Population dynamics L5

2006 自然科学の英語 -ENS-L5

Population dynamicsL5

English in Natural Science

自然科学の英語


Abundance

Birds in river forests (Spain)(Sanchez-Bayo, F. 1985)


Abundance vs body size

• Small animals are more abundant than large ones• Birds are less abundant than mammals

350 mammal and 552 bird species (Silva et al., 1997)

MammalsLog(Y) = 1.3-0.66*log[X]

BirdsLog(Y) = 0.22-0.54*log[X]


Abundance and distributionJim Brown (1984)“Population densities

decrease towards the boundary of the geographical range of a species”

Ilkka Hanski (1982)“Widespread species

tend to be more abundant”

1. Sampling artifact2. Specialization

Generalist - large areaSpecialist - small area

3. Metapopulations and dispersal

Western grey kangaroo(Macropus fuliginosus)(Caughley et al. 1987)


Abundance vs distribution range

Rapoport’s rule (1975)“Geographic range size

decreases from polar to equatorial latitudes, with smallest range sizes in the tropics”

Why?1. Tolerance

2. Dispersal favours generalist species

3. Competition+Dispersal

+ Competition

+Tolerance

523 North American mammals(Pagel et al. 1991)


Population dynamics• Parameters

– Natality (fertility) rate

• Offspring, reproduction

rx = bx ÷ nx

– Mortality rate• Life expectancy

(longevity)

qx = dx ÷ nx

Big mammals

Birds

Fishinvertebrates

Small mammals

• Life tables– Mortality/cohort– Age, sex structure


Intrinsic capacity for increase r (Lotka, 1925)

• Exponential– constant rate (%)

Nt = N0 ert

N population

– Finite rate of increase

= er

individual

– Doubling time: time for a quantity to double

Dt = 70 ÷ r

• Linear– constant amount

y = x + A

Linear

Exponential

• LogisticK = carrying capacity

Nt = K ÷ (1+ ea-rt)


Natural processesExponential growth

– Populations(human, r = 1.7% year)

– Food consumption– Waste production– Economy

(Japan: 1-2% year)

(USA: 5% year)

(China: 7% year)

• Exponential reduction– Radioactive residues– Chemical concentration

(eg. pesticides, pollutants)

– Forest destruction

Linear growth– [CO2] atmosphere

– Food production (?)– industry

1

2

3

4

5

6

Gone!


Limits to population growth• Food resource

– carrying capacity (K)T.R. Malthus (1766-1834)

• Predators

• Abiotic factors– Temperature– Water availability

(Scheffer, 1951)

Reindeer

(Walters et al., 1990)

Daphniarosea


Life strategiesr unrelated to abundance• High r (r strategy)

– Generalist niche– Unstable populations– Quick recovery

• Low r (K strategy)– Specialist niche– Stable populations– Prone to extinction

• Decisive factor:– Mortality rate

High r

Low K

• How to increase r ?– Larger offspring size (r)– Increase longevity (K)

• more times to reproduce

– Younger reproductive age (both r and K)

Rep

rodu

ctiv

e su

cces

s

Reproductive effort

Repeated reproduction(K strategy)

Big-bang reproduction(r strategy)


Stationary distribution

No population increase in timeFertility rate = mortality rate

r = qx


Competition

• Resource competition– Inter or intraspecific

• Interference competition (contest)– Usually intraspecific– Sex: males only

Resources

• Plants– Water– Light– Nutrients in soil

• Animals– Food– Space


Competition: Mathematical models

Lotka (1925) and Volterra (1926)

Species 1dN1 K1-N1-N2

dt K1

Species 2dN2 K2-N2-N1

dt K2

=r1N1

=r2N2

Coexistence

Species 1 wins Species 2 wins

Exclusion


Tilman model (1990)

1

2

3

6

4

Neither species can live

Only species A can live

Species A wins

Species B wins

Only species B can live

5

Species A & B co-exist

Zero growth

• Equilibrium point depends on rate of consumption of resources 1 and 2

R1: rate A > rate B A wins

2006 自然科学の英語 -ENS-L5 Grain beetles in wheat (Birch,1953)

