WNW I! LABORATORY POPULATION STUDIES OF TWO SPECIES OF CHYDORIDAE (CLADOCERA. CRUSTACEA) Thais for the Degree of M. S. MICHIGAN STATE UNIVERSITY ROBERT E. KEEN 1967 Y R A R B .1 L State chh 1.53" _/ (c Ooégjfl’b ABSTRACT LABORATORY POPULATION STUDIES OF TWO SPECIES OF CHYDORIDAE (CLADOCERA, CRUSTACEA) by Robert E. Keen The Chydoridae are a family of small littoral Cladocera. The intrinsic rate of increase, which de- scribes the instantaneous rate of pOpulation growth in a spatially unlimited environment, is a useful statistic in population biology. The intrinsic rate of increase was calculated for two species of Chydoridae, Chydorus sphaericus and Pleuroxus denticulatus, at temperature levels of 25, 15, and 5 C. Twenty-five newborn indivi- duals of each species for each temperature were isolated in culture dishes and raised for their entire life span. Daily observations of births and deaths allowed the cal- culation of £° At 25 and 15 C, E for Chydorus was 0.268 and 0.143; for Pleuroxus, 0.174 and 0.096. Neither spe- cies died or reproduced at 5 C over a period of four weeks. LABORATORY POPULATION STUDIES OF TWO SPECIES OF CHYDORIDAE (CLADOCERA, CRUSTACEA) by Robert E} Keen A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Zoology and the W. K. Kellogg Biological Station 1967 ACKNOWLE DGEMENT S I would like to acknowledge with gratitude the constant advice and encouragement of my major professor, Dr. Donald C. McNaught. The other members of my committee have liberally supplied aid and education of many kinds, but I especially thank Dr. W. E. Cooper for the provision of laboratory facilities, and Drs. G. H. Lauff and R. G. Wetzel for the critical reading of the thesis. For per- mission to include data on Simocephalus from an unpublished M. 8. report, I thank Mr. Dan M. Johnson. The research on the Chydoridae reported here is part of a larger program of work on these animals. These studies have served as a very useful first step towards future work with the chydorids. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . . . . . . . . iV INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1 MATERIALS AND METHODS. . . . . . . . . . . . . . . . 4 RESULTS. . . . . . . . . . . . . . . . . . . . . . . 8 CALCULATIONS . . . . . . . . . . . . . . . . . . . . 8 DISCUSSION . . . . . . . . . . . . . . . . . . . . . 26 CONCLUSION . . . . . . . . . . . . . . . . . . . . . 31 LITERATURE CITED . . . . . . . . . . . . . . . . . . 33 iii 10. LIST OF TABLES Chydorus sphaericus at 25 C. daily observations of births Pleuroxus denticulatus at 25 daily observations of births Chydorus sphaericus at 15 C. daily observations of births Pleuroxus denticulatus at 15 daily observations of births Chydorus sphaericus at 25 C: Pleuroxus denticulatus at 25 Results of and deaths. C. Results and deaths. Results of and deaths. C. Results and deaths. of Age-specific fertility (m ) and survivorship (1x)' with calculations for RD, E, and T. . . . . . . . C: Age-specific fertility (mx) and survival (1X), with calculations for R0, 5, and T. . . . . . . . . Chydorus sphaericus at 25 C: Pleuroxus denticulatus at 15 C: Age-specific fertility (mx) and survival (1x), with calculations for R0, r, and T. . . . . . . . fertility (mx) and mortality (1x), with calculations for R0, E! and T. . . . . . . . . Values for El 32' and T of four laboratory pOpulations of Chydoridae. . . . . . . . . Values of r for small aquatic crustaceans. iv Age-specific Page 10 ll 12 14 16 17 21 27 28 INTRODUCTION The Chydoridae are a family of small Cladocera that principally inhabit the weedy littoral areas of ponds and lakes. With limbs adapted for scraping, they are usually associated with the substrate. Their reproductive capacity is limited by their ability to carry at most two young in the brood pouch (except Eurycercus). The chydorids form a significant part of the littoral fauna of lakes, yet their biology is relative unknown (Flossner, 1964). This study describes quantitatively laboratory popu- lations of some chydorids with some common statistics of population dynamics. The primary objective of the popula- tion studies was to secure information on the reproductive capabilities of the animal and the responses of their popu- lation growth to levels of temperature. The study also served to familiarize the investigator with the animals and provided opportunity for numerous observations of feeding, molting, reproduction, and growth. The results of the popu- lation investigations and the daily observations of these animals over a period of several months have been of sig- nificant value in suggesting how best to conduct future studies. The instantaneous rate of population increase is a term in the common expression of the differential equation for population growth: dN _ E—IN where E = the number of animals, E = time, and E = a con- stant--the instantaneous rate of increase. A value of r - that expresses the rate at which a species can increase in an unlimited environment with a given set of conditions is called the "intrinsic rate of increase". The intrinsic rate of increase is a valuable sta- tistic for describing the potential of a species in