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 737-1086, Scott.Heppell@oregonstate.edu

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.

What happens now?

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)

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.

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

K 2 QET K

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

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.”

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)

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

Effects of stochasticity cool phase warm phase bocaccio

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

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

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?

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?

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

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

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

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

Fertility as a function of sex ratio –Reproductive depensation

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

Population recovery adults 2000000 4000000 6000000 8000000 10000000 2000000 4000000 6000000 8000000 10000000 12000000 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

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

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

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