Download Logistic Growth & Population Dynamics: Exponential Growth, Capacity, & Demography and more Lab Reports Biology in PDF only on Docsity! Ecology Notes Part | B Exponential growth cannot continue forever. The exponential growth of many real populations begins to level off as the density approaches the carrying capacity (K) of the environment. The carrying capacity of a population is the maximum density of a population that the environment can support over a sustained period without damage to the environment. Intrinsic rate of increase then will be high with lower densities and decrease with higher population densities until the population levels out reaching a carrying capacity. 2 Carrying capacity= 6.7 g Deceleration & Inflection point Amount of yeast (maicc) we S Acceleration re 0 2 4 G6 8 10 12 14 16 18 20 Hours Such a growth curve is called an S-shaped or logistic growth curve and results from a changing ratio between births and deaths. In the beginning the rate of increase is accelerating but later as the population increases even though the birth rate is greater than the death rate. At some point in time equilibrium is reached or the carrying capacity and the birth rate equals the death rate. After the curve has leveled off, births and deaths are in balance and the population has zero population growth. This occurs because environmental limitations become increasingly effective in slowing population growth as the population. When the density approaches the carrying capacity , the limitation becomes severe. A density dependent limitation,(think of it as a factor), (K-N)/K, is one whose density is determined by the density of the very population it helps limit. The equation for the logistic growth curve is AN/dt = Fino N((K-N)/K) This inserts the density dependent limiting factor.. At low population densities, population growth is exponential. The rate of increase reaches its maximum at the inflection point of the curve. When the population exceeds the carrying capacity, dN/dt becomes negative , and the population decreases. Growth of a population with r,,,,, of 1.0, K of 100, and an initial size N of 4. It assumes that all individuals in the previous generation survive. In the beginning and N is small, the density limiting factor is very close to 1. If Nis small then ~~ N approximates 1 That means that in the equation AN rex (K-N) y approx- Ade tere (1)N imates or exponential growth. hte N approch es the carrying capacity en (K-N’ oe te ar NO Be sy N AN tra KD approx- Nese (ON imates ak means no rate of increase and a stable population has been reached. The inflection point is where the growth moves from accelerating to decelerating. This point is the maximum sustainable yield. If man wanted to harvest an organism, then the population should be kept at the maximum sustainable yield and not at the carrying capacity.