repro- ducing itself. The statistic E has the units of number of animals by which the total population increases per indi- vidual in the population per unit of time. It corresponds to the instantaneous rate of interest in a compound interest problem (Slobodkin, 1961). It is the difference between the number of animals born per individual per day, and the number of animals dying per animal per day. Smith (1954) has noted that r values differ greatly among species, with the average "harshness" of the environment proportional to the intrinsic rate of natural increase. A p0pulation with a high intrinsic rate of increase is more often faced with the problem of taking advantage of ecological opportunities than a species with a lower intrinsic rate of increase. It is possible to determine the instantaneous rate of population increase for any population, whether increas- ing, decreasing, or fluctuating, with lnNt - lnNo t r: where r is the rate of population increase, NO and Nt rep- resent respectively the size of the population at the be- ginning and end of the period 5. Here, E can be negative, positive, or 0. If the population does not have a stable age distribution, 5 will take on various values, depending upon the origin and length of the time period 2. In a pOpulation with a stable age distribution, the statistic E is a constant (Lotka, 1925) called the "intrin- sic rate of increase" (Birch, 1948). For populations with a stable age distribution, 5 can be calculated with the method outlined by Birch (1948). This technique requires a knowledge of the age-specific survivorship (1X), which is the probability at birth of being alive at age x, and the age-specific fertility (mx), the mean number of off- Spring produced by an animal-at age x. The unlimited environment is perhaps best approxi- mated in the laboratory by isolating individuals or cohorts of animals in comparatively large containers. Observations of the isolated animals at regular time intervals can provide the data for the calculation of lX and mx. This procedure was adopted for the determination of the_intrin- sic rate of increase (E) of two species of chydorids at three temperature levels. MATERIALS AND METHODS Chydorus sphaericus (O. F. Muller) was chosen as one of the animals because it is the most abundant and widely-distributed cladoceran (Brooks, 1959). Pleuroxus denticulatus Birge, while also widely-distributed and com— mon, was selected because it has been investigated by Smirnov (1964) and is currently under study in Dr. David G. Frey's laboratory at Indiana University. Both species are easy to maintain in culture and, unlike most Cladocera, tend not to become trapped in the surface film of the water. The chydorids were collected from Lake Lansing, Ingham County, Michigan on 8 December 1966, with several tows of a Birge cone net (Welch, 1948) among the vegeta- tion and along the bottom. The original collections were warmed from the collecting temperature (3. 5 C) to room temperature over a three-day period. Animals of the two chosen species were separated from the collection and were placed in 50 ml dishes containing abundant food. Twelve dishes were prepared, each with four or more animals from the original collection; Chydorus was isolated in six dishes, and Pleuroxus in the other six. The dishes were put into constant-temperature chambers for three or more generations to allow acclimitization to the prospective temperature and light regimes. Culturing was planned at 25, 15, and 5 C. However, it was difficult to keep the constant-temperature chamber at 5 C, so that culturing at this temperature was delayed as described below. The assembling of the study populations for the fertility-mortality observations commenced on 10 January 1967 for 25 C; the 15 C pOpulations were started on 15 April 1967. The periods between these dates and mid- December 1966, when the 50 ml dishes were established, should have been adequate for acclimation. After the acclimation periods, 12 to 15 adult ani- mals of each species for each temperature were isolated in 5 ml culture dishes. Glass dishes were used at 25 C, and plastic dishes at 15 and 5 C. The 5 ml size was selected because it represented a balance between too large a volume for inspection, and too little volume for the animals. Food was added to these cultures, and the animals were in- spected at 24-hour intervals for the production of young. The dishes were kept covered in trays in the chambers be- tween observation periods. When the isolated adults produced young, the young were similarly isolated in 5 ml culture dishes. Twenty-five of the young were used to make up each study pOpulation for the fertility-mortality determinations. Additional young animals were isolated and used as replacements when any of the first 25 animals were accidentally destroyed. The isolated young were observed at exactly 24- hour intervals, and births and deaths recorded. When young were produced, they were removed from the dishes to main- tain the unlimited environment. Since developing embryos are easily seen through the tranSparent carapace of chy— dorids, the presence of embryos or eggs was also