Population Growth Biology 241 Notes - PDF

Overview of Biology 241 Biology 241 deals with energy flow in biological systems: Unit 1: Molecular Energy Transformations Unit 2: Cellular Energy Transformations Unit 3: Energy Allocation in Organisms Unit 4: Energy Flow in Ecosystems A. Population Growth B. Ecosystem Energetics Fenton et al...

Overview of Biology 241 Biology 241 deals with energy flow in biological systems: Unit 1: Molecular Energy Transformations Unit 2: Cellular Energy Transformations Unit 3: Energy Allocation in Organisms Unit 4: Energy Flow in Ecosystems A. Population Growth B. Ecosystem Energetics Fenton et al (2023): Chapter 26 (p. 689-714) © 2021  Learning Objectives: 1. Explain the difference between exponential and logistic models of population growth 2. Recall the equations for exponential and logistic population growth; given data, be able to use the equations 3. Explain what different values of r indicate (e.g. what does it mean when r = 0?) 4. Define rmax and explain under what conditions it would occur 5. Define carrying capacity (K) 6. Differentiate between density-dependent and density- independent factors and explain how each type of factor can influence population growth 7. Compare and contrast r- and K-selected species © 2021  Population Growth Reproduction results in population growth Your textbook defines a “population” as: – All of the individuals of a given species that live and reproduce in a particular place Population size is the number of individuals alive at a particular time in a particular place and is influenced by: – Births, deaths, immigration and emigration – We will ignore migration in BIOL 241 © 2021  Population Growth We can study the change in the total numbers of individuals in a population B = Number of births ∆𝑁 𝑑𝑁 D = Number of deaths ≈ = 𝐵−𝐷 N = number of individuals ∆𝑡 𝑑𝑡 t = time We can track both the per capita birth rate (b) and per capita death rate (d) in a population b = B/N d = D/N We can use the per capita growth rate (r) to predict population size changes r = b – d = (B-D)/N r > 0 is growing r < 0 is shrinking © 2021 Calculating the Change in Population Growth dN/dt = rN0 r = 0.1 N0 = 1000 𝑑𝑁 If r = -0.1 = 𝑟 ∗ 𝑁0 𝑑𝑡 = -0.1 * 1000 = 0.1 * 1000 = -100 = +100 © 2021  Exponential Model of Population Growth Under ideal conditions: 1. The per capita growth rate (r) will be at a maximum for that population: rmax = intrinsic rate of increase 2. In this model, rmax is always: Constant, positive 3. rmax varies by species: Bacteria can have rmax > 10 Humans have rmax ~ 0.0001 F 29.10 © 2021  rmax Varies by Species F 29.11 © 2021  Calculating Exponential Growth To determine the size of a population growing exponentially, we can use: Nt = N0(1 + rmax)t B = 80 D = 60 N0 = 100 t=1 t=2 rmax = (B – D) / N Nt = N0 (1 + rmax)t = (80 – 60) / 100 N1 = 100 * (1 + 0.2)1 = 0.2 = 120 N2 = 100 * (1 + 0.2)2 = 144 © 2021 © 2021  Organisms Don’t Live Under Ideal Conditions What limits population growth? Temperature, precipitation, predators, disease, food availability, etc Most environments can only support a certain population size = Carrying capacity Factors that limit population growth combine to determine the carrying capacity (K) How close the population size (N) is to the carrying capacity (K) changes As N à K, the growth rate of the population will decrease (less resources/individual available) © 2021  r Changes with N in Logistic Population Growth F 29.12a © 2021  Logistic Model of Population Growth As populations grow, death rates increase, and birth rates decrease r decreases as N increases towards K r is influenced by the fraction of K available: rt = rmax((K-Nt)/K) If N = 90 and K = 100: (K-N)/K = (100 – 90)/100 r = rmax * 0.1 F 29.12b To determine the size of a population growing logistically, we use: Nt+1 = Nt(1 + rt) © 2021 © 2021  Calculating Logistic Growth K = 1000 N0 = 100 rmax = 0.15 What is the population size one year later? We must first determine the value of r: rt = rmax((K-Nt)/K) rt = 0.15 * (1000 - 100) / 1000 = 0.15 * 0.9 = 0.135 Now we can determine Nt+1: Nt+1 = Nt(1 + rt) Nt+1 = 100 * (1 + 0.135) = 100 * 1.135 = 113.5 individuals ~ 114 © 2021 What is the population size after a second year? rt = rmax((K-Nt)/K) rt = 0.15 * (1000 – 114)/1000 = 0.15 * 0.886 = 0.1329 Nt+1 = Nt(1 + rt) Nt = 114 * (1 + 0.1329) = 114 * 1.1329 = 129.162 ~ 129 individuals © 2021  Do Populations Show Logistic Growth? Overshooting the optimum is possible – results in negative growth rate F 29.13 © 2021 © 2021 F 29.21 © 2021 https://population.un.org/wpp/Publications/Files/WPP2019_Highlights.pdf Copyright © 2019 by United Nations, made available under a Creative Commons license (CC BY 3.0 IGO) http://creativecommons.org/licenses/by/3.0/igo/ © 2021  Population Growth is Influenced by Density-Dependent Factors Biotic factors (the importance of each factor depends on what other organisms are also doing – of same species or of different species) Food availability Shelter Mates Predation Disease Have an increasing affect as N becomes large © 2021  Crowding (Density-Dependent) Influences: Reproduction F 29.15 © 2021  Crowding (Density-Dependent) Influences: Growth Rate Adult Size Survival F 29.14 © 2021 Population Growth is Influenced by Density-Independent Factors Abiotic (mainly independent of other organisms): Temperature Precipitation Light Disturbances (hurricanes, landslides, fires) Have an affect at any population size © 2021  Density-Independent Factors Influence Population Growth F 29.18 © 2021 Life History Strategies Influence Population Growth r-Selected Species K-Selected Species Tend to: Tend to: Live in environments Have populations with disturbance close to carrying Go through capacity boom/bust cycles of Be stronger population competitors growth/collapse Be individually larger Be individually in size smaller in size Be long-lived Be early mating Survive extremes Stay near the bottom Live with less of the curve disturbance © 2021 Life History Strategies Influence Population Growth r-Selected Species K-Selected Species (r strategists) (K strategists) Small offspring/adult size Large offspring/adult size Early sexual maturity Late sexual maturity Semelparous Iteroparous High fecundity (lots of offspring) Low fecundity (few offspring) Low parental investment High parental investment Low juvenile survivorship High juvenile survivorship Short lifespan Long lifespan Evolved to reproduce quickly Evolved to compete © 2021  How does rt compare to R in COVID-19? Both values measure the rate of increase of the population size Exponential/logistic depend on the individuals in the population Epidemiology is much more complicated! A “simple” model https://royalsociety.org/-/media/policy/projects/set-c/set-covid-19-R-estimates.pdf © 2021 © 2021