Describing Communities. Species Diversity Concepts. Species Richness. Species Richness. Species-Area Curve. Species-Area Curve

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1 peces versty Concepts peces Rchness peces-area Curves versty Indces - mpson's Index - hannon-wener Index - rlloun Index peces Abundance Models escrbng Communtes There are two mportant descrptors of a communty: ) ts physognomy (physcal structure), as descrbed n the prevous lecture, and ) the number of speces present and ther relatve abundances (speces rchness and dversty). peces Rchness The smplest way to descrbe a communty s to lst the speces n t. peces rchness () s the number of speces on that lst, and s most often used as the frst pass estmate of dversty for a communty. How would one generate such a lst? A smple and wdely used method s to defne the boundares of the communty and then walk through t seasonally, notng all the speces you encounter. Ths s what we call a flora. peces Rchness Whle smply fndng and lstng the speces s useful, ths method has many lmtatons. If we wsh to compare two or more communtes, we need comparable samples, otherwse we mght just fnd a dfference because one was sampled more ntensvely than the other. Ths begs the queston, how much samplng should we do n order to be confdent that we have found most of the speces n each communty? peces-area Curve peces-area Curve One way to make ths nterpretaton s through the use of a speces-area curve. A graph of the total number of speces found as the number of quadrats ncreases explans the relatonshp. We know that we have sampled suffcently when the curve begns to "plateau". No. of peces () 7 No. of m quadrats Concluson: - quadrats would be suffcent to descrbe the vegetaton n ths communty. After many years of study, we now realze that the classcal percepton of the shape of a "typcal" specesarea curve s an artfact of the type of communtes n whch the relatonshp was frst descrbed. Moreover, t s now apparent, that habtat gran, patch sze, and equtablty wll have a substantal nfluence on the shape of the curve and must be evaluated n that context.

2 peces-area Curve Fne-graned; hgh equtablty (classcal condton) peces-area Curve Fne-graned; low equtablty peces-area Curve Coarse-graned; equal patch sze peces-area Curve Coarse-graned; unequal patch sze Gran, Patch ze, Equtablty peces Rchness Whle many studes nclude as a descrptve factor assocated wth the communty, t s largely unnformatve n as much as t does not reflect relatve abundance. Example: suppose two communtes ( & ) each contan ndvduals dstrbuted among fve speces (A-E): A C E Comm- Comm- 6 Are these two communtes equvalent?

3 peces Rchness There are two ways to overcome ths problem: ) ncorporate both speces rchness and abundance nformaton n to one dversty ndex. ) rely on speces rchness but control for the effects of sample sze by a procedure called rarefacton. We wll examne both alternatves as they are wdely used n ecology. One of the fundamental tenants of dversty s that the number of speces found n a gven sample s strongly dependent upon the sze of that sample. Ths makes good ntutve sense n that the more quadrats one samples n a plant communty, the more lkely you are to pck up more and more rare speces. One method of avodng ncompatblty of measurements resultng from samples of dfferent szes s called rarefacton. N - N N n E() - / n Where E() s the expected number of speces n the rarefed sample, n s the standardzed sample, N s the total number of n the sample to be rarefed, and N s the number of ndvduals n the th speces n the sample to be rarefed, summed over all speces counted. The term N n s a "combnaton" that s calculated as: N N! n n! N n! where N! s a "factoral", e.g.,! Ths combnaton s mportant, because t allows us to calculate all the possble numbers of unque speces combnatons... For example, f we have four speces, A,, C,, then we have sx speces pars: A, AC, A, C,, C. Usng the combnatoral equaton:! 6!! Thus N s the number of unque combnatons of N n taken n at a tme;.e., the number of dfferent ways of pckng speces pars from four dfferent speces. Let's look at a fully worked real-world example (taken from Magurran 88). Imagne two moth traps that have been set out n a forest to montor moth dversty. Trap- was nadvertently left out for only about half the tme as Trap-A. We know ths wll be a problem because Trap-A "sampled" the envronment more (longer perod of tme) and s lkely to pck up more speces. To compare between traps would be msleadng and napproprate.

