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### Population dynamics

Today’s outline

- Reading quiz
- Reading discussion
- Field trip briefing/electrofishing safety
- Population dynamics lecture
- Break
- Mark-recapture lab

What limnological relationship was the motivation for this study? (Hint: NOT trophic cascades) (1pt)

- If the population of piscivores increases in a lake, what happens to the density of phytoplankton? (2pts)
- There is a time lag in trophic cascades: why? (2pt)

Nutrients (mg P/L)

How do you interpret this figure?

What piece of information does it convey?

Zoo 511 Ecology of Fishes

Today’s goals

- Understand why and how population dynamics are important in fisheries ecology
- Gain experience in a variety of mark-recapture methods

“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

What are population dynamics?

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

Why study population dynamics?

Atlantic salmon PVA

From Legault 2004

- 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.

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

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?

- Nt+1 = Nt + B – D + I – E
- B = births
- D = deaths
- I = immigration
- E = emigration

Immigration

Stocking

Population

Births

Deaths

Angling

Emigration

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 density-independent?

Density-dependent

Density-independent

Population density

Population density

?

?

Time

Time

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 density-independent?

Density-dependent

Density-independent

Population density

Population density

Logistic

Exponential

Time

Time

Logistic population growth

dN/dt=r0N(1-N/K)

r0 = maximum rate of increase

K= carrying capacity

r0

per capita annual increase

N

K

How do populations change?

- Nt+1 = Nt + B – D + I – E
- B = births
- D = deaths
- I = immigration
- E = emigration

Immigration

Stocking

Population

Births

Deaths

Angling

Emigration

Survival

- Eggs and larvae suffer the largest losses

Recruit!

HATCH

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

Recruitment

- 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
- Somewhat arbitrary, varies among populations
- Major goal of fish population dynamics: understanding the relationship between stock size and recruitment

-Stock size (number and size of females)

Ricker

What determines recruitment?

Recruitment

Beverton-Holt

From: Wootton (1998). Ecology of teleost fishes.

spawning stock biomass (SSB)

Highly variable recruitment results in naturally very variable catches

From: Jennings, Kaiser and Reynolds (2001). Marine Fisheries Ecology

Population Abundance

- On rare occasions, abundance can be measured directly
- Small enclosed systems
- Migration

Catch per unit effort (CPUE)

- 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

- 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
- 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)

Modified Petersen method

- 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?

- 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?

- 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%
- 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

- 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

- Open populations
- Allows 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

- 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
- Precision vs. accuracy

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

Accurate, not precise

Not accurate, precise

Accurate, precise

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