) species-specific scale diagrams in summary publications, and (iv) average adult mass for the appropriate genus, as reported in the source publication providing production and biomass estimates or as calculated from our accumulated data sets. Where necessary, length estimates were converted to mass estimates using the appropriate species-specific length–weight conversion equation as found in the original source reference or in summary publications as described above. Following Morin and Bourassa (1992), we estimated the average mass of an individual in the population (Mav) by dividing the mean annual biomass by the mean annual numerical abundance. We estimated mxsol from latitude using fig. 3.2 in Straskraba (1980). Values for our measures of food resource availability (phos, chl) were obtained from the reference providing zooplankton production data, or other published papers dealing with the same lake. For lakes where both measures are available (N = 27), the relationship between chl and phos is quantitatively similar to the chlorophyll–phosphorus relationships reported for other lake data sets by Pace (1984), Mazumder (1994), and Chow-Fraser et al. (1994). Units, symbols, and summary statistics for all variables are provided in Table 2.

Statistical analysis A tacit assumption built in to equations 2–5 is that dividing population production by population biomass effectively removes the influence of biomass on production. Downing (1984) has argued that this assumption is untenable because of the inevitable reductions in population production at high levels of population biomass as a result of density-dependent restrictions on population growth. He suggested (Downing 1984; Plante and Downing 1989) that differences in total population production rates should be examined directly using regression techniques and the effects of population biomass should be removed empirically by including population biomass as an independent variable in the analysis. © 1997 NRC Canada

Shuter and Ing

363

Table 2. Summary statistics for environmental characteristics of all lakes in the study (maximum N = 38) and characteristics of zooplankton populations included in the annual data set (N = 108) and growing season data set (N = 87). Environmental characteristics of lakes –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– N Standard Symbol (lakes) Minimum Mean Maximum deviation Maximum solar radiation (J cm–2 d–1) Latitude (°N or °S) Maximum depth (m) Mean depth (m) Annual phosphorus (P-PO4, µg L–1) Seasonal chlorophyll (µg L–1) Retention time (yr) Thermocline depth (m) pH

mxsol — — Z

38 38 34 38

phos chl — — —

27 35 18 29 30

2450 0.1 3.5 0.92

2722.4 45.07 32.03 12.73

3000 74.4 250.0 100.00

131.9 20.46 55.61 19.97

102.06 41.11 1.98 6.99 7.91

500.0 795.0 10 75.3 10.5

137.78 137.24 3.21 14.28 1.01

1.3 0.056 0.07 0 5.8

Characteristics of zooplankton populations –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– N Standard Symbol (populations) Minimum Mean Maximum deviation Mean annual biomass (g dw m–2) Annual production (g dw m–2 yr–1) Annual P/B Mean annual water temperature (°C) Mean growing season biomass (g dw m–2) Growing season P/B Mean growing season water temperature (°C) Growing season duration (days) Mean female adult mass (mg dw) Mean individual mass (mg dw)

– B ann

108

1.25 × 10–4

0.311

3.27

0.584

P – P/B ann

108 108

3.86 × 10–3 11.236 2.63 41.914

170.13 220.95

27.526 37.425

Tann

108

0.9

26.2

6.94

– B gs – P/B gs

87 87

7.5 × 10–4 0.505 1.84 20.216

5.36 144.08

0.889 22.687

Tgs gs

87 87

27.5 365

5.87 90.8

Mad Mav

86 39

0.9 62 2.2 × 10–5 1.04 × 10–5

11.21

14.06 194.7 0.0230 7.19 × 10–3

0.848 0.068

0.0939 0.0141

Note: The symbol column lists the symbol used in the main text to identify variables used in particular analyses.

We feel that such nonlinear effects of population biomass on population production can also be dealt with by including population biomass with the other independent variables in regression analyses of observed variation in weight-specific production rates. This approach yields results that are easy to interpret, plus it has some small claim to greater statistical validity. All regression methods assume that dependent and independent variables are estimated independently of each other (Jackson et al. 1991); however, all methods of estimating production incorporate, in their estimates, the basic data used to estimate biomass. Several commonly used methods (e.g., instantaneous growth method, Rigler and Downing 1984, equation 2.12) are structured as follows: weight-specific production and biomass are estimated independently for some segment of the population (e.g., a particular developmental stage), production for this segment is then calculated by multiplying these two estimates, and total production for the population is estimated as the sum of production estimates for all population segments. Thus, it can be argued that weight-specific

production and biomass come closer to the ideal of independently estimated variables than total production and biomass and hence are more appropriate variables to use in regression analyses. Given this argument and the structure of equation 2, it is apparent that annual production is the product of three potentially independent elements ([P/B]daily, Bgs, and gs). Our analyses will focus on these three elements and the various abiotic and biotic factors that may influence them.

Results Weight-specific production rates Daily data set For 30 populations (25 temperate, 5 tropical) in 18 lakes (16 temperate, 2 tropical), we found detailed information on © 1997 NRC Canada

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Can. J. Fish. Aquat. Sci. Vol. 54, 1997

Fig. 1. (A) Individual regression lines generated by fitting the model log([P/B]daily) = a + b(Tdaily) to the data for each population found to have a statistically significant (p < 0.05) production–temperature relationship. (B) Regression lines generated by fitting eq. 6 (log10(median [P/B]daily) = ataxa + b(median Tdaily)) to the median Tdaily and median [P/B]daily associated with each of the 30 population data sets. The lines are differentiated by taxonomic group.

within-year variation in production, biomass, and water temperature, typically derived from biweekly or monthly sampling programs. Table 3 shows the range of daily water temperatures (Tdaily) and daily weight-specific production rates ([P/B]daily) for the 30 populations in the daily data set. Minimum values for Tdaily ranged from 0.4 to 20.8°C, and maximum values ranged from 12.8 to 29.8°C. Minimum [P/B]daily values ranged from 0 to 0.169, and maximum values ranged from 0.040 to 0.8400. Simple regression analysis was used to test each population data set for a positive link between log10([P/B]daily) and Tdaily. Only data sets with at least six points were included in this

analysis. Of the 28 data sets that met this criterion, all exhibited positive correlations and 75% (21) were significant (p < 0.05, one-sided test). Of the populations that exhibited significant correlations, about 70% (14) had R2 values that exceeded 70% and p-values that were less than 0.001 (median p-value = 0.00005). Over 80% had slope estimates ([P/B]daily on temperature) that were similar (i.e., in the range 0.035– 0.055) to the estimates (0.040, 0.049) obtained by Huntley and Lopez (1992) for marine copepods (Fig. 1A; Table 4). A metaanalysis of these 28 independent data sets was performed using Fisher’s x2 test (Sokal and Rohlf 1981; Hedges and Olkin 1985; a procedure that pools the results from several © 1997 NRC Canada

