Largemouth bass, Micropterus salmoides, growth and reproduction in Primera de Palos’ lake (Huelva, Spain)

436 Folia Zool. – 58(4): 436–446 (2009) La gemou h bass, Mic op e us salmoides, g ow h and ep oduc ion in P ime a de Palos’ lake (Huel a, Spain) Vic o ia RODRIGUEZ-SÁNCHEZ*, Lou des ENCINA, Amado a RODRÍGUEZ-RUIZ and Ramona SÁNCHEZ-CARMONA Depa men o Plan Biology and Ecology, Facul y o Biology, Uni e si y o Se ille, Apdo. 1095, 41080 Se ille, Spain; e-mail: [email p o ec ed] Recei ed 8 Oc obe 2007; Accep ed 14 Ap il 2009 Abs ac . Some aspec s o he biology o Mic op e us salmoides such as g ow h, popula ion s uc u e and ep oduc ion, we e s udied in he P ime a de Palos’ lake. A o al o 200 specimens we e cap u ed (98 emales, 86 males and 16 ju eniles) and dis ibu ed in o se en di e en age-classes ( om 0+ o 6+). Specimens 6+ we e exclusi ely emales. The mean alues o male leng h and weigh we e sligh ly highe han emales ones bu he di e ences we e no signi ican be ween sexes. The pa ame e s o he on Be alan y g ow h’s cu e we e L∞=503.6 mm, k=0.19, 0=-1.04 o males and L∞=512.6, k=0.18, 0=-1.05 o emales. The inal alues o he Gompe z g ow h’s cu e o weigh we e: W0=36.35, G=10.61, g=0.06 o males and W0=31.81, G=6.93, g=0.11 o emales. Rep oduc ion ook place in sp ing. Females ma u e olde han males, in age-class 2+. The esul s clea ly indica e ha he la gemou h bass popula ion has acclima ised well o he P ime a de Palos’ lake, ha ing ound en i onmen al and ophic condi ions ha a e a ou able o i s de elopmen . Key wo ds: biology, black-bass, exo ic ish In oduc ion The la gemou h bass (Mic op e us salmoides) is a na i e ish species in No h Ame ica, whe e i inhabi s bo h i e s and s ill wa e s (W h e e l e & A l l e n 2003). La gemou h bass is conside ed he main pisci o ous ish o No h Ame ican eshwa e and one o he mos impo an eshwa e game ish (H e i d i n g e 1975, C a l a n d e 1977, D o a d i o 2001, Wa e s e al. 2005). I has been in oduced in o many coun ies wo ldwide (G a c í a -B e h o u 2002). The la gemou h bass was i s b ough in he Ibe ian Peninsula o ishing pu poses in 1955 (E l i a 1995, G o d i n h o & F e e i a 1996, C o p p e al. 2004). The cu en dis ibu ion in Spain includes mos o he la ge i e basins (D o a d i o e al. 1991, N i c o l a e al. 1996) and i is conside ed as a se ious h ea o na i e Spanish ish (E l i a 1995). P ime a de Palos is a eshwa e small lake o app oxima ely 16 ha, loca ed in he sou h wes o Spain. The small lake is p edominan ly be ween 2 and 2.5 m deep and i s wa e le el su e conside able luc ua ions. Wa e empe a u es anges a e om 15 o 25ºC. The lake has ecen ly been en i onmen ally es o ed and is included in he ne wo k o p o ec ed a eas o Andalusia as a “Na u al Place” (Pa aje Na u al). The main objec i e o he p esen s udy is o esea ch some aspec s o la gemou h bass biology in he P ime a de Palos’ lake, such as i s g ow h, popula ion s uc u e and ep oduc ion. Ma e ial and Me hods The samples we e collec ed mon hly om Sep embe 2002 o Augus 2003. Fishes we e collec ed by boa o om P ime a de Palos’ lake sho es, using a ishing od wi h di e en * Co esponding au ho 437 sizes o a i icial lu es. Cap u ed specimens we e ozen, and o each specimen, o al leng h (TL), o al weigh (W) and e isce a ed weigh (We) we e de e mined (S o i g u e e al. 2000). F om each specimen, eigh o en scales we e collec ed om he body sec ion be ween he la e al line and he do sal in (G o d i n h o & F e e i a 1993, D e i e s & F i e 1996). Scales we e cleaned unde unning wa e and imme sed in NaOH (4%) o emo e mucus and o clean s uc u es. We