recorded. This aided in looking for young at the next time of ob- servation. The water used in culturing of the animals was taken from a large indoor concrete tank. Water was con- tinuously supplied to this tank from tap water filtered through an activated—charcoal filter. The water taken from the tank was kept in a 4-liter jar for at least one day in the constant-temperature chamber prior to using it in the cultures. About half the water in the culture dishes was changed daily at the time of observation. A light regime of 12 hours fluorescent illumination per day was maintained throughout acclimation and the period of observations. "Detritus" was the food used throughout this study, as suggested by Smirnov (1962). The detritus was obtained simultaneously with the collection of the chydorids by dipping up mud from the bottom of the littoral zone of the lake. The mud was placed in a 4-liter glass aquarium and aerated under constant illumination. The detritus evi- dently maintained its food quality for the duration of the population study, for numerous small invertebrates were always observed in the aquarium. Detritus taken from the aquarium was introduced into the cultures every fourth day at 25 C and every fifth day at 15 C. Suffi- cient detritus was introduced with a Pasteur capillary pipette to cover slightly the bottom of the culture dishes. This procedure should have supplied adequate food, in View of the small size of the animals. The de— tritus was not removed when the water was changed. It proved impossible under the conditions of this study to make fertility-mortality observations on popula— tions of either species at 5 C. Difficulty was encountered in establishing a culture for acclimitization. Animals from the 15 C cultures were used to start the 5 C cultures, but all died at 5 C. Two days of acclimitization at the intermediate temperature of 10 C allowed a transfer to 5 C without excessive mortality. After six weeks following the transfer to 5 C, little or no reproduction had occurred. Some of the adults were isolated in the 5 ml dishes, and were observed every other day. After four weeks of obser- vation, with water changes bi-daily and feeding every eighth day, no reproduction had occurred in either species and none had died. Even adults carrying embryos with eyes had not released the young after four weeks. The obser- vations were terminated at the end of four weeks when the constant-temperature unit failed. RESULTS The results of the daily observations of birth and death are given in Tables 1-4 for each individual animal in the four populations. No results are given for either species at 5 C, since the animals were evidently incapable of reproducing in the laboratory at this temperature. It was assumed that all the births and deaths oc- curred at the mid-point between the daily observations. Thus, the animals taken from the adults to start the study populations were assumed to have been released from the blood pouch just twelve hours before they were first ob- served. On the average, this assumption is probably valid. CALCULATIONS The mortality and fertility data of Tables 1-4 were used to calculate the intrinsic rate of population increase (E)! the net reporduction of each animal in the population (R0), and the mean length of a generation (T) by the pro- cedures of Birch (1948), Andrewartha and Birch (1954), and Southwood (1966). The calculation of E requires the ma ma Ha m n m mm mm ma ma ma ma Ha m m w v em om me me mm mm em mm on mm mm mm vm mm ma ha ma ma Ha m h m mm we mm mm em mm am mm mm mm mm Hm om SH ma ma ma m n m mm ov mm mm am mm mm em mm ma ha ma ma m n m am am om 5H ma Ha m m e om mm me ow mm mm mm em Hm ma ea va OH m m m ma ma NH m ma om ma ma ma OH > m ha m m ma em mm om ma ma Ha m m m ma ea NH OH m m «H mm ma ma NH m o ma am we we mm om mm mm Hm mm mm mm mm Hm ma ma HH 5 m NH em mm om me me me ow mm mm mm om nm em mm ma ha ma ma NH 0H m Ha m b m OH ma ma «a HH m o e m em om ha ma ma 5 w m ma HH m m w mm mm mm mm em Hm ma ha Ha m w NH OH 5 v m mm mm om we we we we mm mm mm mm om mm mm em mm ea ma OH m o v v em mm mm mm Hm ma ma m n m w m em mm om mm em om SH ma ma Ha m m m w m we mm om em mm om mm om em wH Ha m o m H summo mo moo omonoonm mumB mono» aoflz3 co nuufln Scum mama .oz Hmfiflnfl .mnummc cam mcuufln mo mGOHum>Hmeo >HHMU mo muHSmom .0 mm um mSOHHmmnmm mDHOUNJU .H GHQMB 10 pmoscoum mmB made» one MHGO 30Hc3 do mmmw n .1 OH NH O ON OH O ON NH *HH O m ON O O NN NH «O *O m HN NH OH ON OH O OH OH O OH ON OON OH OH OH O O OH OH HH O OH wN RON *OH O O ma «H O OH OH «OH OH OH NN OH NH O O NH OH OH O m HH OH NH OH O OH OH «OH OH O O OH OH O O NH O O OH OH O O OH OH O m O OH OH OH O m O OH O OH me m N ON OH NH O H £¢M0© no man UwoDUOHm mHmB mono» £0H£3 do auan ECHO mama .oz HMEHG< .mzummp paw mswan mo mGOHDM>Hmeo OHHMO mo mpHdmwm .0 ON pm ODDMHDOHDGGU meOHdem .N mHQMB ll Umosvoum mmz modem mco OHco BUHSB co mmmv OO OO OO OO OO HO OO OO OO OO OO NO OO OO OO ON ON OH OH HH ON ONH ONH OHH OOH HOH OO NO OO OO OO NO OO OO NO OO OO OO OO HO ON ON OH OH HH ON OO OO OO OO OO OO ON ON ON OH NH ON OO HO OO NO OO OO OO OO ON ON NN OH OH OH NN OOH OHH NHH OOH NOH OO OO OO