WFSC 403 1st Edition Lecture 9 Outline of Last Lecture I Lab Lecture STELLA a Population Growth II Intro a Connections III Theory a 2x2 b r pg 147 IV Lab Experiments V Field Data Outline of Current Lecture I Theory Population Growth a Summary II Logistic Growth a Lab b Field c Rejection d Whooping Cranes III More Realistic Models Current Lecture Discrete generations o Multiplication rate dependent on population size o Function of R0 on population size o Density dependent These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Depending on slope R0 A stable population B Stable oscillation C Chaotic oscillation No trend The oscillations and such change when the R0 changes slope o Flat R0 then stable or stable oscillation o Very R0 steep then chaotic oscillation Even in the simplest forms for discrete generation you can get different forms of population growth Laboratory studies of population growth o Do population of critters grow logistically in lab It really depends Gause 1934 Paramecium Logistic growth Figure 9 5 Pearl 1927 Drosophila Fruit fly Logistic growth Figure 9 6 Chapman 1928 Tribolium and Calandra beetles o o o o Page 149 o Should we reject what occurs in lab o Do we reject the logistic theory of population growth No Theories only work under assumptions and usually do not hold in the real world unless under very controlled circumstances o What good is this then It is useful as a concept A point of departure on why populations do or do not follow the theory A simplification on a way to try and understand nature Field data on population growth o Cormorant Page 150 Figure 9 8 o Ibex Figure 9 9 o Whooping Cranes Page 151 figure 9 10 The theory holds for a little bit then no longer works Not a good logarithmic example More exponential Flower beetles Figure 9 7 Population grows annually which means exponential growth Time o Snow shoe hares and lynx example in book Predation 10 year cycle o Time doesn t drive anything but things do occur in time More realistic models of population growth o Modifications o Why modifications Logarithmic doesn t always work in the field o Theta Page 152 1 is a regular growth rate 4 is convex 4 is concave o Why do we care about theta logistic Gives more flexibility can approach carrying capacity k more rapidly or slowly Doesn t change once hits k but in the mean time there is flexibility Time lag models of population growth o Change between population size and growth rate o The generation takes time to realize what the resource levels are The population thinks it is below carrying capacity resource level but it is not o Once the population realizes it is above k then it slams it s breaks and crashes down Ecological conditions do affect this So far all models in lab and text have been deterministic Stochastic models of population growth o One variable is random o Any variable is random makes graph model stochastic AKA probabilistic o Why is this useful Humans can t predict the future but we give our best guesses add in random unknown since we don t know a lot we have a better shot at being correct Variability increases the further away the graph goes from the deterministic value Good for explicitly incorporating confidence interval Matrix model o Good to project population age structure as well as number into the future