Biol 301 1nd Edition Lecture 5 Outline of Last Lecture I. Population growth modelsII. Density dependent growth modelIII. Carrying capacityOutline of Current Lecture II. Population fluctuationsIII. Cyclic behavior of populationsIV. Extinctions in populationsV. Patchy habitatsCurrent LecturePopulation fluctuations – - All populations experience fluctuations due to factors including availability of resources, predation, competition, disease, parasites, and climate.- Fluctuations include random and cyclic changes through time.- Some populations tend to remain relatively stable over long periods.- Some populations (small organisms) exhibit much wider fluctuations- Small organisms tend to reproduce much faster than larger organisms so their populations often respond faster to favorable and unfavorable conditions- Larger organisms have a lower surface-area-to-volume ratio, which allows them to maintain homeostasis in the face of unfavorable environmental changes.- When an age group contains a high or low number of individuals, the population likely experienced high birth or death rates in the past- Long-term fluctuations in age structure can be determined for a forest by examining tree rings.- Populations in nature rarely follow a smooth approach to their carrying capacity.- Overshoot: when a population grows beyond its carrying capacity; often occurs when the carrying capacity of a habitat decreases from one year to next (e.g., because less resources are produced).- Die-off: a substantial decline in density that typically goes well below the carrying capacity.- Die-offs often occur when a population overshoots its carrying capacity.- Population cycles: regular oscillation of a population over a longer period of time.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.- Some populations can exhibit highly regular fluctuations in size.- Cyclic populations can occur among related species and across large geographic areas (e.g., the synchronous cycles of the capercaillie, black, and hazel grouses in Finland).Cyclic behavior of populations – - Populations have an inherent periodicity and tend to fluctuate up and down, although the time required to complete a cycle differs among species.- Populations behave like a swinging pendulum, which is stable when hanging straight up and down. Gravity will force the pendulum back to the center, but momentum causes it to overshoot the center.- Populations are stable at their carrying capacity; when reductions in population sizes occur, the population responds by growing—often overshooting carrying capacity.- Overshoots can occur when there is a delay between the initiation of breeding and the time that offspring are added to the population.- Population cycles can be modeled by starting with the logistic growth model (continuous):- We can incorporate a delay between a change in environmental conditions and the time the population reproduces. - Delayed density dependence: when density dependence occurs based on a population density at some time in the past.- To incorporate a time delay (τ) into the logistic growth model:- As the time delay increases, density dependence is delayed and the population is more prone to both overshooting and undershooting K.- The amount of cycling in a population depends on the product of r and τ.- Damped oscillations: a pattern of population growth in which the population initially oscillates but the magnitude of the oscillations declines over time.- Stable limit cycle: a pattern of population growth in which the population continues to exhibit large oscillations over time.- Discrete models already incorporate time delays into model.- No need to add τ in discrete population models: - Nt+1=Ntλ[1-(N1/K0]- Delayed density dependence may occur because the organism can store energy and nutrientreserves.- Delayed density dependence can occur when there is a time delay in development from onelife stage to another.Extinctions in populations – - Small populations are more vulnerable to extinction than larger populations.- Although data suggest that small populations are more likely to go extinct, growth models suggest that small populations should have more rapid growth and be resistant to extinction.- This contradiction can be resolved by incorporating random variation of growth rates into growth models.- Deterministic model: a model that is designed to predict a result without accounting for random variation in population growth rate.- Stochastic model: a model that incorporates random variation in population growth rate; assumes that variation in birth and death rates is due to random chance.- Demographic stochasticity: variation in birth rates and death rates due to random differences among individuals.- Environmental stochasticity: variation in birth rates and death rates due to random changes in the environmental conditions (e.g., changes in the weather).- A population that randomly experiences a string of years with low birth rates or high death rates is more likely to go extinct.- With time, there is an increased chance of having a string of bad years.- Smaller populations are at more risk of extinction if they experience a string of bad years.Patchy habitats – - Preferred habitat often occurs as patches of suitable habitat surrounded by a matrix of unsuitable habitat.- Habitat fragmentation: the process of breaking up large habitats into a number of smaller habitats.- Often occurs as a result of human activities (e.g., clearing forests, road construction, draining wetlands).- Some habitat fragments experience extinctions, whereas others are colonized by dispersers.- The basic metapopulation model assumes that all habitat patches are equal in quality and that the matrix between patches is inhospitable.- The source-sink model assumes quality differences between patches.- Sources are high-quality patches that produce a large number of individuals that disperse to other patches.- Sinks are low-quality patches that produce few individuals and rely on dispersers to keep thesink population from going extinct.- If subpopulations rarely exchange individuals, fluctuations in abundance will be independentamong subpopulations.- If subpopulations frequently exchange individuals, the subpopulations will act as one