OO OO OO OO NO OO NO OO OO OO OO HO ON NN OH NH HN OOH «OO OO OO OO OO OO OO OO OO OO NO OO OO OO ON NN OH OH OH ON HOH ONH OOH OOH OO OO OO OO OO OO OO OO OO OO OO NO ON ON ON OH HH OH OO OO NO OO OO OO OO OO OO NO OO OO OO ON NN OH OH OH OH HO *OO NO OO HO OO NO ON ON ON OH HH OH OO OO NO OO OO OO OO OO ON NN OH OH O OH OHH OOH OO OO OO NO OO OO HO OO HO OO OO OO OO OO ON ON OH OH OH OH OO OO OO OO OO OO HO OO OO ON ON HN OH OH O OH ONH OHH OOH OOH OO HO OO OO OO NO OO OO OO OO OO OO OO ON ON OH OH HH OH ONH OOH OOH OOO OO OO OO «OO NO OO OO OO NO OO OO OO ON ON OH OH OH NH OOH HHH OOH HOH OO OO OO OO OO OO OO OO OO OO HO OO OO ON ON ON OH HH HH HNH OHH OOH OOH OO OO OO OO HO OO NO OO NO OO OO OO OO HO ON ON OH OH OH OH OO OO OO OO OO OO OO ON HN OH NH O NOH OHH OOH OOH OO NO OO OO OO OO OO OO NO OO ON ON OH OH OH O OOH OO OO OO OO OO OO OO OO OO OO OO OO HO ON ON OH OH HH O OO OO OO OO OO OO OO OO OO NO OO OO OO ON NN OH OH OH O HNH OOH HOH OO NO OO OO OO OO OO OO HO OO OO OO OO HO ON ON OH HH O HHH *OOH NOH OO OO OO OO OO OO NO OO OO OO OO NO OO OO HO ON ON OH OH OH O HO OO *HO «OO HO OO OO OO OO HO OO OO OO ON NN OH OH OH O ONH *OOH OOH OO OO OO OO OO NO OO OO OO OO NO OO OO HO ON ON OH OH OH N OO OO OO OO OO OO HO ON ON OH OH OH H WWMMWQ Umoswonm mum3 masom QOHQB no nuHHQ ECHO mama Hmwwcfl .npmmw can nuHHQ mo mGOHpm>Hmeo OHHMO mo mpHDmmm .0 OH pm ODOHHmmnmm OSHOUNBU .m GHQMB 12 UmUSOOHm mmz masow moo OHQO QOHQB do mmump k. OO OO NO OO HO «NO HO OO NO OO NO ON ON OH OH ON OO OO OO «OO NO OO HO OO ON HN OH HH ON OO OO OO OO OO OO ON OH «OH ON OO ON ON NN OO ON ON OH HN OO ON ON OO OO OO OO ON ON «OH OH OH OH NH OH OO OO OO «OO ON OH NH OH OO OO «ON «OH NH OH OO OO OO «OO «ON ON OH OH OOH OO OO OO NO «OO «OO OH OO «OO ON ON OH OO «mm ON «OH MH NH OO ON HN OH HH HH HO OO ON ON OH NH OH OO OO OO ON OH OH O OO OO ON ON ON OH HH O ON ON NH O HNH ONH OOH OOH OO OO OO OO OO HO OO HO ON NN OH OH O HO OO OO ON ON OH OH O OO OO OO OO OO OO HO ON NN OH OH O OO OO NO OO OO OO OO «ON HN «OH O OO OO OO OO OO ON NN OH N OO «OO «ON H summw mo mma Omosvoum mHmB @250» noHSB co nyuHQ ECHO mmmo .oz HmEqu .msummw wow mauHHQ mo mGOHum>Hmeo OHHMU mo muHSmmm .0 OH pm msgmHSOHude msxoustm .O mHnme 13 "life table", giving the probability (1X) of being alive at age x, and the age-specific fertility, which is the mean number of young (mX) produced by an animal at age x. The data for 1X and mX of the chydorids are presented in Tables 5-8. _— —— . Column 1 in Tables 5-8 gives the age of the animals in days (x). Column 2 lists, for each x, the number of animals capable of reproducing and/or dying. The number of animals dying at each age 5 is given in the third column, while column 4 gives the total number of young produced by animals of age x. The fifth column is the life table, listing the values for lx’ which is the fraction of the original popu- lation stilI_alive at age x, or the probability at birth of being alive at age x. Values of 1x were obtained for all x's by dividing the number of coIEmn 2 at each x'by the number in column 2 at x = 0. Column 6 provides the age-specific fertility (mx); that is, the number of animals produced by an individu;I at age 5. Fertility for each x was obtained by dividing the total number of animals produced on each day x (column 4) by the number of animals in the population at the same x (second column). As given by Birch (1948), a close approximation of r is obtained with the formula 21 m e-rx = l x x 14 Table 5. Chydorus sphaericus at 25(:: Agewspecific fertility (mx) and survivorship (1x), with calculations for R0, 3, and 3. Age No. of No. No. 1 m l m. =.286 -rx (days) . . x x x x e x animals dying born rx 0 25 0 0 1.00 .000 .000 -—- —-- 1 25 0 0 1.00 .000 .000 --— --- 2 25 0 0 1.00 .000 .000 —-- --- 3 25 O 0 1.00 .000 .000 —-- --- 4 25 0 16 1.00 .640 .640 1.14 320 5 25 0 28 1.00 1.120 1.120 1.43 239 6 25 0 20 1.00 .800 .800 1.72 179 7 25 0 20 1.00 .800 .800 2.00 135 8 25 l 20 1.00 .800 .800 2.29 .101 9 24 l 20 .96 .833 .800 2.57 .077 10 23 0 12 .92 .522 .840 2.86 .057 ll 23 0 22 .92 .957 .880 3.15 .043 12 23 l 12 .92 .552 .480 3.43 .032 13 22 0 20 .88 .909 .800 3.72 .024 14 22 1 6 .88 .273 .240 4.00 .018 15 21 0 20 .84 .952 .800 4.29 .014 16 21 l 12 .84 .517 .480 4.58 .010 17 20 0 16 .80 .800 .640 4.86 .008 18 20 3 12 .80 .600 .480 5.15 .006 19 17 0 10 .68 .588 .400 5.43 .004 20 17 1 10 .68 .588 .400 5.72 .003 21 16 1 10 .64 .625 .400 6.01 .002 22 15 2 8 .60 .533 .320 6.29 .002 23 13 0 6 .52 .426 .240 6.58 .001 24 13 2 16 .52 1.231 .640 6.86 .001 25 11 0 6 .44 .545 .240 7.15 .001 26 ll 0 8 .44 .727 .320 7.44 .001 27 11 0 16 .44 1.455 .640 7.72 .000 28 ll 0 8 .44 .727 .320 29 ll 0 10 .44 .909 .400 30 11 0 10 .44 .909 .400 15 Table 5 continued. Age (days) No. of No. No. 1X mX lxmx x animals dying born 31 ll 0 6 .44 .545 .240 32 ll 0 8 .44 .727 .320 33 ll 0 12 .44 1.091 .480 34 11 2 6 .44 .545 .240 35 9 0 8 .36 .889 .320 36 9 l 8 .36 .889 .320 37 8 O 2 .32 .250 .080 38 8 O 8 .32 1.000 .320 39 8 O 4 .32 .500 .160 40 8 l 4 .32 .500 .160 41 7 0 0 .28 .000 .000 42 7 1 6 .28 .857 .240 43 6 O 2 .24 .333 .080 44 6 1 4 .24 .667 .160 45 5 0 2 .20 .400 .080 46 5 0 4 .20 .800 .160 47 5 