Marine Biology 45, 39-52 (1978) MARINE BIOLOGY 9 by Springer-Verlag 1978 Relationship between Phytoplankton Cell Size and the Rate of Orthophosphate Uptake: in situ Observations of an Estuarine Population E.S. Friebele, D.L. Correll and M.A. Faust Smithsonian Institution, Chesapeake Bay Center for Environmental Studies; Edgewater, Maryland, USA Abstract Orthophosphate uptake by a natural estuarine phytoplankton population was estimated using two methods: (I) 32p uptake experiments in which filters of different pore sizes were used to separate plankton size-fractions; (2) 33p autoradiography of phytoplankton cells. Results of the first method showed that plankton cells larger than 5 ~um were responsible for 2% of the total orthophosphate uptake rate. 98% of the total uptake rate occurred in plankton composed mostly of bacteria, which passed the 5 ~m screen and were retained by the 0.45 Lum pore-size filter. There was no orthophosphate absorption by particulates in a biologically inhibited control containing iodoacetic acid. Orthophosphate uptake rates of individual phytoplankton species were obtained using 33p autoradiography. The sum of these individual rates was very close to the estimated rate of uptake by particulates larger than 5 H/n in the 32p labelling experiment. Generally, smaller cells were found to have a faster uptake rate per bm3 biomass than larger cells. Although the nannoplankton constituted only about 21% of the total algal biomass, the rate of phosphate uptake by the nannoplankton was 75% of the total phytoplankton uptake rate. Results of the plankton autoradiography showed that the phosphate uptake rate per unit biomass is a power function of the surface:volume ratio of a cell; the relationship is expressed by the equation Y = 2x70-11 xi.7, where Y is ~gP ~m-3 h-1 and x is the surface:volume ratio. These results lend support to the hypothesis that smaller cells have a competitive advantage by having faster nutrient uptake rates. Introdu~io. plankton has varied between cells with a diameter of 65 bm to those less than 3bm. The phytoplankton is normally an assemHowever, it is clear from these studies blage of one-celled or multi-celled auto- and from the work of Watt (1971), w h o trophs with diverse shapes and sizes, used autoradiography to measure primary Hutchinson (1961) was puzzled that such production rates of individual phytodiversity could exist in an isotropic en- plankton species, that the smaller cells vironment where competition for reprovide a large fraction of the total sources is supposedly occurring. primary production in the euphotic zone. Phytoplankton species not only disAlthough nannoplankton were the most implay diversity in shapes and sizes, but portant producers in all environments they differ in their contribution to the studied by Malone (1971a), the netplanktotal algal biomass and metabolic activton:nannoplankton productivity and chloity. Nannoplankton (very small algal rophyll ratios were higher in coastal wacells) which, in the past, were overters than in oceanic waters. Nannoplanklooked with net phytoplankton sampling, ton populations varied within a narrow have recently been recognized as very im- margin, but generally netplankton standportant autotrophs in the plankton coming crop increased in areas of upwelling munity, along the California Current (Malone, Many studies have documented the domi- 1971b). Yentsch and Ryther (1959) also nance of "nannoplankton" in algal standreported a stable nannoplankton populaing crop, chlorophyll content, and protion accompanied by fluctuations in netductivity (Yentsch and Ryther, 1959; plankton standing crop. Malone, 1971a, b; McCarthy et al., 1974; These observations suggest that perBerman, 1975). The definition of nannohaps the nannoplankton are the best 0025/3162/78/0045/0039/S02.8O 40 E.S. Friebele et al.: a d a p t e d s p e c i e s of the p h y t o p l a n k t o n comm u n i t y in m a n y a q u a t i c e n v i r o n m e n t s . Possibly they r e p r e s e n t the m o r e o p p o r t u n i s t i c species, since they h a v e f a s t e r g r o w t h and m e t a b o l i c rates than larger s p e c i e s (Fogg, 1965). H o w e v e r , t h e i r a b i l i t y to m u l t i p l y r a p i d l y is d e p e n d e n t upon r a p i d and e f f i c i e n t u t i l i z a t i o n of a v a i l a b l e r e s o u r c e s . Do the n a n n o p l a n k ton h a v e a c o m p e t i t i v e a d v a n t a g e in obt a i n i n g the r e q u i r e d n u t r i e n t s ? M u n k and Riley (1952), who d e v e l o p e d a n u t r i e n t a b s o r p t i o n m o d e l b a s e d on fluid d y n a m i c s , p r e d i c t e d that s m a l l cells h a v e a f a s t e r r e l a t i v e n u t r i e n t abs o r p t i o n rate than large cells. T h e y s t u d i e d m o r p h o l o g i c a l and size v a r i a tions of p h y t o p l a n k t o n cells and conc l u d e d that n e i t h e r the r a t e of s i n k i n g nor n u t r i e n t a b s o r p t i o n i m p o s e s s e v e r e limits upon cells of less than 20 H/n in size. D u g d a l e (1967) p o i n t e d out the p o s s i b i l i t y for c o m p e t i t i v e a d v a n t a g e of one p h y t o p l a n k t o n s p e c i e s over a n o t h e r b a s e d upon M i c h a e l i s - M e n t e n n u t r i e n t u p t a k e k i n e t i c s . E p p l e y e t al. (1969) o b t a i n e d k i n e t i c c o n s t a n t s for a n u m b e r of species t a k i n g up a m m o n i a and n i t r a t e . Their results showed several general trends: (I) large s p e c i e s had h i g h K s values; (2) s m a l l - c e l l e d s p e c i e s f r o m the o c e a n s h o w e d low K s v a l u e s ; (3) fastg r o w i n g s p e c i e s s e e m e d to have lower K s v a l u e s t h a n s l o w g r o w e r s . H o w e v e r , the effect of n u t r i e n t u p t a k e rates on specific g r o w t h rate is m o d i f i e d by e f f i c i e n c y of light u t i l i z a t i o n of the p h y t o p l a n k t o n species. P a r s o n s and T a k a h a s h i (1973) have d e v e l o p e d a m o d e l w h i c h predicts that small cells w i l l o u t g r o w larger cells in all e n v i r o n m e n t s e x c e p t t h o s e w h e r e n u t r i e n t levels and light int e n s i t i e s are high. The w o r k c i t e d a b o v e has i n c l u d e d e i t h e r l a b o r a t o r y s t u d i e s of n u t r i e n t uptake k i n e t i c s w i t h a l g a l c u l t u r e s u n d e r p r e s u m a b l y ideal c o n d i t i o n s , or m o d e l s using k i n e t i c d a t a to p r e d i c t w h i c h cells w i l l h a v e c o m p e t i t i v e a d v a n t a g e in c e r t a i n e n v i r o n m e n t s . T h e p u r p o s e of the f o l l o w i n g study w a s to o b s e r v e t o t a l and i n d i v i d u a l n u t r i e n t a b s o r p t i o n rates of a d i v e r s e g r o u p of p h y t o p l a n k t o n cells u n d e r n a t u r a l c o n d i t i o n s . This w a s a c c o m p l i s h e d by m e a n s of 32p u p t a k e e x p e r i m e n t s e m p l o y i n g f i l t e r s to s e p a r a t e p l a n k t o n sizes and by 33p a u t o r a d i o g r a phy of p l a n k t o n o r g a n i s m s . The latter t e c h n i q u e e n a b l e s the r e s e a r c h e r to m e a sure the rate of a m e t a b o l i c f u n c t i o n in an i n d i v i d u a l o r g a n i s m or species. Thus, we can d e t e r m i n e w h e t h e r small cells do h a v e a c o m p e t i t i v e a d v a n t a g e in n u t r i e n t u p t a k e w h e n they are c o e x i s t i n g and per- Phytoplankton Cell Size and Phosphorus Uptake haps c o m p e t i n g w i t h other cells natural aquatic environment. in a Materials and Methods This s t u d y was c a r r i e d out on the Rhode River, a s u b e s t u a r y on the w e s t e r n shore of the C h e s a p e a k e Bay near A n n a p o l i s , M a r y l a n d , USA. The Rhode R i v e r is a shallow e s t u a r y w i t h a m e a n depth of 2 m. F r e s h w a t e r e n t e r s the r i v e r from the M u d d y C r e e k w a t e r s h e d , and saline w a t e r enters from the Bay. The e x p e r i m e n t s w e r e p e r f o r m e d in the fall, w h e n w a t e r t e m p e r a t u r e s w e r e dropping, s o l u b l e rea c t i v e p h o s p h o r u s levels w e r e d e c l i n i n g after a late s u m m e r peak, and p h y t o p l a n k ton and b a c