BIOL203 Lecture 12: Population Growth - Fall 2024 PDF

Lecture 12 Population growth & regulation BIOL 203 November 13th, 2024 1 Learning objectives 1. Explain why populations can grow rapidly under ideal conditions 2. Explain why populations have growth limits that regulate their populations 3. De...

Lecture 12 Population growth & regulation BIOL 203 November 13th, 2024 1 Learning objectives 1. Explain why populations can grow rapidly under ideal conditions 2. Explain why populations have growth limits that regulate their populations 3. Describe how life tables demonstrate the effects of age, size, and life- history stage on population growth 2  Populations can grow Key Concept rapidly under ideal conditions 3 Populations can grow rapidly under ideal conditions Population growth rate = the number of new individuals that are produced in a given amount of time minus the number of individuals that die Under ideal conditions, individuals can reach maximum reproductive rates and minimum death rates, populations grow rapidly Highest per capita (per individual) growth rate = intrinsic growth rate (r) 4 Mathematical models of population growth Two models for population growth under ideal conditions: Exponential growth model – applies to species that reproduce throughout the year Geometric growth model – applies to species within distinct breeding seasons 5 The exponential growth model The exponential growth model is a model of population growth in which the population increases continuously at an exponential rate 𝑁𝑡 = 𝑁𝑜 𝑒 𝑟𝑡 Where: Nt = size of the population in the future No = current size of the population e = base of natural log r = intrinsic growth rate t = amount of time over which the population grows 6 The exponential growth model 7 The exponential growth model We can also determine the rate of growth (slope) at any point in time by taking the derivative of the exponential growth equation: 𝑑𝑁 = 𝑟𝑁 𝑑𝑡 Where: dN/dt = change in population size per unit time r = intrinsic growth rate N = population size at a given point in time 8 The exponential growth model dN/dt = rN 9 The geometric growth model Most species of plants/animals have distinct breeding seasons Birds/mammals reproduce in spring/summer when resources abundant E.g.) California quail (Callipepla californica) 10 The geometric growth model The geometric growth model is a model of population growth that compares population sizes at regular time intervals: 𝑁1 = 𝑁0 λ Where: N1 = population size at year 1 N0 = population size at year 0 λ = ratio of population’s size in 1 year to its size in the preceding year 11 The geometric growth model λ > 1 means the population size has increased from one year to the next (i.e., births exceed deaths) λ < 1 means the population size has decreased from one year to the next (i.e., deaths exceed births) λ always positive since you cannot have negative number of individuals 12 The geometric growth model We can also predict population size over multiple time intervals: 𝑁2 = (𝑁0 λ)λ 𝑁2 = 𝑁0 λ2 Rewritten for any length of time: 𝑁𝑡 = 𝑁0 λ𝑡 13 Geometric growth example Imagine we have an initial chipmunk population of 100 individuals with an annual growth rate of λ = 1.5. What will the size of the population be after 5 years? 14 Estimating lambda Lambda can be estimated using population sizes from two points in time: 𝑁𝑡 = 𝑁𝑜 λ𝑡 1ൗ λ= 𝑁𝑡 Τ𝑁𝑜 𝑡 Practice: Since European colonization of the Hawaiian islands, the Hawaiian honeycreeper population has declined due to habitat loss, disease, and introduction of predators. In 2003, the remaining 8 individuals were brought into captivity to start a breeding program. By 2015, the captive population had grown to 116 birds. What was the population growth rate over this time? 15 Comparing the exponential and geometric growth models Geometric growth and exponential growth are directly related: 𝑁𝑜 λ𝑡 = 𝑁𝑜 𝑒 𝑟𝑡 λ = 𝑒𝑟 ln λ = 𝑟 16 Comparing the exponential and geometric growth models 17 Comparing the exponential and geometric growth models Decreasing Constant Increasing 18 Population doubling time One way to analyze population growth rate is to estimate the doubling time = the time required for a population to double in size For exponential growth model: ln 2 𝑡= 𝑟 For the geometric growth model: ln 2 𝑡= ln λ 19 Doubling time examples Compare the doubling times for ring-necked pheasants (λ = 2.78), field voles (λ = 24) and flour beetles (λ = 1010) 𝑡𝑝ℎ𝑒𝑎𝑠𝑎𝑛𝑡 = ln 2 ÷ ln λ = 0.69 ÷ 1.02 = 0.67 years or 246 days 𝑡𝑣𝑜𝑙𝑒 = 0.69 ÷ 3.18 = 0.22 years or 79 days 𝑡𝑏𝑒𝑒𝑡𝑙𝑒 = 0.69 ÷ 1.02 = 0.03 years or 11 days 20 Concept check Why does the graph of population increase produce a J-shaped curve even though the intrinsic growth rate is a constant? In what situations should we use the geometric population growth model? 21 Key Concept Populations have growth limits 22 Populations have growth limits In nature, we commonly observe that there are limits on how large a population can grow E.g.) resources, space, mates, predation, pathogens, etc. Growth limits can be grouped into two categories: Density-independent factors Density-dependent factors 23 Density-independent factors Density-independent factors limit population size regardless of the population’s density Include natural disasters, dramatic environmental changes (e.g., droughts) Impact on the population is not related to number of individuals in the population (what random evolutionary process fits in this category?) 