Growth and Death (natality and mortality)

Rates of change (fluxes): Demographics

Death Rate: probability of dying-

=(#deaths/time)/# individuals to start

Life Tables

Horizontal or Cohort LT: following a cohort Table 10.2

Cohorts: group fo individuals born at same time/year

x: age

Nx: number of individuals surviving to that age

lx: survivorship as a proportion of the intial cohort

dx: age specific death

qx: age specific mortality rate, probability of dying.

ex: life expectancy for survivors to age x

Physiological vs. Mean Natural Longeveity

Difficult to obtain life table data on natural populations

Dynamic-composite Life table:

Following several years of markd animals

treating them as a cohort

dx can be estimated from age of natural mortalities

Verticle, time specific, or static life table: Table 10.3

lx can be estimated from random samples of a population:

hunting, natural diasters, allow age structure to be determined

Horizontal/cohort table shows actual survivorship

Verticle/Static shows what survivorship might be.

Differnces shown by tables 10.2 & 10.3

Inverts with multiple life stages: use stages instead of ages

Table 10.4

Survivorship Curves Fig 10.13 lx vs time

Age dependent, age independent

Brooders vs Broadcasters

Fig. 10.15 shows differences between static and cohort LT

(Examples in Figs 10.14, 10.16, 10.17, 10.18)

All three for the same species: Fig 10.19

Mortality curves same concept, Fig 10.20

avoid difficulty of estimating year age class size

most species have "J" shaped curves

Natality

Age specific reproduction/fecundity, mx, Table 10.7

Average number of females produced per female parent at x

Fecundity curves: Fig. 10.21

Bacteria age specific too; Science 289:1131 (Aug 2000)

Net Reproductive Rate Ro: S l_xm_x

number of females produced in a female lifetime

if Ro > 1, female replaces herself

Natality difficult to determine for plants:

variable seed production

dormancy-seed bank

Seed production easiest to measure

Models of Rate of Increase

Population projection table: Table 11.2

Number of offspring added to year 0 each year is

S N_xm_x

Geometric Growth: Finite multiplication rate l= N_t+1/N_t

Projection not prediction N_t = N₀l^t

Population increase is exponential 2:4:8:16 etc.

stable age distibution populations only: stable l

Generation time: T_c birth of parent to birth of offspring

Exponential Growth

Physiological natality “r” per capita specific growth rate

r = lnR₀/T_D

Intrinsic Rate of Natural Increase, Biotic Potential

Instantaneous change in population numbers

Continuous growth

rN = dN/dt

population growth is a function of N (population size) and r

N_t = N₀ e^rt

“r” is the exponential curve equation constant fig 11.2

r can be used to determine T_D, or t for N to double

N_t/N₀ = 2; N₀ e^rt/N₀ = 2; e^rt = 2; rt = log_e2 = 0.693; T_D = 0.693/r

Estimating “r”

l = e^r

Realized natality “m” reflects limitations

m = (lnN_t-lnN₀)/t Slope of the exponential growth curve

range of limiting factors, can estimate “r” as a saturation value

Logistic Growth

Exponential/logarythmic sigmoidal curve

reflecting an upper limit to N

K = carrying capapcity = N supportable on available reources

dN/dt = rN((K-N)/K)

negative feedback term

assumptions limit usefulness of these models:

variability among individuals

instantaneous response

linear response to limitation

Time Lags

Reaction time lag “w”

(K-N_t-w)/K

Reproductive time lag “g”

RN_t-g

Natural populations: discrete generations:

breeding cycles instead of continuous growth

averaged response to K: Fig. 11.10 and Fig. 11.11

Density Dependent Response

Balance of birth and death rates Fig 11.9

Intercompensation: Chincoteague ponies

Possible responses to K:

Direct Equilibrium

Damped oscillations

Stable limit cycles

Chaotic- non-linear: Science 284:83

Density Independent: crash and burn

Thrips on Roses

Cyclical dynamics in populations (more later with predation)

(Fig. 11-12)

Natural Cycles: 3-4 and 9-10 years

cyclic dynamics more prevalent at higher latitudes: muskrats

3-4 year cycle found in Tundra, Eurasia

9-10 year cycles found in Boreal forests

Science 285:1022.

Equilibrium Dynamics: resilience – ability to restablish equilibrium

Cascade effects, dependence of one species on another

More later under community dynamics

Extinction

Small population sizes: genetics later

High rate of extinction this century:

habitat loss, alteration

harvest

introduction of predators, competitors, parasites

Stochastic and Deterministic processes

Deterministic: Uniform, complete loss of habitat

Stochastic: random fluctuations in demographics or K

Environmental noise.