t e r i a l n u m b e r s w e r e d e c r e a s ing. On O c t o b e r 31, 1974, a 24 1 w a t e r sample was taken w i t h a p e r i s t a l t i c p u m p from I m d e p t h at a Rhode River s t a t i o n (Latitude 3 8 o 5 3 ' O O " N; L o n g i t u d e 76032 ' 00" W), w h e r e the d e p t h is 4 m. The water was p l a c e d in glass carboys and t r a n s p o r t e d to the S m i t h s o n i a n I n s t i t u tion C h e s a p e a k e Bay C e n t e r dock w h e r e the e x p e r i m e n t s w e r e p e r f o r m e d . The water was d i v i d e d into e x p e r i m e n t a l bottles w h i c h w e r e s u s p e n d e d from the dock at I m w a t e r depth. The e x p e r i m e n t a l flask for a u t o r a d i o g r a p h y c o n s i s t e d of a 12 1 s p h e r i c a l flask w h i c h had b e e n a c i d - w a s h e d and e q u i p p e d w i t h a s t o p p e r and a w i r e harness, w i t h float and w e i g h t attached. The flask was s u s p e n d e d in the w a t e r on the s o u t h e r n side of the dock at I m depth. The s t o p p e r was p i e r c e d by 3 tubes: I from a p e r i s t a l t i c pump, I from a small air pump, and I for the exit for air. For the d u r a t i o n of the e x p e r i m e n t , air was b u b b l e d g e n t l y t h r o u g h the f l a s k in order to p r e v e n t the p l a n k t o n from settling. 200 ~Ci of 33p as H3P04 was inj e c t e d into the flask t h r o u g h a large s y r i n g e needle. At t i m e d intervals, 1 1 s a m p l e s w e r e p u m p e d f r o m the flask into bottles containing buffered fixative (final c o n c e n t r a t i o n : 0.5% g l u t e r a l d e hyde and O . 0 1 M potassium phosphate buffer at pH 7.0). One ml of each s a m p l e was also p l a c e d in a s c i n t i l l a t i o n vial for c o u n t i n g at the same time. A f t e r each s a m p l e was taken, the p u m p was rev e r s e d in o r d e r to clear the p u m p lines of w a t e r u n t i l the n e x t s a m p l e was taken. One ml of w a t e r was t a k e n at the b e g i n n i n g and at the end of the e x p e r i m e n t for c o u n t i n g to check for leaks in the apparatus. T o t a l p h o s p h o r u s u p t a k e by the p l a n k ton was m e a s u r e d a c c o r d i n g to the m e t h o d of F a u s t and C o r r e l l (1976), in t h r e e 250 ml bottles: light, dark, and one con- E.S. Friebele et al. : Phytoplankton Cell Size and Phosphorus Uptake t a i n i n g the b i o l o g i c a l i n h i b i t o r , iodoacetic acid. In each e x p e r i m e n t , 2 ~Ci of c a r r i e r - f r e e 32p as o r t h o p h o s p h a t e was added at t i m e zero. The b o t t l e s w e r e s u b m e r g e d at I m d e p t h and, at t i m e d intervals, the b o t t l e s w e r e r e t r i e v e d and a s u b s a m p l e was removed. P a r t i c u l a t e s in this s u b s a m p l e w e r e then s e p a r a t e d acc o r d i n g to size w i t h a 5 ~um p o r e - s i z e d N i t e x s c r e e n and a 0.45 bun M i l l i p o r e membrane. The f i l t e r s and I ml of f i l t r a t e w h i c h had p a s s e d the 0.45 Lum m e m b r a n e w e r e p l a c e d in s c i n t i l l a t i o n v i a l s for counting. A u t o r a di o g r a p h y Fixed plankton samples were centrifuged in the l a b o r a t o r y for 30 m i n at 5000 x g at 5oc. The p e l l e t was w a s h e d t h r e e times w i t h 15 ml of 0.002 N HCI at 3000 x g and r e s u s p e n d e d in I ml of d i s t i l l e d water. In order to s e p a r a t e c l u m p e d cells, each cell s u s p e n s i o n was sonic a t e d for 10 sec (Model W 140 C, Heat S y s t e m Co., at 60 W output) and f i l t e r e d via g r a v i t y t h r o u g h 8 ~m p o r e - s i z e N u c l e p o r e filters. The cells w e r e r i n s e d off the f i l t e r s and r e s u s p e n d e d in 2.2 ml of d i s t i l l e d water, Liquid-emulsion autoradiograms were p r e p a r e d a c c o r d i n g to the m e t h o d of B o g o r o c h (1972), s o m e w h a t m o d i f i e d as des c r i b e d by C o r r e l l et ai.(1975). E a c h cell s u s p e n s i o n was s o n i c a t e d for 15 sec and 3 drops w e r e s p r e a d on a g e l a t i n c o a t e d glass slide. S l i d e s of the 8 ~um f i l t r a t e w e r e also made. The slides w e r e a i r - d r i e d for 24 to 48 h. In a dark room, the p h o t o g r a p h i c N T B - 2 e m u l s i o n was d i l u t e d 1:1 w i t h d i s t i l l e d w a t e r and b r o u g h t to 44oc in a w a t e r bath. T w o drops of e m u l s i o n w e r e p l a c e d on each s l i d e and t h e n s p r e a d to an even t h i c k n e s s w i t h a s t a i n l e s s steel r a c l e t t e (Bogoroch, 1972). The slides w e r e allowed to dry for I h at r o o m t e m p e r a t u r e (ca. 23oc), and w e r e then p l a c e d in b l a c k l i g h t - t i g h t , d e s i c c a t e d slide boxes and i n c u b a t e d at 4oc for a 3-day exp o s u r e period. The s l i d e s w e r e d e v e l o p e d in D e k t o l at 15oc for 2 min, r i n s e d for 10 sec, and f i x e d in a c i d fixer for 5 to 10 min, then r i n s e d in r u n n i n g tap w a t e r for 30 min. T h e s l i d e s w e r e c l e a r e d for I h in m e t h y l s a l i c y l a t e , and c o v e r s l i p s were mounted with Permount. G r a i n counts w e r e m a d e u s i n g a Zeiss m i c r o s c o p e at 1OOO X m a g n i f i c a t i o n u n d e r p h a s e - c o n t r a s t optics. The m i c r o s c o p e was f o c u s e d on the top of a cell and the g r a i n s in focus w e r e counted. Then the m i c r o s c o p e was f o c u s e d d o w n u n t i l the next set of g r a i n s was in focus and 41 t h e s e w e r e counted. This p r o c e d u r e w a s r e p e a t e d u n t i l all g r a i n s a b o v e the cell w e r e out of focus. S i n c e 33p is a m o d e r ately h i g h e n e r g y e m i t t e r w h i c h is likely to p r o d u c e g r a i n s at p o i n t s w h i c h do not lie d i r e c t l y over the p o i n t of emission, some i m a g e - s p r e a d i n g due to "crossfire" is to be e x p e c t e d (Perry, 1964). This was t a k e n into a c c o u n t v e r y r o u g h l y by c o u n t i n g g r a i n s w i t h i n 5 ~m of the cell m a r g i n s . G r a i n counts w e r e m a d e for at least 20 cells of each s p e c i e s on each a u t o r a d i o g r a m , i.e., at each time i n t e r v a l of the e x p e r i m e n t . B a c k g r o u n d grains w e r e c o u n t e d for areas w h i c h h a d no cells, u n t i l the s t a n d a r d d e v i a t i o n of g r a i n s per u n i t area was w i t h i n ~ 30% of the m e a n for e a c h a u t o r a d i o g r a m . For each time point, the n u m b e r of b a c k g r o u n d g r a i n s in the a r e a o c c u p i e d by each type of p h y t o p l a n k t o n cell was calc u l a t e d and s u b t r a c t e d from the m e a n number of grains per cell. A n a l y s e s for d i s s o l v e d p h o s p h o r u s w e r e p e r f o r m e d on w a t e r s a m p l e s w h i c h had b e e n f i l t e r e d t h r o u g h a 0 . 4 5 ~un p o r e sized M i l l i p o r e filter. I n o r g a n i c p h o s phorus was determined colorimetrically on w h o l e and f i l t e r e d s a m p l e s by reaction w i t h a m m o n i u m m o l y b d a t e and r e d u c tion w i t h s t a n n o u s c h l o r i d e (American Public Health Association, 1971). T o t a l p h o s p h o r u s was a n a l y z e d by the same m e t h od after d i g e s t i o n w i t h p e r c h l o r i c acid and n e u t r a l i z a t i o n (King, 1932). M e t h o d s for r a d i o i s o t o p e c o u n t i n g w e r e as des c r i b e d by F a u s t and C o r r e l l (1976). P h y s i c a l p a r a m e t e r s w e r e m o n i t o r e d during the e x p e r i m e n t s w i t h r e c o r d i n g ins t r u m e n t s at the C h e s a p e a k e B a y C e n t e r dock. The p o p u l a t i o n of a l g a l s p e c i e s w a s e s t i m a t e d in a I 1 s a m p l e of w a t e r by the d i r e c t - c o u n t p r o c e d u r e of C a m p b e l l (1973). The f i x e d cells w e r e c o n c e n t r a t e d to I ml by c e n t r i f u g a t i o n at 5000 x g for 30 min, s o n i c a t e d for 10 sec, and 0.03 ml was p l a c e d on a m i c r o s c o p e slide. A 2.5 cm s q u a r e c o v e r s l i p was p l a c e d over the l i q u i d and the n u m b e r of cells of each s p e c i e s in a n u m b e r of m i c r o s c o p e fields was c o u n t e d u n d e r 1OOO X m a g n i f i cation. E x c e p t for the r a r e r species, 1OO cells of e a c h s p e c i e s w e r e c o u n t e d in o r d e r to e s t i m a t e cell n u m b e r s w i t h i n 20% w i t h a c o n f i d e n c e c o e f f i c i e n t of 95% (Lund et al., 1958). V o l u m e and surface area of p h y t o p l a n k t o n cells w e r e c a l c u l a t e d f r o m l e n g t h and w i d t h m e a s u r e m e n t s u s i n g s t a n d a r d f o r m u l a s for e i t h e r a rod, a sphere, or o b l a t e spheroid. M o s t of the d i n o f l a g e l l a t e s w e r e a s s u m e d to be o b l a t e s p h e r o i d , w i t h an e c c e n t r i c ity of 0.9. 