24 Density-independent factors E.g.) apple thrip (Thrips imaginis) Hypothesized population was controlled by density- independent factors (e.g., temperature, precipitation) Designed a population growth model to predict population changes (dashed line), included temperature/precipitation 25 Density-independent factors Observed populations (blue bars) matched predicted population size 26 Density-independent factors and climate change E.g.) mountain pine beetle (Dendroctonus ponderosae) Develop faster/reproduce more under warmer conditions Die from unusually cold temperatures Models predict large increases in beetle populations in future; significant damage to conifers 27 Density-dependent factors Density-dependent factors are factors that affect population size in relation to the population’s density Two categories: Negative density dependence = the rate of population growth decreases as population density increases Positive (inverse) density dependence = the rate of population growth increases as the population density increases Also known as the Allee effect (first described by Warder Allee in 1931) 28 Negative density dependence in animals Most common factors include limited supply of resources (food, nesting sites, space) Crowded populations also can have higher levels of stress, disease, predation Cause population growth to slow and eventually stop altogether (or even decline) 29 Negative density dependence in animals E.g.) Drosophila melanogaster Raymond Pearl – raised breeding pairs at different densities with identical amounts of food Increased number of adults led to increased competition, fewer progeny, and shorter lifespans 30 Negative density dependence in animals E.g.) common tern (Sterna hirundo) In 1970s, expanded into Buzzards Bay, MA Colonized three islands Rapid population growth with plateau – limited nesting sites 31 Negative density dependence in plants Plant growth, survival, reproduction also can be affected by density Competition for sunlight, water, soil nutrients 32 Negative density dependence in plants E.g.) flax (Linum usitatissimum) grown at different densities 33 Negative density dependence in plants Under very high densities, competition among conspecifics can cause plants to die E.g.) horseweed (Erigeron canadensis) Seeds sown at high density (100,000 seeds/m2) 100-fold decrease in population density but 1000-fold increase in average plant size 34 Negative density dependence in plants If we graph the changing density of surviving plants versus the change in average dry mass per plant over time, we see a negative relationship = self-thinning curve Can be used to optimize planting of crops, trees, etc. 35 Positive density dependence Positive density dependence occurs when population growth increases as population density increases Typically occurs when population density is very low Low densities make it hard to find mates/obtain pollen, decreased predator detection/defence, more difficult to find/capture food, etc. Low densities can also have harmful effects of inbreeding, uneven sex- ratios (few females means low reproduction) 36 Positive density dependence Observed in many species E.g.) cowslip (Primula veris) Many small populations declining Populations 1, each female replaces herself in the population; population grows How many individuals a female will have at each age (bx), weighted by probability of survival (lx), summed over all age classes: 𝑅0 = ෍ 𝑙𝑥 𝑏𝑥 66 Calculating the net reproductive rate 67 Calculating the net reproductive rate R0 = 2.1 68 Calculating the generation time The generation time (T) of a population is the average time between the birth of an individual and the birth of its offspring We first multiple the age (x) by reproductive rate of each age class (lx x bx) Then, we sum these values and divide by the net reproductive rate: σ 𝑥𝑙𝑥 𝑏𝑥 𝑇= σ 𝑙𝑥 𝑏𝑥 69 Calculating the generation time σ 𝑥𝑙𝑥 𝑏𝑥 4.1 𝑇= = = 1.95 𝑦𝑒𝑎𝑟𝑠 σ 𝑙𝑥 𝑏𝑥 2.1 70 Calculating the intrinsic rate of increase We can use life table data to estimate a population’s intrinsic rate of increase (λ or r) When intrinsic rate estimate from life table, we assume a stable age distribution (rarely occurs) Environmental variation can affect survival/fecundity year over year We can approximate (λ α or rα ; α = approximation) 71 Calculating the intrinsic rate of increase We estimate λ α and rα based on our estimates of net reproductive rate (R0) and generation time (T): 1 1 λ𝛼 = 𝑅0𝑇 = 2.11.95 = 1.46 ln 𝑅0 ln 2.1 𝑟𝛼 = = = 0.38 𝑇 1.95 72 Calculating the intrinsic rate of increase A population’s intrinsic rate of increase depends on both the net reproductive rate and generation time The greater R0 and shorter T, the higher the intrinsic rate of increase A population grows when R0 > 1 (exceeds replacement level) A population declines when R0 < 1 73 Collecting data for life tables To determine the age structure of a population and predict future population growth, we need to collect data on individuals of different ages A cohort life table follows a group of individuals born at the same time and then quantifies their survival and fecundity until death of the last individual A static life table quantifies survival and fecundity of all individuals in a population across all ages during a single time interval 74 Cohort life tables Cohort life tables readily applied to plants and sessile animals Can be marked individually and continually monitored throughout life Does not work well for highly mobile species or species with long life spans Also, a large change in a single year can affect survival/fecundity of cohort; difficult to disentangle effects of age vs changing environments 75 Cohort life tables E.g.) Peter and Rosemary Grant – cactus finches (Geospiza El Niño El Niño scandens) Captured and marked 210 fledglings in 1978, tracked birds throughout their life span Initial survival low, relatively high after that (what survivorship curve does this fit?) 76 Static life tables Static life tables can avoid many problems associated with cohort life tables All calculated at same time, so quantified under same environmental conditions Allows us to examine highly mobile species and species with long life spans Can repeat over multiple time periods as well 77 Static life tables Must be able to assign ages to all individuals (e.g., tree rings, otoliths in fish, etc.) Age-specific data only applies to the environmental conditions when you collected data (might not be representative of other years) Useful to construct tables over multiple years to account for environmental variation 78 Static life tables E.g.) Dall sheep (Ovis dalli) Used growth rings in horns to assess ages of sheep Collected 608 sheep skeletons from recent deaths in single year 79 Concept check Why might a model that contains age structure better reflect the reality of population growth than a model that lacks age structure? What are the patterns of survival with age in the three types of survivorship curves? How would you describe the generation time of a population? 80 Next class Population dynamics (Chapter 12) Next week: Seminar 2: Community Interactions 81