Shuter and Ing

365 Table 3. Range (max.–min.) and median of monthly water temperatures and daily P/B values for all populations in the daily data set. Tdaily range

Tdaily median

[P/B]daily range

[P/B]daily median

Source

Significant Cladocera 9.1 17.0 18.0 8.9 14.5 10.5 18.6 18.1

27.3 10.0 21.0 13.5 11.5 19.5 15.6 12.1

0.276 0.219 0.210 0.741 0.180 0.226 0.199 0.212

0.355 0.132 0.133 0.223 0.085 0.149 0.092 0.098

Lévêque and Saint-Jean 1983 Jones et al. 1979 Hanazato and Yasuno 1985 Forsyth and James 1991 Andrew 1983 King and Greenwood 1992b Vijverberg and Richter 1982a Vijverberg and Richter 1982a

Nonsignificant Cladocera 17.5 17.5 9.0 1.0 11.0 8.9

12.0 12.0 12.0 17.0 19.0 13.5

0.118 0.149 0.060 0.054 0.060 0.777

0.036 0.045 0.030 0.162 0.134 0.137

Mason and Abdul-Hussein 1991 Mason and Abdul-Hussein 1991 Schindler 1972 Borsheim et al. 1988 Babitskiy 1970 Forsyth and James 1991

Significant Calanoida 9.1 13.5 8.9 11.5

27.3 16.0 13.8 16.2

0.063 0.045 0.081 0.036

0.063 0.021 0.034 0.029

Lévêque and Saint-Jean 1983 Burns 1979 Forsyth and James 1991 Green 1976

Nonsignificant Calanoida 9.0 17.3 7.8 12.0

12.0 11.9 9.5 18.0

0.011 0.064 0.032 0.060

0.010 0.008 0.009 0.095

Schindler 1972 Bosselman 1975 Rey and Capblancq 1975 King and Greenwood 1992a

Significant Cyclopoida 9.1 13.0 11.0 18.1 15.8

27.3 22.0 13.0 13.4 16.1

0.168 0.102 0.166 0.215 0.123

0.178 0.109 0.056 0.068 0.079

Lévêque and Saint-Jean 1983 Gophen 1978 Babitskiy 1988 Vijverberg and Richter 1982b Vijverberg and Richter 1982b

Significant Rotifera 14.0 15.0

10.0 5.5

0.249 0.108

0.059 0.038

Andrew and Fitzsimons 1992 Cajander 1983

Nonsignificant Rotifera 13.5

13.0

0.215

0.087

Bosselman 1979a, 1979b

Note: The populations are grouped by significance (p < 0.05) and taxonomic group where significance denotes populations with a statistically significant [P/B]daily–Tdaily relationship. Only time periods with nonzero [P/B]daily values were used in these analyses.

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Table 4. Results of fitting the model log([P/B]daily) = α + βTdaily to data from individual populations in the Daily Data Set.

Taxonomic group

Individual population analysis No. of ––––––––––––––––––––––––––––––––––––––––––––––––––––––– populations N R2 α β

Rotifera

2

Cladocera

8

Cyclopoida

5

Calanoida

4

22 (12, 32) 12 (7, 33) 12 (6, 28) 12 (12, 16)

0.483 (0.23, 0.74) 0.818 (0.56, 0.99) 0.826 (0.74, 0.92) 0.780 (0.67, 0.94)

−1.748 (−1.77, −1.72) −1.725 (−2.75, −1.40) −1.766 (−2.14, −1.69) −2.458 (−3.26, −2.26)

0.052 (0.047, 0.056) 0.044 (0.037, 0.15) 0.040 (0.038, 0.069) 0.050 (0.042, 0.12)

Note: Results are summarized for those populations that exhibited a statistically significant (p < 0.05) temperature effect. Median values and ranges are provided for sample size per population (N), square of the population specific correlation coeficient (R2), α estimates, and β estimates.

independent tests of an hypothesis to provide a single overall test of that hypothesis) and this indicated that the temperature effect was highly significant (p < 0.0001). Results from the simple regression analyses of log10 ([P/B]daily) on Tdaily show that taxonomic groups can be ordered, from high [P/B]daily values to low, as follows: Rotifera/Cladocera, Cyclopoida, Calanoida (Table 4; Fig. 1A). Although most populations exhibited similar slopes, the two populations from Lake Okaro were extreme exceptions. The temperature coefficients (b) from the two Okaro populations are high compared with others from their respective taxonomic groups. The mean slope for the [P/B]daily versus Tdaily relationship among the individual cladoceran populations, with the removal of the Okaro populations, is 0.0476, and the Okaro population yields a slope of 0.1488. A similar discrepancy is found within the calanoid group. The mean slope of the individual populations minus the Okaro population is 0.0474, and the Okaro population shows a slope of 0.1203. For each population, values for [P/B]daily and Tdaily were derived from observational time series, covering one to three annual cycles. Because the degree of autocorrelation in each time series is relatively high (e.g., r lag 1 < 0.7), the possibility exists that the high and consistent P/B–temperature correlations characteristic of these data sets may reflect concurrent, but unrelated, seasonal variation in the variables rather than a strong, direct association between them. We used the procedure described in Sutcliffe et al. (1976) to remove the influence of autocorrelation from our within-population tests of significance: the number of populations exhibiting significant correlations between log10([P/B]daily and Tdaily declined from 75 to 61% and the median p-value declined from 0.00005 to 0.022. However, when we applied Fisher’s metaanalysis procedure to these reduced p-values, it still yielded a highly significant result (p < 0.001). Best subsets multiple regression was used to determine if zooplankton biomass exerted a significant influence on the [P/B]daily–Tdaily correlations evident in most populations. Of the 28 populations studied, only four (one cladoceran, one calanoid, and two cycloploid) exhibited statistically significant

(p < 0.05) biomass effects. In all four populations, biomass had a negative effect on [P/B]daily. In three of the populations, the biomass effect was less important (regression mean square for temperature effect 4–20 times regression mean square for biomass effect) than the temperature effect. In only one (Lake Okaro, Ceriodaphnia dubia) was biomass more important than temperature in explaining variation in weight-specific production. The within-population analyses described above exploit the annual variation in temperature characteristic of each lake to estimate the effect of temperature on [P/B]daily. There are also large interlake differences in annual temperature range (Table 2), and these differences can be exploited to obtain a second, independent estimate of the effect of temperature on [P/B]daily. This was done as follows. Each of the 30 population data sets was characterized by its median Tdaily value and its median [P/ B]daily value. Analysis of covariance (ANCOVA) was then used to fit the following model to these data (Fig. 1B): (6)

log10(median[P/B]daily) = ataxon + b⋅(median Tdaily).

