LECTURE 15: - Despite what politicians and economists would like you to believe, unbridled growth is not possible – all growth in nature has its limits! - Biological populations grow at widely differing rates, and they can grow exponentially (or geometrically) for some time, but the rate of increase will ultimately flatten out (logistic or sigmoidal growth), or the population collapses (irruptive growth); sometimes, oscillations in population density are observed (partial collapses that are followed by recovery) - Both irruptive and oscillatory growth are common among bacteria and viruses, but also occur in mammals (e.g. snowshoe hare and Canadian lynx) - Graphically, geometric growth (Nt = N0 !t; geometric rate of increase: ! = Nt+1/Nt) results in a J-curve pattern resembling exponential growth (Nt = N0 ert, i.e. ! = er), but the former is used to describe J-curve-type growth in discretely-growing populations (e.g. annual plants like many grasses or Phlox, with bursts of seed production, rather then overlapping generations of reproducing individuals; points in such graphs should NOT be connected!), while the latter is observed in populations with overlapping generations (e.g. Scotch pine colonization after the last ice age in Europe, collared doves introduced to Britain; by definition, the e function can only be used to model continuous growth!) - Each environment imposes different limits upon natural population increase: this is known as the carrying capacity (K) of each environment, i.e. the maximal sustainable number of individuals of a population in that environment www.notesolution.com
- The combination of limiting factors (space, food supply, oxygen or carbon dioxide concentration, water availability, number of predators etc.) is referred to as environmental resistance - In irruptive growth, K is being overshot, i.e. growth is so rapid that feedback from the environment usually comes too late: populations tend to decline as rapidly as they become established - Sigmoidal growth usually displays three phases: lag phase – exponential phase – stable equilibrium (reaching carrying capacity, K) - Such growth is mathematically described as: (N is the number of individuals, r is the per capita rate of increase; r considers birth and death rates as well as immigration and emigration) www.notesolution.comLECTURE 15: - Despite what politicians and economists would like you to believe, unbridled growth is not possible all growth in nature has its limits! - Biological populations grow at widely differing rates, and they can grow exponentially (or geometrically) for some time, but the rate of increase will ultimately flatten out (logistic or sigmoidal growth), or the population collapses (irruptive growth); sometimes, oscillations in population density are observed (partial collapses that are followed by recovery) - Both irruptive and oscillatory growth are common among bacteria and viruses, but also occur in mammals (e.g. snowshoe hare and Canadian lynx) t - Graphically, geometric growth (N = N ;tgeom0tric rate of increase: = N N) t+1 t results in a J-curve pattern resembling exponential g

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