42 E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake Calculations The t o t a l rate of p h o s p h a t e u p t a k e by the p l a n k t o n was c a l c u l a t e d from the rate of 32p d i s a p p e a r a n c e from the filtrate. A c c o r d i n g to the e q u a t i o n for a f i r s t - o r d e r r e a c t i o n , the rate c o n s t a n t , k, was o b t a i n e d f r o m t r a c e r m e a s u r e m e n t s : log C o / C -kt - 2.303 ' c o n c e n t r a t i o n . The s p e c i f i c a c t i v i t y of 33p04 d u r i n g the time c o u r s e was calculated f r o m s p e c i f i c a c t i v i t y of 32pO4 using a r a t i o of the counts at the b e g i n ning of the 33p and 32p e x p e r i m e n t s . (The d i s s o l v e d o r t h o p h o s p h a t e c o n c e n t r a tion r e m a i n e d constant.) The rate of P u p t a k e d u r i n g each time i n t e r v a l was then c a l c u l a t e d for each algal species as follows: w h e r e c is the d i s s o l v e d 32p r a d i o a c t i v A cpm iAt ity, c O is the a c t i v i t y at time zero, - ~g P/iAt or ~g P i-i min-land t is time. The slope of a linear recpm/~g P g r e s s i o n t h r o u g h the d a t a p l o t t e d as The P u p t a k e rates w e r e then a v e r a g e d log c v e r s u s t was u s e d to o b t a i n k. The over all time i n t e r v a l s for w h i c h t h e r e s t e a d y s t a t e rate of d i s a p p e a r a n c e of was a slope, and a m e a n rate of p h o s p h o o r t h o p h o s p h a t e f r o m s o l u t i o n was then obrus u p t a k e for each species of p h y t o t a i n e d as follows: p l a n k t o n was obtained. P disappearance rate (~gPl -I h-l) k Co S w h e r e s is the s p e c i f i c a c t i v i t y of the p h o s p h a t e ion (CPM ~g p-l) at t = O. Rates of p h o s p h o r u s u p t a k e by the two p a r t i c u l a t e sizes w e r e c a l c u l a t e d from the slopes of linear r e g r e s s i o n equations of the first p o r t i o n s of the two a p p e a r a n c e curves as follows: P uptake rate (#g P I-[ h -I) = &c/At S ' w h e r e & C / A t is the slope r e p r e s e n t i n g the c h a n g e in the 32p a c t i v i t y on each of the f i l t e r s w i t h time. O b t a i n i n g p h o s p h o r u s u p t a k e rates of i n d i v i d u a l p h y t o p l a n k t o n s p e c i e s from a u t o r a d i o g r a p h y r e q u i r e s a k n o w n relat i o n s h i p b e t w e e n g r a i n counts and a specific a m o u n t of r a d i o a c t i v i t y . No attempt was m a d e to q u a n t i f y the g r a i n y i e l d of 33p on K o d a k N T B - 2 emulsion. Instead, a y i e l d of 1.8 g r a i n s per e m i t t e d B p a r t i c l e was c h o s e n f r o m l i t e r a t u r e v a l u e s for i s o t o p e s w i t h s i m i l a r e n e r g y levels and on films of s i m i l a r s e n s i t i v ity (Herz, 1959; Perry, 1964; Pelc, 1972; P r e s c o t t , 1964). G r a i n counts w e r e first c o r r e c t e d for r a d i o a c t i v e d e c a y to the day of the e x p e r i m e n t . The m e a n n u m b e r of g r a i n s per cell was c o r r e c t e d for the loss of a c i d - s o l u b l e 33p d u r i n g acid w a s h i n g . An a c i d - s o l u b l e f r a c t i o n of 17% of t o t a l cell P, as found in Chlorella pyrenoidosa by B a k e r and S c h m i d t (1964), was used. The (corrected) m e a n n u m b e r of g r a i n s per cell was t h e n conv e r t e d to counts per m i n u t e (cpm) per liter for each s p e c i e s as follows: Results V a l u e s for p h y s i c a l and c h e m i c a l p a r a m eters d u r i n g the e x p e r i m e n t s are pres e n t e d in Table I. The p l a n k t o n labelling e x p e r i m e n t s w e r e c a r r i e d out from a p p r o x i m a t e l y 10.00 to 16.OO hrs, and the a u t o r a d i o g r a p h y e x p e r i m e n t was from 0 9 . 3 0 to 15.30 hrs. The l a r g e s t c h a n g e s in solar r a d i a t i o n and t e m p e r a t u r e took p l a c e in the later stages of the e x p e r i ments. The s o l u b l e r e a c t i v e p h o s p h o r u s c o n c e n t r a t i o n was low at 4 ~g 1-I, and a p p r o x i m a t e l y 50% of the t o t a l d i s s o l v e d P was organic. Most p h o s p h o r u s f r a c t i o n s r e m a i n e d c o n s t a n t t h r o u g h o u t the e x p e r i ments, e x c e p t for an i n c r e a s e in total reactive phosphorus. Turbidity remained at 18 J a c k s o n units t h r o u g h o u t the day. 32p Tracer Experiments 32p u p t a k e was e s t i m a t e d by m e a s u r i n g (I) the rate of 32p d i s a p p e a r a n c e from the d i s s o l v e d o r t h o p h o s p h a t e pool in the filtrate, and (2) the rate of 32p a p p e a r ance in the p a r t i c u l a t e fraction. The results of these e x p e r i m e n t s are s h o w n in Figs. I and 2. V e r y little u p t a k e occ u r r e d in the b o t t l e c o n t a i n i n g iodoacetic acid (IAA), w h e r e b i o l o g i c a l uptake of p h o s p h o r u s was inhibited. C h e c k s of total r a d i o a c t i v i t y at the b e g i n n i n g and at the end of each b o t t l e e x p e r i m e n t c o n f i r m e d that no 32p was lost to the sides of the b o t t l e or by leakage. 32po 4 d i s a p p e a r e d r a p i d l y f r o m the w a t e r in Mean grains/cell x no. of cells/l the dark bottle. S i n c e this u p t a k e was cpm/l = 1.8 grains/count x 4320 rain exposure time" low w i t h IAA p r e s e n t , it was a s s u m e d to be due to b i o l o g i c a l activity. The light S p e c i f i c a c t i v i t y of d i s s o l v e d o r t h o p h o s p h a t e at e a c h time p o i n t in the b o t t l e was lost d u r i n g the e x p e r i m e n t . first 2 h was c a l c u l a t e d f r o m r a d i o a c t i v - However, the u p t a k e in light and dark ity in the f i l t r a t e of the 32p u p t a k e ex- b o t t l e s has r a r e l y d i f f e r e d s i g n i f i c a n t p e r i m e n t and the d i s s o l v e d o r t h o p h o s p h a t e ly in e x p e r i m e n t s of this kind p e r f o r m e d E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake 43 Table i. Physical and chemical parameters during 32p plankton labelling and 33p autoradiography experiments, October 31, 1974 Time (hrs) Solar radiation (g-cal cm-2 min-1) Water temperature (oc) 8.OO 9.OO iO.O0 ii.00 12.00 13.00 14.O0 15.00 16.00 0.24 0.50 0.70 0.78 0.80 0.76 0.64 0.40 0.20 15.2 15.2 15.3 15.5 15.7 16.O 16.4 17.0 17.2 Reactive phosphorus (~g p i-i) Total Dissolved a Total phosphorus (~g P 1-1 ) Total Dissolved 6 4 49 10 16 4 45 7 aAlthough much has been written about other phosphorus compounds which might react with molybdate if they are present in natural waters, we assume for our purposes that dissolved reactive phosphorus and dissolved orthophosphate are synonymous. 4.4 0.45.u m, dark O0 bJ I- 4.3 hl (9 7 --I <4.2 ~~zk-'~ a IK I..- m A 0 6 E) l- n- ~4.1 O. Z U.. z__4.o -- U) 0 _J n m 3.9_ Ig n @ 3 2 13. r .o 3 . 7 _ 5 @ m, dark I 0 3.6_ i 0 4 --I Q E3.a . E) I I I O0 I 200 i I I 300 0 T I M E (MIN) I i , I O0 TI ME I 200 , L 300 (MIN) Fig. i. Disappearance of 32p from the filtrate in dark bottle (circles) and bottle containing the metabolic inhibitor iodoacetic acid, IAA (triangles). The bottles were incubated in the Rhode River at I m depth for 4 h Fig. 2. Appearance of 32p in particulates. Circles: 32p radioactivity on 5 and 0.45 ~m poresized filters in dark bottle; triangles: 32p radioactivity on 0.45 ~m pore-sized filter in IAA bottle in the Rhode River ( C o r r e l l et al., 1 9 7 5 ; Faust and Correll, 1976). The appearance of 32p i n s i z e f r a c t i o n s of p a r t i c u l a t e s is s h o w n in F i g . 