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)

Figure Oscillations occur when population growth occurs faster than density dependence can act – population overshoots

Figure adults larvae Larval food is limited: Larvae do not have enough food to reach metamorphosis unless larval density is low

Figure If food is limited for adults, then they cannot lay high densities of eggs. Low densities of larvae consistently survive.

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)

Kareiva et al Deterministic decline in Pacific salmon across a wide range of densities (r<0)

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 Deterministic extinction from low population size

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons

Population density (N) Births/individual/year No density dependence

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons Population density (N) Births/individual/year Carrying capacity when dN/dt/N=0

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons Population density (N) Births/individual/year Depensation

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 Stochastic extinction

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

What is the minimum viable population of Bighorn Sheep, based on model results? Initial population size

Spatial variation No species is distributed evenly or randomly across all space

Figure Individuals may be clumped due to underlying habitat heterogeneity

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 non- zero) 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

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 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 have high density? Which would contribute more to conservation, high or high density?