did no ake damaged scales o scales wi h doub ul annuli (S c h u l z & L e a l 2005). G ow h was analysed by scale eading and leng h equency dis ibu ion (W e a h e l e y & G i l l 1987). To al o e isce a ed weigh is assumed o indica e condi ion, a ness, o well-being o animals, based on he assump ion ha he hea ies specimens o a gi en leng h a e in be e condi ions han o he ones (B a g e n a l & T e s h 1978). The a ia ion in he condi ion o he specimens h ough he di e en seasons was s udied using an analysis o co a iance (ANCOVA) o he o al weigh , wi h he a iable leng h being he co a ia e. The ins an aneous a es o g ow h in leng h (Li) and he ins an aneous a es o g ow h in weigh (Gi) om mean leng hs and weigh s compu ed o males and emales, we e sepa a ely calcula ed using he exp essions: Li = ln L +1- ln L Gi = ln W +1- ln W Whe e L +1 and W +1 a e mean leng h and mean weigh espec i ely, o he age-class +1, and L and W , mean leng h and weigh o he p e ious age-class (S o i g u e e al. 2000). To desc ibe he g ow h pa e n we ollowed he on Be alan y and Gompe z models (R i c k e 1975, D i c k i e 1978). The equa ion o on Be alan y g ow h unc ion was: L = L∞ (1-exp-k ( - o)) Whe e L is mean s anda d leng h a age (mm), is age (yea s), L∞ is he asymp o ic s anda d leng h (mm), 0 is he o igin o he g ow h cu e and k is some imes conside ed a s ess ac o (M o u e a u 1987). The Gompe z g ow h equa ion was: W = Wo . exp{G (1-exp[-g ])} Whe e W is mean weigh a age (g), is age (yea s), Wo is weigh a he con en ional ime 0. G is he ins an aneous a e a ime 0 and g desc ibes he a e o dec ease o G (P zybylski & G a c í a -B e h o u 2004). The p oduc Gg is he speci ic ins an aneous size a ime 0 (P a g e e al. 1994). Va u g h a n & K a n c i u k (1983) ecommended he use o non-linea - echniques o i he on Be alan y g ow h unc ion. Fo his eason, o i bo h models a non-linea leas -squa es eg ession wi h Ma qua d ´s algo i hm was used (M a q u a d 1963) as implemen ed in he P og am FISHPARM o he Fishe ies Science Applica ions Sys em package (S a i l a e al. 1988). Models ha e been es ima ed o each sex using he mean leng h and weigh alues om all he age g oups wi h a su icien ep esen a ion in he sample (Ga cía-Be hou & Mo eno-Amich 1993). 438 Sex de e mina ion was done by di ec gonad obse a ion. The specimens we e sexed on cap u e in o h ee ca ego ies: males, emales and ju eniles. Gonads we e weighed (Wg) wi h an accu acy o 0.0001g. O a ies we e p ese ed whole in Gilson’s luid a e weighing (Bagenal & B aum 1978). Age a ma u i y was calcula ed by he pe cen age o ma u e emales in each age-class using he o mula o W e a h e l e y & G i l l 1987. The numbe o oocy es p esen in each gonad was coun ed using a sys em o subsampling by a ea (G a n a d o -L o e n c i o 1996). Thei diame e s we e measu ed in mm using a sc eened ule . Po en ial ecundi y was es ima ed by he numbe o oocy es p esen in he o a y and absolu e ecundi y was es ima ed by he numbe o ma u e eggs p esen in he o a y, being ma u e eggs hose hyd a ed eggs wi h diame e s be ween 0.7–1.3 mm. The spawning season was assessed by s udying he a ia ion o he gonadal weigh h ough he di e en s udied seasons, using an analysis o co a iance (ANCOVA) o he gonadal weigh , wi h he a iable leng h being he co a ia e. No analysis was applied on win e da a because e y ew specimens we e caugh . To a oid he use o nega i e alues, all a iables we e p e iously mul iplied by 106 (Ga cía-Be hou & Mo eno- A m i c h 1993). All da a we e analysed wi h he s a is ical package SPSS 13.0 (2004). Mo phome ic da a we e log- ans o med and s