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)