The value of b did not vary significantly (p < 0.05) across taxonomic groups. Estimates for b (0.04336, SE = 0.00773) and for taxon-specific a (rotifers: 21.631; cladocerans: 21.645; cyclopoids: 21.844; calanoids: 22.294) were all relatively similar to the respective medians of the b and a estimates obtained from the within-population analyses (Table 4). Annual and growing season data sets Influence of temperature, population biomass, and body size: We identified useable, annual production estimates for 108 distinct populations found in 38 lakes: 5 arctic lakes with 16 populations, 26 temperate lakes with 73 populations, and 7 tropical lakes with 19 populations. This is our annual data set. Many of these populations were classified to species, but a significant number were only identified to phylum, subclass, or order (i.e., Rotifera, Copepoda, Cladocera). Summary statistics on selected variables are presented in Table 2. © 1997 NRC Canada

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367 Table 5. Regression results from fitting various combinations of the model – log(P/Bann) = αtaxon + β(Tann) + δ(logB ann) + τ(logMad) where αtaxon is an additive constant specific to each taxonomic group.

Regression statistics

Independent variables included in regression –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Tann, Bann, taxa Tann, Bann Tann, Mad Tann, Bann, taxa refined

N R2adj α0 ± SE αrot ± SE αcal/chy ± SE αcyc ± SE αcal ± SE β ± SE δ ± SE τ ± SE

108 0.270 0.960 ± 0.088 — — — — 0.030 ± 0.005 −0.154 ± 0.035 —

86 0.212 0.954 ± 0.115 — — — — 0.025 ± 0.006 — −0.094 ± 0.031

108 0.522 — 1.195 ± 0.097 1.212 ± 0.079 0.888 ± 0.089 0.710 ± 0.083 0.028 ± 0.004 −0.080 ± 0.033* —

90 0.572 — 1.355 ± 0.057 1.288 ± 0.066 0.963 ± 0.073 0.680 ± 0.083 0.029 ± 0.004 — —

Note: α0 = estimate obtained when data from all taxonomic groups are pooled; αrot, Rotifera; αcla/chy, Cladocera/Chydoroidea; αcyc, Cyclopoida; αcal, Calanoida. *0.05 > p > 0.01.

Of the 108 populations in the annual data set, there were 105 with the additional data necessary for estimating length of growing season. Of these 105, 87 could be classified into taxonomically similar groups with relatively large (>10) sample sizes per group. These 87 populations represent the same 38 lakes as were included in the annual data set; however, the numbers of populations in arctic, temperate, and tropical lakes are reduced to 15, 61, and 11, respectively. Four taxonomic groups are represented: (i) Chydoroidea, 30 data sets; (ii) Calanoida, 14 data sets; (iii) Cyclopoida, 20 data sets; and (iv) Rotifera, 23 data sets. Populations classified at higher taxonomic levels (i.e., copepods, cladocerans) were omitted in order to insure some minimal level of similarity among the organisms included within each group. The number of groups was kept at four to insure a reasonable sample size within each group. For example, we chose to limit our analysis of cladocerans to the superfamily Chydoroidea (or Daphnoidea, Hutchinson 1967) consisting of the five families Chydoridae, Macrothricidae, Bosmidae, Moinidae, and Daphniidae because it provided a good sample size (30) of species that were relatively homogeneous in terms of their morphological characteristics. Sample sizes in other cladoceran groups were small (Haplopoda, 1; Sidoidea, 6; Polyphemoidea, 1) and the species represented typically exhibited very distinctive characteristics (e.g., the very large body size of Leptodora kindtii; the gelatinous sheath of Holopedium spp.). The 87 populations, selected as described above, make up our growing season data set (Table 1). We begin by examining whether the proportion of observed variation in P/Bann, associated with variation in adult body size (Plante and Downing 1989), can also be accounted for by splitting the P/Bann values into subsets based on taxonomy. First, models for P/Bann were generated (Table 5) based on Tann and either Mad or Bann because the R2 for a (Tann, Mad, Bann) model was not significantly greater than the R2 for a (Tann, Mad) model or a (Tann, Bann) model. The fits of these models were inferior to the fits of models that took taxonomic groupings into account.

With taxonomy included in the regression model, the influence of body size disappeared and the influence of population biomass was weakened (Table 5). When the analysis was further refined to include only the relatively homogeneous taxonomic groups identified for the growing season data set, the biomass effect disappeared and the overall fit of the model improved (Table 5). Removing nonsignificant terms, we obtain the following final model (N = 90, R2adj = 0.5731) for our annual data set (Fig. 2): (7)

log10(P/Bann) = ataxon + 0.0293⋅Tann

where ataxon equals 1.33 (SE = 0.051) for Rotifera and Chydoroidea, 0.975 (SE = 0.072) for Cyclopoida, and 0.692 (SE = 0.082) for Calanoida. With these results in mind, we then examined the ability of our growing season model (equation 5) to describe the growing season data set. The following equation was fitted to the data: (8)

log10(P/Bgs) = a + b⋅Tgs + F⋅log10(gs)

where a could be influenced by taxonomy, Bgs, Mad, and Mav. We used ANCOVA and best subsets regression analysis on the growing season data set to test the usefulness of this model in accounting for the observed variation in P/Bgs. We found that P/Bgs varied significantly with taxonomic group, Tgs, and gs (Table 6). As expected, both of these effects were positive. The temperature effect was similar across taxonomic groups (ANCOVA tests for interaction effects between taxonomic group and temperature were not significant: p > 0.05), and at a given temperature, P/Bgs declined with taxonomic group in the following sequence: Rotifera, Chydoroidea, Cyclopoida, Calanoida (Table 6); Bgs, Mad, and Mav did not significantly influence P/Bgs. Identical results were obtained with a similar analysis using log10P as the dependent variable: the regression coefficient for log10Bgs was not significantly different from 1, © 1997 NRC Canada

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Fig. 2. Plot of annual P/B and mean annual water temperature estimates. The lines represent the regression model log(P/Bann) = ataxon + 0.029(Tann) for the refined taxonomy data set (N = 90), where ataxon is an additive constant specific to each taxonomic group: arot, Rotifera = 1.355; achy, Chydoroidea = 1.288; acyc, Cyclopoida = 0.963; acal, Calanoida = 0.680.

