1. Lecture 12: Population dynamics
Biology 450: Fish Week
Lecture 12: Population dynamics
Scott Heppell Department of Fisheries and Wildlife Oregon State University 042 Nash Hall ,

3. In order for a population to be sustained over the long term, the equation represented by this conceptual model must balance itself. When a population is at carrying capacity, natural mortality balances reproduction and growth.

4. What happens now?

6. An application of the logistic equation to the U. S
An application of the logistic equation to the U.S. census projection (Pearl et al. 1940)

8. What is MSY?
Maximum Sustainable Yield (MSY): The largest average catch or yield that can continuously be taken from a stock under existing environmental conditions.
Also called: maximum equilibrium catch ; maximum sustained yield; sustainable catch.

9. What is MSY?
The yield obtained when a population is at a density that results in the highest net regeneration rate
For simple logistic models, this is predicted to occur at 50% of original stock biomass
For most fish, it is thought to occur at a little less than B50

10. K 2
QET K

11. Does this curve need to be symmetrical?
Yield = F * Biomass

12. Why MSY is problematic:
The assessments assume that the population is at carrying capacity when MSY is calculated.
The model assumes little change in ecological relationships.
Recruitment and growth are constant/stable.
In order to determine where the peak is, you have to have both very low and very high levels of fishing.
Once you have really high levels of fishing effort, it’s hard to back down, and the fishery may already be in trouble.
“The hardest thing to do in fisheries management is reduce fishing pressure.”

16. Factors affecting population growth rate
Environmental variability
Density (intra-specific competition)
Interactions with other species
These are not mutually exclusive, and we may not be able to distinguish them...
Changes in population growth are a response to changes in vital rates – survival, growth, or fertility (per capita reproduction)

17. What is stochasticity?
Variability that affects mean survival, growth and reproductive rates
Environmental stochasticity
Catastrophes
Variability that affects individuals
Demographic stochasticity
“coin-flipping”

18. Effects of stochasticity
cool phase
warm phase
bocaccio

19. Depensation First described analytically by Allee
A density-dependent effect that causes a reduction in per capita reproductive success at low population densities
May be caused by:
Inability to find mates
Lack of necessary social cues for successful reproduction
Lack of “safety in numbers” from predators

20. Relationship between l and population size (density)1
no Allee effect
strong Allee effect
Growth rate below 1 is a population in decline
Most important, populations with l less than 1 and low population size cannot grow

21. So, there are three things to consider:
Population size
Population growth rate
Variance in population growth rate
What if we could measure population growth and variance, then determine the average population size needed to minimize the risk of extinction?

22. What if...
Populations are regulated by food availability (competition) during poor ocean condition years, but by stochastic fluctuations and predation during good ocean years?
Populations naturally cycle with long periods of negative population growth (deaths exceed births) followed by rapid increases in population size during good ocean cycles?
Does this explain why rockfish live so long?
How does this affect how we designate Essential Fish Habitat?

25. Grouper Sex Ratio Species Sex ratio (M:F) Location Source E. striatus
1.75:1-1:4
Various Caribbean
Sadovy and Colin 1995
and references therein
E. guttatus
1:4-1:115
Puerto Rico
Sadovy et al. 1994
1:4-1:8
Shapiro et al. 1993a
E. morio
1:2-1:6
NE Gulf of Mexico
Coleman et al. 1996
M. microlepis
1:5-1:76

26. Gag Grouper Model Heppell, Heppell, Coleman and Koenig, in revision, Ecological Applications
Examine the effects of harvest on hermaphrodites
Compare the relative impacts of protected areas that are sex-specific and time/location specific
Compare benefits of protected areas with reductions in fishing pressure

28. FISHING MORTALITY RATE
Bag
limits
FISHING MORTALITY RATE
Gear
restrictions
Marine
reserves
POPULATION
recovery or
sustainability?
Size
limits
Seasonal
closures

29. Two models Model I = low fishing mortality rates
Ffemale= 0.4, Fmale= 0.15
Model II = high fishing mortality rates
Ffemale= 0.6, Fmale= 0.6
Z = F(spawn) + F(feed) + M
0.25
0.75
Example: spawning reserve
Z = F(spawn)*0 + F(feed) + M = F(0.75) + M

30. Fertility as a function of sex ratio –Reproductive depensation

31. Management Scenarios A: Status quo – 1996 fishing mortality rates
B: Increase size limit to 24 inches (=age 2-3)
C: Seasonal closure for all size classes January-March (spawning season)
D: Aggregation reserve (protects spawners and males)
E: Aggregation reserve with displaced effort on females
F: Shallow water reserves (protect females May-January)
G: Cut fishing mortality by 50% for all

32. Population recovery adults 2000000 4000000 6000000 8000000 10000000
1995
2005
2015
2025
2035
2045
adults
A - baseline
B - size limit
C - seasonal
closure
D - aggregation
reserve
E - aggregation
reserve with
displaced effort
F - nearshore
G 50% cut in F

33. Sex ratio recovery sex ratio (proportion male) 0.02 0.04 0.06 0.08 0.1
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1995
2005
2015
2025
2035
2045
sex ratio (proportion male)
A - baseline
B - size limit
C - seasonal
closure
D - aggregation
reserve
E - aggregation
reserve with
displaced effort
F - nearshore
G 50% cut in F

34. Comparing effectiveness
Population recovery
Nearshore reserve > 50% cut in F > spawning reserve >= seasonal closure > size limit
Biomass
Nearshore reserve >> 50% cut in F > spawning reserve = nearshore closure = seasonal closure > size limit
Sex ratio (effective population size)
Spawning reserve > nearshore reserve = 50% cut in F > seasonal closure = size limit

35. Conclusions
Relative effectiveness of management scenarios depends on management goals
Reduced fertility with skewed sex ratios can negatively impact population growth, but the level of impact is less than that of changes in mortality rates and depends on management scenario
Maximum recovery rates and biomass occur with female protection and large reductions in fishing mortality, but these strategies do not solve the sex ratio problem in the short term
Marine reserves on spawning aggregations are effective, but recovery is likely to be slow if fishing effort increases in the nearshore