BIO 152 1st Edition Lecture 28Outline of Last LectureI. GeneticsII. Out of AfricaI. Population Ecologya. Ecology Outline of Current LectureIV. Population Ecology continuedV. Population Growth i. Exponential Growth Model Current Lecture**Clicker Question**A population is correctly defined as having which of the following characteristics? I. inhabiting the same general areaII. belonging to the same speciesIII. posesessing a constant and uniform density and dispersion answer = I and II only- III is one of the characteristics of a population (potentially but does notoccur in every population, so it is only one kind of distribution) **Clicker Question**Which of the following groups would be most likely to exhibit uniform dispersion? Remember there were three types: clumped, uniform, randomA. red squirrels who actively defend their territory B. cattails, which grow primarily at edges of lakes and streams C. dwarf mistletoes, which parasitize particular species of forest tree D. moths, in a city at night E. lake trout, which seek out cold, deep water high in dissolved oxygen answer = A (every single squirrel is going to defend a certain area, and they will demonstrate a uniform dispersion pattern) - cattails are going to be clumped around the edges only (not in the center) - dwarf mistletoes are going to be totally dependent on dispersal of thatparticular tree- lake trout = clumped - moths = random (didn’t give you any info about where the moths would go,whereas the squirrels are defending territory so they’re going to set upperimeters which are going to knock up against each other, assuming theterritory is the same size) - all of the red squirrels in a forest each have their own territory thatborders on the territory of the other squirrels Population GrowthGrowth curve for e.coli (two different strains)- at the beginning it shows exponential growth, then becomes logisticgrowth Exponential Growth Model - if N = population - delta N (change in N) = births - deaths - Population ecologists study the change in a population over a given timeso - deltaN /change in time (t) - interested in the PER CAPITA growth rate in a particular time frame - per capita growth rate = (births - deaths)/N - an assumption of this model is that everyone is reproducing together **the per capita growth rate does not vary in this model- the number of individual at any given time varies (so the slow of the curvevaries) - So if growth is 50% and there are 500, you add 250. If you have 1000individuals you add 500 r = per capita growth rater = (births - deaths)/NThis is a model for hypothesis testing (like Hardy-Weinberg) and very rarely will a population grow exponentially, but it could**Clicker Question**1,000 people in population. 200 born, 100 die. What is the per capita growth rate (r)?- births - deaths)/N - 100/1000 = 0.1 **Clicker Question**Assume per capita growth rate (r) is 0.5 and you have 3000 people, how many will you have in the next generation (what will the population be)?- because you have 3000 people and it is growing at a rate of 50%, then thenext year it will increase by half the total population (which is 1500) - so 3000 + 1500 = 4500**Clicker Question**Based on the data at right, which show cod harvest rates over the last 60 years, what should the value of r be over the whole period?- r < 0- the trend is downward, so the population is probably shrinking — within this time period there are periods where it could potentially be increasingexponentially (but over the whole period it is less than zero) Hypothetical population2. starting population of 1000 organisms 3. birth - death = 500 4. per capita growth rate is 0.5 (assume this growth rate is steady) 5. in the first year you have 0.5 * 1000 = 500 **Clicker Question**What have we assumed here?- answer = r is stable and growth over discrete time periods (e.g, year) - # of births is not the same, the births per capita is the same - as r increases, the steepness of your curve will increase (this is whatis doubling every generation) **Clicker Question**If you have an exponentially growing population what will determine the time it will take for a population to increase from 2 to 2000 individuals?- the difference between per capita birth rate and per capita death rate - r is not increasing (it is a constant) - the slope of the exponential growth curve does change over time but itis r that is responsible for the curve. and what gives us r? the birth anddeath rate **Clicker Question**You have two populations of mole rats, one naked and the other blind. There are 2000 naked mole rats and they have a per capita growth rate of 0.25.There are 1000 blind mole rats with per capita growth rate of 1. Which population will be larger after 2 generations?- Blind mole rates will have a larger population - 1000 —> 2000 —> 4000 for blind - 2000 —> 2500 —> 3000 ish for naked - Exponential growth occurs when organisms are introduced into a newplace with plenty of resources and not many predators - This shows elephant seals reintroduced after being hunted to nearextinction and the same for elk.**Clicker Question**But our e. coli experiment doesn’t show exponential growth forever. What happens?- The number of deaths and number of division events (“births”) arebalanced - as far as we know e. coli do not do systematic population controlregimen and manage resources so as to stably support thepopulation - B could be true (not likely) but it could be happening but thatsnot whats happening - Can’t grow exponentially forever, eventually you’ll run into some sort ofbarrier = carrying capacity of the ecosystem - represented by K If K = 1500, you take 1500-N/1500 which gives you the carrying capacity remainingK-N/K is lowing your total population growth (by a little bit at the beginning) - as you approach K, growth slows down — this is called logistic growthIf K is 100,000 and your population is 50,000 what will the difference between the exponential growth and logistic growth be if r is 0.1 per year (so 10% growth). Assume t = 1.- answer = B, the population under logistic growth will be half that of theexponential population - only difference between two equations is the K-N/K part, so whatever value the exponential function gives you, you’re gonna multiply it by 0.5(which is what you get when you add the extra