a is ical signi icance we e de e mina ed as p<0.005 (M e a d o & K e l s o 1990). Resul s A o al o 200 specimens we e caugh (98 emales, 86 males and 16 ju eniles) and dis ibu ed in o se en di e en age-classes ( om 0+ o 6+) (Table 1). The maximum age-class obse ed was 6+. The mos impo an alues o males leng h and weigh we e sligh ly highe (TL: 269 mm, W: 260 g) han o emale ones (TL: 265 mm, W: 250 g) bu he di e ences we e no signi ican be ween sexes in all he s udied age-classes (TL: F1.176=2.107, p>0.05; W: F1,174=3.653, p>0.05). The mos impo an specimen quan i ies o he Mic op e us salmoides popula ion in P ime a de Palos’ lake we e younge han i e yea s old. Specimens 6+ we e exclusi ely eminine. Table 1. Numbe o specimens (n), mean o al leng h (TL) a age, s anda d de ia ion (SD) and mean o al weigh (W) o he s udied popula ion o M. salmoides in P ime a de Palos’ lake. Age-class Ju eniles n TL (mm) SD W (g) SD 0+ 16 89 30 12 7 Males Females nTL (mm) SD W (g) SD n TL (mm) SD W (g) SD 1+ 5 182 17 82 20 10 174 22 68 21 2+ 13 211 14 131 23 19 212 14 132 28 3+ 60 282 14 285 37 47 278 16 270 47 4+ 7 318 16 362 59 20 314 10 336 71 5+ 1 380 - 691 - - - - - - 6+ 2 420 28 934 221 439 Fig. 1. Von Be alan y’s leng h g ow h unc ion calcula ed o bo h, male and emale specimens o la gemou h bass popula ion in P ime a de Palos’ lake. Fig. 2. Gompe z’s weigh g ow h unc ion calcula ed o bo h male and emale specimens o la gemou h bass popula ion in P ime a de Palos’ lake. 440 Leng h-a -age was adequa ely desc ibed by he on Be alan y model. The pa ame e s o he on Be alan y g ow h’s cu e we e: L∞=503.6 mm, k=0.19, 0= -1.04 (R2=0.989) o males and L∞=512.6, k=0.18, 0= -1.05 (R2=0.991) o emales (Fig. 1). Bo h sexes showed a simila g ow h in leng h and he ligh di e ences in g ow h be ween sexes we e no signi ican (F1.128=2.579, p>0.05). The inal alues o he Gompe z g ow h’s cu e o weigh we e: W0=15.76, G=3.66, g=0.49 (R2=0.98) o males and W0=10.66, G=3.84, g=0.58 (R2=0.99) o emales (Fig. 2). Bo h sexes showed a simila g ow h in weigh . F om he age-class 3+ and olde , male ish ge i s maximum weigh ea lie han emales. Howe e , hose di e ences we e no signi ican (F1.128=0.022, p>0.05). Fig. 3. E olu ion o he ins an aneous g ow h a e in leng h (A) and weigh (B) and con idence limi s calcula ed o male and emale specimens o la gemou h bass popula ion in P ime a de Palos’ lake. male ––– emale ––– male ––– emale ––– 441 The de elopmen o he ins an aneous g ow h a e in leng h and weigh (Fig. 3) was simila in males and emales. The highes alue was ob ained in he i s yea o li e, and hen, he ins an aneous g ow h a e su e ed a sudden descen and emained low, wi h small luc ua ions h oughou he li e cycle o he popula ion. On a e age, males ma u ed one yea ea lie han emales in he age-class 1+. Females p esen ed o a ies wi h ma u e eggs om he age-class 2+. The esul s o ANCOVA and analysis o he simple e ec s ca ied ou on la gemou h bass gonadal weigh da a (Table 2) showed no signi ican in e ac ion season*sex (F2.147=1.054, p>0.05). The e ec o sex was signi ican on gonadal weigh , a e lea ing ou he co a ia e e ec . Th oughou he whole ep oduc i e pe iod, emales in es ed mo e ene gy in gonadal de elopmen han males. Va iables wi h signi ican seasonal a ia ion could be accu a ely desc ibed by a Bon e oni con as . Thus, o ma u e ish in bo h sexes, he maximum alue o gonadal weigh was go du ing he sp ing season. The oocy e diame e s we e signi ican ly di e en h oughou he annual cycle. The smalles oocy es, belonging o class 1 and 2 (wi h diame e s be ween 0.1–0.3 mm and 0.4–0.6 mm, espec