1. Populations: Variation in time and space Ruesink Lecture 6 Biology 356

2. Temporal variation Due to changes in the environment (e.g., ENSO, seasons) OR Due to inherent dynamics –Lag times –Predator-prey interactions (LATER)

3. Figure 15.11 Oscillations occur when population growth occurs faster than density dependence can act – population overshoots

4. Figure 15.13 adults larvae Larval food is limited: Larvae do not have enough food to reach metamorphosis unless larval density is low

5. Figure 15.14 If food is limited for adults, then they cannot lay high densities of eggs. Low densities of larvae consistently survive.

6. 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

7. 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)

8. Kareiva et al. 2000 Deterministic decline in Pacific salmon across a wide range of densities (r<0)

9. 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

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

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

12. 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

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

14. 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

15. 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

16. 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

17. Minimum viable population Population size that has a high probability of persisting into the future, given deterministic dynamics and stochastic events

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

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

20. Figure 15.15 Individuals may be clumped due to underlying habitat heterogeneity

21. Individuals may also occur in a clumped distribution due to habitat fragmentation by human activities

22. Population Group of regularly-interacting and interbreeding individuals

23. Metapopulation Collection of subpopulations Spatially structured –Previously we’ve talked about population structure in terms of differences among individuals: Age structure

24. Metapopulation Dynamics of subpopulations are relatively independent Migration connects subpopulations (Immigration and Emigration are non- zero) Subpopulations have finite probability of extinction (and colonization)

25. 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

26. 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)

27. Metapopulation dynamics

34. 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

35. 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

36. In real populations… Subpopulations can vary in –Size –Interpatch distance –Population growth type D-D or D-I value of r –Quality

37. Figure 15.16

38. Figure 15.17a

39. Figure 15.17b

40. Classic metapopulation Subpopulations have independent dynamics and are connected by dispersal

41. Mainland-Island metapopulation R. MacArthur and E.O. Wilson 1967 1 area persists indefinitely and provides colonists to other areas that go extinct

42. Source-Sink metapopulation R. Pulliam 1988 In sources, R>1 In sinks, R<1 Sinks persist because they are resupplied with individuals from sources

43. Source-Sink metapopulation Do all subpopulations with high have high density? Which would contribute more to conservation, high or high density?