2. In t h e I A A b o t t l e , t h e r e w a s n o P u p t a k e by either size fraction. The majority of dark-bottle uptake was by organisms passing the 5 ~m screen and retained on the 0.45 ~m membrane. Disappearance of 3 2 p f r o m t h e w a t e r appeared to follow a pseudo first-order reaction. I n F i g . I, it c a n b e s e e n t h a t 44 E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake Table 2. Estimates of population numbers and biomass of phytoplankton species from Rhode River station at i m depth on October 31, 1974 Species Size (~m) Volume (~m 3) Peridineum trochoideum 25 x 28 10300 4.9 O.O5[ 2.5 Gymnodinium sp. 2 25 x 18 5890 [40.0 0.825 41.8 Gymnodinium gracilentum 20 x iO 2090 72.3 O.151 7.6 Gymnodinium sp. 1 15 x 11 1300 68.3 0.0~9 4.5 Gyrodinium mundulum 15 x iO 1180 22.3 0.026 1.3 Gymnodinium galesianum ~5 x 15 i170 a 42.7 0.050 2.5 Gymnodinium subroseum 11 x 8 546 33.4 O.018 0.9 Flagellate IO x IO 523 50.0 0.050 2.5 Euglena ascus 20 x 392 117 0.046 2.3 19oa ],300 0.247 12.5 34 12,400 0.422 21.4 14,3OO 1.98 5 Katodinium rotundatum 10-15 x 3-10 Nannoplankton <5 Total avalues from Campbell Cells 1-I (x iO3) Biomass (mm 3 1-1) % total biomass (1973). t h e log 32p in s o l u t i o n d e c r e a s e s linearly f o r a p p r o x i m a t e l y t h e f i r s t 2 h. It t h e n l e v e l s off t o an e q u i l i b r i u m value w h e n 32p r e l e a s e i n t o t h e w a t e r b y planktonic organisms has begun. As in a n y f i r s t - o r d e r reaction, the appearance of t h e " p r o d u c t " (i.e., 32p in p a r t i c u l a t e s ) is a c u r v e d line. A l t h o u g h t h e r a t e of p h o s p h a t e u p t a k e is c o n s t a n t , t h e r a t e of a p p e a r a n c e of 32p in p a r t i c u l a t e s decreases as t h e s p e c i f ic a c t i v i t y of o r t h o p h o s p h a t e decreases. T h e f i r s t p o r t i o n of t h e c u r v e is f i t t e d to a s t r a i g h t line. The total P uptake rate calculated from the disappearance of 3 2 P 0 4 f r o m sol u t i o n is 1.07 bg P 1 -I h-1. U p t a k e rates calculated f r o m t h e r a t e of 32p appearance in p a r t i c u l a t e s on t h e 5 a n d 0 . 4 5 Lum f i l t e r s a r e 2% (0.024 u g p 1-I h -I) a n d 98% (1.O6 ~ g P 1 -I h - l ) , r e s p e c t i v e ly, of t h e t o t a l P u p t a k e rate. Phytoplankton Population The phytoplankton in t h e R h o d e R i v e r o n t h e d a y of t h e e x p e r i m e n t s w a s n o t as a b u n d a n t as d u r i n g t h e w a r m e r m o n t h s of the year, but the species composition w a s q u i t e d i v e r s e . T e n m a j o r s p e c i e s of a l g a e w e r e o b s e r v e d , of w h i c h m o s t w e r e dinoflagellates. Phytoplankton populat i o n n u m b e r s a n d b i o m a s s are g i v e n in T a b l e 2. O n l y o n e s p e c i e s , Katodinium rotundatum, n u m b e r e d o v e r o n e m i l l i o n c e l l s p e r liter. T h e n a n n o p l a n k t o n , which was c o m p o s e d of m a n y s m a l l f l a g e l l a t e s , chrysophytes, and green algae, was most abundant. Small diatoms were quite numerous, b u t m o s t of t h e c e l l s a p p e a r e d t o be senescent. It c a n b e s e e n f r o m T a b l e 2 t h a t Gymnodinium s p e c i e s 2, K. rotundatum, and the n a n n o p l a n k t o n m a d e up t h e l a r g e s t p o r t i o n s of t h e a l g a l b i o m a s s : 41.8, 21.4, a n d 12.5%, r e s p e c t i v e l y . 33p Autoradiography Fig. 3 s h o w s the a p p e a r a n c e of 33p in fixed, a c i d - w a s h e d cells (concentrated f r o m I i of w a t e r b y c e n t r i f u g a t i o n and l a t e r u s e d for a u t o r a d i o g r a p h y ) with time. T h e r a t e of p h o s p h o r u s incorporation into acid-insoluble c o m p o u n d s inside plankton cells (including bacteria) was calculated f r o m Fig. 3 as 0 . 7 6 8 ~g P I-I h - l , w h i c h is a p p r o x i m a t e l y 75% of t h e t o t a l u p t a k e r a t e o b t a i n e d in t h e 32p u p t a k e e x p e r i m e n t . We observed that autoradiograms of the Rhode River samples contained a g r e a t e r n u m b e r of b a c k g r o u n d grains than E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake 45 w a s f o u n d in p l a n k t o n p r e p a r a t i o n s by B r o c k a n d B r o c k (1968) 9 T h i s p r o b l e m w a s a t t r i b u t e d to t h e l a r g e n u m b e r of b a c t e r i a p r e s e n t in e s t u a r i n e w a t e r s 9 A u t o 4 radiograms of p l a n k t o n at t h e f i r s t t i m e 9 points were relatively f r e e of b a c k g r o u n d c o u n t s , b u t t h e n u m b e r of b a c k g r o u n d I ~9 9 f grains increased steadily with time during the f i r s t 2 h; t h e n u m b e r t h e n re:3 m a i n e d c o n s t a n t d u r i n g t h e r e m a i n d e r of the experiment. Therefore, it w a s n e c e s O s a r y to s u b t r a c t b a c k g r o u n d g r a i n s at K each time-point as d e s c r i b e d in " M a t e r i als a n d M e t h o d s " 2 Fig 4 illustrates t h e i n c r e a s e in t h e m e a n n u m b e r of g r a i n s p e r c e l l w i t h O t i m e for o n e d i n 9 species. Generally, the s t a n d a r d d e v i a t i o n of g r a i n c o u n t s for a s p e c i e s at o n e t i m e p o i n t w a s w i t h i n ~ 30% of the m e a n . T h e i n c r e a s e in g r a i n s w a s r a p i d at f i r s t and then leveled off when the specific a c t i v i t y of the o r t h o p h o s p h a t e p o o l in the water had decreased 9 Similar curves w e r e o b t a i n e d for a l l 10 s p e c i e s of p h y 0 ( toplankton. All curves had shapes simiI I I I I I lar to t h e o n e s h o w n , w i t h t h e a b s o l u t e 6 0 120 180 2 4 0 3 0 0 3 6 0 0 n u m b e r of g r a i n s a n d t h e s l o p e d i f f e r i n g for each species. TIME (MIN) R a t e s of p h o s p h o r u s u p t a k e for all phytoplankton s p e c i e s w e r e c o m p u t e d , as Fig. 3. Autoradiography experiment. Appearance described in t h e " M a t e r i a l s a n d M e t h o d s " of 33p in acid-washed plankton cells and partis e c t i o n , f r o m t h e i n c r e a s e in g r a i n culates with time. Rhode River water was inc o u n t s p e r c e l l o v e r time. T h e s e u p t a k e cubated with 33p in 12 1 bottle in the light at rates are presented in T a b l e 3, w i t h i m depth. Each I 1 subsample was fixed, centriseveral parameters of c e l l d i m e n s i o n s 9 fuged, and washed with dilute HCI. Solid line U p t a k e r a t e p e r c e l l is l a r g e s t for represents a least-squares regression equation l a r g e c e l l s ; h o w e v e r , it is o b v i o u s f r o m giving best fit of first 7 data points; broken t h e d a t a in t h e f i f t h c o l u m n of T a b l e 3 line is arbitrarily drawn that the phosphorus uptake rate per ~m 3 c e l l v o l u m e is h i g h e s t for s m a l l e r c e l l s . The relationship between size and uptake r a t e is i l l u s t r a t e d m o r e c l e a r l y in Fig. 5. A p l o t of log P u p t a k e p e r c e l l m a s s a g a i n s t log s u r f a c e : v o l u m e ratio ~150 o _ _ @ / for t h e v a r i o u s p h y t o p l a n k t o n s p e c i e s is / / linear. The line represents the b e s t f i t / / (r 2 = 0.93) of t h e l i n e a r r e g r e s s i o n (D equation, log Y = (-10 7) + (I 7 log x) ~I00 w h e r e Y is u p t a k e in u g P p e r ~un3 c e l l v o l u m e p e r h o u r for a s p e c i e s a n d x is z the s u r f a c e : v o l u m e ratio 9 Taking the ~ 50 antilogarithm, the equation becomes Y = (2 x 10-11) x 1.7, a n d w e c a n see t h a t P u p t a k e of t h e s e a l g a l c e l l s is a p o w e r 0 f u n c t i o n of t h e i r s u r f a c e : v o l u m e ratio 9 I I I I t I To t e s t w h e t h e r t h e o b s e r v e d r e l a t i o n 0 60 120 180 240 500 560 ship between uptake and surface:volume TIME (MIN) r a t i o is t r u e f o r o t h e r R h o d e R i v e r p h y toplankton populations rather than just Fig. 4. Gymnodinium species i. Mean number of for the one, w e a n a l y z e d t h e 33p a u t o grains per cell with time. Whole water samples radiography d a t a of J u l y 9, 1973 f r o m containing this species were incubated with C o r r e l l et al. (1975) in t h e s a m e w a y . 