4 What is a population?A population is a group of potentially interbreeding individuals of the same species living in the same area at the same time and sharing a common gene pool.Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment. It is the study of how the population sizes of species living together in groups change over time and space.Carabus coriaceus in a forestCarabidae in a forestBasic characteristics of populations:Absolute density (individuals per unit area)Relative density (Proportion of individuals with respect to some standard)Abundance (size; total number of individuals)Age structure (triggered by natality and age dependent mortality)Dispersal (spatial dynamics)
5 Main axiom of population ecology: Organisms in a population are ecologically equivalent.Ecological equivalency means:Organisms undergo the same life-cycleOrganisms in a particular stage of the life-cycle are involved in the same set of ecological processesThe rates of these processes (or the probabilities of ecological events) are basically the same if organisms are put into the same environment (however some individual variation may be allowed)
6 Sometimes species of different species interbred. These do not form a population per definitionIn Sulawesi seven species of macaques (Macaca spp.) interbreed where their home ranges overlap.Interbreedin is the cause of endangerment of Macaca nigra.Adapted from Riley (2010) The endemic seven: four decades of research onth Sulawesi Macaques. Evol. Anthr. 19: 22.
7 Spatially separated individuals do not form true populations Raven (Corvus corax)A species occurring on four islands that are isolated is divided into four independently evolving populations.Ravens in different continents do not form a single population.There is no (or only limited) gene flow.Due to limited gene flow populations on two islands might be considerd as foring a single genet ically structured populations
8 Temporary separated individuals do not form populations Omphale lugensMikiola fagiMacrotera arcuataNNumber of bees hatching from eggsNSpringSummerSpringSummer123SummerEggsHatching yearSpring and summer generations have only limited overlap and thus form partly separated populations.Overlaying is connected with host change. M. fagi is univoltine.Overlaying is a strategy to reduce risk due to unfavourable conditions. If overlaying is genetically fixed the genotypes of the three hatching cohorts never meet.
9 North atlantic salmon is semelparous Life cyclesNorth atlantic salmon is semelparousMan is iteroparousImportant questions:What is the population rate of growth or decline?To what factor is the population growthrate most responsive?Will the population eventually go extinct?What happened to the population in thepast?Iteroparous populations are of age structured with each age cohorte having a different reproductive output.
10 Differences in life history EggSemelparous species reproduce only once and can be described by simple growth modelsEggLarva 1JuvenileIteroparous species reproduce at least two times and might form age structured populationsLarva nAdults 1Fertility = number of eggs per femaleAdultAdult nFertility = number of eggs per femaleSome species have age cohorts after the reproductive phaseSenexWhy grandparents?
11 Some basic definitions Females onlyTotal fertility rate (TFR) is the total number of children a female would bear during her lifetime.Gross Reproduction Rate (GRR) is the potential average number of female offspring per female.Net Reproduction Rate (NRR) is the observed average number of female offspring per female. NRR is always lower than GRR. When NRR is less than one, each generation is smaller than the previous one. When NRR is greater than 1 each generation is larger than the one before.In semelparous species age specific fertility (ASF) is the average number of offspring per female of a certain age class.Males and femalesPopulation growth is the change in population size over time. Growth can be negative.Population growth rate is the multiplication factor that describes the magnitude of population growth. Growth rate is always positive.
12 Fertility versus population growth rate Bacterial growthAnimal growth𝑁 𝑡+1 =2 𝑁 𝑡𝑁 𝑡+1 =𝑅 𝑁 𝑡MalesFemales𝑁 𝑡+1 =𝑅 𝑁 𝑡𝐹 𝑡+1 =𝑅 𝐹 𝑡R describes the population growth rateR describes the net reproduction rateR is the average number of daughters of each female in the populationIn demographic analysis only females are counted.The number of females in reproductive age is called the effective population size.Net refers to the number of daughters, which reach reproductive age.
