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From individuals to populations

The basic entities of ecological research

Bees, ants, and other insect societies form superorganismsthat behave as an ecological unit.

Single information coding strand of DNA

Single celled Bacteria

Clonal organisms might have extreme longivity

Unitary organisms have genetically prescribed longivity

Clonal Populustremuloides forests

Modular organized Brown fungi

A clonal colony or genet is a group of genetically identical individuals, such as plants, fungi, or bacteria, that have grown in a given location, all originating vegetative, not sexually, from a single ancestor. In plants, an individual in such a population is referred to as a ramet.

A modular organism has an indeterminate structure wherein modules of various complexity (e.g., leaves, twigs) may be assembled without strict limits on their number or placement.

Life cycles

All organisms have life cycles from single celled zygotes through ontogenetic stages to adult forms. All organsims finally die.

k2

k4

k1

k3

k5=1

Often stages of dormancy

Mortality

Type I, high survivorship of young individuals: Large mammals, birds

Type II, survivorship independent of age, seed banks

Type III, low survivorship of young individuals, fish, many insects

Age dependent survival in annual plants

Type I

Type II

Surviving individuals

Surviving individuals

Type III

Individual age

Individual age

K-factor analysis

k2

k4

k1

k3

k5

Each life stage t has a certain mortality rate dt.

The k-factor is the difference of the logarithms of the number of surviving indiiduals at the beginning and the end of each stage.

A simple life table

k-factors calculated for a number of years

Densityseries

Time series

2000

2001

Density

Cleartemporaltrends in mortalityrates

No densitydependencein mortalityrates

Allometric constraints on life history parameters

Mammals

Body size is an important determinant on life history.

Insects

Microorganisms

Birds

Various vertebrates

Life history trade-offs

Optimal food intaketime

Optimaloffspringnumber

Fitness

Quality of food

Survivalprobability

Degree of starvation

Number of offspring

Time

Trade-offs: Organisms allocate limited energy or resources to one structure or function at the expense of another.

Allspecies face trade-off.

Trade-offs shape and constrain life history evolution.

Complex life histories appear to be one way to maximize reproductive success in such highly competitive environments.

The importance of individualistic behaviour

Th perceived food value migh remain more stable than food quality

The value of food is the product of food quality and the difference of total amount N and amount consumed C).

Amount of food consumed

Food quality

Food value

Food quality

X

For different individuals it pays to use resources of different quality.

Trade-offs between resource quality and resource availability at a given point of time mark the beginn of individualistic behaviour.

Individualistic behaviour is already observable in bacteria.

The precise estimation of resource value is one of the motors of brain evolution.

Trade-off decisions during life history

At each time step in life animals take decisions.

These decisions determine future reproductive success and ae objects of selective forces

How large to grow?

When to begin reproducing?

How fast to grow?

Each step is a decision on resource allocation.

How often to breed?

(semelparous, iteroparous)

How long to live?

How many offspring?

When to change morphology?

Caring for offspring?

How long to live after reproduction?

What size of offspring?

How fast to develop?

Different selective forces might act on different stages of life.

Contrary forces might cause the development of subpopulations.

Contrasting selective forces on life history

r-selection and K-selection describe two ends of a continuum of reproductive patterns.

r refers to the high reproductive rate.

K refers to the carrying capacity of the habitat

Rana temporaria

Brookesia desperata

High reproduction rate

High population growth

Low parental investment

No care of offspring

Often unstable habitats

Low reproduction rate

Low population growth

High parental investment

Intensive care of offspring

Often stable habitats

r

Continuum

K

In many species different developmental stages,the sexes and particulalry subpopulations range differently on the r/K continuum!

K selected

mature more slowly and have a later age of first reproduction

have a longer lifespan

have few offspring at a time and are iteroparous

have a low mortality rate and a high offspring survival rate

have high parental investment

Have often relatively stable populations

r selected species

mature rapidly and have an early age of first reproduction

have a relatively short lifespan

have few reproductive events, or are semelparous

have a high mortality rate and a low offspring survival rate

have minimal parental care/investment

are often highly variable in population size

Literature: Reznick et al. 2002, Ecology 83.

The growth of populations

+N(t)

Equilibrium

Birth rate:

Death rate:

Birth excess

Number of births

Population size

Number of deaths

Time

The net reproductive rate R is the number of reproducing female offspring produced per female per generation.