4 Moth lght traps are typcally suspended above the vegetaton and contan a battery powered lght. The trap s set to operate only durng the evenng hours. Moths are drawn to the lght and become entrapped n the canster below. As expected, Trap-A has more speces. The best way to correct for the dfference n samplng tme s to ask, How many speces would we expect to fnd n Trap-A f t too contaned ndvduals? peces N No. of Indvduals Trap-A Trap- 6 Frst, take the number of ndvduals of each speces from Trap-A and nsert them nto the formula. For speces n Trap-A: N, n, N, N-N N! n! ( - )! N-N! n! -! ( ) therefore:!! - / /66..!!!! { [ ] } Contnue ths same set of calculatons for each speces (to determne the expected number) and then sum the values (as per the Σ n the equaton). Zero values need not be ncluded as they have no nfluence on the estmate. E() Expected Concluson: If Trap-A contaned ndvduals, we would expect t to contan 6.8 speces--about the same as Trap-. N versty Indces As already alluded to, the dversty of a communty needs (n most nstances) to account for both speces rchness and the evenness wth whch ndvduals are dstrbuted among speces. One way to do ths s through the use of a proportonal abundance ndex. There are two major forms of these ndces: domnance ndces and nformaton ndces. Whle more than 6 ndces have been descrbed, we wll look at the three most wdely used n the ecologcal lterature: mpson's, hannon-wener, and rlloun. mpson's Index mpson's Index s consdered a domnance ndex because t weghts towards the abundance of the most common speces. mpson's Index gves the probablty of any two ndvduals drawn at random from an nfntely large communty belongng to dfferent speces. For example, the probablty of two trees, pcked at random from a tropcal ranforest beng of the same speces would be relatvely low, whereas n boreal forest n Canada t would be relatvely hgh.

5 mpson's Index mpson's Index The bas corrected form of mpson's Index s: ( n ( n ) ) ( N( N ) ) where n s the number of ndvduals n the th speces. A worked example for trees of speces assessed n several quadrats: Tree spp. A C E Total No. Indvduals nce s and dversty are negatvely related, mpson's ndex s usually expressed as the recprocal (-) so that as the ndex goes up, so does dversty Then / /.88.6 hannon-wener Index The hannon-wener Index belongs to a subset of ndces that mantan that dversty can be measured much lke the nformaton contaned n a code or message (hence the name nformaton ndex). The ratonale s that f we know a letter n a message, we can know the uncertanty of the next letter n a coded message (.e., the next speces to be found n a communty). hannon-wener Index The hannon Index assumes that all speces are represented n a sample and that the sample was obtaned randomly: H' - p ln p where p s the proporton of ndvduals found n the th speces and ln s the natural logarthm. The uncertanty s measured as H', the hannon Index. A message coded bbbbbb has low uncertanty (H' ). hannon-wener Index A worked example from a communty contanng trees dstrbuted among speces: Total peces A C E Abund p p ln p hannon-wener Index The most mportant source of error n ths ndex s falng to nclude all speces from the communty n the sample. Ths makes a speces-area curve assessment very mportant at the begnnng of a study. Values of the hannon dversty ndex for real communtes typcally fall between. and.. H'.

6 hannon-wener Index The hannon ndex s affected by both the number of speces and ther equtablty, or evenness. A greater number of speces and a more even dstrbuton OTH ncrease dversty as measured by H'. The maxmum dversty (H max ) of a sample s found when all speces are equally abundant. H max ln, where s the total number of speces. Evenness We can compare the actual dversty value to the maxmum possble dversty by usng a measure called evenness. The evenness of the sample s obtaned from the formula: Evenness H'/H max H'/ln y defnton, E s constraned between and.. As wth H', evenness assumes that all speces are represented wthn the sample. rlloun Index When the randomness of a sample cannot be guaranteed, the rlloun Index H s preferable to the H': ln N! - ln n! H N where N s the total number of ndvduals and n s the number of ndvduals n the th speces. A worked example follows... rlloun Index peces No. Indvduals ln n! N Σ. ln N! - ln n! ln! -. H.6 N Evenness Evenness for the rlloun Index s estmated as: H E H where H max represents the maxmum possble rlloun dversty, that s, a completely equtable dstrbuton of ndvduals between speces. In our example, we had complete equtablty, therefore, H max H.. versty Indces As you have probably fgured out, the choce of a partcular ndex s chosen wth respect to the goals of the study (emphass on abundant vs rare speces) and to what extent samplng can be assured to be random. There are other factors that come n to play, but these are the most wdely used measures of dversty that ncorporate both rchness and evenness nto the determnaton. Note: There s generally NO relatonshp between one ndex and another. 6

7 peces Abundance Models One of the earlest observatons made by plant ecologsts was that speces are not equally common n a gven communty. ome were very abundant, other were uncommon. A graphcal way was sought to descrbe ths pattern, and so arose speces abundance models. These models are strongly advocated among some ecologsts because they emphasze abundance whle utlzng speces rchness nformaton and therefore provde the most complete mathematcal descrpton of the data. peces Abundance Models A speces abundance model s generated by graphng the abundance of each speces aganst ts rank order abundance from hghest to N lowest. One of four dstrbutons usually arse: Log normal dstrbuton Geometrc seres Logarthmc seres McArthur's broken stck model peces Abundance Models peces Abundance Models (Changes through successon - azzaz 7) 7

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