Population Models Flashcards
Surplus production Models
Aggregate biomass, undifferentiated by age, size, or sex.
complex biological processes implicit in model structure
e.g., natural mortality, fecundity, somatic growth,
recruitment not explicitly modeled
Rely on a few key parameters (r, K, q)
external factors assumed non-dominant (not modeled)
What are the data requirements for surplus production models?
Time series index of relative abundance (catch per unit effort, survey)
Time series of catch/harvest/removals
Why are surplus models used?
have simple data requirements and are inexpensive.
used in roughly 12% of US assessed stocks
often used in tropical fisheries and data limited fisheries.
Why are surplus models used in tropical fisheries?
Even in tropical fisheries that are data rich, its hard to determine age structure since there is no seasonality clear growth rings.
Surplus production definition
is the difference between production (recruitment + growth) and natural mortality, or the additional population production above that necessary to maintain a constant population size
Explain this equation:
Biomass next year is greater than biomass this year when recruitment plus growth are greater than natural mortality.
Maximum Sustainable Yield (MSY)
is the largest amount of productivity (biomass, individuals) that can be continuously removed from a population without affecting population size
what does B_msy refer to?
The biomass needed to generate MSY is referred to as BMSY
Schaefer Model (1954)
Logistic growth model
Density dependence (birth/death rates) linear function of population size.
Pella-Tomlinson (1969)
Modified logistic growth model
density dependce non-linear
Fox (1970)
Gompertz growth model
Density dependence non-linear
What species would be better with the fox model? AKA – MSY occurs at a lower population level.
First developed with sardines and tunas that have really high fecundity and really productive at low population sizes.
It could be sustainably fished at lower abundance levels. The population will be more productive.
Surplus production and fishing
Biomass next year equal to biomass this year plus surplus production and minus fishery yield
What surplus production model is used most frequently?
Schaefer
What should be noted in the Schaefer model?
yield becomes catch (catch is exactly equal to excess population productivity (surplus))
What do you target in surplus production and fishing?
Target MSY
Why target MSY in surplus production models?
Two reasons:
1. The most productive a stock – yields the most biomass or protein that can be drawn from the resource.
2. Sustainable – keep removing that excess productivity (surplus) year after year, the population abundance levels will not change.
Why is MSY important for fishery management?
MSY guides a lot of management but almost always the management level is almost slightly less than MSY for precautionary reasons.
Reference point that is either a target or a limit. It informs harvest allocations. If a stock overfished, would want to fish under MSY.
Removing surplus production…
Exploiting unfished biomass will draw down stock until equilibrium reached (surplus production = harvest)
Assuming no change in underlying habitat, biological conditions, etc.
Process likely not smooth, though some models make this assumption
Why were surplus models developed in the first place?
Regulate effort and catch/harvests to achieve MSY (or other yield target)
Fish stock down so it is more productive
What are some useful management values based on Schafer specifications?
MSY = rK/4
Biomass @ MSY: BMSY = K/2
Fishing mortality @ MSY: FMSY = r/2
Effort @ MSY: EMSY = r/2q
What data do we need to use surplus models?
Want information on biological parameters (r, K) to set management targets (e.g., BMSY , FMSY)
What is a critical assumption for surplus production models?
index of abundance is an accurate measure of true abundance, e.g., It=qBt (index = catchability coefficient x true abundance)
What are the two general approaches for surplus production models?
Equilibrium methods
Non-Equilibrium methods
Equilibrium Methods
assume population is at steady state at all times (catch always = surplus production) → changes in CPUE driven by density dependent population response (strong and unrealistic assumption)
Non-equilibrium methods
relax steady-state assumption and allow for variability or error in response
assume some error
Explain what happened with the Peruvian anchoveta fishery and the equilibrium method.
