Biol. 356 Lab 8. Moraliy, Recruimen, and Migraion Raes (modified from Cox, 00, General Ecology Lab Manual, McGraw Hill) Las week we esimaed populaion size hrough several mehods. One assumpion of all hese mehods was ha he populaion we were esimaing was a closed populaion. In oher words, we assumed ha here was no immigraion or emigraion, and furher ha here was no recruimen (birhs) ino he populaion. Some moraliy may have occurred during our populaion esimaes, bu we assumed ha moraliy occurred equally in he marked sample and in he populaion as a whole, and we were unable o deermine how much moraliy was occurring. (This is why our populaion esimaes were esimaes a he ime ha he marked individuals were released, and no esimaes a he ime he marked individuals were recapured). This week, we will learn abou a simple way o use mark-recapure echniques o esimae moraliy raes as well as birh raes, immigraion and emigraion raes. This ype of mark-recapure echnique requires ha collecions be made from a populaion on hree separae daes. Addiionally, i requires ha he area of collecion be uniform and se up in a specific manner. The sudy area needs o be divided ino wo sub-areas: an inner area and an ouer area, and he inner area needs o have a boundary lengh exacly one-half ha of he ouer area s boundary. The simples way o accomplish his is o have an inner area in he shape of a square, wih an ouer area being anoher square wih sides exacly wice as long as he inner square. Thus, you will have nesed squares, wih he inner square being exacly ¼ he area of he oal. We will call hese he inner area, ouer area and oal area respecively. (The oal area is he sum of he inner and ouer areas). Ouer area Inner area Dae 1. Animals are capured in boh inner and ouer areas, and marked so ha we can disinguish when and where hey were capured. In oher words, we need o be able o ell where an animal was colleced (inner or ouer area) and on wha dae i was colleced.
Then, hese animals are released in he area where hey were colleced. These marked animals are designaed as: M1a = marked and released in inner area M1b = marked and released in ouer area Dae. Animals are again capured in boh inner and ouer areas. Animals ha are capured ha are unmarked are again marked and released in he area of capure. These are marked differenly han he previous collecion, so ha we can again disinguish where and when hey were colleced. These newly marked animals are designaed as: Ma = marked and released in inner area Mb = marked and released in ouer area Also, because we (hopefully) were able o recapure some of he animals ha we marked on Dae 1, we need o ally hese animals separaely and keep rack of where hey were originally marked and where hey were subsequenly capured. Thus we have he number of M1a capured in inner, he number of M1a capured in ouer, he number of M1b capured in inner, and he number of M1b capured in ouer. Dae 3. One final ime, animals are capured in boh inner and ouer areas. However, his ime we do no mark and release anyhing (hough everyhing can be released once we re done couning and recording hem). This ime we coun he oal number of individuals colleced in boh inner and ouer areas. We also coun he number of individuals marked from Dae 1 colleced in boh inner and ouer areas (M1a in inner, M1a in ouer, M1b in inner, and M1b in ouer), as well as he number of individuals marked from Dae in boh areas (Ma in inner, Ma in ouer, Mb in inner and Mb in ouer). We ll record hese daa in a able like he one below: Table 1. Dae 1 Capured Marked and Released Inner Ouer Toal M1a M1b M1a + b a 1 1 Dae Capured Marked and Released Inner Ouer Toal Ma Mb Ma + b n a Recapured from Dae 1 M1a inner M1b inner M1a ouer M1b ouer M1a + b oal r 1 1 Dae 3 Capured Inner Ouer Toal n 3 3 Recapured from Dae 1 M1a inner M1b inner M1a ouer M1b ouer M1a + b oal r Recapured from Dae Ma inner Mb inner Ma ouer Mb ouer Ma + b oal r
You should noice ha here are subscrips lised in some of he cells. I urns ou ha hese are he imporan cells in he analysis below. Using he daa in hese cells, we will calculae esimaes of populaion size (P), disappearance rae (i), and addiion rae (k) for he inner and oal areas separaely (we ll ignore he ouer area by iself we only needed o keep rack of i so ha we could separae he inner from he oal). Remember, wha we re ineresed in here is esimaes of immigraion, emigraion, birh (naaliy), and moraliy. These esimaes will be single esimaes for he enire populaion under sudy. We can ge populaion size esimaes (for eiher inner or oal area) by he equaions below: anr P i = P o = where P i = inner and P o = ouer r r 1 1 This is called he Bailey Triple Cach Esimae, and ells us how many organisms are in our sudy area. The disappearance rae (i) is calculaed for he inerval beween daes 1 and (again separaely) as: i i = log a1 log x e e 1 i o = log x e 1 log e ' 1 Firs, however, we mus calculae x 1 (he number of a 1 sill in he populaion) as: ar x 1 = x 1 = r In hese wo equaions for disappearance, is he ime period beween daes 1 and. For our purposes, we ll assume i was one year, so = 1, so he equaions are simple. Now we have he disappearance rae, and we need o calculae he addiion rae, k (he rae a which new individuals come ino he populaion by eiher immigraion or birh). We sar by calculaing he diluion rae d as below (again for boh areas separaely): n3r1 d = nr The addiion rae is hus: log d k i = e Again will be assumed o be one. and d = and k o = 3 1 log e d' for inner and ouer areas.
