Population EcologyRemember from last time:Today:Is the Population Increasing, or Decreasing?Threatened Species:Western Snowy PloverPopulations across the landscapeSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Controls on immigrationSample Metapopulation DataMathematical ModelsPopulation GrowthSlide 17Projecting Population SizeDoubling TimeLet’s Try It!When Is Exponential Growth a Good Model?Environmental StochasticityPowerPoint PresentationPlover Population Model with Stochasticity Nur, Page and Stenzel: POPULATION VIABILITY ANALYSIS FOR PACIFIC COAST SNOWY PLOVERSWhat Controls Population Size and Growth Rate (dN/dt)?Slide 26Slide 27Slide 28Slide 29Slide 30What does (1-N/K) mean?Slide 32Slide 33Population Size as a Function of TimeLast Time…At What Population Size does the Population Grow Fastest?Fisheries Management: MSY (maximum sustainable yield)Assumptions of Logistic Growth Model:Lets Try It!Population EcologyES 1008/21/07Remember from last time:•Population ecology•Life Tables•Cohort-based vs. Static•Identifying vulnerable growth stages•Age-specific birth rate•Computing fitness, net reproductive rate and generation time•Population projectionsToday:Metapopulation TheoryImmigration and EmigrationSource and Sink PopulationsMaintaining Genetic DiversityPopulation ModelsExponential and Logistic growthAssumptionsDoubling timeWhen should this model be used?Is the Population Increasing, or Decreasing?Fitness is one indication….. But…Populations vary dramatically over time (boom/bust cycles)Individuals move in (immigration) and out (emigration) of populationsMetapopulations (18.5 Bush) Nt+1 = Nt + (B-D) + (I-E)Threatened Species:Western Snowy PloverBefore 1970, 53 breeding locations in CA (including Santa Barbara)Now, 8 breeding sites support 78% of the CA metapopulationPopulations across the landscapeMetapopulation: sum of multiple interacting sub-populations sub-population Asub-population Bsub-population Dsub-population CPopulations across the landscapeGenetic diversity is maintained by exchange of genes between the sub-populations sub-population Asub-population Bsub-population Dsub-population CPopulations across the landscapeMost mating occurs within a sub-populationsub-population Asub-population Bsub-population Dsub-population CPopulations across the landscapeSome habitat patches are better than others hot and drymost idealmanypredatorsfew nesting sitesPopulations across the landscapeSub-populations can be source populations or sink populationshot and drymanypredatorsfew nesting sitesmost idealsourcesinksinksinkPopulations across the landscapeIn source population habitats:•living conditions are good, so births meet or exceed deaths•competition may be great, forcing some members outhot and drymanypredatorsfew nesting sitesmost idealsourcesinksinksinkPopulations across the landscapelocally extinctsource of recruitssourcesinkIf a sub-population goes extinct, it can be revived by recruits from a source population….But sinks are important too!Controls on immigrationDistance to source populationmainlandLots of immigrationLittle immigrationObstacles•Mountains•WaterwaysmountainshillsAge Stagesub-population A sub-population Bsub-population C Total dN/dt = Nx-Nx-10-1 60 25 489 -----------1-2 24 30 1266 -232-3 14 26 1050 -163-4 10 20 434 -164-5 7 13 121 -13Number of individuals•Is this population assessment static or cohort based?•Which sub-population(s) are sources? Sinks?•Can you develop a life table for each sub-population?•Can you develop a life table for the total population?Sample Metapopulation DataMathematical ModelsUses:•synthesize information•look at a system quantitatively•test your understanding•predict system dynamics•make management decisionsPopulation Growth•t = time•N = population size (number of individuals)• = rate of change in population size (ind/time)•r = maximum/intrinsic growth rate (1/time) = fractional increase, per unit time, when resources are unlimiteddN dtPopulation Growth•Lets build a simple model (to start) = r * N•Constant growth rate  exponential growth•Assumptions:•Closed population (no immigration, emigration)•Unlimited resources•No genetic structure•No age/size structure•Continuous growth with no time lagsdN dtProjecting Population Size Nt = N0ertN0 = initial population sizeNt = population size at time te  2.7171r = intrinsic growth rate t = timeDoubling Timertdouble)2ln(=Let’s Try It!The brown rat (Rattus norvegicus) is known to have an intrinsic growth rate of: 0.015 individual/individual*daySuppose your house is infested with 20 rats. How long will it be before the population doubles?How many rats would you expect to have after 2 months?Is the model more sensitive to N0 or r?When Is Exponential Growth a Good Model?•r-strategists•Unlimited resources•Vacant nicheEnvironmental StochasticityOur exponential growth model is deterministicOutcome is determined only by model inputsIntrinsic growth rate varies with ‘good’ and ‘bad’ environmental conditions:Often we know the mean growth rate and the variance in the growth rate,These can be incorporated into our model!r2rσHerd Size with Environmental Stochasticity0500100015002000250030000 2 4 6 8 10YearHerd SizeHerd Size (Deterministic Model)050010001500200025000 2 4 6 8 10YearHerd SizePlover Population Model with Stochasticity Nur, Page and Stenzel: POPULATION VIABILITY ANALYSIS FOR PACIFIC COAST SNOWY PLOVERSWhat Controls Population Size and Growth Rate (dN/dt)?•Density-dependent factors:Population Density:# of individuals of a certain # of individuals of a certain species in a given areaspecies in a given area•Intra-specific competition•food•Space•contagious disease•waste production•Interspecific competition•Other species interactions!•Density-independent factors:•disturbance, environmental conditions•hurricane•flood•colder than normal winterTime (t)Population size (N)Can the population really grow forever?What should this curve look like to be more realistic?Population Growth•Logistic growth•Assumes that density-dependent factors affect population•Growth rate should decline when the population size gets large•Symmetrical S-shaped curve with an upper asymptotePopulation Density:# of individuals of a certain # of individuals of a certain species in a given areaspecies in a given areaPopulation