Population Ecology: Growth & Regulation Photo of introduced (exotic) rabbits at “plague proportions” in Australia from Wikimedia Commons.

Life Cycle Diagram seed 1 to 2 yr old adult 2 to 3 yr old adult seedling age survival fecundity

Life Table (a.k.a. Actuarial Table) Cain, Bowman & Hacker (2014), Table 10.3 Demographic rates often vary with age, size or stage

Life Table (a.k.a. Actuarial Table) Cohort Life Table Fates of individuals in a cohort are followed from birth to death Static Life Table Survival & reproduction of individuals of known age are assessed for a given time period

Life Table (a.k.a. Actuarial Table) S x = Age-specific survival rate; prob. surviving from age x to x+1 Cain, Bowman & Hacker (2014), Table 10.3 l x = Survivorship; proportion surviving from birth (age 0) to age x F x = Age-specific fecundity; average number of offspring produced by a female at age x

Life Table (a.k.a. Actuarial Table) Population growth from t 0 (beginning population size) to t 1 (one year later) Cain, Bowman & Hacker (2014), Table 10.4 F 1 = 2, so 6 x 2 = 12 F 2 = 4, so 24 x 4 = offspring

Life Table (a.k.a. Actuarial Table) Population growth from t 0 (beginning population size) to t 1 (one year later) Cain, Bowman & Hacker (2014), Table 10.4 N t+1 NtNt Population growth rate = = = =

Life Table (a.k.a. Actuarial Table) Cain, Bowman & Hacker (2014), Fig B If age-specific survival & fecundity remain constant, the population settles into a stable age distribution and population growth rate 11 = = = = 1.32 etc. = 1.32

Leslie Matrix Age-structured matrix model (L) of population growth parameters Example of a Leslie matrix from Wikimedia Commons Age structure at t+1Age structure at t Dominant Eigenvalue of L = Dominant Eigenvector of L = stable age distribution Age-specific survival & fecundity

Lefkovitch Matrix Stage-structured matrix model (L) of population growth parameters Example of a Lefkovitch matrix adapted from Leslie matrix from Wikimedia Commons Stage structure at t+1Stage structure at t Dominant Eigenvalue of L = Dominant Eigenvector of L = stable stage distribution Stage-specific survival & fecundity

Population Age Structure Age structure for China in 2014 from Wikimedia Commons; China implemented a “one-child policy” in 1960s Useful for predicting population growth

Survivorship Curves Cain, Bowman & Hacker (2014), Fig Which is most likely to characterize an r-selected species? K-selected species?

Geometric growth when reprod. occurs at regular time intervals Exponential Growth Cain, Bowman & Hacker (2014), Fig N t+1 = N t Population grows by a constant proportion in each time step N t = t N 0 = Geometric population growth rate or Per capita finite rate of increase

Exponential Growth Cain, Bowman & Hacker (2014), Fig Exponential growth when reproduction occurs “continuously” Reproducing is not synchronous in discrete time periods dN dt = rN N(t) = N(0)e rt r = Exponential growth rate or Per capita intrinsic rate of increase

Exponential Growth Cain, Bowman & Hacker (2014), Fig = e r N t = t N 0 N(t) = N(0)e rt = e rt N(0) Geometric Exponential r = ln( ) Exponential decline / decay Constant population size Exponential growth

Peter Turchin The Fundamental Law of Population Ecology Original idea from Turchin (2001) Oikos “A population will grow… exponentially as long as the environment experienced by all individuals in the population remains constant.” In other words, as long as the amount of resources necessary for survival & reproduction continues expanding indefinitely as the population expands.

Laws of Thermodynamics Image of Carnot engine from Wikimedia Commons Earth Bio-geo- chemical processes 1 st Law of Thermodynamics  Law of Conservation of Energy Related to Law of Conservation of Mass E=mc 2 Sun

Limited Scope for Population Increase Quote from Cain, Bowman & Hacker (2014), pg. 227 “No population can increase in size forever.” < <  Number of particles in the universe

Limits to Exponential Growth Cain, Bowman & Hacker (2014), Fig Density independent Density dependent Density-independent factors can limit population size

Limits to Exponential Growth Cain, Bowman & Hacker (2014), Fig Density independent Density dependent Density-independent factors can limit population size Density-dependent factors can regulate population size

Logistic Growth Cain, Bowman & Hacker (2014), Fig K = Carrying Capacity r = Intrinsic Rate of Increase

r- vs. K-selection Cain, Bowman & Hacker (2014), Fig K = Carrying Capacity r = Intrinsic Rate of Increase