i ely) a ied signi ican ly h oughou he seasons (K-W: χ2=54.155, p<0.05 o class 1 and K-W: χ2=44.080, p<0.05 o class 2) (Fig. 4). Simila ly, classes 3 and 4 (wi h diame e s be ween 0.7–0.9 mm and 1–1,3 mm, espec i ely) p esen ed signi ican di e ences h oughou he annual cycle (K-W: χ2=59.199, p<0.05 o class 3 and K-W: χ2=59.199, p<0.05 o class 4). The mean, maximum and s anda d de ia ion o po en ial and absolu e ecundi y in emale specimens, du ing he di e en s udied seasons, a e in Table 3. In sp ing, absolu e Table 2. Resul s o ANCOVA and analysis o he simple e ec s ca ied ou on Mic op e us salmoides gonadal weigh da a. Bon e oni con as (α=0,05) co esponds o he di e en s udied seasons: μ1 is he mean gonadal weigh o specimens cap u ed du ing au umn, μ3 is he mean gonadal weigh o specimens cap u ed du ing sp ing and μ4 is he mean gonadal weigh o specimens cap u ed du ing summe . μ emale co esponds o he mean gonadal weigh o emale ish and μmale is he mean gonadal weigh o male ish. To al leng h is he co a ia e. All a iables (dependen and co a ia e) we e log- ans o med. d : deg ees o eedom. d F p Reg ession 1.147 336.851 <0.001 Sex 1.147 221.565 <0.001 Time 2.147 72.196 <0.001 In e ac ion 2.147 1.054 0.351 μ emale > μmale Males: μ1= μ3 > μ4 Females: μ1= μ3 > μ4 * Ju eniles we e excluded om he analysis. 5+ and 6+ indi iduals we e elimina ed because ep esen a i e o bo h sexes we e no a ailable. Analyses we e no applied on win e da a because e y ew specimens we e caugh . Table 3. Po en ial ecundi y (PF) and absolu e ecundi y (AF), mean, maximum and s anda d de ia ion o emales o Mic op e us salmoides. Au umn Sp ing Summe PF AF PF AF PF AF 19 36 32 31194.64 0.87 9981.81 690.82 8253.35 - 51246.00 84.00 69258.00 16580.00 35603.00 - 21084.43 8.53 15456.11 2145.70 11010.47 - 442 ecundi y alues we e bigge han hose in au umn. Du ing he summe pe iod we did no ind any ma u e eggs. Class 1 was p edominan in la e summe and ea ly au umn. Classes 3 and 4 we e mo e nume ous in sp ing. The maximum gonadal de elopmen ook place du ing sp ing, wi h 15.10% o class 3 oocy es and 33.45% o class 4 oocy es. The highes absolu e ecundi y alue was egis e ed in a emale specimen cap u ed in Ma ch p esen ing a o al leng h o 440 mm and a o al weigh o 1 090 g, wi h a gonadal weigh o 41.60 g and a o al o 16 580 ma u e eggs (belonging o class 3 and 4). Resul s om gonadal de elopmen and egg size equency dis ibu ion showed ha spawning ook place in sp ing when wa e empe a u e we e wa me han in o he seasons. In la e sp ing and ea ly summe , gonadal de elopmen came in a quiescen phase. Egg o ma ion began in la e summe , wi h p edominance o oocy es wi h diame e s be ween 0.1 and 0.3 mm (class 1). Discussion The ish communi y o P ime a de Palos’ lake in eg a es popula ions o la gemou h bass (Mic op e us salmoides), common ca p (Cyp inus ca pio), eel (Anguilla anguilla), mosqui o ish (Gambusia holb ooki) and ibe ian loach (Cobi is paludica), bu la gemou h bass popula ion domina es he communi y (95% o he sample) (L. Encina, pe s. comm.). In his small lake, he la gemou h bass popula ion is ageing well, wi hou agmen a ion and wi h indi iduals in all he age-classes. The size- equency dis ibu ion o la gemou h bass p esen s an ampli ude o age-classes in e media e o hose ound in o he s udied Fig. 4. Oocy e size his og am calcula ed o emale o la gemou h bass in P ime a de Palos’ lake. (Class 1: oocy e diame e be ween: 0.1 and 0.3 mm; Class 2: 0.4–0.6 mm; Class 3: 0.7–0.9 mm; Class 4: 1.0–1.3 mm). 