0 2 .20 .400 .080 48 5 0 4 .20 .800 .160 49 5 l 4 .20 .800 .160 50 5 l 4 .20 .800 .160 51 4 1 0 .16 .000 .000 52 3 O 3 .12 1.000 .120 53 3 1 0 .12 .000 .000 54 2 1 O .08 .000 .000 55 l 0 0 .04 .000 .000 56 1 0 0 .04 .000 .000 57 l O 0 .04 .000 .000 58 l 0 O .04 .000 .000 59 1 0 2 .04 2.000 .080 60 1 0 0 .04 .000 .000 61 l 0 0 .04 .000 .000 62 1 1 1 .04 1.000 .040 63 0 .00 R = 21 m = 19.04 animals 0 x x 21 m e"rX = 1.000 x x _ 1nRO _ 2.944 _ T- ——f--— m— 10.29 days l6 Table 6. Pleuroxus denticulatus at 25 C: Age-specific fertility (mX) and survival (1X), with calculations for RD, E! and T. DaySO- 'No. of No. of No. of r=.174 (x) animals deaths births lx mx lxmx rx e rx 0 25 0 0 1.00 .000 .000 --— ——- l 25 0 0 1.00 .000 .000 ——- —-- 2 25 0 0 1.00 .000 .000 -—— ——- 3 25 0 0 1.00 .000 .000 -—- --- 4 25 0 0 1.00 .000 .000 ——- ——- 5 25 0 14 1.00 .560 .560 0.87 .419 6 25 0 20 1.00 .800 .800 1.04 .353 7 25 0 9 1.00 .360 .360 1.22 .295 8 25 0 9 1.00 .360 .360 1.39 .249 9 25 l 8 1.00 .320 .320 1.57 .208 10 24 0 14 .96 .583 .560 1.74 .176 11 24 0 3 .96 .125 .120 1.91 .148 12 24 4 8 .96 .333 .320 2.09 .124 13 20 1 7 .80 .350 .280 2.26 .104 14 19 1 1 .76 .053 .040 2.44 .087 15 18 5 5 .72 .278 .200 2.61 .074 16 13 3 7 .52 .538 .280 2.78 .062 17 10 2 0 .40 .000 .000 —-— --- 18 8 3 0 .32 .000 .000 —-- -—- l9 5 1 0 .20 .000 .000 ——- --- 20 4 2 2 .16 .500 .080 3.48 .031 21 2 0 0 .08 .000 .000 ——— --- 22 2 l 0 .08 .500 .040 3.83 .022 23 l O 0 .04 .000 .000 --- -—- 24 l 1 O .04 .000 .000 --- --- 25 0 .00 R = 21 m = 4.32 animals 0 x x 21 m e‘rX = 1.004 x x _ lnRo 1.463 _ — —HF— — 07T74 — 8.41 days 17 Table 7. Chydorus sphaericus at 25 C: Age—specific fertiliEy (mXYand survival (1x), with calculations for R0, 3, and 2. Days No. of No. of No. of r—.143 (x) animals deaths births lx mx lxmx rx e-rx 0 25 0 0 1.00 .000 .000 —-- --— l 25 0 0 1.00 .000 .000 -—- --- 2 25 O 0 1.00 .000 .000 --- ——- 3 25 0 0 1.00 .000 .000 ~-- -—— 4 25 O O 1.00 .000 .000 --- --— 5 25 0 0 1.00 .000 .000 —-- -—- 6 25 0 O 1.00 .000 .000 --- --- 7 25 0 0 1.00 .000 .000 -—- --- 8 25 0 0 1.00 .000 .000 --- --- 9 25 0 4 1.00 .160 .160 1.29 .275 10 25 0 24 1.00 .960 .960 1.43 .239 11 25 0 16 1.00 .640 .640 1.57 .208 12 25 0 6 1.00 .240 .240 1.72 .179 13 25 O 6 1.00 .240 .240 1.86 .156 14 25 O 16 1.00 .640 .640 2.00 135 15 25 O 16 1.00 .640 .640 2.15 .116 16 25 0 10 1.00 .400 .400 2.29 .101 17 25 0 4 1.00 .160 .160 2.43 .088 18 25 0 16 1.00 .640 .640 2.57 .077 19 25 0 18 1.00 .720 .720 2.72 066 20 25 0 10 1.00 .400 .400 2.86 .057 21 25 0 4 1.00 .160 .160 3.00 .050 22 25 0 14 1.00 .560 .560 3.15 .043 23 25 0 20 1.00 .800 .800 3.29 .037 24 25 0 8 1.00 .320 .320 3.43 .032 25 25 0 6 1.00 .240 .240 3.58 .028 26 25 0 18 1.00 .720 .720 3.72 .024 27 25 0 16 1.00 .640 .640 3.86 .021 28 25 0 8 1.00 .320 .320 4.00 .018 29 25 0 8 1.00 .320 .320 4.15 .016 30 25 O 18 1.00 .720 .720 4.29 .014 18 Table 7 continued. Days No. of No. of No. of m l m r=.143 -rx (x) animals deaths births x x x x rx e 31 25 0 18 1.00 .720 .720 4.43 .012 32 25 0 4 1.00 .160 .160 4.58 .010 33 25 O 10 1.00 .400 .400 4.72 .009 34 25 0 14 1.00 .560 .560 4.86 .008 35 25 0 20 1.00 .800 .800 5.01 .007 36 25 0 4 1.00 .160 .160 5.15 .006 37 25 0 8 1.00 .320 .320 5.29 .005 38 25 0 16 1.00 .640 .640 5.43 .004 39 25 0 18 1.00 .720 .720 5.58 .004 40 25 0 6 1.00 .240 .240 5.72 .003 41 25 0 8 1.00 .320 .320 5.86 .003 42 25 0 16 1.00 .640 .640 6.01 .002 43 25 0 16 1.00 .640 .640 6.15 .002 44 25 0 4 1.00 .160 .160 6.29 .002 45 25 0 8 1.00 .320 .320 6.44 .002 46 25 0 22 1.00 .880 .880 6.58 .001 47 25 0 10 1.00 .400 .400 6.72 .001 48 25 0 8 1.00 .320 .320 6.86 .001 49 25 0 6 1.00 .240 .240 7.01 .001 50 25 0 18 1.00 .720 .720 7.15 .001 51 25 0 4 1.00 .160 .160 7.29 .001 52 25 0 12 1.00 .480 .480 7.44 .001 53 25 O 10 1.00 .400 .400 7.58 .001 54 25 0 16 1.00 .640 .640 7.72 .000 55 25 0 0 1.00 .000 .000 56 25 0 12 1.00 .480 .480 57 25 0 8 1.00 .320 .320 58 25 0 24 1.00 .960 .960 59 25 0 3 1.00 .120 .120 60 25 0 6 1.00 .240 .240 61 25 1 6 1.00 .240 .240 62 24 0 10 .96 .417 .400 63 24 0 4 .96 .167 .160 64 24 0 8 .96 .333 .320 65 24 0 3 .96 .125 .120 19 Table 7 continued. Days No. of No. of No. of m 1 m (x) animals deaths births x x x x 66 24 l 6 .96 .250 .240 67 23 0 2 .92 .087 .080 68 23 1 2 .92 .087 .080 69 22 0 0 .88 .000 .000 70 22 l 2 .88 .091 .080 71 21 0 3 .84 .143 .120 72 21 0 4 .84 .190 .160 73 21 O 2 .84 .095 .080 74 21 0 10 .84 .476 .400 75 21 0 9 .84 .429 .360 76 21 0 4 .84 .190 .160 77 21 0 2 .84 .095 .080 78 21 l 10 .84 .476 .400 79 20 0 10 .80 .500 .400 80 20 O 6 .80 .300 .240 81 20 1 2 .80 .100 .080 82 19 0 4 .76 .211 .160 83 19 0 6 .76 .316 .240 84 19 l 8 .76 .421 .320 85 18 0 6 .72 .333 .240 86 18 0 8 .72 .444 .320 87 18 0 6 .72 .333 .240 88 18 2 8 .72 .444 .320 89 16 1 10 .64 .500 .320 90 16 1 8 .64 .500 .320 91 15 0 2 .60 .133 .080 92 15 0 6 .60 .400 .240 93 15 0 10 .60 .667 .400 94 15 0 8 .60 .533 .320 95 15 0 5 .60 .333 .200 96 15 0 4 .60 .267 .160 97 15 0 6 .60 .400 .240 98 15 0 2 .60 .133 .080 99 15 0 5 .60 .333 .200 100 15 1 6 .60 .400 .240 20 Table 7 continued. Days No. of No. of No. of (x) animals deaths births x mX lxmx 101 14 0 6 .56 .429 .240 102 14 0 4 .56 .268 .160 ._ 103 14 