Population growth and intra-specific competition in duckweed

Transcription

1 Populaion growh and inra-specific compeiion in duckweed We will use a species of floaing aquaic plan o invesigae principles of populaion growh and inra-specific compeiion, in oher words densiy-dependence. Proocol 1) Label each ub wih your lab secion using ape and a marker 2) Number each cup wih a unique number so ha daa can be recorded for each cup, or experimenal uni. 4) The base-level growing condiions will be 50mL of he prepared Swedish Sandard Growh Medium and 50mL of disilled waer. You can use he graduaions on he side of he specimen cups for his measuremen. 5) As a class, design an experimen o describe densiy-dependence in his species. You wan o examine growh raes a a range of densiies. You have 90 experimenal unis (i.e. cups) wih which o design your experimen. Consider wha should be conrolled, versus random, versus manipulaed. Think abou how your design deermines your analysis (noe, you may need o read ahead o he daa analysis secion). 6) Serilize inoculaing loop wih 70% ehanol by dipping loop in ehanol (ETOH) dish and hen rinsing he loop wih disilled waer over he rinse dish. Serilizaion only needs o be done once a beginning of lab no afer every frond is moved. 7) Add plans according o your experimenal design. Remember when couning ha Lemna and Spirodela ypically grows in clumps of 2-4 plans each frond couns as an individual. Coun fronds if hey are a leas 50% healhy (i.e no covered in dark green algae, and no grey indicaing hey are dead. Coun hose ha are green or yellow). Daa collecion Record he number of plans placed ino each cup a he sar of he experimen (N 0 ). A he end of he experimen, record he number of plans in each cup (N 7 ). The subscrip 7 here denoes he 7 days. A visual guide such as he edge of a piece of paper may be useful when couning. Use ally clickers o assis in couning. Selec abou 5 of he cups across your range of densiies and re-coun he cups. This will give you a sense of your experimenal error when inerpreing your resuls. You can use he average of he 2 couns for your bes esimae of he iniial cup coun. Oher informaion The ligh ower has been placed on a cycle of 16 hours of ligh and 8 hours of dark. 1

2 Daa Shee Cup # N 0 N 7 Cup # N 0 N 7 2

3 Daa Analyses Here is he expression for per-capia growh rae given a general equaion for densiyindependen growh. The populaion size is N and f(n) is he pre-capia growh rae as a funcion of he densiy. dn d dn d f ( N ) N 1 N f ( N ) (1) Assume for a momen ha he per-capia growh rae is a consan over he ime period of our experimen, f (N) = r. We can use he soluion for densiy-independen growh o derive a formula for he per-capia growh rae, r, based on measures of duckweed populaion size a 2 paricular ime poins. r N N e 0 N r e N0 N (2) ln r N 0 ln N ln( N0) r Take he final expression and subsiue back ino our funcion for per capia growh rae, f. ln N ln( N0) f ( N0) (3) Use equaion 3 o plo he per capia growh raes of your daa versus he iniial densiy. We arbirarily choose N 0 o plo agains f, alhough we could have chosen N. Now compare he shape of your daa o ha modeled in he logisic model of densiydependence, equaion 4. Noe ha o avoid confusion I am using m o equal he maximum per capia growh rae (a low densiy). N f ( N) m 1 k (4) m f ( N) m N k Noice how he expression for per-capia growh rae in he logisic model can be re-arranged o form a sraigh line. By fiing a sraigh line o your daa (i.e. regression analysis), you can now esimae he parameers m and k from he logisic model. Wha are he caveas for your esimaes? To wha condiions do hey apply? 3

4 You can find he slope and inercep from daa using regression. You can simulaneously examine he slope of wo differen facors using GLM. In R Commander choose Saisics/Fi models/linear model. Choose he response variable on he lef-hand side of he ~. On he righ-hand side, choose boh facors separaed by a *. A significan ineracion indicaes ha he slope of densiy dependence is differen a a leas some of he nurien levels. If he ineracion is no significan, he slopes are he same across nurien levels. 4

5 Design your own experimen The nex ime you work wih duckweed, you will design and conduc your own experimen based on your own quesion or hypohesis. Your experimen could be designed o examine a coninuous facor or a discree facor. A number of poenially imporan condiions could be examined. Ligh levels can be adjused wih shade cloh. Differen levels of nurien soluion a he beginning of he experimen. Talk o your TA abou wha nuriens can be modified. Compeiion wih anoher species. Aack by a duckweed herbivore. Wrie down your hypohesis or quesions now, and communicae wih your TA abou he equipmen and organisms needed for your experimen. 5