443 sys ems. Compa ing o o he Eu opean sys ems, he analysed popula ion p esen s mo e age- classes han hose egis e ed in se e al popula ions o Po ugal (G o d i n h o & F e e i a 2000) and is simila o hose ound in Lake T asimeno in I aly (L o e n z o n i e al. 1996, 2002). Ou side he Eu opean con inen , s udied popula ion shows less age-classes han hose known in lake Manyame, Zimbabwe (B e a m i s h e al. 2005). On he o he hand, he e we e ce ain simila i ies wi h he obse ed s uc u es o he la gemou h bass popula ions o Tadenae lake, Canada (M a a l d o & M a c C i m m o n 1979). The g ow h o la gemou h bass in P ime a de Palos’ lake egis e ed he highes alues du ing he i s yea , p esen ing highe leng hs han he Ame ican mean leng h (B e a m e s d e e & N o h 1995) and lowe leng hs han he Po uguesse mean leng h (G o d i n h o & F e e i a 1993, 2000) and simila leng hs o hose ound in sou he n s a es o he Uni ed S a es (B e a m e s d e e & N o h 1995). The e o e, he g ow h is as e han in o he eshwa e ish species, wi h male and emale specimens ge ing a 50% o hei maximum leng h in hei i s h ee yea s o li e, wi h as g owing o he la al ish in o size classes less ulne ables o p eda ion (W o o o n 1990, W i n i e l d & N e l s o n 1991) and ea ly s ages cha ac e ized by high g ow h a es (J o b l i n g 1995). In addi ion, among o he ac o s, he g ow h o la gemou h bass depends on he wa e empe a u e, begins in empe a u es o e 10ºC and eaches maximum alues wi h empe a u es o e 25ºC (Cou an 1975). These empe a u es happen in o e en mon h long pe iods in Spanish sou he n wa e s, and his ex ended g ow h pe iod is p obably he main eason o he high g ow h a es ound. The la ges ish eco ded du ing his s udy was a emale o 440 mm in leng h (age-class 6+) and 1 090 g in weigh . Al hough sexual dimo phism in he size o la gemou h bass was al eady deba ed in he i s s udies published on his species (H e i d i n g e 1976) and la ge emales we e obse ed only occasionally (A l e s s i o 1981), in P ime a de Palos’ lake, he compa ison be ween sexes did no show signi ican di e ences. The L∞ alues o he on Be alan y g ow h’s equa ion ob ained o he popula ion o la gemou h bass s udied we e bigge han hose ound in Zimbabwe (B e a m i s h e al. 2005) o Japan (F o e s e & P a u l i 1998) and we e simila o he ob ained alues in I aly (L o e n z o n i e al. 1996), in Lake Rebeca, USA (F o e s e & P a u l i 1998) and hose ound in high la i ude Ame ican popula ions (B e a m e s d e e & N o h 1995). Ne e heless, k alues we e lowe han hose ound in o he Eu opean popula ions. In P ime a de Palos’ lake, he la gemou h bass popula ion g ows slowly eaching a big size (weak k and high L∞) like he popula ions s udied in No h Ame ica. Acco ding o he esul s o B e a m i s h e al. (2005), sexual ma u i y is eached a 180 mm and 75 g in he case o males (age-class 1+) and a 230 mm and 125 g in he case o emales (age-class 2+). In P ime a de Palos’ lake, like in o he s udied popula ions (B e a m i s h e al. 2005), emales o la gemou h bass in es ed mo e ene gy han male specimens in gonadal de elopmen . Sex- a io changed h oughou he li e span o his popula ion p obably as a esul o he di e en ep oduc i e s ess su e ed by males and emales (G a n a d o -L o e n c i o 2000). In P ime a o Palos’ lake he wa e empe a u e is ge ing high om Ma ch o Augus , being he sp ing he mos a ou able pe iod in he ecosys em o ep oduc ion, when empe a u es a y be ween 20–25 ºC. As epo ed in he li e a u e, la gemou h bass can ini ia e i s ep oduc i e pe iod in empe a e zones be ween la e win e and ea ly sp ing, due o his wa e empe a u e is a p ima y ac o in ep oduc ion o his species (K e & G a n 1999, L o e n z o n i e al. 2002). 