Table 6. Comparison of regression results obtained by fitting the model – log(P/B gs) = αtaxon + β(Tgs) + Φ(log(gs)) to our most comprehensive growing season data set and to two refined subsets of the data where αtaxon is an additive constant specific to each taxonomic group.aaa Regression statistics

Complete growing season dataset

Subset 1

Subset 2

N R2adj αrot ± SE αchy ± SE αcyc ± SE αcal ± SE β ± SE Φ ± SE

87 0.700 −0.634 ± 0.267 −0.784 ± 0.262 −1.019 ± 0.281 −1.191 ± 0.295 −0.042 ± 0.004 −0.629 ± 0.124

64 0.764 −0.637 ± 0.266 −0.803 ± 0.267 −0.892 ± 0.291 −1.200 ± 0.303 −0.045 ± 0.004 −0.600 ± 0.124

45 0.768 −0.809 ± 0.440 −0.956 ± 0.404 −1.197 ± 0.451 −1.479 ± 0.486 −0.042 ± 0.006 −0.712 ± 0.209

Note: αrot, Rotifera; αchy, Chydoroidea; αcyc, Cyclopoida; αcal, Calanoida. Subset 1 represents populations in which water temperatures were directly measured; subset 2 represents those production estimates that were derived using methods that did not assume food-saturated development times.

the coefficient for Tgs was similar for all taxonomic groups, and the group effects themselves were similar to those identified in the P/Bgs analysis. Given the overriding importance of temperature in the growing season data set, we examined the possibility that a more accurate model could be developed from that portion of the data set where Tgs was estimated directly from water temperature data provided in the original references. Analysis of this subset of 64 cases does produce a model that fits the data better: the structure of the best model was identical with that fitted to the full growing season data set, but its residual mean square was smaller (0.033 versus 0.040) and its R2 value was

higher (Table 6; Fig. 3). In addition, this increase in accuracy is not accompanied by a reduction in the range of values for the independent variables over which the model can be legitimately applied: the ranges for the independent variables in the reduced data set were identical with the ranges found in the full growing season data set. The structure of eq. 5 implies that F (eq. 8) should have a value close to 1. Our best estimate for F (0.6054, SE = 0.122) is close to, but significantly less than, 1. A plot of standardized residuals against log(gs) exhibited strong negative curvature at high (>2.45) log10(gs) values. If F is reestimated (ANCOVA of cases with direct Tgs estimates) from that subset © 1997 NRC Canada

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369

Fig. 3. Plot of corrected P/Bgs values against mean growing season water temperature estimates: corrected P/Bgs = observed P/Bgs 2 0.600(log(gs) 2 mean log(gs)), where mean log(gs) = 2.2423 and 0.600 comes from the regression model log(P/Bgs) = ataxon + 0.045(Tgs) + 0.600(log(gs)) fitted to the refined taxonomy data set (N = 64). The lines represent the same model where ataxon is an additive constant specific to each taxonomic group: arot, Rotifera = 20.637; achy, Chydoroidea = 20.803; acyc, Cyclopoida = 20.892; acal, Calanoida = 21.200.

(N = 49) of the data with gs values less than 300, the new estimate (0.800, SE = 0.17) is not significantly different from 1. Similar results are obtained when cases with both direct and indirect Tgs estimates are included in the analysis. These results strongly suggest that our procedure for estimating gs is biased high for estimated values greater than 300 days. In fact, the distribution of gs estimates is strongly bimodal: 83% have values less than 300 days and are normally distributed around a mean value of 160 days; the remaining 17% form a relatively uniform subset, with almost all values (12 of 15) equal to 365 days. A rough estimate of the bias associated with this subset of the data can by obtained by refitting the regression models of Table 6, with F set to 1.0 and a new categorical variable (long gs) added that splits the data into two subsets at a gs value of 300 days. The regression coefficient estimated for long_gs then provides a direct measure of the potential bias associated with gs estimates greater than 300 days. These new models provide improved descriptions of their respective data sets (i.e., small increases in R2adj values). In both, long_gs is statistically significant (p < 0.0001) and has fitted values indicating that gs estimates in the neighbourhood of 365 days overestimate the “true” gs values by about 60%. Also, by fixing F at 1, estimates of ataxon and b derived from the growing season data sets can be compared directly with estimates of ataxon and b obtained by fitting eq. 6 to the [P/B]daily data (Table 7). The similarity among all three sets of estimates confirms the prediction, inherent in eq. 4, that the relationship linking [P/B]daily values to daily temperatures can be recovered by fitting eq. 5 to P/Bgs values. Influence of food resource availability and lake morphometry: All subsets regression analysis and stepwise regression analy-

sis were used to determine if addition of the independent variables phos, chl, and Z to the models listed in Table 6 would produce a significant (p < 0.05) increase in their adjusted R2 values. No such increase was observed. Therefore, we conclude that none of these variables improves on the explanatory power of the models in Table 6. Comparing empirical predictors of production: We compared the predictive capability of our “best” taxonomically differentiated model for annual production: (9)

log10(P) = ataxon + log10(Bgs) + 0.045⋅Tgs + 0.600⋅log10(gs)

(where arot = 20.634, achy = 20.784, acyc = 21.019, and acal = 21.191) with the Plante and Downing (1989) annual production model: (10)

log10(P) = 0.06 + 0.79⋅log10(Bann) 2 0.16⋅log10(Wm) + 0.05⋅Tann

where Bann = mean annual biomass (grams dry weight per square metre), Wm = maximum adult size, and Tann = mean annual water temperature (degrees Celsius). The comparison was limited to the subset of 48 cases that contained all variables necessary for applying both equations. For our growing season model, the R2 calculated from observed and predicted values for log10(P) was 0.9521, the mean residual was – 0.0093, and the standard deviation of the residuals was 0.2087. Predictions derived from the Plante and Downing (1989) model were not as accurate: the R2 was 0.8679, the mean residual was 0.1928, and the standard deviation of the © 1997 NRC Canada

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Table 7. Comparison of three sets of estimates for the relationship log([P/B]daily) = αtaxon + β log(Tdaily) where αtaxon is an additive constant specific to each taxonomic group.

