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# Adv EcolPopulComm PCB 5423

FIU

GPA 3.72

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This 9 page Class Notes was uploaded by Eve Mayert PhD on Monday October 12, 2015. The Class Notes belongs to PCB 5423 at Florida International University taught by Thomas Philippi in Fall. Since its upload, it has received 31 views. For similar materials see /class/221715/pcb-5423-florida-international-university in Biology at Florida International University.

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Date Created: 10/12/15

Dens1tyDependent Population Growth DensityDePendent Population Growth Logistic Population Growth consider dNdt hudw Densityindependent models assume here 5 EN o h hinhrat underideal uncrowded enndianns unlimited resources such that b and d are 25txength ufdensltyllmltahun N constant and was at e n an and parameters as in h thus per eapita death rate 0 Conglder inereases Wth N when e is pnsiave at b d Nate these are the must simple funetinnal forms linear ufresuurce limitation N Can he cunslda ed as Taylur expansions nfhinlripeally enneet tuneanns DensityDependent Population Growth DensityDependent Population Growth Reality check density dependence is E probably not linear for example Allee Effect A313 Zipmem to logistic dNdt rN1NKE Richter model in sheries i4 Insects Logistic quot Generally g 9 Fish attributed to g a problems in the E social system at low density H Allee fect N DensityDependent Population Growth DenSItyDependent Populatlon GTOWth Back to the logistic model Why do we care dNdt b d N dNdt baN r dcNN substituting dNdt bd e acNN Multiply through bdbdl bdaCNlN bdlbdbd aCbdNlN et b a dNdt rN1acbdN Note a b c d are all constants so Kbdac which is called Carrying Capacity t b amp d rates wo resouce limitation aamp c measure strength of densit dependence DensityDependent Population Growth Growth is most rapid at N K2 Note tlme to reach K m r Z Steepest slope at N Kz Exponential g g dNdt N1NK rNraltN2 N A parabola pointing down DensityDependent Population Growth Why do we care Maximum sustainable harvest is at N39 DensityDependent Population Growth Assumptions 0 K is constant 0 Density dependence is a linear function of N lN dNdt lN dNdt N N Logistic Exponential DensityDependent Population Growth b rate K max sustainable pop size where l K bgtdbelow bltd above g 2 1 Gotelli N Substitute into logistic dNdt rN1NK rhis is the classic eqn from Verhulst 1838 where 1NK is the unused portion o IfKZIOO but N7 17100 0 93 or 93 ofresource is unused this is a damping functi on exponential growth LfNgtK then 1 NK is negative and population declines dNdt 0 when N K a stable equilibrium no matter how far N is perturbed it returns to K DensityDependent Population Growth K by lntegratlon Nt W 0 Which is S shaped Tune 0 per capita growth rate declines one unit for each individual added lNdNdt 2 bd r whenN is small max growth rate DensityDependent Population Growth Variations 1 Time Lags 1 control attirne from N in past NH t Thus dNdt rN1 NHK So solution depends on r and 1 and response time is inversely 0c r response lr Ratio of time lag to response controls growth rr 8 gradual increase toward K rt 0 368 lt rt lt157 damped oscillation rr rr gt157 stable lirnit cycles DensityD ependent Population Grow1l1 Rana Drums lag m response controls growth r u lt nltu m gamalmcrusetwwardK r n362lt nlt157 dampedascillahm r gt157 mm mm cycles sublehmn cycle hasK as midpoint wii stun ifpemxbed Cyclic population charanenzedby mime andpenadbztwemhlga andlaw asn atmn Period time betweenpeaks Amplitude range hawzen high anle Amplitude increases x r how much overshoot Penad541fm 5 AN DensityD ependent Population Grow1l1 2 Discrete time model NH N raNJlNtKD AN NmNF raNJlNKD J Graph NHl V N z N DensityD ependent Population Growth 2 Discrete time model 5 g Ni DensityD ependent Population Grow1l1 2 Discrete time model 9 Np DensityD ependent Population Growth 2 Discrete time model 5 z iZ Ni m DensityD ependent Population Grow1l1 9 2 Discrete time model 9 Np D ensityD ependent Population Grow1l1 2 Discrete Lime model Slope AN Nm39NF riiN1NK Graph NM v Ni memes 99 isms Wimmm e mummies sxsm emsswim isms mwmmmixu m mi mm ereem numam suszrpn hh in mud mum DensityD ependent Population Grow1l1 Why do we care DensityD ependent Population Growth 3 Random variation in K Note die appioach to K is asymmetrical decline faster NgtK aim increase NltK 2 i so always ltK Z K more variable environmentleads to smallei N Also size ofr ac to tracking ofwn39ation bigger i closer tracking ofvan39able K is smaller Oi same a with small i DensityD ependent Population Grow1l1 Minnie Variz nn in K 0 sezsmmy Aasiike um lag depends mi Andpenad uf cycle 5 Leggepap txackchyclesat NltK ect Tranhrlgcumegnmtnmyuxd