Intrinsic Rate of Increase - Principles of Ecology - Lecture Slides, Slides of Ecology and Environment

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Lecture 9: Population Growth and

Regulation

9.5 Intrinsic rate of increase can be

estimated from the life table

Crude birthrate (demographers): # of birth over a period of time divided by population size at the beginning of the period*

Age-specific birthrates, b x Mean # of females birth to a female in each age group. (Only females give birth; birth rates vary with ages) Gross reproduction rate: sum of the bx values across all age classes, provides an estimate of average offspring born to a female over her lifetime. Docsity.com

Birth rate and survivorship determine net

reproductive rate

• Net reproduction rate, R 0 : number of female offspring a female at birth can produce (or average # of females that will be produced (left) during a lifetime by a newborn females.)

 R 0 : depends on survivorship and fecundity  R0=1, >1 or <  Generation time: average age at which an individual gives birth to its offspring  T=Sum(xlxb x )/sum(l x b x )  N(t)/N(0)= λt^ (T=1.95)  If t=T, then R0=^ λt,^ λ =R 0 1/T^ =1.46; r =^ ln (λ)=0.

The growth potential of populations

• Capacity of population growth examples
• Pheasants: 2 males +6 females in 1937
• in 5 years,  1325 (r=1.02, λ =2.78)
• Elephant seal: 100, 1900

2000: 150,000 (r=0.073, λ=1.076) 2100: 225 millions Doubling time: t2 =ln(2)/ln(λ) or t2 =ln(2)/r

• Pheasants: t2=246, water flea, t2=3.6 days

Birth rate and death rate change with

population size N

dN/dt=rN r=b-d b=b0-aN d=d0+cN

dN/dt=[(b0-d0)- (a+c)N]N dN/dt=(b0-d0)[1- (a+c)/(b0-d0)*N]N

dN/dt=r N(1-N/K) K=(b0-d0)/(a+c) K: carrying capacity: maximum sustainable population size under prevailing environmental environment. Docsity.com

From exponential growth to logistic growth

Logistic Population Growth

Logistic Population Growth

• As resources are depleted, population growth rate

slows and eventually stops: logistic population

growth.

• Sigmoid (S-shaped) population growth curve.
• Carrying capacity (K) is the number of individuals of a population the environment can support.
• (r) is per capita increase rate.