13 Discrete population growth Birth and death dynamicsDiscrete population growthNatalityA population growth process considers four basic variables (BIDE model)B: number of births D: number of deaths I: number of immigrationsE: number of emigrationNImmigrationEmigration𝑁 𝑡+1 = 𝑁 𝑡 + 𝐵 𝑡 − 𝐷 𝑡 = 𝑁 𝑡 + 𝑏 𝑡 𝑁 𝑡 − 𝑑 𝑡 𝑁 𝑡Mortality𝑏 𝑡 = 𝐵 𝑡 𝑁 𝑡𝑑 𝑡 = 𝐷 𝑡 𝑁 𝑡I, E = 0𝑁 𝑡+1 𝑁 𝑡 = 𝑅 𝑡𝑁 𝑡+1 = 𝑁 𝑡 (1+ 𝑏 𝑡 − 𝑑 𝑡 ) = 𝑅𝑁 𝑡𝑁 𝑡+1 = 𝑅 𝑡 𝑁 𝑡 = 𝑏 𝑡 − 𝑑 𝑡 𝑁 𝑡 + 𝑁 𝑡𝑅 𝑡 = 1+𝑏 𝑡 - 𝑑 𝑡The population increases if Rt > 1.R: fundamental net population growth rateThe population decreases if Rt < 1.𝑟 𝑡 = (𝑏 𝑡 - 𝑑 𝑡 )The population increases if rt > 0.The population decreases if rt < 0.r: intrinsic rate of population change
14 Simple population growth processes 𝑁 𝑡+1 = 𝑅𝑁 𝑡 = 𝑏 𝑡 − 𝑑 𝑡 𝑁 𝑡 + 𝑁 𝑡Discrete growth modelThe growth model has only one free parameter:R: fundamental net growth rateThe model is simple.The model parameter has a clear and logical ecological interpretation.The parameter r can be estimated from field data.𝑁 𝑡 =𝑓( 𝑁 𝑡−1 )Change equation∆𝑁=𝑁 𝑡 − 𝑁 𝑡−1 =𝑓( 𝑁 𝑡−1 )Difference equationRecurrence functions𝑁 𝑡 𝑁 𝑡−1 =𝑓 (𝑁 𝑡−1 )Ratio equation
15 Recurrence functions𝑓 𝑥 =𝑓(𝑥−𝑛)𝑓 𝑥 =𝑓 𝑥−1 +𝑓 𝑥−2Leonardo Pisano (Fibonacci; ) developed this model to describe the growth of rabbit populations.Fibonacci series1=1+02=1+13=2+15=3+28=5+313=8+5 This is the first model in population ecology.Assume a couple of immortal rabbits that five birth to a second couple every month.Start11. month12. month23. month34. month5
16 The discrete form of the exponential growth model 𝑁 𝑡 = 𝑅𝑁 𝑡−1 = 𝑅 2 𝑁 𝑡−2 … =𝑅 𝑡 𝑁 𝑜The discrete form of the exponential growth modelExponental growth is a very fast increase in population size.𝑁 𝑡 =𝑅 𝑡 𝑁 𝑜 = 𝑁 𝑜 𝑒 𝑙𝑛𝑅×𝑡R: fundamental net population growth rate𝑅 0 =𝑅 𝑡Basic reproductive rateN0𝑟=𝑙𝑛𝑅= 𝑏−𝑑 = 𝑙𝑛 𝑅 0 𝑡Intrinsic rate of increase per unit of timetWhooping crane (Grus americana) population in North America after protection in 1940Scots pine (Pinus sylvestris) population in Great Britain after introduction (7500 BC)
17 The Human population growth Human growth was hyperexponential until about 1970.Net growth rate was not constant but increase until about 1970Since 1970 net growth rate declined
18 Continuous population growth Exponential growth model 𝑁 𝑡 =𝑅 𝑡 𝑁 𝑜 = 𝑁 𝑜 𝑒 𝑟𝑡𝑑𝑁 𝑑𝑡 = 𝑟𝑁 0 𝑒 𝑟𝑡 =𝑟𝑁𝑁 𝑡+1 = 𝑅𝑁 𝑡 = 𝑏 𝑡 − 𝑑 𝑡 𝑁 𝑡 + 𝑁 𝑡𝑁 𝑡+1 − 𝑁 𝑡 =∆ 𝑁 𝑡 = 𝑏 𝑡 − 𝑑 𝑡 𝑁 𝑡Exponential growth modelIf r > 0: population increasesIf r < 0: population decreases𝑟= 𝑏 𝑡 − 𝑑 𝑡 =𝑙𝑛𝑅Intrinsic rate of increaseIn the lack of resource limitation a population will exponentially grow.In this case population grows is density independent.Nln Nln 𝑁 𝑡 =𝑙𝑛 𝑁 0 +𝑟𝑡ln N0atan a = (r-1)atan a = (r-1)tN0t0tt
19 Discrete logistic growth N𝑁 𝑡 = 𝑁 𝑡−1 + 𝑟𝑁 𝑡−1 𝐾− 𝑁 𝑡−1 𝐾KThe Pearl – Verhulst model of logistic population growthK/2t0t1/2tContinuous logistic growth𝑁 𝑡 = 𝐾 1+ 𝑒 −𝑟(𝑡− 𝑡 0 ) = 𝐾 1− 𝐾 𝑁 0 −1 𝑒 −𝑟𝑡𝑑𝑁 𝑑𝑡 =𝑟𝑁 𝐾−𝑁 𝐾Solution to this differential equation
20 𝑑𝑁 𝑑𝑡 =𝑟𝑁 𝐾−𝑁 𝐾The logistic growth model has only two free parameters:r: net reproductive rateK: the carrying capacity.The model is simple.The model parameters have a clear and logical ecological interpretations.The parameters can be estimated from field data.The model does not refer to a specific group of species, but applies to all populations from Bacteria to vertebrates amd plants.The model is based on realistic assumptions about population growth.The model is sufficiently precise.Constraints:The model refers to homogeneous environments.Reproductive rates are supposed to be constant.Carrying capacity is supposed to be constant.Generations do not overtlap.Limitation:The model is symmetrical around the point of inflection.
21 The logistic growth function is a discrete recursive model The discrete version of logistic growth𝑁 𝑡 = 𝑁 𝑡−1 + 𝑟𝑁 𝑡−1 𝐾− 𝑁 𝑡−1 𝐾The logistic growth function is a discrete recursive modelr = -0.05K = 500r = 0.1K = 500
24 High reproductive rates imply: high population fluctuations pseudochatotic population sizeno density dependent population regulationr = 3.01K = 500Local extinctionPseudochaos does not mean that population size is unpredictable.Very simple determinstic processes might cause pseudochaos.r-strategists often have pseudochaotic population fluctuations.A random walk is a pure stochastic process that causes unpredictable population sizes.𝑁 𝑡+1 = 𝑁 𝑡 +𝑟𝑎𝑛(−𝑥,𝑥)
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