33PO4 in the Rhode River at i m depth for 6 h. Their data shows a similar correlation Solid line gives best-fit linear regression of b e t w e e n g r a i n d e n s i t y p e r bm3 c e l l v o l first 5 data points; broken line is arbitrarily ume p e r h o u r a n d s u r f a c e : v o l u m e ratio drawn 9 _ _ Table 3. Surface areas, surface:volume ratios, and phosphorus uptake rates for Rhode River phytoplankton species, October 31, ~974. Uptake rates were computed from grain counts of autoradiograms. For phytoplankton cell counts and biomass estimates, see Table 2 Species Surface area (~m2 cell-l) Surface: volume ratio uptake rate Uptake rate Uptake rate (~g P cell -I (~g P ~m -3 (~g P 1-I h-i x 10-9) h-i x 10-12 ) h-i x 10 -3 ) 1927 O. 188 1 i. 84 1 . 15 0.058 O. 15 981 O. 167 7.74 i .31 1.084 2.84 Gymnodinium gracilentum 739 O. 353 8.52 4.O7 0.616 1.62 Gymnodinium sp. i 490 O. 378 3.63 2 .80 O.248 0.65 Gyrodinium mundulum 464 O. 394 2.60 2.21 0.058 O. 15 Gymnodinium galesianum 707 0.604 6.28 5 .37 0.268 0.69 Gymnodinium subroseum 261 O.512 4.43 8.76 0.148 0.38 Flagellate 314 0.600 3.48 6.65 O. 174 O. 45 Euglena ascus 314 O. 801 5.92 15.1 0.692 I .81 Katodinium rotundatum 266 1 .400 5.02 26.4 6.539 17.14 50 i .480 2.30 67.7 Peri dineum trochoi deum Gymnodinium sp. 2 Nannoplankton 28.52 % Total phytoplankton uptake rate per liter 74.75 38.41 = 0.038 ~ g P l - l h -I Total uptake rate (uptake rates were not available). The regression equation is Y = O . 1 7 x 2 . 4 (r 2 = 0 . 9 9 ) . T h e c o n v e r s i o n from grains -i0 t o u p t a k e in ~ g P i n v o l v e s several constants which account for the difference between the coefficients of x i n t h e jequations for the 1973 and 1974 data. However, the similarity between expoICJ n e n t s of x (1.7 f o r o u r d a t a , a n d 2 . 4 E f o r t h e 1 9 7 3 d a t a ) is i n t e r e s t i n g . O. T h e d a t a in t h e s i x t h a n d s e v e n t h c o l umns in Table 3 shows that nannoplankton were responsible for the largest part of ,.-Ii the phosphorus uptake by the phytoplankU.I t o n i n t h e R h o d e R i v e r at t h i s t i m e of year. Other species which showed signifiI-9 Q. c a n t P u p t a k e a r e Katodinium rotundatum, Gymnodinium graciientum, Gymnodinium s p e c i e s 2, Q. a n d Euglena ascus. T h e s e s p e c i e s , w h i c h comprise the largest portions of t h e p h y L9 toplankton b i o m a s s b e c a u s e of e i t h e r 0 ..I l a r g e n u m b e r s of c e l l s o r l a r g e c e l l size, are also responsible for the greate s t p a r t of t h e t o t a l p h o s p h o r u s uptake -t2 per liter. However, no clear-cut relationship between the total biomass and I J I I I I I I I I the rate of phosphate uptake by each spe0 +Q3 - 1.0 - 0.5 c i e s is i n d i c a t e d . With the correlation in F i g . 5 in LOG (SURF/VOL) m i n d , an e x a m i n a t i o n of t h e r e l a t i o n s h i p between total cell surface area for a Fig. 5. Relationship between phosphorus uptake per ~m 3 cell volume per hour for various phytos p e c i e s a n d i t s P u p t a k e p e r l i t e r is plankton species and their surface:volume ratios, m o r e e n l i g h t e n i n g . Nannoplankton a n d KatoLine drawn is linear regression of data: log Y = dinium rotundatum h a d t h e h i g h e s t s u r f a c e : (-1o.7) + 1.7 log x (r2 = 0.93) volume ratios ( 1 . 4 8 a n d 1.4) a n d h i g h e s t % E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake cell n u m b e r s ; these o r g a n i s m s w e r e res p o n s i b l e for 75 and 17% r e s p e c t i v e l y , of the t o t a l p h y t o p l a n k t o n P uptake rate. In contrast, species w i t h low surface: volume ratios, such as Gyrodinium mundulum (0.394) and Peridineumtrochoideum (O.188) and r e l a t i v e l y low cell numbers, had P u p t a k e rates w h i c h w e r e O.15% of the total. Thus, we found that in the w a t e r column, the P u p t a k e rate by a species is c o r r e l a t e d w i t h its t o t a l s u r f a c e area. The e q u a t i o n Y = (-1.4 x 10-3) + (4.15 x 10-5 x), w h e r e x = s u r f a c e area in m m -2 1-I for a species and Y P uptake in ~g P 1-I h-1 for that species, is the linear r e g r e s s i o n of the data, w i t h r 2 = 0.90. The sum of i n d i v i d u a l p h y t o p l a n k t o n P uptake rates as given in T a b l e 3 is 0.038 ~g P 1-I h-1. The rates were calc u l a t e d a s s u m i n g that a c i d - s o l u b l e P was 17% of t o t a l cell P. If the a c i d - s o l u b l e P f r a c t i o n w e r e a s s u m e d to be 50% as it is in some diatoms, the t o t a l u p t a k e rate w o u l d be 0.063 ~g P 1-I h-1. The sum of the rates of i n d i v i d u a l species o b t a i n e d from a u t o r a d i o g r a p h y is in v e r y good a g r e e m e n t w i t h the rate of 0 . 0 2 4 ~g P 1 -I h -I for p l a n k t o n cells "larger than 5 %~m" o b t a i n e d in the 32p u p t a k e e x p e r i ments. 47 f r a c t i o n a t i o n by this m e t h o d is not perfect by any means, however. S h e l d o n and S u t c l i f f e (1969) have s t u d i e d the accuracy of size s e p a r a t i o n of p l a s t i c particles w i t h d i f f e r e n t types and pore sizes of filters. Their r e s u l t s show that m a n y p a r t i c l e s w i t h a d i a m e t e r less than the s t a t e d p o r e size of the f i l t e r are r e t a i n e d due to c l o g g i n g of pores and o b s t r u c t i o n of p a r t i c l e p a t h t h r o u g h the filters. The type of f i l t e r used, as w e l l as its pore size, d e t e r m i n e d the q u a l i t y of s e p a r a t i o n obtained; s c r e e n s rather than m e m b r a n e filters g a v e the best separation. In our e x p e r i m e n t , particles s m a l l e r than 5 ~m (including the n a n n o p l a n k t o n ) w e r e p r o b a b l y r e t a i n e d by the 5 ~m screen. B a c t e r i a are n o t o r i o u s for a t t a c h i n g to surfaces, i n c l u d i n g s u s p e n d e d s e d i m e n t s and other p l a n k t o n cells. This p h e n o m e n o n m i g h t lead to o v e r e s t i m a t i o n of p h o s p h a t e u p t a k e by p l a n k t o n "larger than 5 H/n" in size. A n d e r s o n (1965) r e p o r t e d e x p e r i m e n t s w i t h size f r a c t i o n a t i o n of p l a n k t o n off the O r e g o n Coast. He found that large f r a c t i o n s of p h y t o p l a n k t o n p a s s e d t h r o u g h a 5 Lum filter, w h i l e v e r y little p a s s e d t h r o u g h a 0.8 ~m filter. B e r m a n (1975), w o r k i n g in the Gulf of C a l i f o r n i a , found 13 to 83% of total carbon f i x a t i o n of n a t u r a l p h y t o p l a n k t o n p o p u l a t i o n s was a s s o c i a t e d w i t h o r g a n i s m s p a s s i n g a 3 ~m Discussionand ~nclusions N u c l e p o r e filter. The r e s u l t s of these size f r a c t i o n a t i o n e x p e r i m e n t s depend, The e x p e r i m e n t s p r e s e n t e d here w e r e deof course, upon the size d i s t r i b u t i o n of s i g n e d to m e a s u r e the p h o s p h o r u s u p t a k e natural phytoplankton populations. While of a n a t u r a l e s t u a r i n e p h y t o p l a n k t o n com- these two s t u d i e s w e r e c a r r i e d out in m u n i t y u n d e r n a t u r a l c o n d i t i o n s . E n v i r o n - open m a r i n e waters, size f r a c t i o n a t i o n m e n t a l v a r i a b l e s in t h e s e e x p e r i m e n t s e x p e r i m e n t s w i t h p l a n k t o n from a s h a l l o w such as solar r a d i a t i o n , w a t e r t e m p e r a e a s t - c o a s t e s t u a r y showed m o s t a l g a l ture, salinity, and n u t r i e n t levels, cells to be r e t a i n e d by a 5 ~m N i t e x w e r e t h o s e o c c u r r i n g n a t u r a l l y in the screen (Faust and Correll, 1976). Also, Rhode River. T h e r e f o r e , the n u t r i e n t upa u t o r a d i o g r a m s of the f i l t r a t e of our take rates o b s e r v e d in this study are cell s u s p e n s i o n s f i l t e r e d via g r a v i t y likely to be t h o s e w h i c h occur w h e n a t h r o u g h an 8 ~m N u c l e p o r e f i l t e r cond i v e r s e g r o u p of a l g a e is p r e s e n t and ex- t a i n e d few p h y t o p l a n k t o n cells. A l t h o u g h cess n u t r i e n t s are not available. m i c r o s c o p i c e x a m i n a t i o n of the f i l t e r s The rate of t r a n s f e r of p h o s p h o r u s was not m a d e in this study, it is asfrom the d i s s o l