Class Note for ECOL 406R at UA
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Date Created: 02/06/15
What is population Viability analysis PVA Population Viability analysis is a quantitative analysis of population dynamics with the goal of assessing extinction risk Demographic Data gt Mathematical Prediction of Analysis extinction risk osurvival and fertility throughout an organism s life cycle opopulation size over time obirth and death rates omatrix model time series analysis obranching process 0stochastic birth death process oreactiondiffusion equation opopulation growth rate A extinction probability time to extinction ofuture population size or structure Table 11 Potential uses of PVA quotproductsquot Category of Use Specific Use Examples Assessment of extinction risk G uiding management Assessing the extinction risk of a single population Comparing relative risks of two or more populations Analyzing and synthesizing monitoring data Identifying key life stages or demographic processes as management targets Determining how large a reserve needs to be to gain a desired level of protection from extinction Determining how many individuals to release to establish a new population Setting limits on the harvest or take from a population that are compatible with its continued existence Deciding how many popula tions are needed to protect a species from regional or global extinction Shaffer 1981 Shaffer and Samson 1985 Lande 1988a Manges 1990 Forsman et a1 1996 Allendorf et a1 1997 Menges and Gordon 1996 Gerber et al 1999 Crouse et al 1987 Shaffer 1981 Armbruster and Lande 1993 Bustamante 1996 Howells and Edwards Jones 1997 Marshall and Edwards Jones 1998 South et a1 2000 Nantel et a1 1996 Ratsirarson et a1 1996 Caswell et a1 1998 Tufto et a 1999 Menges 1990 Lindenmayer and Possingham 1996 Why do we do population viability analysis U S Endangered Species Act 1973 codi es in law a national policy of avoiding the extinction of species U S National Forest Management Act 1976 fish and Wildlife habitat shall be managed to maintain viable populations of existing native and desired nonnative vertebrate species in the planning area In order to insure that viable populations Will be maintained habitat must be provided to support at least a minimum number of reproductive individuals and the habitat must be well distributed so that those individuals can interact With others in the planning area U S Marine Mammal Protection Act 1994 amendments stock assessment process What do I mean by population dynamics populations are dynamic not static Grizzly 60 bears 55 in Yellowstone so National Park 45 40 35 Estimated number of adult females 30 I I I I I I 1958 1963 1968 1973 1978 1983 1988 Year populations are dynamic not static Sheep on the island of Tasmania Number of sheep ons M I I I I I I I I L I I I 1820 3940 60 3980 1900 20 Year lemmings per hectare 4O 27 13 populations are dynamic not static l 19291930 1931 1932 19331934 1935 1936 1937 1938 19391940 1941 1942 1943 year Index of abundance populations are dynamic not static Whales in the Antarctic Fin whaes Sei whales Blue whales 1 945 6 1949 50 1959 60 1 969 70 Population sizes change over time Why What causes change in population size What regulates population size If we can answer these questions we might be able to make changes that increase populations of declining endangered species Many things affect population size competition populatlon within a species structure among species other interactions predation herbivory chance events gt populatlon pollination etc demographic genetic SIZC habitat attributes enVqunmental quantity quality succession 01 varlatlon con guration and good years bad years connectivity d1sturbance Exponential growth densityindependent deterministic In a closed population no immigration or enngra onx population grownhisa function of birth and death rates d N bdN dt Population size 2000 1000 0 arnhmetic 3938 3940 3942 Ringnecked pheasant on Protection Island exponential growth an unrealistic model Humans on planet Earth 6 1997 Modern 5 times 5 Middle New Stone Age Bronze Age Iron Age Ages 1 970 Population billions 1 930 8000 6000 4000 2000 lt uc A Di D 2000 Years 2 Logistic growth densitydependent deterministic intraspecific competition dN 2 N KN r dt K stabilizes population Size birth rates go down andor death rates go up with increasing population size