0 6 .56 .268 .160 ‘\ 104 14 0 4 .56 .268 .160 7 105 14 l 4 .56 .286 .160 106 13 0 4 .52 .308 .160 107 13 0 4 .52 .308 .160 108 13 O 4 .52 .308 .160 109 13 1 2 .52 .154 .080 110 12 0 4 .48 .333 .160 111 12 1 2 .48 .167 .080 112 11 0 2 .44 .182 .080 113 11 1 0 .44 .000 .000 114 10 0 2 .40 .200 .080 115 10 0 2 .40 .200 .080 116 10 0 0 .40 .000 .000 117 10 0 0 .40 .000 .000 118 10 0 2 .40 .200 .080 119 10 0 0 .40 .000 .000 120 10 0 0 .40 .000 .000 121 10 2 0 .40 .000 .000 122 8 0 0 .32 .000 .000 123 8 2 0 .32 .000 .000 124 6 0 4 .24 .667 .160 125 6 l O .24 .000 .000 126 5 0 O .20 .000 .000 127 5 l 0 .20 .000 .000 128 4 0 0 .16 .000 .000 129 4 0 0 .16 .000 .000 130 4 2 0 .16 .000 .000 131 2 1 0 .08 .000 .000 132 1 1 O .04 .000 .000 133 0 .00 R = 21 m = 34.96 animals 0 x x 21 m e'rX = 0.993 x x lnR _ 3.555 T = ‘ 0.143 = 24.86 days HI. 21 Table 8. Pleuroxus denticulatus at 15 C: Age-specfic fertility (mX) and mortality (1X), with calcula— tions for R0, r, and 2. Days No. of No. of No. of l r=0.096 (x) animals deaths births x mx xmx rx e-rx 0 25 O 0 1.00 .000 .000 --— --- 1 25 O O 1.00 .000 .000 --- --- 2 25 0 0 1.00 .000 .000 —-— —-— 3 25 0 0 1.00 .000 .000 --— --- 4 25 0 0 1.00 .000 .000 --- --- 5 25 0 0 1.00 .000 .000 --- --- 6 25 0 0 1.00 .000 .000 --— --— 7 25 0 0 1.00 .000 .000 --- —-— 8 25 0 0 1.00 .000 .000 -—- --— 9 25 0 0 1.00 .000 .000 --- —-- 10 25 0 0 1.00 .000 .000 --- --- 11 25 0 4 1.00 .160 .160 1.06 .346 12 25 0 10 1.00 .400 .400 1.15 .317 13 25 0 7 1.00 .280 .280 1.25 .287 14 25 O 6 1.00 .240 .240 1.34 .262 15 25 0 4 1.00 .160 .160 1.44 .237 16 25 0 8 1.00 .320 .320 1.54 .214 17 25 0 10 1.00 .400 .400 1.63 .196 18 25 1 6 1.00 .240 .240 1.73 .177 19 24 0 6 .96 .250 .240 1.82 .162 20 24 O 12 .96 .500 .480 1.92 .147 21 24 0 6 .96 .250 .240 2.02 .133 22 24 0 6 .96 .250 .240 2.11 .121 23 24 1 12 .96 .500 .480 2.21 .110 24 23 0 l .92 .043 .040 2.30 .100 25 23 0 9 .92 .391 .360 2.40 .090 26 23 0 6 .92 .261 .240 2.50 .082 27 23 O 7 .92 .304 .280 2.59 .075 28 23 0 8 .92 .348 .320 2.69 .068 29 23 O 7 .92 .304 .280 2.78 .062 30 23 0 8 .92 .348 .320 2.88 .056 mi- ., -~ >r-O—'- .. 22 Table 8 continued. Days No. of No. of No. of 1 m 1 m r=0.096 e'rx (x) animals deaths births x x x rx 31 23 l 4 .92 .174 .160 2.98 .051 32 22 0 2 .88 .091 .080 3.07 .046 33 22 0 6 .88 .273 .240 3.17 .042 34 22 0 2 .88 .091 .080 3.26 .038 35 22 0 8 .88 .364 .320 3.36 .035 36 22 2 5 .88 .227 .200 3.46 .031 37 20 0 5 .80 .250 .200 3.55 .029 38 20 1 3 .80 .150 .120 3.65 .026 39 19 0 6 .76 .316 .240 3.74 .024 40 19 0 2 .76 .105 .080 3.84 .021 41 19 1 4 .76 .211 .160 3.94 .019 42 18 0 2 .72 .111 .080 4.03 .018 43 18 0 4 .72 .222 .160 4.13 .016 44 18 0 6 .72 .333 .240 4.22 .014 45 18 1 4 .72 .222 .160 4.32 .013 46 17 1 9 .68 .529 .360 4.42 .012 47 16 0 2 .64 .125 .080 4.51 .011 48 16 0 0 .64 .000 .000 —-— --— 49 16 0 4 .64 .250 .160 4.70 .009 50 16 1 6 .64 .375 .240 4.80 .008 51 15 0 2 .60 .133 .080 4.90 .007 52 15 0 4 .60 .267 .160 4.99 .007 53 15 0 0 .60 .000 .000 ——— ——- 54 15 3 0 .60 .000 .000 -—— —-- 55 12 2 0 .48 .000 .000 —-— ——— 56 10 l 4 .40 .400 .160 5.38 .005 57 9 0 2 .36 .222 .080 5.47 .004 58 9 0 2 .36 .222 .080 5.57 .004 59 9 0 0 .36 .000 .000 ——— --— 60 9 1 0 .36 .000 .000 —-— —-— 61 8 O 1 .32 .125 .040 5.86 .003 62 #8, 0 1 .32 .125 .040 5.95 .003 63 8 1 2 .32 .250 .080 6.05 .002 64 7 l 0 .28 .000 .000 —-- --— 65 6 1 0 .24 .000 .000 ——— --- 23 Table 8 continued. Days No. of No. of No. of 1 m l m r=0.096 e'rx (x) animals deaths births x X x x rx 66 5 0 0 .20 .000 .000 --- -—- 67 5 0 1 .20 .200 .040 6.43 .002 68 5 0 0 .20 .000 .000 -—- --— 69 5 1 0 .20 .000 .000 —-- --- 70 4 0 0 .16 .000 0000 ——- —-— 71 4 0 2 .16 .500 .080 6.82 .001 72 4 0 0 .16 .000 .000 —-— --— 73 4 0 0 .16 .000 .000 --- —-- 74 4 0 0 .16 .000 .000 --- —-— 75 4 0 l .16 .250 .040 7.20 .001 76 4 0 2 .16 .500 .080 7.30 .001 77 4 0 0 .16 .000 .000 —-- -—— 78 4 0 0 .16 .000 .000 --- -—— 79 4 0 0 .16 .000 .000 -—- --- 80 4 0 2 .16 .500 .080 7.68 .000 81 4 0 O .16 .000 .000 82 4 0 4 .16 1.000 .160 83 4 0 0 .16 .000 .000 84 4 0 0 .16 .000 .000 85 4 0 0 .16 .000 .000 86 4 0 0 .16 .000 .000 87 4 0 2 .16 .500 .080 88 4 0 4 .16 1.000 .160 89 4 0 0 .16 .000 .000 90 4 0 0 .16 .000 .000 91 4 0 0 .16 .000 .000 92 4 0 0 .16 .000 .000 93 4 0 2 .16 .500 .080 94 4 O 0 .16 .000 .000 95 4 1 0 .16 .000 .000 96 3 0 0 .12 .000 .000 97 3 0 l .12 .333 .040 98 3 l 0 .12 .000 .000 99 2 0 2 .08 1.000 .080 100 2 0 0 .08 .000 .000 24» Table 8 continued. Days No. of No. of No. of 1 m l m (x) animals deaths births x x x x 101 2 0 0 .08 .000 .000 102 2 0 0 .08 .000 .000 103 2 0 2 .08 1.000 .080 104 2 0 0 .08 .000 .000 105 2 0 0 .08 .000 .000 106 2 0 0 .08 .000 .000 107 2 O 0 .08 .000 .000 108 2 0 O .08 .000 .000 109 2 1 2 .08 1.000 .000 110 1 0 0 .04 .000 .000 111 1 0 0 .04 .000 .000 112 1 0 0 .04 .000 .000 113 l 0 0 .04 .000 .000 114 1 0 0 .04 .000 .000 115 1 0 0 .04 .000 .000 116 1 0 0 .04 .000 .000 117 1 0 0 .04 .000 .000 118 l O 0 .04 .000 .000 119 l 0 O .04 .000 .000 120 1 0 2 .04 2.000 .080 121 1 1 0 .04 .000 .000 122 0 .00 R = 21 m = 10.96 animals 0 x x 21 m e"rX = 1.005 XX T __ lnRO _ 2.398 _ — r' _ 0.096 _ 24.98 days 25 where e is the base of the natural