Equilibrium method was used until the 70s with this fishery
Notice that the only one point touches the surplus production curve and points are concentrated on one side. Do not have a good understanding of the shape of the parabola. In 1972 there was a strong el nino, recruitment was not stable (growth rate), and started to school in dense aggregations which means the catchability (q) was not stable. Causing major overfishing and economic colapose. Stopped using equilibrium methods because of this.
Example of a fishery that today still uses surplus production models (non-equilibrium method):
North Atlantic albacore
CPUE data in an observation-error production model to estimate the intrinsic rate of growth (r), carrying capacity (K), and biomass dynamics
Estimating surplus production parameters
Do not have information on r & K until actual fishing occurs. If it’s a virgin fishery, then carry capacity (K) may be known. However, intrinsic grown rate (r) is the population at really levels of abundance. Wont know r until the population is fished down.
What is critical when estimating surplus production parameters?
Contrast in data
Fisheries data is frequently characterized by a “one-way trip” → increasing effort and declining CPUE
Ideally, want catch and effort over broad range and with effort both increasing and decreasing (several times even better!)
What is the difference between age-structured stock assessments and surplus production models?
Surplus production models do not include – age, size, or sex structures in the models
Where surplus production model lumped all of the stuff (growth, recruitment, mortality) together into the collection of r & K. Age structure models splits it all up.
Why are age-structured stock assessments important?
Many population processes may differ across age groups (fecundity, natural mortality, fishing vulnerability)
What portion of the federally managed species use age-structure models?
2/3
What are the two general approaches to age-structured models?
Backward projection
Forward projection
Backward Projection
start out with a terminal age or year class and say ok, if there were this many fish alive at age 4 then that is the most that could be caught. From there, work our way backwards to determine what recruitment could have been to determine that many age 4 species.
Often called BPA
Forward projection models –
predict recruitment and track fishing mortality through time.
What is the standard approach for backward projection?
– virtual population analysis is the standard approach.
Uses fishing mortality at terminal age to backward project.
Virtual population analysis
For a given age-class, fish alive in the previous year must equal (at minimum) those fish caught this year plus those that died from natural causes
What is the goal of a Virtual population analysis?
estimate stock sizes and fishing mortality of individual cohorts using commercial catch data
Cohort
class or group of fish spawned during a given time period (typically 1 year)
What is the standard approach for Backward Projection?
Virtual population analysis.
Virtual population analysis.
Uses fishing mortality at terminal age to backward project.
The idea is that cant more fish that were alive at the end of the previous year.
What do you need to do a virtual population analysis?
need time series of catch-at-age and (frequently) fishing effort
What is standard ___ = ___ -___-___ for VPA: backward projection?
In the equation presented above, what is oftentimes unknown? What equation can you substitute to estimate number of alive at beginning of next year?
Generally, dont know the number alive at the beginning of this year (aka cohort).
Use this equation instead:
When is VPA a good model to use?
When most of the mortality is from fishing since this is observed, and the dominate driver is population dynamics.
Statistical catch-at-age methods
Combines multiple types of data and sub-models to simulate population dynamics of stocks and fisheries
What are the main differences between statistical catch-at-age and VPA methods?
Forward looking → catch dependent on recruitment
Utilize statistically robust methods for finding parameter values rather than ad-hoc numerical approach
Natural mortality is a parameter that can be estimated (does not require modeler to specify a prior)
Can handle gaps in data, e.g., missing years of catch
Allows for error in catch-at-age (e.g., due to measurement/ageing)
Statistical catch-at-age example
Model incorporates data on catch-at-age, fishing effort, recruits and spawning stock → estimates mortality parameters, catchability, and parameters of spawner-recruit relationship
Yield-per-recruit analysis
Yield-per-recruit (YPR) models track a recruit (or cohort) through time
Evaluate how changes in exploitation rate affect lifetime expected yield (YPR) and spawning-biomass (SBPR)
f msy
fishing pressure
What is YPR analysis used for
When growth overfishing is a potential, YPR is the analysis often used.