carrying capacity K Population size N 80 90 100 Time t Alternatively The population growth rate may increase with population size positive densitydependence Allee effect growth rate negative minimum Viable population size Allee effect How group defense against predators 100 Goshawk attack success as Number 01 pigeons In ock FIGURE 1317 Success rate of goshawk attacking pigeons in ocks mka by a mined gushka rarely resulted in capture uf a pigcuh from 1 large ock although most attacks on single pigeons were successful Allee effect 37 Passenger Pigeon adult male How In animals group defense against predators group attack of prey mates difficult to find critical number to stimulate breeding behaVior In plants pollinator limitation selfincompatibility inbreeding depression The two categories of models we have considered thus far assume that all individuals in a population have the same birth and death rates no genetic developmental or physiological differences among individuals under some circumstances this might cause us to inaccurately predict population size 3 Structured population models densityindependent deterministic This is the type of model most often used in population viability analysis What is meant by structure A population is unstructured if all individuals have the same rates of survival and fertility A population is structured if differences among individuals in age developmental stage or size cause them to have different survival or fertility rates TABLE 63 Survival data for redcockaded woodpeckers in different reproductive stages from Walters 1990 Fate at the end ofa oneyear interval Total number Proportion Stage of birdyears Dead Alive surviving one year Fledglings 616 345 271 044 Solitary males 131 50 81 062 Helpersat thenest 273 60 213 078 Breeding males 838 201 637 076 Floaters 29 11 18 062 Loggerhead turtles 3 Densityindependent deterministic structured population growth What can structured population models tell us 1 Eigenvalues The dominant eigenvalue 7 will eventually govern population growth 3 Densityindependent deterministic structured population growth What else can structured population models tell us 2 Sensitivity The sensitivity of QM to each matrix element quanti es how much 7L will be affected by a change in that transition probability 3 Densityindependent deterministic structured population growth What else can structured population models tell us 2 Sensitivity The sensitivity of QM to each matrix element describes how much 7L will be affected by a change in that transition probability Would it be better to focus conservation efforts on improving the survival of hatchlings or large juveniles or adults 3 Densityindependent deterministic structured population growth What else can structured population models tell us 3 Elasticity Elasticities quantify the proportional change 1 in the asymptotic growth rate that can be expected given a particular proportional change 1 in each life history transition Many things affect population size competition populatlon within a species structure among species other interactions predation herbivory chance events gt populatlon pollination etc demographic genetic SIZC habitat attributes enVqunmental quantity quality succession 01 varlatlon con guration and good years bad years connectivity d1sturbance Two possible predictions given a single transition matrix exponential growth 7tgt1 extinction probability O 0139 exponential decline 7K1 extinction probability 10 Two possible predictions given a single transition matrix exponential growth 7tgt1 extinction probability O 0139 exponential decline 7K1 extinction probability 10 Longterm average 4 Stochastic models A Environmental stochasticity The environment varies from one year to the next IABLE 65 Size ransilions fur mountain golden haakher over four yearsmi 51 in was rcm39 Size in ms mi N 25 50400 gt100 025 21 084 2 01333 2 001333 0 0 2550 4 016 7100057 5 02003 1 02 50100 0 0 5 03333 15 10 525 1 10 2 gt100 0 0 1 00557 2 100533 3 100 TOTAL 25 15 21 5 Size m 1955 mquot Size In 1007 km 025 2550 50100 gt100 Ms 12 0 6316 4 02353 1 n 05 00 2amp5 7 0 3684 x 04700 3 015 0 0 5mm 0 o 5 02941 9 005 0 0 gt100 0 0 00 71035 b 0 TOTAL 19 17 20 a size in 197 mil Size in 195 an H 257511 50400 gt100 025 131013 5 03333 1 01029 0 0 2550 2 02 9 05 2 01129 1 0 0709 504 00 0 n 1 10 0057 710 5 5103046 gt100 u 11 0 0 3 02113 7 053135 