logarithms. The process of finding the correct value of E is one of trial—and—error; various values of E are used in solving the right—hand side of the equation, until a value is selected such that the summation approximates unity. Column 7 lists the product (1XmX) of the fifth and sixth columns at each age x. These—pfgducts are used in finding both E and R0. Four to six—trials usually were required before finding suitable values of E for each of the four popula— tions. Graphical methods aided in approximating Er once it was bracketed (Southwood, 1966). Column 8 in Tables 5—8 gives the products of each age x, and the most suit— able value of E' Column 9 shows the values of the eighth column expressed as the negative exponential of 3 obtained from tables of negative exponentials of e. For the value of E given at the top of column 8, the sum of the products of the seventh and ninth columns (leXe’rx) more nearly approaches unity than any other third decimal place number. Values for Ex and e'rX were not calculated where leX = 0, —rx §___ nor continued beyond that x where Ex was so large that was less than 0.000. Net reproduction per individual, Ro’ is given by Birch (1948) as 21 m = R . x x o 26 Values for R0 were obtained by summing column 7 over all values of 5. The mean length of generation, T, is given by 1 R = erT or by T = n O . T for each population was calculated with the values ob- tained for E and R0. In the case of the chydorids, T takes units of days. Values of 5, R0, and T for the four populations studied are summarized 1; Table 9. Confidence intervals of 95% were calculated for the values of E by dividing each of the populations into five groups of five animals each. Since the animals are not listed in any particular order in Tables 1-4, these cohorts were made of animals numbered 1-5, 6-10, etc. Age- specific fertility and mortality tables were then prepared for the 20 populations thus created. Values of £_were cal- culated for each of these populations. Using these values, mean E and 95% confidence intervals were determined for each species at 25 and 15 C (Table 9). DISCUSSION The values of E determined for the two species of Chydoridae are similar to those found for other small aquatic crustaceans (Table 10). The E given for Daphnia puTeg was found for the control population of Marshall's (1962) experiments with the influence of radiation on £° 27 OHo.o fl OOo.o O0.0N O0.0H OOo.o 0 OH #m meOstHm Ooo.o H OOH.o O0.0N O0.00 OOH.o 0 OH um mDHOUMSO OOO.o H OOH.o H0.0 N0.0 OOH.o 0 ON #6 meOHSOHm OHo.o H OON.o ON.OH O0.0H OON.O 0 ON #6 mDHOUNQU mHmEHcm w>am . . Amhmwv AmHmEHcmv mo mpnonpw Mom B o .H.0 OOO . H saws m .mmvHHOUOS0 mo meHpMHsmom OHODMHOQMH usom mo H van .om .M Mom mmsHm> .m anme TIT}. .111 28 meHm> me mo Gme ««« 6 HH pm quflaumpmc 4. o ON um Omcflagwhmw * mHo>wH 000% 30H cam .w#mmeOE .QOHQ "A0 .AQ 4AM AOOOHO Hmmooo m>flummma oao.o *4.mOo.o HOo.o momuum mamHHmmm hwsum Dammmum OO0.0 OOH.O mopMHDOHuch msxousmHm %©d#m gammwum OOH.O OON.O mSUHmezmw mSHOUOQU 0v O0.0 .Qsmcd .COm:£0O .S.Q my OO.O .Qm demnmmooEHm ««ov O0.0 UV ON.O 0v O0.0 ««Qv OH.O QV O0.0 9V O0.0 I AOOOHV HHmm ««mv NH.O my O0.0 mv H0.0 wwpoccmfi mummHmw .Q AOOOHO nuflam OmN.o mamma .m ANOOHV HHmanmz «O0.0 wasm MHcammo OH OH ON ON wOHDom 0 @803 meommm .mcmwomgmsuo UHumswm HHmEm Mom m mo mmsHm> .OH mHQme 29 The value for Q. magna is the maximum 5 at which Smith (1963) maintained populations of the animal with continuous culture techniques. The values for Simocephalus are un- published determinations by Mr. Dan Johnson of Michigan State University. Values for the amphipod, Hyalella azteca, are presented for comparison with the Cladocera that com- prise the remainder of the list. While the E values for the chydorids are not greatly different from the other values, they are lower than those found for other Cladocera at a given temperature 3.3. 25 C. The explanation for this is relatively simple, for, as Slobodkin (1961) points out, in an animal that matures early, the number of young in the first reproductive period has a much greater impact on E than other reproductive fac— tors. The chydorids of this study are limited anatomically to two young per brood; the other Cladocera in Table 10 have no such limitation. Since the Cladocera begin to re— produce at about the same time after hatching, it is not surprising that the multi-egg animals have higher values of E than do the Chydoridae. It is not yet possible to speculate on the influ— ence of the littoral and limnetic environments in selecting for high and low values of 3, because there is a lack of determinations of E for a range of animals living in these two environments. With the exception of the Chydoridae, the E values of the littoral and pond forms (Simocephalus, 30 Q. pulex) are very similar to those of the limnetic form (2. galeata mendotae). The values of E determined from the entire pOpu- lations of 25 animals are all close to the average values of E for the cohorts of five animals. In all cases, they lie well within the confidence intervals about the mean value. There is no overlap of the confidence intervals, so that the differences in the calculated values