Population dynamics
L5
English in Natural Science
自然科学の英語
2006
自然科学の英語-ENS-L5
Abundance
Birds in river forests (Spain)
(Sanchez-Bayo, F. 1985)
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Abundance vs body size
Mammals
Log(Y) = 1.3-0.66*log[X]
Birds
Log(Y) = 0.22-0.54*log[X]
350 mammal and 552 bird species (Silva et al., 1997)
• Small animals are more abundant than large ones
• Birds are less abundant than mammals
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自然科学の英語-ENS-L5
Abundance and distribution
Jim Brown (1984)
“Population densities
Western grey kangaroo
(Macropus fuliginosus)
(Caughley et al. 1987)
decrease towards
the boundary of the
geographical range
of a species”
Ilkka Hanski (1982)
“Widespread species
tend to be more
abundant”
1. Sampling artifact
2. Specialization
Generalist - large area
Specialist - small area
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自然科学の英語-ENS-L5
3. Metapopulations
and dispersal
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?
523 North American mammals
(Pagel et al. 1991)
1. Tolerance
2. Dispersal favours
generalist species
3. Competition
Tolerance
Dispersal
+
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自然科学の英語-ENS-L5
+
+
Competition
Population dynamics
Big mammals
• Parameters
– Natality (fertility)
rate
Birds
• Offspring,
reproduction
r x = bx ÷ nx
Fish
invertebrates
Small mammals
– Mortality rate
• Life expectancy
(longevity)
qx = dx ÷ nx
• Life tables
– Mortality/cohort
– Age, sex structure
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自然科学の英語-ENS-L5
Intrinsic capacity for increase r (Lotka, 1925)
• Exponential
– constant rate (%)
Nt = N0 ert
Exponential
N population
– Finite rate of increase
 = er
Linear
 individual
– Doubling time: time for
a quantity to double
Dt = 70 ÷ r
• Logistic
K = carrying capacity
Nt = K ÷ (1+ ea-rt)
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• Linear
自然科学の英語-ENS-L5
– constant amount
y=x+A
Natural processes
• Exponential reduction
Exponential growth
– Populations
– Radioactive residues
– Chemical concentration
(human, r = 1.7% year)
– Food consumption
– Waste production
– Economy
(Japan: 1-2% year)
(USA: 5% year)
(China: 7% year)
(eg. pesticides, pollutants)
– Forest destruction
1
2
3
Linear growth
2006
Gone!
4
– [CO2] atmosphere
5
– Food production (?)
6
– industry
自然科学の英語-ENS-L5
Limits to population growth
• Food resource
– carrying capacity (K)
T.R. Malthus (1766-1834)
• Predators
• Abiotic factors
– Temperature
– Water availability
Reindeer
Daphnia
rosea
(Scheffer, 1951)
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自然科学の英語-ENS-L5
(Walters et al., 1990)
Life strategies
– Generalist niche
– Unstable populations
– Quick recovery
• Low r (K strategy)
– Specialist niche
– Stable populations
– Prone to extinction
• Decisive factor:
– Mortality rate
High 
Low 
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Repeated reproduction
(K strategy)
Reproductive success
r unrelated to abundance
• High r (r strategy)
Big-bang reproduction
(r strategy)
Reproductive effort
• How to increase r ?
– Larger offspring size (r)
– Increase longevity (K)
r
K
• more times to reproduce
– Younger reproductive age
(both r and K)
自然科学の英語-ENS-L5
Stationary distribution
No population increase in time
Fertility rate = mortality rate
r = qx
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自然科学の英語-ENS-L5
Competition
• Resource
competition
– Inter or intraspecific
• Interference
competition
(contest)
– Usually intraspecific
– Sex: males only
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Resources
• Plants
– Water
– Light
– Nutrients in soil
• Animals
– Food
– Space
自然科学の英語-ENS-L5
Competition: Mathematical models
Species 1 wins
Species 2 wins
Lotka (1925) and
Volterra (1926)
Species 1
dN1
K1-N1-aN2
=r1N1
dt
K1
Coexistence
Exclusion
Species 2
dN2
K2-N2-bN1
=r2N2
dt
K2
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Zero growth
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Tilman model (1990)
1
Neither species can live
2
Only species A can live
3
Species A wins
4
Species A & B co-exist
5
Species B wins
6
Only species B can live
• Equilibrium point depends on
rate of consumption of
resources 1 and 2
R1: rate A > rate B
自然科学の英語-ENS-L5
A wins
Co-existence

Species must
occupy different
niches (Gause,
1934)
1. resource partitioning
(share)
Saccharomyces + Schizosaccharomyces yeast
(Gause, 1932)
2. Spatial
segregation
outside
inside
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自然科学の英語-ENS-L5
Grain beetles in wheat (Birch,1953)
Segregation
• Efficient utilization of
the same resource
– Habitat (space)
– Size of prey (diet)
– Time
• Day - night
• Seasons (migration)
• Mechanism of
evolution
Tern species in Christmas Island
(Ashmole, 1968)
2006
– r and K selection theory
(MacArthur & Wilson,
1967)
自然科学の英語-ENS-L5
Predation & parasitism
• 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
– External
– Big size
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• Parasites
– Internal - live on host
– Small size (i.e.larvae)
自然科学の英語-ENS-L5
Predators and parasites depend on prey/host
Abundance
Prey (lemming)
abundance
bird predators
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Models
• Discrete populations: one generation/year
– Prey Nt+1 = (1-B zt)Nt-C NtPt
– Predator
Pt+1 = Q NeqPt
B = prey reproductive rate
C = predator efficiency
Q = predator
reproductive rate
Parasitic wasp
Prey = Host
(Utida, 1957)
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Continuous generations
• Lotka (1925) and Volterra (1926): unrealistic
• Rosenzweig-MacArthur (1963)
Predator equilibrium
Predation
Food shortage
equilibrium
Environmental pressure
(Carrying capacity)
Predator density (P)
Intraspecific
competition
Prey population density (N)
Caribou (Bergerud 1980; Sinclair 1989)
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自然科学の英語-ENS-L5
Net reproductive rate (R0) =
number of female offspring / female / generation
Population regulation
Birth rate (b) UP
Death rate (d) DOWN
Stochastic variation
Humans
R0 = 1.1
Stable populations
Birth rate (b) DOWN
Death rate (d) UP
predation
disease
food shortage
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Extinction
• Species ceases to exist
• Causes
– Habitat loss
– Introduced species
(competition, predation)
– Overkill
– stochasticity
• Human impact
– Habitat destruction
– Overkill (e.g. Dodo,
Mammoth, Moa)
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Probability of extinction
(Pielou, 1969)
P = (d/b)N0
d = death rate
b = birth rate
N0 = initial population size
1) b > d
2) b < d
3) b = d
P > 1.0 survival
P < 1.0 extinction
P = 1.0 extinction
because of stochastic changes
in a lifetime
(e.g. disease, climate)
自然科学の英語-ENS-L5
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?
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Historical extinction events
15% families
50% genera
52% families
95% species
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Cretaceous-Triasic boundary
extraterrestrial iridium layer
Italy
Caribbean
2006
(Alvarez et al. 1980, 82)
自然科学の英語-ENS-L5
meteorite
Denmark
(Kastner et al. 1984)
Mass extinctions…recovery
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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!
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自然科学の英語-ENS-L5
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 CretaceousTertiary extinction. Science 208: 1095-1108
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