Population fluctuations

Equilibrium density

If R > 1: population size increases

If R = 1: population remains stable

If R < 1: population size decreases

Population size

The density of a population is the average number of individuals per unit of area.

Abundance is the total number of individuals in a given habitat.

Amplitude

Time

The exponential growth of populations

Population size

The intrinsic rate of population growth r (per-capita growth rate) is fraction of population change per unit of time.

Time

If r > 0: population size increases

If r = 0: population remains stable

If r < 0: population size decreases

North atlantic gannets in north-western England (Nelson 1978)

Population doubling time

Under exponential growth there is no equilibrium density.

Exponential growth is not a realistic model since populations cannot infinite sizes.

The growth rate is r = 0.057

The logistic growth of populations

Populations do not increase to infinity. There is an upper boundary, the carrying capacity K.

The logistic model of population growth

The logistic growth function is the standard model in population ecology

Pierre Francois Verhulst (1804-1849)

Raymond Pearl (1879-1940)

The logistic growth of populations

Maximum population growth

The equilibrium population size

Time t0 of maximum growth

The logistic growth of populations

How to estimate the population parameters?

Growth of yeast cells (data from Carlson 1913)

K = 665

K/2

t0

t0=7.70

Logistic growth occurs particularly in organisms with non-overlapping (discrete) populations, particularly in semelparous species: e.g. bacteria, protists, single celled fungi, insects.

Logistic population growth implies a density dependent regulation of population size

If N > K, dN/dt < 0: the population decreases

Natural variability in population size

Density dependence means that the increase or decrease in population size is regulated by population size.

The mechanism of regulation is intraspecific competition.

The number of offspring decrease with increasing population size due to resource shortage.

The Allee effect

Logistic growth is equivalent to a quadratic function of population growth

No Allee effect

Weak Allee effect

Strong Allee effect

Population growth

K

K

K/2

K

N

N

N

At low population size propolation growth is in many cases lower than predicted by the logistic growth equation.

Allee extension of the logistic function

Most often Allee effects are caused by mate limitation at low population densities

A is an empitical factor that determines the strength of the Allee effect

Variability in population size

Proportional rescaling

Poisson random

Density regulated

J=1.14

J=0.91

J=0.82

We use the variance mean ratio as a measure of the type of density fluctuation

Aphids

Butterflies

Birds

Proportional rescaling

The Lloyd index of aggregation needs m > > 1.

Taylor’s power law

The metapopulation of Melitaeacinxia

In fragmented landscapes populations are dived into small local populations separated by an inhostile matrix.

Between the habitat patches migration occurs.

Such a fragmented population structure connected by dispersal is called a metapopulation.

Illka Hanski

Glanville fritillary

Melitaea cinxia

The Lotka – Volterra model of population growth

Dispersal in a fragmentedlandscape

Levins (1969) assumed that the change in the occupancy of single spatially separated habitats (islands) follows the same model.

Assume Pbeing the number of islands (total K) occupied. Q= K-Pis then the proportion of not occupied islands. m is the immigration and e the local extinction probability.

Emigration/Extinction

Colonisations

The Levinsmodel of meta-populations

Fragments differ in population size

Colonisation probability is exponentially dependent on the distance of the islands and extinction probability scales proportionally to island size.

The higher the population size is, the lower is the local extinction probability and the higher is the emigration rate

150

100

Distance

If we deal with the fraction of fragments colonized

90

80

The canonical model of metapopulation ecology

200

Metapopulation modelling allows for an estimation of species survival in fragmented landscapes and provides estimates on species occurrences.

Distance

Extinction times

If we know local extinction times TL we can estimate the regional time TR to extinction

When is a metapopulation stable?

1200

1000

800

Median time to extinction

600

400

The meta-population is only stable if m > e.

200

0

0

1

2

3

4

5

6

7

0.5

p K

The condition for long-term survival

What does metapopulation ecology predict?

Occurrences of Hesperia comma in fragmented landscapes in southern England (from Hanski 1994)

Occurrences

Absences

Predictedextinctionthreshold

In fragmentedlandscapesoccupancydeclinesnonlinear with decreasingpatcharea and with decreasingconncetivity (increasingisolation)

Extinction times of ground beetles on 15 Mazurian lake islands

Local extinction times (generations) are roughly proportional to local abundances

Population should be save if they occupy at least 12 islands.

SPOMSIM

Populationecologyneedslong-term data sets

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