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### 26 Cards in this Set

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 ____ ____ ____ (lambda) - change in population size over a specific time interval (eg. 1 year) finite growth rate best for individuals that don't reproduce continuously (distinct "breeding" season) called "geometric growth" or "discrete growth" _____ ____ ____ - theoretical rate of change as the "time step" becomes smaller and smaller, approaching zero instantaneous growth rate appropriate for continuously reproducing populations (bacteria, some tropical insects, humans) called "exponential growth" or "continuous growth" equation for geometric growth Nt = N0 * lambda(t) equation for exponential growth Nt = N0 * e^rt r per capita growth rate r = b - d computational form of r formula r = [ln(Nt) - ln(N0)] / t lambda = 1 r = 0 population size is constant lambda > 1 r > 0 population is growing lambda < 1 r < 0 population is declining conversion of lambda to r r = ln(lambda) equation for finding doubling time in an exponentially growing population rt = 0.693 continuous reproduction stable age distribution constant "b" and 'd' (constant 'r') implies constant environment and unlimited resources assumptions for exponential growth model when are exponential growth requirements met in nature? introduction of species into new habitat (zebra mussel) population recovering from disturbance modern humans Thomas Malthus came up with these ideas in an essay on the principle of population in 1798 reproductive powers exhaust means of sustenance increasing death rates and decreasing birth rates must limit population populations do not increase exponentially w/o bound population growth varies w/ population size describes a population limited by resources logistic population growth equation for logistic population growth model dN/dt = r max(N) * [(K-N)/K] rate of population increase = max possible rate * proportion of resources available the realized growth rate of the population (dN/dt) depends on the ____ ____ population size example of density-dependent population regulation density-dependent regulation requires... -- birth rates (b) that ____ w/ increasing N and/or... -- death rates (d) that _____ w/ increasing N decrease increase what happens if b or d are non-linear functions of N? can have stable and unstable equilibrium points unstable equilibrium point = "critical minimum N" population growth rates decline if N drops below a minimum critical value Allee effect due to a decline in birth rates (b) at low and high values of N b declines at high N due to density-dependent effects (competition) b declines at low N due to difficulty in: mate location social interactions (group defense, foraging, etc.) allee effect important implications for conservation biology humans in 1975, the population was growing at an annual rate of nearly __% 2% at this rate, a population will double in size every 35 years, and we would reach 32 billion by 2080 growth rate has slowed recently, to about ____% per year 1.21% if this rate is maintained, there would be roughly 16 billion ppl on earth in 2080 current population size about 7 billion at current rate... how many ppl are added/day how long to add 1 billion? what is doubling time? 230,000 /day 1 billion every 13 years 58 yr doubling time in net reproductive rate went to r0 = 1 right now, would the population stop growing tomorrow? NO it would take several decades (probably a few generations) for the population age structure and growth rate to stabilize