of E for the four chydorid populations are significantly different. It was expected that the animals would exhibit the different rates of population growth for the various tem— peratures, but there was no expectation that the E values for the two species of Chydoridae would differ as much as observed. In contrasting the two Species, Pleuroxus was a more erratic producer of young than Chydorus (Tables 1—4). The most striking example is the Pleuroxus popula- tion at 25 C where the animals grew to maturity, produced about two broods of young (R0 = 4.32), and then died. Certain individuals of Pleuroxus seemed capable of match— ing the fertility of Chydorus, however. Perhaps the greatest factor in the difference between the values of E for the two species is the difference of average ages when the first young were produced, which affects E greatly. Perhaps one of the reasons for this delay in re- production of Pleuroxus can be attributed to its tendency to become stuck in the experimental surface film during 31 its early instars. This tendency is almost entirely ab- sent in Chydorus. For this reason, the E values for Pleuroxus may be somewhat lower than the animal is capable of achieving under natural conditions of unlimited popu— lation growth. Reproduction by older animals is rather sporadic (Tables 1—4). The older animals did not follow the usual pattern of cladoceran reproduction, in which the eggs are extruded into the brood pouch almost immediately after the previous brood has been released. Often, in the older animals, a considerable period of days would elapse between emptying and refilling of the brood pouch. None of the previous studies of Cladocera has noted whether this er— ratic production is normal in old individuals or whether this is an artifact of laboratory culture. Only Marshall (1962) has similarly carried the 1X and mX through until all the animals of the original population had succumbed. CONCLUSION The statistics of population growth determined in laboratory studies such as these have only limited value in themselves. They can serve as bases for the comparison of the potential rate of increase of organisms widely dif— fering in life span, g.g. bacteria and man (Smith, 1954). They can also serve as a measure of the response to varia— tions of environmental factors, such as food or temperature. 32 The laboratory population studies have little direct bearing on field studies of the same animals. Determinations of E for Daphnia galeata mendotae (Hall, 1964) and fiyallella azteca (Cooper, 1965) had little practical value in the subsequent studies in the field. Perhaps the study re- ported here can be applied to a field situation somewhat more easily than others, because of the limitation on brood size in the chydorids. They are probably not capable of demonstrating the wide response of other Cladocera to feed— ing levels. Laboratory studies such as this can, however, im- part direction and purpose to studies of the dynamics of natural populations. The numerous observations are a fer- tile source of ideas of methods and techniques of field study. In suggesting approaches to the study of the Chy- doridae in the littoral zone of lakes, this study in the laboratory has proved invaluable. LITERATURE CITED Andrewartha, H. G. and L. C. Birch. 1954. The distribution and abundance of animals. Univ. Chicago Press, Chicago. 782 p. Birch, L. C. 1948. The intrinsic rate of natural increase of an insect population. J. Anim. Ecol. 17:15-26. Brooks, J. L. 1959. Cladocera, p. 587-656. TE_W. T. Edmondson (ed.), Ward & Whipple's Fresh-water Biology. J. Wiley and Sons, New York. COOper, W. E. 1965. Dynamics and productivity of a natural population of a fresh-water amphipod, Hyalella azteca. Ecol. Monogr. 35:377—394. Fldssner, D. 1964. Zur Cladocerenfauna des Stechlinsee— Gebietes. II. Okologische Untersuchungen uber die litoralen Arten. Limnologica 2:35-103. Hall, D. J. 1964. An experimental approach to the dynamics of a natural population of Daphnia galeata mendotae. Ecology 45:94—112. Lotka, A. J. 1925. Elements of physical biology. Williams & Wilkins, Baltimore. 460 p. Marshall, J. S. 1962. The effects of continuous gamma ra- diation on the intrinsic rate of natural increase of Daphnia pulex. Ecology 43:598-607. Slobodkin, L. B. 1961. Growth and regulation of animal populations. Holt, Rinehart, and Winston, New York. 184 p. Smirnov, N. N. 1962. Eurycercus lamellatus (0. Fa Muller) (Chydoridae, Cladocera): Field observations and nutrition. Hydrobiologia 20:280-294. . 1964. Pleuroxus (Chydoridae): Field observa- tions and growth. Hydrobiologia 23:305-320. Smith, F. E. 1954. Quantitative aspects of population growth. In E. Boell, (ed.), Dynamics of growth processes, Princeton Univ. Press, Princeton, N. J. 33 34 . 1963. Population dynamics in Daphnia magna and a new model for population growth. Ecology 44:651- 663. Southwood,TH R. E. 1966. Ecological methods, with particu— lar reference to the study of insect populations. Methuen and Co., London. 391 p. Welch, P. S. 1948. Limnological methods. McGraw-Hill Co., N. Y. 381 p. MICHIGAN STATE UNIV. LIBRARIES mWITHINWTWIlIHIWHTWIWTWHW 31293102529769