emmnmemgmi See gl I Population Regulation B ackground What determines the nnrnher and kinds ofanimals and plants in an area Why don t minds and plants 111511 their potential to grow exponentially What does pepiiation regulation rnean7 Can we detect densitydependent regulation in real populations How frequent TheoIies 7 Regulation in natural populations Maitus 1798 Essayun Prinnp1esefpepu1auen39 EXpunEntlal pep gumh Wth u1tirnate reseuree 1irnits Darwin 1m invekea Maithus as rneehanisrn furnatural se1eetien Mueb1us187 natural enemies Heward and Fiske 1911 DD vs D1 faetersrnake up 3 v1runment39 Niehn1sen 1999 DD fund avai1ahi1ity intraspeniie eernpentinn h1uw 1es ntraspeeiiie eernpentinn ve1es lemmings Laek 1954 intraspeei e acinterspeei e enrnpeuuen birds Adrewanha and 5111110954 dmsitymdependmtrmn nut uf nrne tn M1511 petennai r Lhnps Strong 1986 density Vague reg Population Regulation Mi1ne 1957 imperfect density dependence chitty 1950 selfregulation through genetically es in individual vitality se1ect for s individuals at different densities Pimental 1951 regiiation by coevolu on ofpredator an prey genetic feedback for Nicholsonianresponse WynneEdwards 1952 mm dispersion and social ehavior leads to selfregulating pepiiatiens ulation with oors and ceilings ulation density independent uctuation except for extremes density de endence with non 1inearities and noise Population Regulation Can we detect ung dependent regu1ataen m unrea1 pupulahuns397 Been there done that lledthe mayonnmsejar Population Regulation Population Regulation Detecting Density Dependence with statistical 1 Key factor analys1s by l1fe stages Nlorns 1959 Varley and Gradwell 1960 logNH1 logNt logF logs log 52 here F fecundity s Klllmg pewer39 1e elugSL Tutal k111ing puwer39 1lt k k1 kn survrvership 39um factor 1 Q Which lg1s rnest correlated Wth K7 European spruce sawcly in New Brunswick Canada dancers based an twneperyear nan 1911952 11 Mame insert 1 armyysar N 1 vap snmvmg madam d e mi snmvmg disease 1 precipitation pram CbrkL 1 1967 macalaey iiiinsect Paynth mmury and practice Methiert Lordoxl Key Factor Analysis parasitism e disease p arasiusm Detecting Density Dependence Problem 1 seldorn have data detailed enough for this approach Problem 2 densitydependence at one life stage is not adequate for regulation Hassell 1986 TREE 19093 Could be counteracted by inverse density dependence in another stage Current analyses focus on intergenerational change in population size Detecting Density Dependence Analyses ofTime Series ems Low power can t distinguish from random walk Usually only 1 replicate Standard Fsta sdc is inappropriate Non lineanty and lags obscure relationships However new tests are available that overcome these problems Detecting Density Dependence Some consensus has been reached because 1 Improvedtheory and statistical techniques 2 More and better data longer time series 3 More studies that combine observational data eld experiments and mathematical theory Population Regulation De nitions A population regulation a on stali onary probability distribution of population densities some mean density around which population size uctuates anance is bounded nonregulated time series has increasing wriance overtime Also unregulated time series not characterized by mean population size Note mean goes up not a stationary system though uctuations are goyeined by endogenous 1 Random walkis a special case ofunregulated tiine se 39es inh Death so no long te 39 iease oi decieaseBUT no stationary probability distribution ie yanance of expectation incieases with time nN ZInNH 5 at Note NHFAN Where R1 MN 7 lnNH note magilaud dues noteoualnnaan bntmtnrldum note moonwalk described as oathadnnk News as when lat eachsetm39steyi Pmeeds in enansnaal pawn in ileclins is magilaud waliaac amiss a onions znrldumdmctwnbnishm attie eni iiitie last set mm can go too high mw a1 d stocks and 2 CEerlgiaonrtrI numhei stnng is not a iandoin walk yanance is will selfregulate back down 7 Ni at Other De nitions and issues Other De nitions and issues 1 Regulated populationis one that ietuins to an 3 equililiiium density attei de e partur Reouiies a stable point ouliloiun as non LotRaeVoltena oi dsoete logsic models ignoiesiole afexagenaus enmonnental yanalales on stable point and nmse39 2 Regulated population is one that uctuates within li 39t nnpiesiioonanaeeingsp ouiityaanoaoon ninesoaeonaoenes inn pannnoninn systems eaiieaan loaned saoonay poouiitynsnooion apopuoion onstyteniiionon natapon out a clo ufpmnls Geek speak amacioiis a cmnpacl set thaiamacis initial conditionstion Egan aiound it a siange ntuacwns special case that leadsianmexepuh g dynamics called chaos Stochastic boundedness Chesson 78 82 nooaoityoipeiass on owei bound of densty Not a stationaiy halality dstnouion 4 Finite population