Parameters

Estimates from daily data set

N R2adj αrot ± SE αcla ± SE αcyc ± SE αcal ± SE β ± SE

30 0.737 −1.631 ± 0.141 −1.645 ± 0.132 −1.844 ± 0.170 −2.294 ± 0.138 0.0434 ± 0.008

Estimates from growing season data set –––––––––––––––––––––––––––––––––––––– Subset 1 Subset 2 64 0.776 −1.482 ± 0.058 −1.651 ± 0.084 −1.732 ± 0.093 −2.047 ± 0.096 0.0451 ± 0.004

87 0.704 −1.424 ± 0.060 −1.565 ± 0.085 −1.825 ± 0.088 −2.005 ± 0.094 0.0419 ± 0.004

Note: αrot, Rotifera; αcla, Cladocera; αcyc, Cyclopoida; αcal, Calanoida. The estimates in the first column were obtained by fitting eq. 6 to the daily data set. Estimates derived from the growing season data set were obtained by fitting eq. 8, with Φ set to 1 and the long gs term included. Subset 1 was derived from Tgs estimates based on direct water temperature measurements; subset 2 was derived using all available estimates of water temperatures. Coefficient estimates for the long gs term were −0.22 (SE = 0.062) for subset 1 and −0.172 (SE = 0.063) for subset 2.

residuals was 0.3237. When we confined our comparison to those cases (N = 28) with direct estimates of temperature, predictions from the growing season model (R2 = 0.9803, mean residual = 20.0468, standard deviation of residuals = 0.1740) were still more accurate than those derived using the Plante and Downing (1989) model (R2 = 0.8865, mean residual = 0.1037, standard deviation of residuals = 0.3253). Average biomass over the growing season Stepwise regression analysis produced the following empirical model for Bgs: (11)

log10(Bgs) = 20.139 + 0.538⋅log10(Mad) + 0.346⋅log10(chl) + 0.412⋅log10(Z)

(N = 71, R2adj = 0.580) with all terms highly significant (p < 0.01). In this analysis, about 48% of the overall variation in log10(Bgs) was accounted for by log10Mad, 6% was accounted for by log10chl, and 4% by log10Z. The group of observations with long (>300 days) gs values did not stand out from all the other data. Length of the growing season Stepwise regression analysis produced the following empirical model for gs: (12)

log10(gs) = 2.16 + 0.165⋅log10(chl) 2 0.059⋅(log10(chl))2 2 0.113⋅clad + 0.334⋅long gs

(N = 85, R2adj = 0.61) with all terms highly significant (p < 0.001). In this analysis, about 10% of the overall variation in log10(gs) was accounted for by the chl terms, 14% was accounted for by the clad term, and 37% by the long gs term. The value (0.344, SE = 0.038) of the long gs term in this model is not significantly (p > 0.05) different from the estimate

(0.221, SE = 0.062) of its value obtained from the P/Bgs model (Table 7). Thus, both analyses (i.e., P/Bgs and gs) generate similar estimates for the positive bias present in gs estimates greater than 300 days.

Discussion Is the association between weight-specific production and water temperature a methodological “artifact”? All our analyses demonstrate a strong and consistent correlation between water temperature and weight-specific production. This could be the product of the direct effects of temperature on the biological processes of production or it could simply reflect the fact that “adjustments” for temperature were included in the calculations used to generate the original production estimates. One of the most common methods for estimating production assumes that individual development rates in the field match food-saturated development rates measured in the laboratory (Rigler and Downing 1984). This assumption is included in production calculations by estimating field development rates from field water temperatures using temperature functions defined in the laboratory under food-saturating conditions. Although this assumption may be generally true for the development times of life stages that do not feed independently (eggs, Edmondson 1974 and references therein; early naupliar stages, Hart 1990 and references therein), there is good evidence that the development times of life stages that do feed independently (later naupliar and copepodite stages) are significantly extended by large reductions in food supply (Rigler and Downing 1984; Hart 1990; McCauley et al. 1990a). If a large percentage of authors generated their production values from individual development times estimated from field water temperatures, then these production values should exhibit strong dependence on field water temperatures, everything else being equal. The presence of such an effect would be a simple consequence of the © 1997 NRC Canada

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methodological assumption of the authors, and would in no way provide independent evidence of the validity of that assumption. To assess this possibility, we identified those production estimates in our data set that were free of this assumption and then examined the character of the temperature effect exhibited by those estimates alone. The methods in our data set fall into two broad categories: (i) those based on growth rate estimates for individual organisms (increment–summation and related methods, Waters 1977) and (ii) those based on population growth rate estimates, including turnover time methods and removal–summation methods (Waters 1977). Among studies using type i methods, in 15, development times were estimated directly in the field by timing the passage of individual cohorts through their developmental stages; in 13, field development times were assumed equal to laboratoryestimated development times measured under food, water quality, and temperature conditions set to match those existing in the field; and in 16, field development times were assumed equal to laboratory-estimated development times measured under food-saturating conditions at field temperatures. Among studies using type ii methods, 17 used nonequilibrium variants of the removal–summation approach, where production estimates are generated from direct estimates of shortterm variation in population growth rate in the field, coupled with indirect estimates of population birth rate from egg densities and estimated egg development times. Typically, egg development times were estimated from field water temperatures using a laboratory-derived function. Such methods generate production estimates that should be quite comparable with those generated by type i methods (Crisp 1984; Gillespie and Benke 1979; Herzig et al. 1980). Consider our analyses of the [P/B]daily data. Of the 28 data sets analyzed, six were based on direct estimates of field development times. In all six, [P/B]daily was positively correlated with Tdaily. In three, the correlation was statistically significant at the 1% level, and in the remaining three, it was significant at the 10% level. In regression analyses of these data sets, the median value for the temperature coefficient (0.055) was similar to the value derived from the entire daily data set (0.0434 ± 0.008, Table 7). A further six data sets were based on development times estimated from laboratory simulations of field conditions: all six exhibited positive and statistically significant (p < 0.01) correlations between [P/B]daily and Tdaily, with the median estimate (0.040) of the temperature coefficient again very similar to the value derived from the entire data set. Thus, the finding of a strong and consistent association between daily, weight-specific production rates and temperature does not simply reflect assumptions buried within the production estimation methods. Now consider our analyses of P/Bgs values. Of the 87 estimates in the original data set, 15 were based on direct estimates of field development times. This subset of the complete data set exhibited a statistically significant (p < 0.02) association with water temperature; the estimate for the temperature regression coefficient (0.0421 ± 0.017) was essentially identical with the estimate derived from the entire data set (0.0425 ± 0.004). An additional 13 estimates were based on development rates derived from laboratory simulations (food availability, water quality, temperature) of field conditions. In this larger subset (N = 28) of the data, the temperature effect