v e d o r t h o p h o s p h a t e pool sumed that the m a j o r i t y of p h y t o p l a n k t o n into p l a n k t o n o r g a n i s m s was m e a s u r e d by was r e t a i n e d by the 5 ~m screen as shown (I) t r a c i n g the m o v e m e n t of 32p04 into by p r e v i o u s studies in the same e s t u a r y size f r a c t i o n s of p a r t i c u l a t e s , and (2) (Faust and Correll, 1976). by f o l l o w i n g the m o v e m e n t of 33po 4 into A l t h o u g h t h e r e are no r e s u l t s f r o m i n d i v i d u a l s p e c i e s of p h y t o p l a n k t o n . the light bottle, we h a v e f o u n d that toUsing the first method, the total phostal P u p t a k e and u p t a k e by d i f f e r e n t parp h o r u s u p t a k e rate of the p l a n k t o n was t i c u l a t e sizes g e n e r a l l y do not vary sigd e t e r m i n e d to be a p p r o x i m a t e l y I ~g P n i f i c a n t l y b e t w e e n light and dark bot1-I h-1. A c o n t r o l e x p e r i m e n t w i t h biotles in 32p t r a c e r e x p e r i m e n t s on the logical i n h i b i t o r s h o w e d very little adRhode River (Correll et al., 1975; F a u s t s o r p t i o n of the r a d i o a c t i v e t r a c e r to and Correll, 1976). T a f t et al. (1975) n o n - l i v i n g p a r t i c l e s . P l a n k t o n cells realso o b t a i n e d i d e n t i c a l r e s u l t s w i t h t a i n e d on the 5 ~m screen w e r e r e s p o n s i light and dark b o t t l e s in 32p t r a c e r exble for about 2% of the u p t a k e (0.024 ~g p e r i m e n t s w i t h p l a n k t o n of C h e s a p e a k e P 1-I h-l), w h i l e those p a s s i n g the 5 ~um Bay. Thus, it a p p e a r s that the o b s e r v e d screen d i s p l a y e d 98% of the uptake. Size P u p t a k e does not r e q u i r e light and is = 48 E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake not d i r e c t l y d r i v e n by p h o t o s y n t h e s i s ~ this u p t a k e also is not i n h i b i t e d n o t i c e ably by light. The m a j o r i t y of u p t a k e is by small o r g a n i s m s w h i c h i n c l u d e few algae; light or the a b s e n c e of light has l i t t l e effect u p o n t h e i r P uptake. T h e r e f o r e , m o s t of the p h o s p h a t e u p t a k e m u s t be att r i b u t e d to b a c t e r i a . M a n y l a b o r a t o r y s t u d i e s have e s t a b l i s h e d the r a p i d uptake of i n o r g a n i c p h o s p h e r u s by b a c t e r i a (Rigler, 1956; Harris, 1957; J o h a n n e s , 1964; Rhee, 1972; B e u c h l e r and Dillon, 1974). We h a v e less k n o w l e d g e of this p r o c e s s o c c u r r i n g in nature. R i g l e r ' s exp e r i m e n t s (1956) w i t h lake p l a n k t o n ind i c a t e d a h i g h p h o s p h a t e u p t a k e by b a c teria. Taft (1974) and T a f t et el. (1975) argue that b a c t e r i a are not i m p o r t a n t c o n s u m e r s of i n o r g a n i c p h o s p h a t e in est u a r i n e waters. T h e y n o t e that p a r t i c u lates a b s o r b i n g p h o s p h a t e in their studies had N and P to c h l o r o p h y l l a r a t i o s w h i c h are close to t h o s e of m o s t a l g a l cells. In c o n t r a s t , F a u s t and C o r r e l l (1976) h a v e shown a h i g h c o r r e l a t i o n bet w e e n p h o s p h a t e u p t a k e rates by p a r t i c u lates s m a l l e r than 5 Lun and b a c t e r i a l b i o m a s s in e s t u a r i n e w a t e r s at v a r i o u s times of the year. The s e c o n d c o n s i d e r a t i o n was the effect of cell size and s h a p e upon g r a i n density. For a p o i n t source of r a d i o a c tivity l o c a t e d at the c e n t e r of a disc, the n u m b e r of g r a i n s r e s u l t i n g f r o m the e m i t t e d ~ p a r t i c l e w h i c h are c o u n t e d over a large disc w i l l be h i g h e r than those c o u n t e d over a small disc. H o w e v e r , this e f f e c t is g r e a t l y r e d u c e d by counting grains at the m a r g i n s and s e v e r a l m i c r o m e t e r s beyond. The data p r e s e n t e d by K n o e c h e l and K a l f f (1976) shows that the g r a i n c o u n t i n g e f f i c i e n c y over a cell 10 Lum in d i a m e t e r , w h e n c o u n t i n g is e x t e n d e d 5 Lum b e y o n d cell m a r g i n s , is 75%. Thus, since g r a i n c o u n t i n g was ext e n d e d that far in this study, the effic i e n c y was r e d u c e d v e r y little. Also, since our cells w e r e w i t h i n a n a r r o w size range, any r e d u c t i o n in e f f i c i e n c y w o u l d be n e a r l y c o n s t a n t for all the cells. The a u t h o r s also note that selfa b s o r p t i o n of r a d i a t i o n by the cells m a y cause error. However, s e l f - a b s o r p t i o n is g r e a t e r in large cells; since m o s t of our cells w e r e less than 20 Lum in diameter, this e f f e c t w o u l d r e d u c e a c t u a l g r a i n counts by 15% at most, a c c o r d i n g to e s t i m a t e s by K n o e c h e l and K a l f f (1976). For the s m a l l e s t cells, s e l f - a b s o r p t i o n w o u l d r e s u l t in a r e d u c t i o n in g r a i n Only 2% of the p h o s p h a t e u p t a k e was counts of only a few percent. by o r g a n i s m s r e t a i n e d on the 5 %um screen, F i n a l l y , error is i n t r o d u c e d in estip r e s u m a b l y algae. A l t h o u g h the algal abm a t i n g the g r a i n y i e l d of a r a d i o a c t i v e s o r p t i o n rate seems a r e m a r k a b l y small i s o t o p e on a p a r t i c u l a r e m u l s i o n or film. part of the t o t a l uptake, it is conIdeally, an i n t e r n a l s t a n d a r d i z a t i o n bef i r m e d by the sum of i n d i v i d u a l s p e c i e s t w e e n g r a i n s and d i s i n t e g r a t i o n s h o u l d rates o b t a i n e d f r o m a u t o r a d i o g r a p h y . The be m a d e using cells w i t h a k n o w n radiop h y t o p l a n k t o n r a t e f r o m the f i l t r a t i o n activity. As s t a t e d before, no a t t e m p t t e c h n i q u e is 0.024 ~g P 1-I h-l, as comat this was m a d e in this study. However, p a r e d w i t h 0 . 0 3 8 to 0 . 0 6 3 ~g P 1-I h-1 the c o m p a r i s o n b e t w e e n algal species is from a u t o r a d i o g r a p h y , d e p e n d i n g u p o n the not a f f e c t e d by any e r r o r in the g r a i n v a l u e u s e d for the a c i d - s o l u b l e P conyield, as it is m e r e l y a c o n s t a n t used tent of the p h y t o p l a n k t o n cells. in c a l c u l a t i o n of all u p t a k e rates. The The t e c h n i q u e of a u t o r a d i o g r a p h y was sum of i n d i v i d u a l p h o s p h a t e u p t a k e rates, u s e d to c o m p a r e the p h o s p h o r u s u p t a k e i.e., the total p h y t o p l a n k t o n u p t a k e rates of i n d i v i d u a l s p e c i e s of p h y t o rate, m i g h t r e f l e c t an error in the p l a n k t o n . K n o e c h e l and K a l f f (1976) h a v e g r a i n yield, but the g r a i n y i e l d used c r i t i c a l l y r e v i e w e d the use of g r a i n (1.8) w o u l d have to be u n d e r e s t i m a t e d by d e n s i t y a u t o r a d i o g r a p h y for c o m p a r i s o n an o r d e r of m a g n i t u d e b e f o r e a s i g n i f i of m e t a b o l i c a c t i v i t y in p l a n k t o n specant d i f f e r e n c e in the total p h y t o p l a n k cies. T h e y s u b m i t that errors r e s u l t ton u p t a k e rate w o u l d be observed. The from s e v e r a l sources: (I) i n a d e q u a t e s o u r c e s of error w h i c h K n o e c h e l and cell p r e p a r a t i o n ; (2) f a i l u r e to conK a l f f list are s i g n i f i c a n t only if autosider the e f f e c t of cell size and geomr a d i o g r a p h y is used for s t u d y i n g large etry on g r a i n d e n s i t y ; (3) i n a d e q u a t e p h y t o p l a n k t o n cells w i t h a high e n e r g y m e t h o d s of d e t e r m i n i n g g r a i n yield. isotope, or if one is c o m p a r i n g the results of s e v e r a l d i f f e r e n t a u t o r a d i o g In this study, the m e t h o d of cell r a p h y e x p e r i m e n t s in w h i c h there are difp r e p a r a t i o n was not d e t r i m e n t a l to the f e r e n c e s in t o t a l r a d i o a c t i v i t y . cells, as no a c e t o n e , h a r s h f i x a t i v e s , As n o t e d in the results, the autoheat, or h i g h c e n t r i f u g e speeds