Transcript Population dynamics - Center for Limnology

POPULATION DYNAMICS
Zoo 511 Ecology of Fishes
Today’s goals
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Understand why and how population dynamics are
important in fisheries ecology
Gain experience in a variety of mark-recapture
methods
What are population dynamics?
“A population is a group of fish of the same
species that are alive in a defined area at a
given time” (Wootton 1990)
Population dynamics: changes in the number of
individuals in a population or the vital rates of a
population over time
Major role of ecology: understand change
250
Rusty
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1000
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800
100
600
400
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0
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0
Rusty catch
Bluegill catch
200
Bluegill
Why study population dynamics?
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Often most relevant response
to ecosystem
manipulation/perturbation
Endangered species
(population viability analysis,
PVA)
Fisheries management
(sustainable yield)
Understand ecosystem
dynamics and ecological
processes
Why study population dynamics?
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Often most relevant response
to ecosystem
manipulation/perturbation
Endangered species
(population viability analysis,
PVA)
Fisheries management
(sustainable yield)
Understand ecosystem
dynamics and ecological
processes
PVA: Modeling the probability that a
population will go extinct or drop below
the minimum viable population size
within a given number of years.
Atlantic salmon PVA
From Legault 2004
Why study population dynamics?

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Often most relevant response
to ecosystem
manipulation/perturbation
Endangered species
(population viability analysis,
PVA)
Fisheries management
(sustainable yield)
Understand ecosystem
dynamics and ecological
processes
from Hilborn and Walters 1992
Why study population dynamics?




Often most relevant response
to ecosystem
manipulation/perturbation
Endangered species
(population viability analysis,
PVA)
Fisheries management
(sustainable yield)
Understand ecosystem
dynamics and ecological
processes
When do ecological shifts occur?
Are they stable?
How do populations change?
Population
Density Dependence
Rate of
Change
(per capita)
Population Density
per capita annual increase
Rate of population increase
Density independent
Density dependent
N
Small group exercise
Population starts at low density.
What happens to density over time under
density-dependent rate of increase?
What happens if rate of increase is densityindependent?
Density-independent
Population
density
Population
density
Density-dependent
Time
Time
Logistic population growth
r0 = maximum rate of increase
K= carrying capacity
per capita annual increase
dN/dt=r0N(1-N/K)
r0
N
K
R-selected vs. K-selected
r-selected
K-selected
Environment
variable and/or
unpredictable
constant and/or
predictable
Lifespan
short
long
Growth rate
fast
slow
Fecundity
high
low
Natural mortality
high
low
Population dynamics
unstable
stable
How do populations change?
Nt+1 = Nt + B – D + I – E
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B = births
D = deaths
I = immigration
E = emigration
Immigration
Stocking
Births
Deaths
Population
Angling
Emigration
Survival
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Predation
Disease
“Natural Mortality”
Prey availability
Competition for food
Harvest
Age 1 Age 2 Age 3
Year 1
N1,1
N1,2
Year 2
N2,1
N2,2
N2,3
Year 3
N3,1
N3,2
N3,3
S
N1,3
Survival
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Eggs and larvae suffer the largest losses
Egg
HATCH
Larva Viable & Competent
Not Fertile
Starvation
Inviable
Eaten
Eaten
Other
2 cohorts each produce 10,000,000 eggs
90.5% survivorship/day yields 24,787 survivors at 60 days
95.1% survivorship/day yields 497,871 survivors at 60 days
Recruit!
Recruitment
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Can mean many things!
 Number
of young-of-year (YOY) fish entering
population in a year
 Number of fish achieving age/size at which they are
vulnerable to fishing gear
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Somewhat arbitrary, varies among populations
Major goal of fish population dynamics:
understanding the relationship between stock size
and recruitment
What determines recruitment?
-Stock size (number and size of females)
Density-independent
Ricker
Recruitment
What determines recruitment?
Beverton-Holt
spawning stock biomass (SSB)
From: Wootton (1998). Ecology of teleost fishes.
The problem? Stochasticity!
From: Cushing (1996). Towards
a science of recruitment in fish
populations
Highly variable recruitment results
in naturally very variable catches
From: Jennings, Kaiser and Reynolds (2001). Marine Fisheries Ecology
Population Abundance
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On rare occasions, abundance can be measured directly
 Small
enclosed systems
 Migration
Catch per unit effort (CPUE)
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Very coarse and very common index of abundance
1
Catch= 4 fish
CPUE=4/48=0.083
Effort= 4 nets for
12 hours each=
48 net hours
2
Catch=8 fish
CPUE=8/48=0.167
Effort= 4 nets for
12 hours each=
48 net hours
We conclude population 2 is
2X larger than population 1
Population abundance
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Density estimates (#/area)
 Eggs
estimated with quadrats
 Pelagic larvae sampled with modified plankton nets
 Juvenile and adult fish with nets, traps, hook and line, or
electrofishing
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Density is then used as index of abundance, or
multiplied by habitat area to get abundance
estimate
Depletion methods
Closed population
Vulnerability constant for each pass
Collection efficiency constant
Often not simple linear regression
*
N
*
*
*
Time (or pass)
Mark recapture
M=5
N=population size=????
C=4
R=2
Modified Petersen method
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Assumptions:
 Closed
population
 Equal catchability in first sample
 Marking does NOT influence catchability
 Marked
and unmarked fish mix randomly
 Mortality rates are equal
 Marks
are not lost
How to avoid violation of
assumptions?
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Two sampling gears
Distribute marked individuals widely; allow time for
mixing
Can be separated into different groups
 Length
 Sex
 Geographic
regions
How many to mark/recapture?
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Requires some knowledge of population size!
Trade-off between precision and sample size
 Population
of 10,000: Mark 400 and examine 600 for
+/- 50% OR mark 1,000 and examine 1,500 for +/10%
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Trade-off between marked and recapture sample
size
 Population
of 10,000: Mark 1,000 and examine1,500
OR Mark 4,500 and examine 500
Schnabel method
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Closed population
Equal catchabilty in first sample
Marking does NOT influence catchability
Multiple recaptures
 Easier
to pick up on violation of assumptions
Jolly Seber method
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Open populations
 Allows
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estimation of births and deaths
Three or more sampling periods needed
Equal catchability of all individuals in all samples
Equal probability of survival
Marks are not lost
Sampling time is negligible compared to intervals
between samples
Importance of uncertainty
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Confidence intervals
 Long-term
frequency, not probablity!
 95% confidence intervals  if you repeated
procedure an infinite number of times, 95% of the time
the interval you create would contain the “true” value
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Precision vs. accuracy
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Accurate, not precise
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Not accurate, precise
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Accurate, precise
Lets count some beans!