Demography. Demography. Future Population Size. Population Change. Population Change. Instantaneous Rate of Change. Examples: Future Population Size

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1 Demography Demography Fuure populaion is a resul of he inerplay beween inernal characerisics and processes and erinsic forces and processes. We will begin by focusing on he inernal facors - he demographics. Fuure Populaion Size Predicing fuure populaion size requires undersanding he inernal workings of he populaion. We learn abou hese workings by observing changes in populaions and looking for principles which would allow us o predic hem. Populaion Change Speed of populaion change is referred o as rae of increase. Change resuls from inerplay beween fecundiy rae, moraliy rae, and composiion (age disribuion and se raio). Populaion Change Fuure populaion size can be prediced from curren populaion size and is rae of change: + = (rae of change) + = λ λ = finie rae of increase λ = + / If populaion is consan λ =. Insananeous Rae of Change Someimes is beer o epress he finie rae of increase as an insaneous (or eponenial) rae of increase (r): λ = + / = e r ln λ = log e λ = r If populaion is consan hen r = Fuure Populaion Size Eamples: If rae of change is consan hen = N e r ln = ln N + r Equaion for a sraigh line: y = a + b

2 Esimaing rae of increase Finie rae of increase: λ = + / Insananeous rae of increase: Regress ln on r = (ln - ln N ) / Rae of change Wha really deermines he rae of change (increase or decrease) in a populaion? Birhs? Deahs? Immigrans? Emigrans? Rae of change Change resuls from balance beween raes of increase and decrease Increase: Birhs + Immigrans Decrease: Deahs + Emigrans N = (B + I) - (D + E) Immigrans and Emigrans are samll in number and depend on oher populaions so we ll simplify i by ignoring hem (for a while). Deahs = Moraliy Wha do moraliy raes depend on? Age? Populaion size? Resources? Summarize moraliy in a life able Life able = age (years) f = n = Survival frequency = Survivorship d = Moraliy q = Moraliy rae Cohor Life Table Survival of male Song Sparrows hached in 976 on Mandare Island, BC Saic Life Table (Cach Curve) Ages of male reindeer, Souh Georgia Island Consrucing a Life Table Sandardize o l =. Male reindeer, Souh Georgia Island f / f d 78 78/ / / / / /

3 Consrucing a Life Table Male reindeer, Souh Georgia Island d q Graphing a Life Table: Survivorship Survivorship Graphing a Life Table: Moraliy Rae Eamples of Survivorship.8.6 q.4 Moraliy Rae Epanded Life Table - Females Add fecundiy ( =female offspring per female age ) Age() Sum (finess) Populaion R = Ne Reproducive Rae (Finess) No. daughers generaion + = No. females generaion Σ.78 = = =.78 l. Finess Finess defined as Σ for a genoype This fundamenal formula is a he hear of boh demographic and geneic analyses for a populaion I is very clever because i combines boh survival( ) and fecundiy( ) Populaion G = Mean lengh of a generaion = Mean period elapsing beween birh of parens and birh of offspring Σ 3.68 = = = 2.7 Σ.78

4 Populaion ln (R ) ln (.78) r = = =.28 G 2.7 λ = e r = e.28 =.32 = Σ e -r Noe: Firs 2 equaions are approimaions, bu solving his las equaion ieraively is eacly correc. So Wha? Wha is value of his? λ and r are good descripions for eiher a simple populaion or a more comple populaion. Our simple models o predic (or analyze) populaion growh migh work surprisingly well. + = λ Finie Growh Rae λ = Finie Growh Rae N Coninuous Growh = N e r 2.5 Coninuous Growh ln = ln N + r 2 Plo of ln vs. is a sraigh line slope of line is r ln.5.5 ln N 5 Is his correc? Wha assumpions mus be rue? Rae of increase (λ or r) is consan. Sable age disribuion in he populaion. Sable Age Disribuion Loka (922) showed ha a populaion ha is subjec o a consan schedule of birh and deah raes will gradually approach a fied or sable age disribuion, whaever he iniial age disribuion may have been, and will mainain his age disribuion indefiniely.

5 Sable Age Disribuion C = proporion of populaion in age caegory o + Merz (97) showed ha C = λ - / Σ λ - Even if a populaion sars ou wih a differen age disribuion i will aain his sable age disribuion afer a while Sable Age Disribuion Age() λ - λ - C Sum Is he rae of increase consan? Rae of increase declines wih If resources are unlimied, such as inroducion of species o new area OR if populaion remains a fairly similar numbers over ime (i.e. r= or λ=. approimaely), bu even here random environmenal variaion will produce random changes in r (or ). Typically resources are limied and more animals consume more resources, reducing amoun available for each animal. A simple case would be if he rae of increase declined wih each animal in he populaion. λ (or r) = (Ma λ or r) - b