w e r e r a d i o g r a m s c o n t a i n e d a n u m b e r of backused. F i x a t i o n was complete: F r o t a r g o l g r o u n d g r a i n s w h i c h i n c r e a s e d w i t h time. s t a i n i n g of the g l u t e r a l d e h y d e - f i x e d A u t o r a d i o g r a m s of the f i l t r a t e o b t a i n e d cells s e v e r a l m o n t h s later s h o w e d e x c e l by f i l t e r i n g 3 3 p - l a b e l l e d cell s u s p e n lent f i x a t i o n and no d e t e r i o r a t i o n of sions t h r o u g h an 8 H/n p o r e - s i z e f i l t e r cell o r g a n e l l e s . E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake also c o n t a i n e d grains w i t h o u t any v i s i ble cells u n d e r them, and t h e s e g r a i n s also i n c r e a s e d w i t h time. A r e a s o n a b l e source for t h e s e g r a i n s is b a c t e r i a , w h i c h are not r e s o l v e d in a u t o r a d i o g r a m s at 1000 X m a g n i f i c a t i o n w i t h o u t staining, C e r t a i n l y , a d s o r p t i o n of 33p to sediments or i n c o m p l e t e d w a s h i n g of s o l u b l e 33p is r u l e d out b e c a u s e the n u m b e r of b a c k g r o u n d grains i n c r e a s e d w i t h time. Fuhs and C a n e l l i (1970) o b s e r v e d s i m i l a r c l u s t e r s of b a c k g r o u n d grains in 33p a u t o r a d i o g r a m s . They s u s p e c t e d that clumps of b a c t e r i a w e r e the cause, but they could not p r o v e that b a c t e r i a l cells w e r e present. F a u s t and C o r r e l l (1977) w e r e able to o b s e r v e g r a i n s over b a c t e r i a l cells in 33p a u t o r a d i o g r a m s by s t a i n i n g their cell p r e p a r a t i o n s . As exp l a i n e d in " M a t e r i a l s and M e t h o d s " , a c o r r e c t i o n for b a c k g r o u n d counts was m a d e for each a u t o r a d i o g r a m . However, no c o r r e c t i o n for the a d h e r i n g and c l u m p i n g of b a c t e r i a on p h y t o p l a n k t o n cells could be made. This could r e s u l t in o v e r e s t i m a tion of p h o s p h o r u s u p t a k e by p l a n k t o n cells. R e s u l t s from a u t o r a d i o g r a p h y show that u p t a k e of p h o s p h o r u s by the nannop l a n k t o n (algal cells less than 5 ~m in size) a c c o u n t s for a l m o s t 75% of the total u p t a k e by p h y t o p l a n k t o n . The importance of n a n n o p l a n k t o n in the t o t a l p r i m a r y p r o d u c t i o n of m a n y p l a n k t o n i c c o m m u n i t i e s has b e e n d i s c u s s e d in the "Int r o d u c t i o n " . Taft (1974) s h o w e d that there was no d i f f e r e n c e in i n o r g a n i c p h o s p h a t e u p t a k e rates of p l a n k t o n passing a 35 bm and a 10 V/n filter. He also c o n c l u d e d that s m a l l e r p l a n k t o n cells (which c o u l d i n c l u d e bacteria) w e r e res p o n s i b l e for the m a j o r i t y of the p h o s p h o r u s u p t a k e in C h e s a p e a k e Bay. The f r a c t i o n of the t o t a l rate of uptake by the n a n n o p l a n k t o n exceeds their c o n t r i b u t i o n to the t o t a l p h y t o p l a n k t o n biomass. W a t t (1971) found this to be true for n a n n o p l a n k t o n p r o d u c t i v i t y in 14C a u t o r a d i o g r a p h y e x p e r i m e n t s . E a r l i e r 33p a u t o r a d i o g r a p h y of Rhode River p l a n k ton was p e r f o r m e d d u r i n g a b l o o m of large d i n o f l a g e l l a t e s (Correll et al., 1975). A l t h o u g h the d i n o f l a g e l l a t e s m a d e up 90% of the p h y t o p l a n k t o n b i o m a s s , the rate of p h o s p h o r u s u p t a k e per <un3 of cell v o l u m e by the n a n n o p l a n k t o n was 300 to 500 times the rate of the d o m i n a n t larger p h y t o p l a n k t o n cells. Thus, the total p h o s p h a t e u p t a k e rate of the nannop l a n k t o n was still h i g h e r than that of the n u m e r o u s large d i n o f l a g e l l a t e s . Fuhs et al. (1972) o b s e r v e d the e f f e c t of cell s u r f a c e : v o l u m e ratio on n u t r i e n t u p t a k e and m a x i m u m g r o w t h rate. They found that m a x i m u m g r o w t h rates of two d i a t o m s p e c i e s o c c u r r e d at the same p h o s - 49 phate c o n c e n t r a t i o n b e c a u s e the lower a f f i n i t y for p h o s p h a t e (larger K s ) of the s m a l l e r s p e c i e s was o f f s e t by its g r e a t er s u r f a c e : v o l u m e ratio. Our r e s u l t s of the a u t o r a d i o g r a p h y e x p e r i m e n t i n d i c a t e that the algal p h o s p h o r u s u p t a k e r a t e per b i o m a s s unit is r o u g h l y a f u n c t i o n of the s q u a r e of cell s u r f a c e : v o l u m e ratio: u/v ~ K' (s/v) 2. We m a y ask why this s h o u l d be so. Is there a simple r e l a t i o n s h i p b e t w e e n cell d i m e n s i o n or g e o m e t r y and n u t r i e n t uptake rate u n d e r l y i n g these r e s u l t s ? Let us a s s u m e that the P u p t a k e rate per cell is linear w i t h cell radius for s p h e r i c a l cells. (There was no i n d i c a tion from our data that u p t a k e rate was a linear f u n c t i o n of cell s u r f a c e area.) U=Kr then for a sphere, Kr u/v = ~ / 3 ~ r 7 and, 4~r2 4/3zr-~ = 3/r S/V- r -- - 3 (s/v) - ! therefore, u/v = K = K ' (S/V) 2 T a k i n g an a v e r a g e radius for each cell in this study, we e x a m i n e d the ass u m p t i o n of l i n e a r i t y b e t w e e n r a d i u s and P u p t a k e per cell. L i n e a r r e g r e s s i o n of the data gave u = -0.7 + 0.8 r w i t h r 2 = O.76. The s c a t t e r in the d a t a is p r o b a bly due to the fact that m o s t of t h e s e cells are not true spheres. The r e l a t i o n ship b e t w e e n axial d i m e n s i o n and v o l u m e is, of course, m o r e c o m p l e x for dinof l a g e l l a t e s than for p e r f e c t spheres. The m o d e l of M u n k and Riley (1952) p r e d i c t s that the time r e q u i r e d for an algal cell to a b s o r b as m a n y grams of nut r i e n t as are a l r e a d y c o n t a i n e d i n c r e a s e s w i t h i n c r e a s i n g size. A c c o r d i n g to their c a l c u l a t i o n s , n u t r i e n t a b s o r p t i o n rate per unit mass is d o u b l e d to q u a d r u p l e d w h e n cell d i m e n s i o n is halved, d e p e n d i n g upon cell shape. This is r o u g h l y confirmed for s p h e r e s by our results. If 1 U/r ~K, and r/V = 4 / 3 ~ r ,then U/V a ~ K = K' -~ , and it is o b v i o u s that w h e n cell dimension is halved, n u t r i e n t u p t a k e per cell mass is q u a d r u p l e d . The h i g h rate of p h o s p h a t e u p t a k e by b a c t e r i a l o r g a n i s m s w o u l d be e x p e c t e d from the o b s e r v e d r e l a t i o n s h i p b e t w e e n u p t a k e and s u r f a c e : v o l u m e ratio. Fuhs et al. (1972) s h o w e d that b a c t e r i a h a v i n g 50 E.S. Friebele et al. : Phytoplankton Cell Size and Phosphorus Uptake lower a f f i n i t y for p h o s p h a t e than a l g a e (higher Ks and lower Vma x per unit surface area) w e r e able to o u t g r o w the algae b e c a u s e of t h e i r f a v o r a b l e surface: v o l u m e ratio. H o w e v e r , Lewis (1976) reports that b a c t e r i a l s : v r a t i o s can be e q u a l e d or e x c e e d e d by algae. U n f o r t u nately, no data on b a c t e r i a l n u m b e r s and s u r f a c e : v o l u m e r a t i o s w e r e o b t a i n e d in our e x p e r i m e n t s , and the c o r r e l a t i o n found for a l g a e c o u l d not be t e s t e d further. W i t h t h e s e r e s u l t s in mind, the "paradox of the p l a n k t o n " remains. Why, if n a n n o p l a n k t o n h a v e such a d i s t i n c t adv a n t a g e over large cells in a b s o r b i n g n u t r i e n t s , do larger p h y t o p l a n k t o n cel~s exist? One a n s w e r is that in some env i r o n m e n t s w h e r e all n u t r i t i o n a l res o u r c e s are p l e n t i f u l , a l g a l cells may not be c o m p e t i n g for n u t r i e n t s , but this c o n d i t i o n is not one that occurs cons t a n t l y in m a n y e n v i r o n m e n t s . Second, if p h y t o p l a n k t o n p o p u l a t i o n n u m b e r s are low, c o m p e t i t i o n for n u t r i e n t s m a y not occur, H u r l b u r t (1970) f o l l o w e d f