Now we have calculaed he disappearance raes (i) and addiion raes (k) for boh inner and ouer areas. Disappearance raes equal he sum of moraliy and emigraion. Moraliy raes should be similar (on a per individual basis) beween he wo areas, bu emigraion raes should differ by he facor of he difference in heir relaive boundary size. Thus, we expec ha he inner area, wih half he boundary lengh bu only onequarer he acual area should have wice he loss o emigraion han he oal area. Therefore, we can se up wo more equaions ha show how moraliy and emigraion conribue o disappearance for each area. These equaions are: i i = Z + m and i o = Z + m Where Z is he moraliy rae and m is he emigraion rae. Now we have wo equaions and wo unknowns, and we can solve for each of he unknown (and ineresing) variables. The emigraion rae, m = i i i o and he moraliy rae, Z = i o -i i Likewise, he addiion rae is he amoun of immigraion plus he birh rae. The birh rae (on a per individual basis) should be consan beween he wo areas, bu again, he immigraion rae should be proporional o heir relaive boundary lengh. So, we can wrie he equaions k i = b + j and k o = b + j Here, b is he birh rae, and j is he immigraion rae. Solving for b and j gives us he following equaions The immigraion rae, j = k i k o and he birh rae, b = k o - k i OK now o your ask for nex week. I ve decided o ask you o use his echnique and wrie i up. I ll aach some daa o hese insrucions, and I wan you o run hrough he calculaions and urn hem in as your lab repor. This repor will be worh 0 poins, jus like always, bu I don wan you o pu i ino he forma ha we ve been using. All I wan you o do is o fill ou he able above (you can Xerox i and cu ou all he ex if you wan or reproduce i yourself) wih he daa and oals in he appropriae cells. Then, I wan you o produce a second able wih separae esimaes (for inner and oal areas) for P, x 1, i, d and k, and hen single esimaes of Z, m, b, and j. I also wan you o include a SHORT discussion of which of he facors is mos imporan (immigraion, emigraion, birh, or deah) in changing populaion size, and an assessmen of he differen parameers esimaed for boh areas (paricularly in regard o he differen proporions of area remember, he inner area is one-quarer of he oal so we should expec some of hese parameers o scale as a quarer, while ohers will scale on order of a half, righ?). Do he values you calculae fi our expecaions? Wha assumpions do you hink ha his analysis makes? The daa are nex.
Here are he daa ha you can use. Dae 1. Colleced Inner area = 155 Colleced Ouer area = 438 Dae. Toal Colleced Inner area = 145 Toal colleced ouer area = 465 Number of M1a colleced in inner area = 47 Number of M1b colleced in inner area = 36 Number of M1a colleced in ouer area = 38 Number of M1b colleced in ouer area = 95 Dae 3. Toal colleced in Inner area = 10 Toal colleced in ouer area = 419 Number of M1a colleced in inner area = 18 Number of M1b colleced in inner area = 11 Number of M1a colleced in ouer area = 16 Number of M1b colleced in ouer area = 51 Number of Ma colleced in inner area = 8 Number of Mb colleced in inner area = 16 Number of Ma colleced in ouer area = 30 Number of Mb colleced in ouer area = 38 For daes 1 and, assume ha all individuals ha were colleced ha had no been previously marked were marked and released in he areas where hey were caugh. Again, when he equaions ask for, jus assume ha = 1. (wheher i is years, or weeks, or monhs or days is immaerial for his exercise bu i would maer for real work, righ?)