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Populations: Variation in time and space Ruesink Lecture 6 Biology 356 Temporal variation • Due to changes in the environment (e.g., ENSO, seasons) OR • Due to inherent dynamics – Lag times – Predator-prey interactions (LATER) Oscillations occur when population growth occurs faster than density dependence can act – population overshoots Figure 15.11 Larval food is limited: Larvae do not have enough food to reach metamorphosis unless larval density is low adults larvae Figure 15.13 If food is limited for adults, then they cannot lay high densities of eggs. Low densities of larvae consistently survive. Figure 15.14 Three reasons why populations may fail to increase from low density • r<0 (deterministic decline at all densities) OR • Depensation: individual performance declines at low population size (deterministic decline at low densities) OR • Below Minimum Viable Population: stochastic decline Depensation • Form of density dependence where individuals do worse at low population size – Resources are not limiting, but… – Mates difficult to find – Lack of neighbors may reduce foraging or breeding success (flocking, schooling) Deterministic decline in Pacific salmon across a wide range of densities (r<0) Kareiva et al. 2000 Deterministic extinction from low population size Passenger Pigeon Millions to billions in North America prior to European arrival 1896: 250,000 in one flock Probably required large flocks for successful reproduction 1900: last record of pigeons in wild 1914: “Martha” dies Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons Births/individual/year Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons No density dependence Population density (N) Births/individual/year Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons Carrying capacity when dN/dt/N=0 Population density (N) Births/individual/year Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons Depensation Population density (N) Stochastic extinction Heath hen (Picture is related prairie chicken) 1830: only on Martha’s Vineyard 1908: reserve set up for 50 birds 1915: 2000 birds 1916: Fire eliminated habitat, hard winter, predation, poultry disease 1928: 13 birds, just 2 females 1930: 1 bird remained Small populations • Dynamics governed by uncertainty – Large populations by law of averages • Demographic stochasticity: random variation in sex ratio at birth, number of deaths, number reproducing • Environmental stochasticity: decline in population numbers due to environmental disasters or more minor events Small populations • Genetic problems also arise in small populations – Inbreeding depression – Reduction in genetic diversity • Genetic problems probably occur slower than demographic problems at small population sizes Minimum viable population • Population size that has a high probability of persisting into the future, given deterministic dynamics and stochastic events Initial population size What is the minimum viable population of Bighorn Sheep, based on model results? Spatial variation • No species is distributed evenly or randomly across all space Individuals may be clumped due to underlying habitat heterogeneity Figure 15.15 • Individuals may also occur in a clumped distribution due to habitat fragmentation by human activities Population • Group of regularly-interacting and interbreeding individuals Metapopulation • Collection of subpopulations • Spatially structured – Previously we’ve talked about population structure in terms of differences among individuals: Age structure Metapopulation • Dynamics of subpopulations are relatively independent • Migration connects subpopulations (Immigration and Emigration are nonzero) • Subpopulations have finite probability of extinction (and colonization) Metapopulation dynamics • Original “classic” formulation by R. Levins 1969 • dp/dt = c p (1-p) - e p • p = proportion of patches occupied by species • 1-p = proportion of patches not occupied by species Metapopulation dynamics • dp/dt = c p (1-p) - e p • c = colonization rate (probability that an individual moves from an occupied patch to an unoccupied patch per time) • e = extinction rate (probability that an occupied patch becomes unoccupied per time) Metapopulation dynamics Metapopulation dynamics Metapopulation dynamics Metapopulation dynamics Metapopulation dynamics Metapopulation dynamics Metapopulation dynamics Classic metapopulations • At equilibrium, dp/dt = 0 and p =1 - e/c • Metapopulation persists if e<c • Specific subpopulation dynamics are not modeled (but can be); only model probability of extinction of entire metapopulation Classic metapopulations • Lesson 1: Unoccupied patches or disappearing subpopulations can be rescued by immigration (Rescue Effect) • Lesson 2: Unoccupied patches are necessary for metapopulation persistence In real populations… • Subpopulations can vary in – Size – Interpatch distance – Population growth type • D-D or D-I • value of r – Quality Figure 15.16 Figure 15.17a Figure 15.17b Classic metapopulation • Subpopulations have independent dynamics and are connected by dispersal Mainland-Island metapopulation • R. MacArthur and E.O. Wilson 1967 • 1 area persists indefinitely and provides colonists to other areas that go extinct Source-Sink metapopulation • • • • R. Pulliam 1988 In sources, R>1 In sinks, R<1 Sinks persist because they are resupplied with individuals from sources Source-Sink metapopulation • Do all subpopulations with high l have high density? • Which would contribute more to conservation, high l or high density?