1	Cell Division and Population Growth The simpliest form of population growth is binary cell division.
2	Reading Assignment Read pages 227-235 (emphasising the genetic relationship of the two daughter cells to each other and to their parent) Read pages 1192-1201 (sections 52.1 & 52.2) emphasizing the parameters and variables of different equations of growth. Figure 14.11b showing DNA duplication in the bacteria is also useful.
3	Growth and Reproduction In the exponential growth phase of the cultural life cycle there is an increase in mass of the population and an increase in the number of cells. Both building new macromolecules from acquired materials and assembling the macromolecules into new individuals are the essence of reproduction.
4	Population Growth In BioS 100 the processes of acquiring materials and energy and the building of new macromolecules is emphasized. In BioS 101 we focus on the number of individuals - the size, N, of the population and rates of change of N.
5	Cell division in bacteria Bacteria have circular DNA. The 2 strands of the DNA run in opposite directions (5´-3´ & 3´-5´). Bacterial DNA starts replication at a single spot and proceeds in both directions around the circle (Figure 14.11b).
6	Bacterial Division After DNA duplication there are two identical circular pieces of DNA in a single cell. When the cell divides in two, the crucial step is to assure that each daughter cell gets one and only one of the chromosomes. Cellular parts besides DNA are not always divided equally among the daughter cells.
7	Eukaryotes DNA in eukaryotes is organized in pieces called chromosomes. The DNA is linear (rather than circular). A complete set of information for a species requires many chromosomes, called the haploid number, n. For humans n=23, for dogs n=36, for the fruit fly n=4.
8	Cell Division in Eukaryotes I Eukaryotic cell reproduction can be considered as repeated cycles. After duplication the DNA in the chromosome is in two strands called sister chromatids.
9	Cell Division in Eukaryotes II The separation of the sister chromatids of the chromosome is done in mitosis (within cell membrane). The physical separation of the cell into two ‘daughter’ cells is called cytokinesis.
10	Ploidy Both haploid and diploid cells (and other ploidies) can undergoes mitosis. Tetraploids have four sets of chromosomes. Haploid is the minimum complete set.
11	Increase in cell number Given binary cell division, we expect the number of cells thru time to follow the powers of 2, namely 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, etc. This is basic pattern of geometric growth. There are variations among cells in the length of the cell cycle, and the pulsed nature of the increase in N smoothes into exponential growth.
12	Exponential growth In exponential growth, the per capita growth rate ΔN/(N•Δt) is constant (r). ΔN = N_final – N_initial = increase in population size. ΔN/Δt is the growth rate, where Δt is the time interval. Dividing the growth rate by N gives the per person or per capita growth rate.
13	Equation of Exponential Growth N_t = N₀•e^r•t Where N_tis the number at time t, N₀is the number at time zero (initial number), e is 2.718…, r is a parameter of the species (with units of per time) and t is time (in same units that r is given).
14	Geometric Growth equation N_t+1 = l• N_t where N_t+1 is the number of individuals in the next (t + 1) generation, l is the growth rate parameter, and N_t is the number of individuals in the t^th generation, where t is any integer.
15	Geometric Growth, many generations If the initial number of individuals is N₀ and the discrete growth goes on for n generations then the following equation applies: N_n = lⁿ• N₀ The number of generations is indicated by t in your text (only integer values are OK).
16	Growth rate parameters Each species has a characteristic per capita growth rate, r & l, when resources are abundant. Bacteria can double in as short as 20 minutes (=26,280 times in a year), but humans take 15 or 16 years (0.064 times per year). l = e^r when matches time units
17	Improved models of growth The previous models assume that all N individuals in the population are equivalent. Age of an individual seems intuitively important in modeling population growth. Age is symbolized by the variable x to distinguish age from time, t. A birth cohort (all individuals born in same year) is studied as they age.
18	Age specific patterns of death Let N(0) be the total number of newborns in the cohort with N(x) the number of individuals surviving to age x. As all individuals eventually die, N(x) = 0 for some large value of age = x. Survivorship, l(x) (shown in text as l_x) = N(x)/N(0), survivorship tells the probability a new born will survive to age X.
19	Age specific patterns of births Fecundity, m(x), is the average number of births a female of age x will have in next interval (by x+1). Symbol is m(x) or m_xbased on the word maternity. For population growth demographers just keep track of females (text is incorrect in saying male offspring are counted).
20	Growth in age-structured populations Later in the semester you will learn how to predict future population size, if age specific survivorship and fecundity are known and constant. In the lab you will learn that survivorship values have dramatically changed –people live longer- and fecundity has dropped –people have less children.
21	A Life Table
22	Vocabulary Age specific Cycle Exponential growth Fecundity Haploid number growth rate Mitosis per capita growth rate Reproduction Survivorship