TOTAL 10 15 1A 12 Size in 1950 cu1 52 in 198N001 025 25517 501110 gt100 025 1010 7062 2011029 010 0 0 25750 3 102308 0 042255 0 0 0 10 50100 0 a 1 012130 3 0615 1 10 1 gt100 O l U D 5 E3545 9 9 TOTAL 13 14 13 in Number of realizations 450 400 350 300 250 200 150 100 50 39 500 39 0 7 2001 2500 3000 100 Population size ml 50 initial population size 4343 4 Stochastic models A Disturbance and succession The environment varies from one year to the next in a cyclical or predictable manner I I A wan mm m m um wc w m m m wvnaltmpmnl u r my rum 4 in mm 5 SunKner A lt s 3 m mm m 7 u a a M W D WWW m V n m m a a u a a 1 a o m m m an 2 a 3 m 3 2 3 l 1 a g g g 3 OPEN CLOSED m CANOPY CANOPY n m m a a m w mm m 4 Stochastic models B Demographic stochasticity Tossing a coin seX ratio survival Rolling a dice clutch size 4 Stochastic models B Demographic stochasticity T0ss1ng a 02 coin 022 02 sex ratlo 018 survival 0m 014 012 m Rolllng a 008 006 dlce clutch size 002 Number of individuals 4 Stochastic models C Genetic stochasticity Small populations tend to lose genetic diversity heterozygosity allelic diversity Via inbreeding drift or combinations of the two This may have tness consequences 5 a v o a Plant height 53 z ve o P m tqa 101 53 260Control Inbred Comgosite 2 4 8 2 8 m m o Tiller number a 7quot 140 CV Figure 14 The effect olexperlmental boltlcnecks on plant heighl cm and tiller number in Lollurn multtflorum Experlmental populallnns nt restricted size t2 4 and at were main tained lur three generations and then grown in a contnmn garden wilh a unlrol treatment and Lumpugtie mixture of genotypes from the inbred treatments The mean and cuerticient ol variation for each treatment are illustrated Alter Folans and Allard 19897 Rule of thumb genetic and demographic stochasticity important in populations lt 50 environmental stochasticity still important in populations gt 50 5 Landscapescale or metapopulation models 0 amount of habitat 0 quality of habitat 0 distribution or con guration of habitat connectivity of habitat 5 Landscapescale or metapopulation models Patch size matters populations in smaller habitat patches islands are more likely to go extinct than populations in larger habitat patches Patch isolation matters the more isolated an unoccupied habitat patch is from occupied habitat patches the less likely that it will be colonized The Theory of Island Biogeography MacArthur and Wilson 1967 Metapopulation Theory Levins 1969 and others 5 Landscapescale or metapopulation models Norlhem Monterey 100 O 50 km V Soulhern Monterey 60 Cerro Alto 6 Soulhern Santa Lucia 32 Sierra ngwa Tehachap r 24 Madre 24 San Pmus Halael amw 39 Pelano 40 l San Gabriel 190 San Bernardino 266 Santa Ynez 36 Cobbleslone 20 LOS ANGELES I San Jacmto 40 Santa Ana 24 Thomas 20 F alomar 60 Pacilic Ocean Black Volcan 32 10 SAN DIEGO I Laguna 30 Cuyamaca 20 Which population is mostleast likely to go extinct 5 Landscapescale or metapopulation models Patch quality matters populations in habitat patches of higher quality are less likely to go extinct than populations in patches of lower quality A source is an area Where bgtd Excess individuals may emigrate from a source patch A sink is an area Where dgtb Populations in sink patches are certain to go extinct Sink populations may be rescued by immigration from source populations the rescue effect Many things affect population size competition populatlon within a species structure among species other interactions predation herbivory chance events gt populatlon pollination etc demographic genetic SIZC habitat attributes enVqunmental quantity quality succession 01 varlatlon con guration and good years bad years connectivity d1sturbance Last thoughts on PVA PVA requires lots of data which takes time work and money whereas managers want answers predictions about extinction now Few species will get thorough PVA When should PVA be used and what type of PVA how complex Predictions from PVA can only be as good as the data that go into the analysis We can only have degrees of con dence in the predictions from PVA Populations should not be managed to their minimum viable population size One of the greatest strengths of PVA is the ability to play what if games with the model That is what if management were to increase patch sizes or connectivity What if adult survival were improved
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