ehj351 lec_2 - 13/01/2011 Populationgrowthinecology...

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13/01/2011 1 Population growth in ecology EHJ351: January 13 Lecture 2 Remember to review James Thomson BIO150 lecture slides and notes! Headline of National Geographic article (Jan. 2011) by Robert Kunzig: "By 2045 global population is projected to reach nine billion. Can the planet take the strain?" Population growth is an inherently multiplicative process Simplest case=Each individual within a species (or some category within the species) has a probability of birth and death More individuals mean more net reproduction when birth exceeds death, thus more individuals, more birth. ...etc. Leads to two basic models when all individuals are similar r = b–d; R = (B + 1)(1–D) dN dt rN or N t 1 RN t Time Population () (0 ) ( ) Nt N Expr t r is the instantaneous growth rate; its units are numbers (or density) per unit time ( t ) Exp( rt ) is e to the rt power where e is the base of the natural logarithms 2.71828. .. Any positive r means infinite growth! Reducing r from x to 0.1x means that it will take ten times longer to reach any given population size. Human population growth is usually measured in % per year: 1.It is a relatively small number; < 4% a year 2.The rate Ehrlich used in 1968 was about 2% a year 3.For low rates the exponential model with r = % in decimal form N(t) = N(0)Exp(.02t) 4.N(t) = N(0)Exp[rt] or N(0)R t (r=0.02 and R=1.02 are almost equivalent Doubling time approximately 70/(% growth per year)
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13/01/2011 2 What is wrong with this model? 1. No resources or other factors that can be used up or become scarce 2. No time lag in the effects of density (e.g., due to time required to reach maximum reproductive rate) 3. No age structure, spatial structure, genetic variation, or other structure (e.g., no sexes—female may be assumed) 4. No predators or diseases 5. No culture or learning It is possible that positive effects of higher population size via #5 will cancel the probable net negative effects of 1-4 in humans Over a short enough time interval, these modifying factors usually won't change too much. .. What is the impact of age structure? Obvious that distribution of individuals into age classes matters if they have different b, d. Numbers can always be calculated based on life table, assuming constant per capita birth and survival rates for each age; Life table gives births at age x (m x ), and probability of survival from age x to x+1 (p x ) ; survival from birth to age x is l x = p 0 p 1 ...p x 1
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ehj351 lec_2 - 13/01/2011 Populationgrowthinecology...

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