371

was again statistically significant (p < 0.0001) and the regression coefficient estimate was very similar (0.0451 ± 0.007) to the estimate derived from the entire data set. In addition, this subset exhibited (p < 0.05) the difference, between calanoid species and other species, that was strongly apparent in the entire data set. Finally, consider the larger subset (N = 45) of data, obtained by including the 17 production estimates derived from removal–summation methods. Analysis of these data produced a regression model that was essentially identical with the model generated by our analysis of the entire data set (Table 6). We used this model (Table 6, subset 2) to predict P/Bgs values for the 16 studies that were explicitly based on the assumption that field development times equalled temperature-corrected food-saturated development times. There was a strong association (r = 0.8, p < 0.001) between predicted and observed values and no sign of systematic bias in the predicted values: the regression of observed values on predicted values had slope and intercept estimates not significantly (p > 0.05) different from 1 and 0, respectively. These findings show that the character of the temperature effect resident in the growing season data set is not a product of methodological assumptions buried in the production calculations themselves. Our analyses of daily and annual production data suggest that simple strong relationships, linking weight-specific production rate to temperature, underlie a substantial portion of the variation in production observed in natural populations of limnetic zooplankton. When we examined variation in [P/B]daily values within populations, we found that 75% of the populations examined exhibited such relationships. The similarity of slope estimates and the distinctiveness of intercept estimates (Table 4; Fig. 1) clearly characterize the ways in which different taxonomic groups vary in terms of both their characteristic daily weight-specific production values and the sensitivity of those values to changes in temperature. A second independent analysis, founded on between-population differences in [P/B]daily and Tdaily values, produced a quantitatively similar picture (Fig. 1). A third independent analysis, founded on between-population differences in annual production values, produced a picture that was both qualitatively and quantitatively consistent (Figs. 2 and 3; Table 7) with the results obtained from the analyses of [P/B]daily values. All of these results are consistent with the view that the combined influence of temperature and taxonomy on annual production rates in the wild is strong, pervasive, and accurately described by a model of the following form: (13)

log10(P) = ataxon + log10(Bgs) + b⋅Tgs + F⋅log10(gs)

or (14)

log10(P/Bgs) = ataxon + b⋅Tgs + F⋅log10(gs)

where a varies with taxonomic group. Our most accurate version of this model (Table 6, direct Tgs estimates) has the following properties: (i) it accounts for a very large (77%) proportion of observed variation in P/Bgs values; (ii) a varies significantly among taxonomic groups, reflecting the same ordering of production rates (highest to lowest: Rotifera, Cladocera/Chydoroidea, Cyclopoida, Calanoida) observed in our analysis of the daily production data; and (iii) variation in b (0.0458, SE = 0.0039) across taxo© 1997 NRC Canada

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nomic groups was undetectable; the estimated value for b was very similar to independent estimates derived from analyses of [P/B]daily values (i.e., pooled b value from between-population analysis = 0.04336, SE = 0.0077; median b values from within-population analyses: Rotifera, 0.0516; Cladocera, 0.0442; Cyclopoida, 0.0399; Calanoida, 0.0499). Our estimate for b is very similar to recent b estimates (0.048 ± 0.001; 0.041 ± 0.005) reported by Huntley and Lopez (1992) for marine copepods. It also reflects a temperature effect that is quantitatively similar to the temperature effect evident in Hart’s (1990) compilation of individual development times among marine and freshwater copepods, under food-saturated conditions. Regression analyses of these data, assuming a Van’t Hoff temperature relationship (i.e., eq. 1), generated temperature coefficient estimates (freshwater calanoids, 0.039 ± 0.002; marine calanoids, 0.041 ± 0.004; freshwater cyclopoids, 0.048 ± 0.006) that overlap our b estimates and those of Huntley and Lopez (1992). In addition, some of the differences in development time between subsets of Hart’s (1990) data are qualitatively similar to differences in weightspecific production rates noted in our analyses: (i) the weightspecific production rates for freshwater calanoids in our data set were substantially lower than those noted for marine copepods by Huntley and Lopez (1992); similarly, in Hart’s (1990) data, development times for freshwater calanoids are significantly (p < 0.01) longer (by about 65%) than those for marine calanoids; and (ii) in our data set, calanoid weight-specific production rates are significantly (p < 0.05) lower than cyclopoid rates; similarly, in Hart’s (1990) data, freshwater calanoid development times are significantly longer (by about 17%) than freshwater cyclopoid development times. Associations among population density, food resource availability, body size, and lake mean depth Many authors have reported a positive association between chlorophyll concentration and total biomass density of zooplankton. Our analysis of population-level biomass density (grams dry weight per square metre of lake surface area) also revealed a positive link to chlorophyll concentration, with our slope estimate for chl (0.35, SE = 0.090, in our log–log regression of Bgs on chl) not significantly different (p > 0.05) from estimates obtained in earlier studies of total zooplankton biomass density: 0.51 (McCauley and Kalff 1981), 0.43–0.53 (Hanson and Peters 1984), and 0.47 (Cyr and Pace 1993). Empirical studies of a wide range of organisms (Damuth 1981; Peters 1983; Strayer 1994) have reported statistical associations between population density and individual body size. Typically, numerical density declines with increasing body size, and biomass density increases. Both types of relationships are allometric with characteristic body weight exponent values of –0.75 for numerical density and +0.25 for biomass density (Blackburn et al. 1993). The few reported studies of zooplankton (or related organisms) are consistent with this general finding. Peters and Wassenberg (1983) looked at the biomass density of invertebrate populations and found a positive allometric relationship, with a body weight exponent of +0.45. Cyr and Pace (1993) looked at the total biomass density of zooplankton communities and found a positive allometric relationship with mean community body weight (exponent value = +0.75), coupled with a positive relationship with chlorophyll concentration. Our