size and spatial scale Tiaolitional analyses Canada population scale as in nite exunman is inn an popunonseaie nosioento penance gm autononstcoesnnan 5 Temporal scale of environmental uctuations s cales lt l yeai model as stochastic 2 decadal may yield non sationaiity gadual tiends cm oi noie too long to be inpoatant toi most data sets lnezn yeais Alternative Definitions Regulation action of factors that function in a density dependent inann i to cieate an equilibrium density one thatis iegained following apenuiliation Limitation the extent to which a popula apita giowthiate is depiessed by the particular factor e piedation nsk don s pei action ofa g iesouice availability oi Control factors that set the equilibrium at a particular density need not lie density dependent on was c man mo moan nameannmmnnaanm onenesn anae antenna a Minn nnwaa mmnmamua s in w Dmbug c w on c c mush iwa manna mam aieaon moonminimian tannin lat has a ans max at mums l7deth mmnm a ma ins ml in DensityDependence Tests 0 Dependence of per capita growth rate on present andor past population densities L K N N Direct DD Indirect DD F E smith 1961 published a criticism ofAndrewatha and Birch h L A 4b analysis nfr i i 7 as in Davidson and Andrewanha 48 DensityDependence Tests Mixture of direct and inverse effects possible summarized by ret39urn tendency No DD of r no return tendency no stationary distribution of population densities Also DD is necessary but not suf cient condition for regulation 3 conditions are39 1 DD ofcorrect sign negative 2 DD strong enough to counteract disruptive effects ofdensity independent factors 3 Lag for return must not be too long SeeNisbet and Gumey 1982 most analyses ignore strength and lag issues most look for immediate DD in per capita growth rate DensityDependence Tests 1e1 lnN e lnNH RN a where fis typically a linear function ofNH or lnNH and e is random density independent factors Dennis and Taper 94 Criticisms linear no delay assumes errors are additive and independent Properly used on sernelparous univoltine organisms must measure population size at one point each generation BUT this equation permits for atest ofregulated dynamics Could be generalized szH nonlinear more complicated periodic or autocorrelated 2 Wld Density dependence What data are needed and available Long time series heighten probability of detecting DD Reviews I WoiWood amp Hanski 92 6000 pops ofinsects aphids 94 spp and moths 263 spp 7 sign DD in 69 aphids 29 moths e Excluded time series less than 20 years and 84 of aphids and 54 ofmoths with DD I Holyoak 93 171 examples also found that With signi cant DD increases With length oftime series 0 a and Dennis 93 Concluded freq ofDD positively correlated With power to detect it Density dependence What data are needed and available Note DD and random walk may correspond for relatively large number of generations 10 years 7 prob of detecting DD different from random mlk 10 30 years 7 Pr detection 6070 strength ofDD and magnitude of exogenous variability Turchin 95 regulation is ubiquitous though any pop may not be regulated especially if environment changes 39 h es it Role ofDD test is to determine ifstochastic equilibrium should be added to model ofpop dynamics Density dependence What data are needed and available Turchln 95 continued Key questions Are dynamics stationaryv 7 Can add mnrhnmr and time lag eumpunents to model Puule 78 AnnRevEculampSyst 9427448 What arethe relative role ofendogenous and awgmous controls of dynamics7 What is the degree ofpenodlclty7 autocorrelatlon at is degree of stablllty7 1s regulation the result of local or regional metapopulatlon processes7 7 old topic Ehrlich and Birth 1957 The balance ufnature39 andupnpulaann controlquot Am Nat 1U197rl 7 Andrew39th and Birch 1984 The Eculugcal Web Univ l rA 2 n E r e Huffaker and Kennett 1955 deserves special mention though usually discussed in predrprey context Well consider in predaturrprey amp metapupulaaun Population Regulation De nitions A Population regulation a longterm ta 39 y and bounded probability distribution of population densities some mean density around which population size fluctuates But stationary pdf can be around an unstable equilibrium point eg limit cycles or chaotic dynamics Stationary alone could include h a faadcham V Am amp Ha w Alternative De nitions Regulation action of factors that function in a density dependent manner to create an equilibrium density one that is regained following a perturbation Limitation the extent to which a population s per capita growth rate is depressed by the action of a particular factor eg resource availability or predation risk Control factors that set the equilibrium at a particular density need not be density dependent Mmh h

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