Lecture 2 review

• Compensatory rate change is the ecological basis for sustainable populations and harvesting

• Compensatory change may involve– Increases in adult survival rate at low N– Increases in juvenile survival rate at low N– Increases in growth and mean fecunity at low N

• Generally mean fecundity decreases dramatically in harvested populations, so compensation is mainly in juvenile survival

• A good measure of compensation in juvenile survival is the “Goodyear compensation ratio” K=(maximum survival rate)/(survival rate in unharvested population)

Limits to compensatory responses• Most populations exhibit high juvenile

survival at very low densities

• But occasionally (5-10%?) compensation fails at low densities, leading to low equilibrium or extinction

N

SJ

SJ

N

-Allee effect (eggs don’t get fertilized, eg scallops); rare

-Cultivation/depensation (competitors/predators of juveniles increase when N is low, eg bass-bluegill)

-Trophic cascades (green water/clear water states)

-Botsford’s effect (size dependent cannibalism)

(Invasive species have to exhibit this ability)

Is the Beverton-Holt invariant M/K=1.6 a valid generalization based on your

analysis of the data in Fishbase?

y = 2.1161x

R2 = 0.5872

y = 1.6372x

R2 = 0.3182

y = 2.0041x

R2 = 0.8567

y = 1.1363x

R2 = 0.2195

0.01

0.1

1

10

100

0.01 0.1 1 10

vonBertalanffy K

Na

tura

l mo

rta

lity

ra

te M Age structure data

Length converted catchcurve

Tagging

Z vs E plot

Life history trajectories

• Whenever you handle a fish, ALWAYS ask yourself these questions:– How old is it?– Where was it spawned?– Where will it spawn?

Life history stanzas (partitions of the life history trajectory)

The eggie

Larval drift, density-independent mortality

Juvenile migrationFirst juvenile nursery area: small, strong density-dependence in mortality

Spread into larger juvenile nursery area(s), mortality much lower

Adult foraging areas, most often with complex seasonal migration patterns

Spawning migration

Fractal, complex diurnal movement

Characteristics of LHT

• There is typically very strong selection for behaviors that take fish back to spawn in the places where they were successfully produced (this is not just a salmon thing)

• Seasonal migrations become more pronounced as fish grow

Time

Random model

Distance from tagging site

Migration model

Distance from tagging site

Time

Characteristics of LHT

• Natural mortality rates vary as M=k/(body length), starting at a few percent per day and often falling to a few percent per year

• Body growth typically follows a vonBertalanffy length curve of the form

length=L[1-e-K(a-ao)]• Sometimes there is a “kink” in the growth curve,

with small juveniles either showing extra fast growth (if they seek warm microhabitats) or extra slow growth (if they face very high predation risk).

Characteristics of LHT• Maturation typically occurs at 50%-70% of maximum

body length, with fecundity then being proportional to body weight

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

Age (years)

Len

gth

(cm

)

0

500

1000

1500

2000

2500

3000

3500

4000

Wei

gh

t (g

)

Length (cm)

Hayes model Length

wt (kg)

Hayes Model weight

But some fish like these New Zealand brown trout practically stop growing at maturity, and make massive (45%) investments in eggs (Hayes et al TAFS 2000)

Representing LHT in models

• Age structure accounting (block trajectory by even age intervals)

• Stanza structure accounting (Ecosim)

• Individual-based models (track movement)

[N1 N2 N3 …]t [N1 N2 N3…]t+1 (easy in spreadsheets)

Log Numbers at age

Age (months)

Weight at age

Log Numbers at age

Age (months)

Weight at age

X,Y positions and fates of large sample of individuals