Can. J. Fish. Aquat. Sci. Vol. 54, 1997

analysis of population biomass density also revealed an allometric relationship with body weight. Our estimate for the weight exponent (0.53, SE = 0.070) was somewhat lower than that found by Cyr and Pace (1993) but somewhat higher than its characteristic value of 0.25. This finding is consistent with the fact that numerical density is allometrically related to body size in our data set, with an exponent value (20.25, SE = 0.12) that is also higher than its characteristic value (20.75). The presence of body size and chlorophyll terms in our biomass regression equation (eq. 11) is consistent with the hypothesis (Damuth 1981; Lawton 1989; Blackburn et al. 1993) that population density – body size correlations largely reflect the reciprocal effects of food availability and individual food requirements on population carrying capacity: more food can support more animals of any size, and because larger animals often have lower weight-specific energy requirements than smaller animals and larger animals may acquire a greater proportion of available resources than smaller animals, a fixed amount of food will usually support a greater biomass density of larger animals. The positive link between population biomass density (measured as grams dry weight per square metre of lake surface area) and lake mean depth is likely a simple result of the increases in average water volume per unit surface area that accompany increases in lake mean depth. Much recent work (e.g., McQueen et al. 1989; Carpenter and Kitchell 1993) has shown that the activity of both predators and competitors can strongly influence zooplankton biomass density in lakes, at both the community level and the population level. Because we were unable to capture these potentially important effects in our analyses, it is not surprising that we could only account for a moderate amount (58%) of the observed variation in population biomass density. Also, in our analysis, variation in adult body size accounted for a larger share of observed biomass variation than did variation in chlorophyll concentration. This is partly a reflection of the fact that adult body size exhibits greater variation in our data set than does chlorophyll concentration. Interpreting the associations between weight-specific production, population biomass, and body size Our analysis of annual production rates suggests that the statistical associations linking weight-specific production rates to both population biomass and adult body size may simply reflect large, roughly parallel taxonomic differences in all three variables rather than direct influences of population biomass and adult body size on production rates. This conclusion is supported by the following observation. Ordering (from lowest to highest) our four taxonomic groups by median population biomass yields the same sequence (Rotifera, Cyclopoida, Chydoroidea, Calanoida) as ordering them by median adult body weight. A similar sequence (Rotifera, Chydoroidea, Cyclopoida, Calanoida) is obtained if the groups are ordered from the highest weight-specific production rate to the lowest. The similarity in these three separate orderings should produce relatively strong negative correlations between production rate and adult body weight and between production rate and population biomass, if all the data are pooled and analyzed without recognizing taxonomic groupings. This is exactly what we observed in our analyses of the pooled pro© 1997 NRC Canada

Shuter and Ing

duction data and what Plante and Downing (1989) observed in their analyses. There are also process-level interpretations (Peters 1983; Downing 1984) of such empirical associations. Negative effects of population biomass could be interpreted in terms of density-dependent growth processes operating at the population level, and negative effects of body size could be interpreted in terms of the size dependence of energy metabolism (e.g., respiration, maximum growth rate: Peters 1983; Schmidt-Nielsen 1984) commonly observed at the individual level. Our analysis of production data from limnetic zooplankton populations is not consistent with either of these interpretations: (i) if our entire zooplankton P/Bann data set is analyzed without accounting for the distribution of observations among taxonomic groups, we obtain a strong biomass effect; (ii) if we conduct a similar analysis on a reduced data set containing only data from the smallest (Rotifera) and largest (Copepoda) individual sized groups, we obtain a strong body size effect and no biomass effect (log10(P/Bann) on Tann, log10(Mad); R2 = 0.525); (iii) if we account for taxonomic groupings explicitly in our statistical model, then both the biomass and body size effects disappear, overall model fit improves (Table 5), and similar results are obtained no matter what the distribution of observations among taxonomic groups; and (iv) analyses of within-population variation in [P/B]daily values showed that negative effects of population biomass were rarely detectable. We reanalyzed the original Plante and Downing (1989) set of production data for freshwater invertebrates and also found that results differed depending on how internal groupings within the data were recognized: (i) with all data pooled, regression analysis identified strong negative biomass and body size effects on total production; (ii) if the analysis was limited to the benthic data alone, the body size effect disappeared and the biomass effect weakened; and (iii) if the analysis was limited to the zooplankton data alone, both biomass and body size effects were weakened; however, the continuing presence of the body size effect was due to the presence of a single representative of the Mysidacea in the data set, an organism with a body mass at least 100 times larger than almost all other organisms present; with this observation eliminated, the body size effect disappeared. Given a functional interpretation of the biomass and body size effects, one would expect that a statistical analysis that allowed for taxonomic differences would permit such effects to emerge more clearly. One would also expect to see strong evidence for density-dependent effects on production in analyses of the seasonal cycle of daily production rates. Neither of these expectations was met in our work. The absence of body size effects on population P/B values is consistent with the following observations on zooplankton: (i) among cladocerans (Paloheimo et al. 1982; McCauley et al. 1990a, 1990b; Glazier and Calow 1992; Paloheimo et al. 1982) and copepods (van den Bosch and Gabriel 1994), weight-specific rates of metabolism, ingestion, and assimilation are almost independent of body mass; (ii) among cladocerans, intrinsic rates of population increase (Lynch 1980) and population P/B (Banse 1982) values, observed under laboratory conditions, are almost independent of adult body size; (iii) regression analysis of data in Hart (1990) shows that life cycle development times (food saturating conditions) for

