Chapter 12 Population Growth and Regulation Under ideals conditions populations can grow rapidly Vocab Demography The study of populations Growth Rate of individuals that are born minus of individuals that die Intrinsic growth rate r the highest possible per capita growth rate for a population Exponential growth model aka Continuous Growth Model model in which the population increases continuously at exponential rate J shaped curve shape of the Exponential Growth graph Geometric growth model model in which population growth are compared at different time intervals Expressed as as ratio of a population s size in 1 year to its size in the preceding year or some other year Fig 12 2 The discrete breeding events of the California quail Each generation of new quail produced each spring is represented Because births only happen in the spring the growth of the California quail is better modeled by a geometric growth model than an exponential The exponential growth model equation tell us how population will change under ideal conditions By taking the derivative of the exponential growth equation to determine the rate of growth at any time The Geometric Growth Equation uses the symbol lambda to determine population at a regular growth interval Using the geometric growth equation we can also calculate how the size of a population changes between time intervals N t N 0 ert dN dt rN N t N 0 t N N 0 t N 0 er or r ln R and are directly related and can be converted between one another How to calculate population doubling time 1 N t N 0ert 2 e rt 23 rt ln 2 4 t ln 2 r 5 t ln 2 ln the equation Populations have growth limits Vocab Density Independent factors that limit enhance population size regardless of population density Fig 12 5 Density Dependent factors that limit enhance population size that are affected by population density Negative Density Dependence limiting population based on population density Positive Density Dependence aka inverse density dependent or the Allee effect population size increases as density increases Self Thinning Curve shows how decrease in population density over time lead to increases in the size of each individual in the population Carrying Capacity K maximum size of population that environment can support Logistic Growth Model describes slowing growth of populations based on density S shaped curve the shape of the curve when a population is graphed over time using logistic growth derivative of logistic growth Inflection Point point on the S shaped curved where growth rate is highest but afterwards slows down Fig 12 5 Apple thrift growth is independent of density and scientists found it is proportional to temperature and rainfall variables Fig 12 7 Larger populations cause increased competition in fruit flies As density increases they experience a decline in progeny and the adults life span decreases Fig 12 8 Bird known as the common tern expanded into Buzzard s Bay in Massachusetts in 1970 Their population grew very quickly and eventually the birds expanded to Ram Island which then became dense as well and the terns moved to Penikese Island Fig 12 9 When flax seeds are sown at high densities the average plant is smaller Smaller flax plants are less fecund so high densities cause the population to increase at slower rate Fig 12 10 Horse weed seeds were sown at a density of 100 000 per m2 and over time the number of survivors declined while the average mass of plants increased Plotting density against Average dry mass results in a line with slope 3 2 Fig 12 11At low densities plants appear to be pollen limited which limits seed production At high densities each plant produces more seeds Fig 12 13 Positive and negative density dependence can be seen in We may think of positive and herring negative density dependence as isolated however populations can be regulated by both process At small population an increase in density will increase growth rate but eventually growth rate will get too large and get lower Fig 12 15 a The overall rate of population increase inflection point is at K 2 shown beside b the per capita rate of increase 12 16 Georgyi Gause in 1934 grew two different protists paramecium Aurelia and paramecium caudatum in test tubes giving each sample an equal amount of food each day and observed their carrying capacity He repeated the experiment giving the protists more food and observed an increase in carrying capacity Logistic Growth Equation begins with exponential growth which eventually will shrinks and falls to zero We can adjust the Logistic Growth Equation to get equation the per capita rate of increase derivative of the derivative of logistic dN dt rN 1 N K 1 N dN dt Populations growth rate is influenced by the proportions of individuals in a different age size and life history classes Vocab Age Structure the proportion of individuals that occur in different age classes Life Tables contain class specific survival and fecundity data Stable Age Distribution When age structure of a population remains constant over time Net Reproductive Rate total of female offspring that we expect an average female to produce over the course of her life Generation Time T average time between the birth of an individual and the birth of its offspring Cohort Life table life table that follows a group of individuals born at the same time from birth to the death of the last individual Static Life table A life table that quantifies the survival and fecundity of all individuals in a population during a single time interval The different columns on a life table Fecundity fruitfulness and fertility it is a measure of how many newborn an individual can produce birth rate Survivorship chance of individuals of a population to survive measured in age groups on life table Survivorship Curve Type I HIGH survivorship among young but drops off after certain age bears Species on this curve usually take care of their young for a long time Survivorship Curve Type II Equal survivorship among each group in a population 1 slope Species on this curve usually take care of their young for a short time squirrels Survivorship Curve Type III LOW survivorship among young that balances out as individuals age dandelions and oak trees X age Nx initial population Sx survival rate likelihood that an individual will survive to the next age Bx of offspring produced at certain age NxSx of individuals who survive that year and make it to next age level at age 0 this is 0 Multiply the Nx and Sx of the age