Download Self-extinction due to adaptive change in foraging and anti

Self-extinction due to adaptive change
in foraging and anti-predator effort
• Matsuda H, Abrams PA (1994a) Runaway
evolution to self-extinction under asymmetric
competition. Evolution 48:1764-1772.
• Matsuda H, Abrams PA (1994b) Timid
consumers: self-extinction due to adaptive change
in foraging and anti-predator effort. Theor Pop
Biol 45:76-91.
• Matsuda H, Abrams PA (2004) Effects of
predator-prey interactions and adaptive change on
sustainable yield. Can J Fish Aq Sci in press
Matsuda & Abrams (1994a, b)
• Frequency dependent selection may
decrease the population size and the
population growth rate.
• Therefore, self-extinction due to frequencydependent selection is possible.
• e.g., Timid herbivores (Matsuda & Abrams
1994, Theor. Pop. Biol. )
Tradeoff between antipredator effort
and foraging time
benthos
(constantdensity
densityR)R)
plant (constant
flatfish (change
herbivore
(changeinintrait
traitĈĈ&&
population size N)
fishery (constant
carnivore
(constantdensity
densityP)P)
Model I: Harbivore’s fitness W
• W(C) = B(CR) - M(C,P) - d
W (C )  1  bCR  eCP  d
• Optimal foraging time
W
bR
 0  C  2 2
C
4e P
–always decreases as predator increases;
Optimal foraging time
dN 
CR
CP 
  ( D   N ) 

N

dt 
1  bCR 1  hCN 
• I = ĈR: Foraging intake rate I
= (individual’s foraging time)(plant density),
• B = ĈR/(1 + bĈR)
Benefit B from intake saturates with intake,
• Risk M of predation (type II functional response)
M = ĈP / (1 + hCN)
• C is population mean trait value
h: handling time
Population & evolutionary dynamics
dN
CP
 CR

 (W * 1) N  

 (D   N ) N
dt
1  bCR 1  hCN

dC
dW
 g (C )
dt
dCˆ Cˆ C
• Equilibrium population
– N* = Ns (stable level)
– N* = Nu (unstable critical level)
– N* = 0 (extinct)
figures
ESS
ESS
ESS
ESS
A model for exploitation of predator
dR
R
fCR

 r 1   R 
N
dt
1  hCR
 K
dN  d
bfCR

 

 e1qC  N
dt  1  C 1  hCR



dC
d
bfR
 VC (1  C )  

 e1q 
2
2
dt
 (1  C ) (1  hCR)

R: prey density; N: consumer density;
e1: fishing effort; C: foraging time;
q: catchability; V; evolution velocity;
Stock & yield
Non-standard fisheriesstock/yield relationship
fishing effort may
increase stock.
P
Y
Fishing effort
Stock△ and
yield○ are
maximized
just before
stock collapse.
Feedback control may result in
stock collapse.
dR
R
fCR

 r 1   R 
N
dt
1  hCR
 K
dN  d
bfCR

 

 E1qC  N
dt  1  C 1  hCR



dC
d
bfR
 VC (1  C )  

 E1q 
2
2
dt
 (1  C ) (1  hCR)

dE1
 U  qCN  S  N
dt
Target CPUE
Feedback control may result in
stock collapse.
We should take account of adaptation in
managing endangered species.
• Does evolutionary response of species
always increase its population size?
– No
• “the fish may become poorer foragers as the
result of fishing, and that this may result in
extinction, or at least contribute to reducing
their population size.” (Matsuda & Abrams
1994b)