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marine and freshwater copepods are strongly dependent on temperature and independent of adult body size; (iv) Huntley and Lopez (1992) found that weight-specific rates of production by marine copepods were strongly dependent on temperature but were essentially independent of adult body size; and (v) in copepods, individual growth over the life cycle can often be approximated by a simple exponential model (Huntley and Lopez 1992); given this, age structure effects on population biomass growth should be minimal. Because many of the processes that contribute to population production do not exhibit the size dependence characteristic of other animal groups, it is perhaps to be expected that population P/B values for cladocerans and copepods do not exhibit the size dependence characteristic of other animal groups. Biomass stability and the length of the growing season Our protocols for estimating gs appear to yield positively biased estimates as gs approaches its upper bound of 365 days. For all populations with gs values >300 days (the long gs group), gs was estimated from the annual biomass cycle. Given our protocol for estimating gs, a relatively stable (i.e., minimum annual biomass >20% maximum annual biomass) biomass cycle guarantees a gs estimate of 365 days. The positive bias in such estimates suggests that a stable annual biomass cycle does not provide useable information on the duration of the productive period for the population. This would arise if biomass stability resulted from mortality rates low enough to prevent rapid loss of accumulated biomass. Cyclopoids, and particularly calanoids, are overrepresented in the long gs group. Population production and food resource availability Our analyses suggest that the average durations of developmental stages in the field are not very different from foodsaturated values observed in the laboratory. However, this finding does not remove the possibility that field production rates are influenced by food availability. Stage duration is a relatively insensitive indicator of food-limited growth: quite large reductions in food availability are required to produce even moderate increases in duration (Ban 1994; Jamieson and Burns 1988; Makarewicz and Likens 1979). Thus, production rates could be suffering from moderate levels of food limitation while still exhibiting stage durations similar to those characteristic of food-saturated conditions. Production estimates would reflect the effects of food limitation through more sensitive population parameters such as body size (Geller 1989; Hart 1991; Lynch 1989; McCauley et al. 1990a, 1990b; Santer and van den Bosch 1994) and particularly egg production (Ban 1994; Lynch 1989; Makarewicz and Likens 1979), both of which are usually measured directly in the field. Our examination of within-population variation in [P/B]daily values suggests that compensatory links between population biomass and production are rarely strong enough to be detectable. Few populations (four, less than 20% of those examined) exhibited such relationships, and in only one was this negative effect of population biomass on production strong (i.e., of more importance than temperature in explaining variation in production) and consistently expressed throughout the growing season. © 1997 NRC Canada

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Our examination of growing season production rates indicates that the growing season average for [P/B]daily is independent of Bgs. This suggests that if strong intraspecific effects of population density on daily weight-specific production rates do occur, they must be restricted to relatively short segments of the growing season. We were unable to use our data set to test for the effects of interspecific competition on population-specific production rates because most studies did not report biomass levels for other segments of the zooplankton community. Taken together, our empirical analyses of the elements of the annual production cycle for limnetic zooplankton suggest that (i) weight-specific rates of production during the cycle are primarily driven by temperature; the influence of food resource availability is probably only evident over relatively short portions of the cycle; and (ii) the level of biomass reached during the cycle is influenced by food resource availability and adult body size; temperature exerts little influence on these elements of the cycle. This view of the production cycle is similar to that reached by Geller (1987), after his study of zooplankton populations in Lake Constance: “... juvenile development was prolonged by up to a factor of 2 with low food concentrations. In natural populations, however this may be of minor importance, because nearly no offspring is produced during times of severe food shortage (clear-water phase; winter) and because the bulk of a population’s annual production occurs under optimum food conditions during the spring maximum of phytoplankton.” This view suggests a very simple model to illustrate how the interactive effects of temperature and food resource availability (R) may shape the annual production cycle of a particular population. If we assume that (i) biomass carrying capacity (Bmax) for the population is proportional to food resource availability (i.e., Bmax ∝ R), (ii) population biomass at the start of the annual production cycle (B0) is small relative to Bmax and is unrelated to either temperature or resource availability, (iii) weight-specific growth follows a simple Van’t Hoff function of temperature (i.e., eq. 1) for B < Bmax, and (iv) the length of the production cycle (gs) is set by the time required to reach Bmax, then gs is roughly proportional to (loge[R]/exp[b⋅Tgs]) and thus both increases in temperature and decreases in food resource availability can act separately, or together, to shorten the annual cycle. We can include the effect of adult body size in this model by making Bmax proportional to R⋅Mcad, where c > 0. The new Mcad term captures the hypothesis (Damuth 1981; Lawton 1989) that a fixed level of food resources will support a greater biomass density of larger animals. The extended model predicts that gs should be positively related to chl and Mad and negatively related to Tgs. Further analysis of the observed variation in gs confirmed these predictions. After removing the biased gs values of the long gs group plus one other atypical point from our growing season data set, we obtained the following model (N = 62, Radj2 = 0.45, all terms highly significant: p < 0.004): (15)

log10(P) = ataxon 2 0.020⋅Tgs + 0.133⋅log10(chl) + 0.047⋅log10(Mad)

where ataxon equals 2.37 for Chydoroidea and 2.50 for the other taxonomic groups.

Fig. 4. Schematic plot of seasonal biomass growth illustrating how an increase in temperature and a decrease in resource availability will interact to produce a decrease in the length of the growing season. We assume that biomass growth is exponential and temperature dependent before reaching carrying capacity (Bmax), carrying capacity varies with resource availability, and when carrying capacity is reached, biomass growth ceases and mortality rapidly depletes biomass.

Our results suggest that the annual production cycle for at least some freshwater zooplankton populations is driven by both temperature and food availability. The interactive effects of these two factors (as summarized in Fig. 4) may be such that a simple increase in temperature, unaccompanied by changes in food availability, would produce a decrease in the length of the annual production cycle, with little change in the overall amount of zooplankton biomass produced and thus made available for transfer up the trophic chain to fish and ultimately to humans. This suggests that predictions of increased fish production from climate change (e.g., Hill and Magnuson 1990) may not be realized in some lake systems.

Acknowledgments We would like to thank H. Cyr, D. Jackson, J. Stockwell, J. Wong, and an anonymous reviewer for their comments on earlier versions of this manuscript. We are particularly grateful to John Roff for his extensive and perceptive critique. Thanks to the COMPMECH Group at Oak Ridge for getting us interested in the issue. Financial support for this work was provided by the Ontario Ministry of Natural Resources.

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