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Basics in population ecology It is not the strongest of the species that survives, nor the most intelligent, but the one most responsive to change. Charles Darwin.

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Our program 1.Simple growth processes 2.Outbreaks 3.Age structured populations 4.Harvesting and viability analysis 5.Competition, predation and parasitism 6.Populations in space: Metapopulation and spatial dynamics 7.Populations in space: Metapopulation and spatial dynamics

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Literature

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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. Carabus coriaceus in a forestCarabidae in a forest 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. Basic 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)

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Main axiom of population ecology: Organisms in a population are ecologically equivalent. Ecological equivalency means: Organisms undergo the same life-cycle Organisms in a particular stage of the life-cycle are involved in the same set of ecological processes The 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)

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Sometimes species of different species interbred. These do not form a population per definition In 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.

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Spatially separated individuals do not form true populations A species occurring on four islands that are isolated is divided into four independently evolving populations. Due to limited gene flow populations on two islands might be considerd as foring a single genetically structured populations Raven (Corvus corax) Ravens in different continents do not form a single population. There is no (or only limited) gene flow.

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Temporary separated individuals do not form populations Number of bees hatching from eggs Hatching year N Macrotera arcuata 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. Omphale lugens Mikiola fagi SpringSummer N Eggs Summer Spring Spring and summer generations have only limited overlap and thus form partly separated populations. Overlaying is connected with host change. M. fagi is univoltine.

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North atlantic salmon is semelparous Man is iteroparous Iteroparous populations are of age structured with each age cohorte having a different reproductive output. Important questions: What is the population rate of growth or decline? To what factor is the population growth rate most responsive? Will the population eventually go extinct? What happened to the population in the past? Life cycles

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Egg Larva 1 Larva n Adult Egg Juvenile Adults 1 Adult n Senex Iteroparous species reproduce at least two times and might form age structured populations Semelparous species reproduce only once and can be described by simple growth models Some species have age cohorts after the reproductive phase Fertility = number of eggs per female Differences in life history Why grandparents?

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Total 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. Some basic definitions Population 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. Females only Males and females

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Fertility versus population growth rate Bacterial growth R describes the population growth rate Animal growth R describes the net reproduction rate Males Females R is the average number of daughters of each female in the population Net refers to the number of daughters, which reach reproductive age. In demographic analysis only females are counted. The number of females in reproductive age is called the effective population size.

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Birth and death dynamics A population growth process considers four basic variables (BIDE model) B: number of births D: number of deaths I: number of immigrations E: number of emigration I, E = 0 Discrete population growth N Natality Emigration Immigration Mortality R: fundamental net population growth rate The population increases if R t > 1. The population decreases if R t < 1. r: intrinsic rate of population change The population increases if r t > 0. The population decreases if r t < 0.

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Simple population growth processes Change equation Difference equation Ratio equation Recurrence functions Discrete growth model The growth model has only one free parameter: R: fundamental net growth rate The model is simple. The model parameter has a clear and logical ecological interpretation. The parameter r can be estimated from field data.

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Recurrence functions Fibonacci series 1=1+0 2=1+1 3=2+1 5=3+2 8=5+3 13=8+5 Leonardo Pisano (Fibonacci; ) developed this model to describe the growth of rabbit populations. Start 1. month 2. month 3. month 4. month This is the first model in population ecology. Assume a couple of immortal rabbits that five birth to a second couple every month

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The discrete form of the exponential growth model N t N0N0 Exponental growth is a very fast increase in population size. Scots pine (Pinus sylvestris) population in Great Britain after introduction (7500 BC) Whooping crane (Grus americana) population in North America after protection in Basic reproductive rate Intrinsic rate of increase per unit of time R: fundamental net population growth rate

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The Human population growth Human growth was hyperexponential until about Net growth rate was not constant but increase until about 1970 Since 1970 net growth rate declined

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Continuous population growth If r > 0: population increases If r < 0: population decreases In the lack of resource limitation a population will exponentially grow. In this case population grows is density independent. N t N0N0 tan = (r-1)t ln N t ln N 0 tan = (r-1) t0t0 Exponential growth model Intrinsic rate of increase

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The Pearl – Verhulst model of logistic population growth K K/2 t 1/2 N tt0t0 Logistic growth Discrete logistic growth Continuous logistic growth Solution to this differential equation

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The logistic growth model has only two free parameters: r: net reproductive rate K: 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.

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The logistic growth function is a discrete recursive model r = 0.1 K = 500 r = K = 500 The discrete version of logistic growth

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r = 1 K = 500 r = K = 500 Density dependent population regulation Stable cycling

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r = 1.95 K = 500 r = 2.70 K = 500 r = 2.85 K = 500 r = 2.87 K = 500 Pseudochaos

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Local extinction r = 3.01 K = 500 High reproductive rates imply: high population fluctuations pseudochatotic population size no density dependent population regulation r-strategists often have pseudochaotic population fluctuations. Pseudochaos does not mean that population size is unpredictable. Very simple determinstic processes might cause pseudochaos. A random walk is a pure stochastic process that causes unpredictable population sizes.

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