Download The struggle for existence

Module BIO-­‐M1-­‐S06 “Evolu3onary ecology” The struggle for
existence
David Claessen!
Institut de Biologie de l’ENS!
Equipe Eco-Evolution Mathématique
Thomas
Robert
Malthus
•  The increase of popula0on is necessarily limited by the means of subsistence; •  The popula0on does invariably increase when the means of subsistence increase; •  The superior power of popula0on is repressed, and the actual popula0on kept equal to the means of subsistence, by misery and vice. Logistic growth
Mathéma0cien, inspiré par le « principe de popula0on » de Malthus, il proposa en 1838 ce modèle pour la dynamique des popula0ons animales grâce à un modèle qui ne soit pas exponen0el. K = capacité de charge r = taux intrinsèque de croissance Redecouvert en 1920 par Raymond Pearl et Lowell Reed, depuis très répandu en écologie Charles Darwin (1859) identified the
« struggle for existence »,"
in combination with heritable
variation,"
as the driving force of evolutionary
change.
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The origin of this struggle
(« It is the doctrine of Malthus applied with manifold force to the
whole animal and vegetable kingdoms »)
Two basic observations:
1.  All populations tend to
grow exponentially"
2.  Exponentially growing
populations are kept in
check by regulatory
mechanisms
–  Food depletion, predation, disease,
competition, etc
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Struggle for existence
•  As a population grows exponentially, its impact
on the environment is such that conditions get
less favorable for population growth"
•  This results in population regulation
•  In combination with heritable variation, this also
results in natural selection "
(or: survival of the fittest)
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Resource
Time
Time
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Population
Population
Resource
Time
Struggle for
existence
Time
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Feedback loop
•  The struggle for existence corresponds to a
feedback loop:
–  The environmental "
conditions determine the "
population growth rate"
–  The population size "
determines the "
environmental conditions"
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A very simple model example
Exponential growth
with
Constant mortality
Food-dependent
reproduction
Population impact on the
environment
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The « Environment » formulation
•  Why use such a complicated model formulation,
if we can write the same model like this:
with
•  Answers:
–  to obtain a linear model for the population dynamics
–  to make the feedback loop explicit
–  to use a generic model formulation for modelling
density-dependence
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The environmental feedback loop
Individual
(realised life history,
behaviour)
Environment
(resources, ecological
interactions, physical
environment)
Population
(dynamics,
structure,
demography)
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The environmental feedback loop
Individual
(realised life history,
behaviour)
ics
m
a
n
y
on d
i
t
a
l
u
y the
b
Pop
d
e
vern
are go graphic
demo ies of
rt
prope , such as
als
u
d
i
v
i
ival,
v
r
ind
u
s
ity,
fecund al growth,
du
indivi tion rate.
migra
Environment
(resources, ecological
interactions, physical
environment)
Population
(dynamics,
structure,
demography)
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Indi
The environmental
feedback loop
part vid
, on ual prop
th
er
(food e state o ties dep
e
f
pred density the env nd, in
,a
ir
ators
, tem bundan onment
c
pera
ture, e of
etc).
Individual
(realised life history,
behaviour)
Environment
(resources, ecological
interactions, physical
environment)
Population
(dynamics,
structure,
demography)
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The environmental feedback loop
Individual
(realised life history,
behaviour)
Environment
(resources, ecological
interactions, physical
environment)
Population
(dynamics,
structure,
demography)
Colle
ct
indiv ively,
id
influe uals
nce th
envir
e
o
thoug nment, e.g
.,
h exp
l
o
i
ta
of res
ource tion18
s
How can we use the idea of the environmental
feedback loop to model evolutionary dynamics?
It provides us with a ‘‘free’’ fitness definition
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Adaptive dynamics
•  The starting point is to consider the fate of
a rare mutant that arrives in an established
resident population
–  Can the mutant invade? (increase)
–  Can the mutant replace the resident?
Trait u → •  Use these questions to determine the path
of evolution
Evolu0onary 0me → 20
The environmental feedback loop
Individual
(realised life history,
behaviour)
Environment
(resources, ecological
interactions, physical
environment)
Population
(dynamics,
structure,
demography)
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The environmental feedback loop
Individual
(realised life history,
behaviour)
Individual
Environment
(realised life history,
behaviour)
(resources, ecological
interactions, physical
environment)
Population
Population
(dynamics,
structure,
demography)
(dynamics,
structure,
demography)
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Fitness
•  The mutant initially does not impact the
environment
•  Hence its population growth is exponential:
•  And its invasion fitness is given by the
exponential growth rate r that we now write as
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Fitness
Adaptive dynamics
The fitness landscape
changes after each
successive mutant
invasion & replacement
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Trait
0
The resident always
has fitness=0
(The struggle for
existence)
Metz et al (1992, 1996), Geritz et al (1998), etc…
Evolutionarily
stable strategy
(CSS)
0
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Fitness
Adaptive dynamics
Evolution towards
disruptive selection
0
Trait
0
Evolutionarily
branching
point (EBP)
0
Metz et al (1992, 1996), Geritz et al (1998), etc…
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Fitness
Adaptive dynamics
Evolution towards
disruptive selection
0
Trait
0
Evolutionarily
branching
point (EBP)
« If Muhammed will not go to the mountain pass,
the mountain pass will come to Muhammed »"
0
"
(Francis Bacon paraphrased)
Metz et al (1992, 1996), Geritz et al (1998), etc…
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