l u c t u a t i o n s in a b u n d a n c e of m a r i n e p h y t o p l a n k t o n species and c a l c u l a t e d that the m a x i m u m n u t r i e n t - d e p l e t e d zones a r o u n d algal cells c o u l d not o v e r l a p at the cell densities found in the o p e n oceans; h o w e v e r , overlap, and thus c o m p e t i t i o n for n u t r i ents, o c c u r r e d at cell d e n s i t i e s a b o v e 3 x 108 cells 1-I, w h i c h are s o m e t i m e s f o u n d in e s t u a r i e s and c o a s t a l w a t e r s . He found that e s t u a r i n e p h y t o p l a n k t o n forms w e r e s i g n i f i c a n t l y smaller, w i t h less d i v e r s i t y and g r e a t e r numbers. A n o t h e r l o g i c a l a n s w e r to the q u e s tion p o s e d is that other f a c t o r s as w e l l as n u t r i e n t a b s o r p t i o n rate act as s e l e c tive forces on the shapes and sizes of p h y t o p l a n k t o n cells. Lewis (1976) s h o w e d that t h e r e is c o n s e r v a t i o n of s : v r a t i o s for the g r e a t e s t axial d i m e n s i o n of phyt o p l a n k t o n cells. C e r t a i n l y a lower limit of the s : v r a t i o is u n d e r s t a n d a b l e , but o b v i o u s l y some u n k n o w n s e l e c t i v e p r e s s u r e s are p r o d u c i n g an u p p e r limit on the s : v ratio, S e m i n a (1972) d e s c r i b e s some i n t e r e s t ing m u t u a l e f f e c t s of p h y s i c a l f a c t o r s on p h y t o p l a n k t o n cell size in the oceans, In general, she f o u n d i n c r e a s i n g cell size w i t h i n c r e a s i n g v e l o c i t y of a s c e n d ing w a t e r , and this e f f e c t was a m p l i f i e d by i n c r e a s i n g d e n s i t y g r a d i e n t in the p y c n o c l i n e and i n c r e a s i n g p h o s p h a t e conc e n t r a t i o n . M a l o n e (1971b) s u g g e s t s t h a t i n c r e a s e s in n e t p l a n k t o n s t a n d i n g crop in areas of u p w e l l i n g c o u l d r e s u l t f r o m the v e r t i c a l w a t e r m o v e m e n t as w e l l as from i n c r e a s e s in n i t r a t e c o n c e n t r a t i o n . Thus, c e r t a i n p h y s i c a l factors can select large cells h a v i n g low S : V ratios. P a r s o n ' s and T a k a h a s h i ' s m o d e l (1973) p r e d i c t s that small cells w i l l be dominant u n d e r m o s t light and n u t r i e n t regimes. H o w e v e r , the k i n e t i c c o n s t a n t s used in t h e i r m o d e l w e r e o b t a i n e d w i t h c u l t u r e s in the l a b o r a t o r y , and are dep e n d e n t upon m a n y factors, i n c l u d i n g env i r o n m e n t a l h i s t o r y and p h y s i o l o g i c a l state of the cells. A c c o r d i n g to observ a t i o n s of C a r p e n t e r and G u i l l a r d (1971), algal cells are a p p a r e n t l y able to a d a p t n u t r i e n t u p t a k e rates to a g e n e r a l range of n u t r i e n t c o n d i t i o n s e n c o u n t e r e d in their e n v i r o n m e n t . E x i s t i n g d a t a on the r e l a t i o n s h i p between p h y t o p l a n k t o n cell size and M i c h a e l i s - M e n t e n k i n e t i c c o n s t a n t s is c o n f u s i n g . E p p l e y et ai.(1969) note a t r e n d of d e c r e a s i n g K s for n i t r o g e n compounds w i t h d e c r e a s i n g cell size. M a l o n e ' s (1971b) o b s e r v a t i o n that nannop l a n k t o n p r o d u c t i o n i n c r e a s e s r a p i d l y at very low n i t r a t e c o n c e n t r a t i o n s , w h i l e netplankton productivity increases more r a p i d l y at n i t r a t e levels g r e a t e r t h a n 1.5 V/n, lends s u p p o r t to this h y p o t h e s i s . In contrast, Fuhs et al. (1972) found that the larger of two d i a t o m species had a lower Ks for p h o s p h a t e than the smaller. The r e s p o n s e of n a t u r a l p h y t o p l a n k t o n p o p u l a t i o n s to n u t r i e n t levels also a p p e a r s to be ambiguous. M a c I s a a c and D u g d a l e (1969) s h o w e d that the uptake of n i t r o g e n c o m p o u n d s by n a t u r a l p h y t o p l a n k t o n p o p u l a t i o n s is d e p e n d e n t upon n u t r i e n t c o n c e n t r a t i o n at the lower c o n c e n t r a t i o n s , but that m a x i m u m u p t a k e v e l o c i t y is r e p r e s s e d at h i g h e r c o n c e n t r a t i o n s by o t h e r l i m i t i n g factors. Taft et al. (1975) o b s e r v e d t y p i c a l M i c h a e l i s M e n t e n k i n e t i c s of p h o s p h a t e u p t a k e by n a t u r a l p h y t o p l a n k t o n of C h e s a p e a k e Bay. H o w e v e r , in their l o n g - t e r m study, rate c o n s t a n t s for p h o s p h a t e u p t a k e by natural p h y t o p l a n k t o n p o p u l a t i o n s f l u c t u a t e d r a n d o m l y t h r o u g h o u t the year, r e g a r d l e s s of p h o s p h a t e c o n c e n t r a t i o n ; the only pattern o b s e r v e d was an i n v e r s e r e l a t i o n ship b e t w e e n s o l u b l e r e a c t i v e p h o s p h o r u s c o n c e n t r a t i o n and p h o s p h o r u s u p t a k e rate c o n s t a n t s in the w i n t e r months. The r e l a t i o n s h i p b e t w e e n Ks for diss o l v e d n u t r i e n t s and cell size is thus c o m p l e x and at this p o i n t unclear. Our r e s u l t s do not r e s o l v e this problem, but they do show that s m a l l cells u n d e r natural c o n d i t i o n s and at low n u t r i e n t levels do h a v e m u c h f a s t e r P u p t a k e rates per cell m a s s than larger cells. It w o u l d be i n t e r e s t i n g to use a u t o r a d i o g r a p h y to o b s e r v e the n u t r i e n t u p t a k e of i n d i v i d u a l s p e c i e s at d i f f e r e n t (naturally occurring) n u t r i e n t levels; h o w e v e r , we w o u l d e x p e c t the r e l a t i o n s h i p b e t w e e n u p t a k e rate and n u t r i e n t c o n c e n t r a t i o n to be c o m p l i c a t e d by other factors, such E.S. Friebele et al.: Phytoplankton Cell Size and Phosphorus Uptake as p h y s i o l o g i c a l s t a t e of t h e p h y t o p l a n k ton and limiting factors repressing maximum nutrient uptake. F i n a l l y , G a v i s (1976) r e c a s t t h e M u n k a n d R i l e y m o d e l in t h e l i g h t of r e c e n t knowledge of algal nutrient uptake kinetics a n d t h e e f f e c t of n u t r i e n t d i f f u s i o n limited transport (Pasciak and Gavis, 1 9 7 4 ) . In h i s m a t h e m a t i c a l m o d e l , t h e d i m e n s i o n l e s s p a r a m e t e r P ( w h i c h inc l u d e s V m a x a n d K s) i n c r e a s e s w i t h d e c r e a s i n g c e l l size; as a r e s u l t , t h e inf l u e n c e of d i f f u s i o n t r a n s p o r t l i m i t a t i o n is d i m i n i s h e d . H e s u g g e s t s t h a t t h i s is w h y o c e a n i c r e g i o n s w i t h l o w n u trient levels contain cells which are s m a l l in s i z e a n d h a v e l o w K s v a l u e s . A l t h o u g h t h e e u p h o t i c z o n e is a s o m e what homogenous environment, we can see from the literature that regional differe n c e s in l i g h t , d e n s i t y g r a d i e n t s , v e r tical currents, and nutrient levels do exist. However, each local environment u s u a l l y s u p p o r t s a d i v e r s e g r o u p of p h y toplankton cell shapes and sizes. From o u r r e s u l t s , t h e r e l a t i v e n u t r i e n t abs o r p t i o n r a t e s of t h e c e l l s m u s t c o n v e y a competitive advantage on smaller cells, but other selective forces must also be at w o r k to b a l a n c e t h i s m e t a b o l i c a d v a n t a g e of s m a l l c e l l s . C e r t a i n l y z o o plankton grazing, which was not discussed, must play a large role. More research with natural phytoplankton populat i o n s in c o m p l e t e l y n a t u r a l c o n d i t i o n s is n e e d e d in o r d e r to d e t e r m i n e t h e f a c tors most strongly influencing the types of p h y t o p l a n k t o n w h i c h s u c c e s s f u l l y coexist. Acknowledgements. This paper includes part of an MA thesis submitted to the Johns Hopkins University by E. Friebele. We would like to thank Dr. J.F. Ferguson for his careful reading of that manuscript and his comments. We are also grateful to Mr. G. Chirlin for his helpful thoughts on the results. Mr. R.L. 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