2. Spatial segregation

Co-existence

Saccharomyces + Schizosaccharomyces yeast(Gause, 1932)

inside

outside

Species must occupy different niches (Gause, 1934)1. resource partitioning

(share)


Tern species in Christmas Island(Ashmole, 1968)

Segregation

• Efficient utilization of the same resource– Habitat (space)– Size of prey (diet)– Time

• Day - night• Seasons (migration)

• Mechanism of evolution– r and K selection theory

(MacArthur & Wilson, 1967)


Predation & parasitism

• Predators– External– Big size

• Parasites– Internal - live on host– Small size (i.e.larvae)

• Natural agents to control populations– Exponential increase logistic model

• Exponential reproduction ‘biomass waste’– Producers: plants, phytoplankton– Predation: one species eats another

• Herbivores: eat plants• Carnivores/parasites: eat herbivores (prey)

• Predators/parasites USE that extra biomass


Predators and parasites depend on prey/host

AbundancePrey (lemming)

abundancebird predators


Models• Discrete populations: one generation/year

– Prey Nt+1 = (1-B zt)Nt-C NtPt

– Predator Pt+1 = Q NeqPt

(Utida, 1957)

Parasitic wasp

Prey = Host

B = prey reproductive rateC = predator efficiencyQ = predator reproductive rate


Prey population density (N)

Pre

dat

or

den

sity

(P

)

Caribou (Bergerud 1980; Sinclair 1989)

Continuous generations• Lotka (1925) and Volterra (1926): unrealistic• Rosenzweig-MacArthur (1963)

Intraspecificcompetition

En

viron

men

tal pre

ssure

(Carrying capacity)

Predator equilibrium

Food shortage equilibrium

Predation


Population regulation

Birth rate (b) DOWNDeath rate (d) UPpredationdiseasefood shortage

Birth rate (b) UPDeath rate (d) DOWN

Net reproductive rate (R0) =number of female offspring / female / generation

HumansR0 = 1.1

Stable populations

Stochastic variation


Probability of extinction (Pielou, 1969)

P = (d/b)N0

d = death rateb = birth rate

N0 = initial population size

1) b > d P > 1.0 survival2) b < d P < 1.0 extinction3) b = d P = 1.0 extinction

Extinction

• Species ceases to exist• Causes

– Habitat loss– Introduced species

(competition, predation)– Overkill– stochasticity

• Human impact– Habitat destruction– Overkill (e.g. Dodo,

Mammoth, Moa)because of stochastic changes

in a lifetime (e.g. disease, climate)


Natural extinction• Geological eras and periods

– Characterised by changes in biodiversity• Extinction of old forms• Apparition of new forms

• Natural causes– Atmospheric composition

• Plants increased O2 and decreased CO2

– Astronomic - Milankovitch cycles• Climate variation (i.e. iceage)

– Catastrophes (Cuvier, 1769-1832)• Five major extinction events• Cause: asteroids? Earth’s geochemistry?


Historical extinction events

52% families95% species

15% families50% genera


extraterrestrial iridium layer meteoriteCretaceous-Triasic boundary

ItalyCaribbean Denmark

(Alvarez et al. 1980, 82) (Kastner et al. 1984)


Mass extinctions…recovery


Evolution and extinction

• Extinction is an irreversible process

• Extinction events have a founder effect– New taxa appear– Biodiversity flourishes, even more than before

• Eventually all species go extinct– Evolve to generate another species

(average lifetime of species is 10 m years)– Stop existing - gone!


References

• Charles J. Krebs. 2001. Ecology 5th ed. / 応用動物昆虫学　 B-226

• Tokeshi M. 1999. Species coexistence: ecological and evolutionary perspectives / 応用動物昆虫学 B-207

• Alvarez, L. W., W. Alvarez, et al. 1980. Extraterrestrial cause for the Cretaceous-Tertiary extinction. Science 208: 1095-1108

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Population dynamics L5