Population EcologyWhat really cool ecologists doWhat is population ecology? The study of how populations interact with the environment and other populations Population Genetics Population Dynamics Behavioral Ecology MetapopulationsWhere does it fit?PopulationBiologyConservationBiologyResourceManagementRestorationEcologyEvolutionMathematicsCommunityEcologyDiseaseEcologyBehavioralEcologyAgricultureWhere is population ecology? Fisheries Stock recruitment Marine Reserves Conservation Population Viability Analysis Population Genetics Restoration Crop Improvement ConservationPopulation Biology Theory rich Physics like (?) (see Berryman 2003, Turchin 2001) Conflicted (see Kingsland, Modeling Nature) Open vs. Closed Density Dependent vs. Density Independent Chaos vs. Noise Spatial vs. nonspatial Top Down vs. Bottom upA brief history of population ecologyA brief history G. F. Gause Competitive exclusion principle Antibiotics developmentMathematics in population biology Models are maps of reality Maps omit details Reveal essential truths Models should be testableMaps based on knowledge – There be dragonsThe mathematics of change Continuous models Differential or Partial Differential Equations Change is continuous and implicit is the notion of infinitesimals and limits Can be continuous in time and space Discrete models Difference Equations Synchronized generations Hybrids  Integrodifference equations Discrete time / continuous space  Individual Based ModelsModels Linear Malthusian Growth Age / Size structured models Leslie Matrix Euler Equation Nonlinear  Density Dependence Delay Equations Lattice ModelsPopulation Biology – some concepts Malthus (1798)rtteNN00NRNtt0 5 10 15 20010203040506070GenerationPopulationR=1.1R=1R=0.9Population Biology – some concepts Pearl – Verhulst –Logistic (1835 and 1930s)KNrNdtdN10 5 10 15 2002004006008001000TimeNEmergence – Why Ecology is So CoolBifurcation DiagramPopulation Biology – some concepts Logistic Growth with lags Cycles of period ~4T  KTtNtrNdtdN1Population Biology – some concepts Discrete time, density dependent models Logistic, Ricker, etc. Stable, Period Doubling, and Chaos Sensitivity to initial conditions0 20 40 60 80 10005001000150020002500GenerationN2 4 6 8 10012345678910rpopulation densityChaos Deterministic Sensitive to initial conditions Time series analysis How can we tell the difference between random noise and chaos?Individual Based Models Lattice or Cellular Automata Algorithm rather than a single equation Mean field approx can be poor Emergent dynamics Examples Sandpiles Earthquakes Forest FiresSpace Matters Spatial synchrony Transient chaos Self organized dynamicsMetapopulations Levins, 1969, 1970 Populations connected by dispersal are ephemeral with patch extinctions and colonizations occurring over time Defined by:Metapopulations Examples Butterflies (Hanski and Harrison) Daphnia Silene Genetics Population Structure Evolution of Metapopulations Effective Population SizeMetapopulations to Dispersal Ecology Metapopulations have a discrete structure Extinctions and colonizations are distinct events True Levins metapopulations not strongly supported in natural systems Dispersal Ecology Study of the effects of dispersal on populations Reaction-Diffusion Equations PDEs Turing’s Chemical Basis of MorphogenesisDispersal Ecology Discrete Time, Continuous Space Models Integrodifference Equations Size of tail of kernel determines the rate of spread Leptokurtic dispersal causes accelerating invasions Size of tail not important for persistence, mean dispersal distance is Tail becomes important for dispersal in a flow regime, analogous to invasions at this point     N x k x y f N y y dyt tD1, ,Population Growth FunctionDispersal KernelOutbreaks matter Insects Spruce Budworm Pine Beetle Locusts Grasshoppers Mosquitoes Thrips Diseases Influenza Cholera Dengue Fever Billions of dollars in damage Food security Public Health Billions of dollars in damage Food security Public HealthModern Responses to outbreaksOutbreaks – schools of thought Density dependent Feedback loops Food limitation Predation Density independent Weather Direct effects – moisture and temperature Indirect effects – Effects on food/pathogens Disease Pesticides Both factors work synergistically Deterministic skeletons coupled with envrionmental fluctuationsOutbreaks linked to abiotic effects Weather ENSO effects and cholera Grasshoppers Thrips Seasonality Measles School yearPopulation biology – Density independence Andrewartha and Birch: They rejected the subdivision of the environment into physical and biotic factors because they did not believe it was a useful framework. They did work on 2 species in particular: Swarm forming grasshopper, Austroicetes cruciata. Hypothesized that its distribution and abundance was determined by weather. Thrips imaginis - pest of apples in South Australia studied a population for 14 years - daily counts used multiple regression analysis and explained 78% of the variation in number with weather measurements.Outbreaks linked to density dependence Grasshoppers Food limited Feedback loops Forest insects Secondary chemicals react slowly as defensive mechanisms in treesGrasshopper infestations - IdahoGrasshopper Infestations - WyomingTribolium populationsCostentino et al. 1997DipteraFrom Ylioja et al. 1999(77% of total variance is exogenous)Rangeland Grasshoppers 15 species Different forbs and grasses Generally univoltine Melanoplus sanguinipes –migratory grasshopper Swarms travel miles Historic densities >2000 per yd2 400 eggs per adult per season Melanoplus femurrubrum –redlegged grasshopper Can migrate great distances 336 eggs per adult per seasonGrasshopper food web56 species of hoppersGrasshopper food web56 species of hoppers+plants they eat andcannibalism/necrophagyGrasshopper food web56 species of hoppers+plants they eat andcannibalism/necrophagy+insect