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 frequency-dependent selection is possible.
• e.g., Timid herbivores (Matsuda & Abrams 1994, Theor. Pop. Biol. )
Tradeoff between antipredator effort and foraging time
plant (constant density R)
herbivore (change in trait Ĉ & population size N)
carnivore (constant density P)
benthos (constant density R)
flatfish (change in trait Ĉ & population size N)
fishery (constant density P)
Model I: Harbivore’s fitness W
• W(C) = B(CR) - M(C,P) - d
( ) 1W C bCR eCP d
2 20
4
W bRC
C e P
• Optimal foraging time
–always decreases as predator increases;
Optimal foraging time
( )1 1
dN CR CPD N N
dt bCR 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 valueh: handling time
Population & evolutionary dynamics
• Equilibrium population– N* = Ns (stable level)
– N* = Nu (unstable critical level)
– N* = 0 (extinct)
( * 1) ( )1 1
dN CR CPW N D N N
dt bCR hCN
ˆ
( )ˆ
C C
dC dWg C
dt dC
figures
ESS ESS
ESS ESS
A model for exploitation of predator
11
dR R fCRr R N
dt K hCR
11 1
dN d bfCRe qC N
dt C hCR
12 2(1 )
(1 ) (1 )
dC d bfRVC C e q
dt C hCR
R: prey density; N: consumer density;
e1: fishing effort; C: foraging time;
q: catchability; V; evolution velocity;
Sto
ck &
yie
ld
Fishing effort
Y
P
Non-standard fisheries-stock/yield relationship
fishing effort may increase stock.
Stock and △yield○ are maximized just
before stock collapse.
Feedback control may result in stock collapse.
11
dR R fCRr R N
dt K hCR
11 1
dN d bfCRE qC N
dt C hCR
12 2(1 )
(1 ) (1 )
dC d bfRVC C E q
dt C hCR
1dEU qCN S N
dt Target CPUES
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)