444 Po en ial ecundi y mean alues we e simila o hose desc ibed o his species in he Ibe ian Peninsula, wi h alues anging om 10 000 o 11 000 eggs (D o a d i o 2001). The maximum absolu e ecundi y alue in P ime a de Palos’ lake was 16 580 ma u e eggs ound in a 440 mm long emale, a high alue in compa ison wi h he mean alue e e enced. The maximum gonadal weigh o emales was eco ded in sp ing jus be o e spawn and he inc ease in es icula weigh occu ed a he same ime ha in o a ies. Spawning akes place in sp ing once a yea , like in o he Eu opean communi ies (L o e n z o n i e al. 2002) when egg sizes a e big, he wa e empe a u e is wa me han in o he seasons and he nu i ional esou ces in he small lake ha e inc eased conside ably. The d op o gonadal weigh in bo h sexes a e sp ing sugges s ha ep oduc ion akes place in a na ow pe iod, his ac has also been desc ibed in o he popula ions o la gemou h bass (W o o o n 1990, R o s e m b l u m e al. 1994, L o e n z o n i e al. 2002). In he P ime a de Palos’ lake, la gemou h bass popula ion has been acclima ised well. The sou he n Spanish wa e s p esen excellen possibili ies o la gemou h bass g ow h, wi h a ou able en i onmen al and ophic condi ions o i s de elopmen . Un o una ely, he di e si y o he na i e eshwa e ish communi ies is h ea ened wi h he in oduc ion o exo ic species (E l i a 1995). The knowledge o he al e a ion caused by exo ic species could be he base o p e en successi e in oduc ions and o decide me hods o con ol hem. On he o he hand, o limi u he ecological damage, ec ea ional angle s a e u ged o s op addi ional in oduc ions o Mic op e us salmoides. Acknowledgemen s We would like o hank o Ra ael Benjumea o his help wi h he ieldwo k. We a e also g a e ul o Ja ie Camacho o pe mission o s udy he P ime a de Palos’ lake. Finally we would like o hank o Ma hew J. L. and Ma y R. R. o hei assis ance in he English e sion. LITERATURE Alessio G. 1981: Rice che sul pe sico o a Mic op e us salmoides (Lacep.) nel bacino medio-supe io e del F. Po (Pisces Cen a chidae). Na u a 72: 197–220. Bagenal T.B. & B aum E. 1978: Eggs and ea ly li e his o y. In: Bagenal T.B. (ed.), Me hods o assessmen o ish p oduc ion in esh wa e s. Blackwell Scien i ic Publica ions, Ox o d. Bagenal T.B. & Tesch F.W. 1978: Age and g ow h. In: Bagenal T.B. (ed.), Me hods o assessmen o ish p oduc ion in esh wa e s. Blackwell Scien i ic Publica ions, Ox o d. Beamesde e R.C. & No h J.A. 1995: G ow h, na u al mo ali y and p edic ed esponse o ishing o la gemou h bass and smallmou h bass popula ions in No h Ame ica. No h Am. J. Fish. Manage. 15: 688–704. Beamish C.A., Boo h A.J. & Deacon N. 2005: Age, g ow h and ep oduc ion o la gemou h bass, Mic op e us salmoides, in lake Manyame, Zimbabwe. A . Zool. 40: 1–11. Ca lande K. 1977: Handbook o eshwa e ishe y biology. Idowa S a e Uni e si y P ess. Idowa. Cou an C.C. 1975: Responses o bass o na u al and a i icial empe a u e egimes. In: Cleppe (ed.), Black bass biology and managemen . Washing on, DC. Spo ishing ins i u e: 272–285. Copp G.H., Fox M.G., P zybylski M., Godinho F.N. & Vila-Gispe A. 2004: Li e- ime g ow h pa e ns o pumpkinseed Lepomis gibbosus in oduced o Eu ope, ela i e o na i e No h Ame ican popula ions. Folia Zool. 53: 237–254. DeV ies D.R. & F ie R.V. 1996: De e mina ion o age and g ow h. In: Mu phy B.R. & Willis D.W. (eds.), Fishe ies echniques, 2nd ed. AFS, Be hesda, Ma yland: 483–512. Dickie L.M. 1978: Ma hema ical models o g ow h. In: Bagenal T.B. (ed.), Me hods o assessmen o ish p oduc ion in esh wa e s. Blackwell Scien i ic Publica ions, Ox o d: 130–136.