Population Models

Question 1

Surplus production Models

Answer 1

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)

Question 2

What are the data requirements for surplus production models?

Answer 2

Time series index of relative abundance (catch per unit effort, survey)

Time series of catch/harvest/removals

Question 3

Why are surplus models used?

Answer 3

have simple data requirements and are inexpensive.

used in roughly 12% of US assessed stocks

often used in tropical fisheries and data limited fisheries.

Question 4

Why are surplus models used in tropical fisheries?

Answer 4

Even in tropical fisheries that are data rich, its hard to determine age structure since there is no seasonality clear growth rings.

Question 5

Surplus production definition

Answer 5

is the difference between production (recruitment + growth) and natural mortality, or the additional population production above that necessary to maintain a constant population size

Question 6

Explain this equation:

Answer 6

Biomass next year is greater than biomass this year when recruitment plus growth are greater than natural mortality.

Question 7

Maximum Sustainable Yield (MSY)

Answer 7

is the largest amount of productivity (biomass, individuals) that can be continuously removed from a population without affecting population size

Question 8

what does B_msy refer to?

Answer 8

The biomass needed to generate MSY is referred to as BMSY

Question 9

Schaefer Model (1954)

Answer 9

Logistic growth model
Density dependence (birth/death rates) linear function of population size.

Question 10

Pella-Tomlinson (1969)

Answer 10

Modified logistic growth model
density dependce non-linear

Question 11

Fox (1970)

Answer 11

Gompertz growth model
Density dependence non-linear

Question 12

What species would be better with the fox model? AKA – MSY occurs at a lower population level.

Answer 12

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.

Question 13

Surplus production and fishing

Answer 13

Biomass next year equal to biomass this year plus surplus production and minus fishery yield

Question 14

What surplus production model is used most frequently?

Answer 14

Schaefer

Question 15

What should be noted in the Schaefer model?

Answer 15

yield becomes catch (catch is exactly equal to excess population productivity (surplus))

Question 16

What do you target in surplus production and fishing?

Answer 16

Target MSY

Question 17

Why target MSY in surplus production models?

Answer 17

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.

Question 18

Why is MSY important for fishery management?

Answer 18

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.

Question 19

Removing surplus production…

Answer 19

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

Question 20

Why were surplus models developed in the first place?

Answer 20

Regulate effort and catch/harvests to achieve MSY (or other yield target)

Fish stock down so it is more productive

Question 21

What are some useful management values based on Schafer specifications?

Answer 21

MSY = rK/4
Biomass @ MSY: BMSY = K/2
Fishing mortality @ MSY: FMSY = r/2
Effort @ MSY: EMSY = r/2q

Question 22

What data do we need to use surplus models?

Answer 22

Want information on biological parameters (r, K) to set management targets (e.g., BMSY , FMSY)

Question 23

What is a critical assumption for surplus production models?

Answer 23

index of abundance is an accurate measure of true abundance, e.g., It=qBt (index = catchability coefficient x true abundance)

Question 24

What are the two general approaches for surplus production models?

Answer 24

Equilibrium methods
Non-Equilibrium methods

Question 25

Equilibrium Methods

Answer 25

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)

Question 26

Non-equilibrium methods

Answer 26

relax steady-state assumption and allow for variability or error in response

assume some error

Question 27

Explain what happened with the Peruvian anchoveta fishery and the equilibrium method.

Answer 27

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.

Question 28

Example of a fishery that today still uses surplus production models (non-equilibrium method):

Answer 28

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

Question 29

Estimating surplus production parameters

Answer 29

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.

Question 30

What is critical when estimating surplus production parameters?

Answer 30

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!)

Question 31

What is the difference between age-structured stock assessments and surplus production models?

Answer 31

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.

Question 32

Why are age-structured stock assessments important?

Answer 32

Many population processes may differ across age groups (fecundity, natural mortality, fishing vulnerability)

Question 33

What portion of the federally managed species use age-structure models?

Answer 33

2/3

Question 34

What are the two general approaches to age-structured models?

Answer 34

Backward projection
Forward projection

Question 35

Backward Projection

Answer 35

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

Question 36

Forward projection models –

Answer 36

predict recruitment and track fishing mortality through time.

Question 37

What is the standard approach for backward projection?

Answer 37

– virtual population analysis is the standard approach.
Uses fishing mortality at terminal age to backward project.

Question 38

Virtual population analysis

Answer 38

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

Question 39

What is the goal of a Virtual population analysis?

Answer 39

estimate stock sizes and fishing mortality of individual cohorts using commercial catch data

Question 40

Cohort

Answer 40

class or group of fish spawned during a given time period (typically 1 year)

Question 41

What is the standard approach for Backward Projection?

Answer 41

Virtual population analysis.

Question 42

Virtual population analysis.

Answer 42

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.

Question 43

What do you need to do a virtual population analysis?

Answer 43

need time series of catch-at-age and (frequently) fishing effort

Question 44

What is standard ___ = ___ -___-___ for VPA: backward projection?

Answer 44

Question 45

In the equation presented above, what is oftentimes unknown? What equation can you substitute to estimate number of alive at beginning of next year?

Answer 45

Generally, dont know the number alive at the beginning of this year (aka cohort).

Use this equation instead:

Question 46

When is VPA a good model to use?

Answer 46

When most of the mortality is from fishing since this is observed, and the dominate driver is population dynamics.

Question 47

Statistical catch-at-age methods

Answer 47

Combines multiple types of data and sub-models to simulate population dynamics of stocks and fisheries

Question 48

What are the main differences between statistical catch-at-age and VPA methods?

Answer 48

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)

Question 49

Statistical catch-at-age example

Answer 49

Model incorporates data on catch-at-age, fishing effort, recruits and spawning stock → estimates mortality parameters, catchability, and parameters of spawner-recruit relationship

Question 50

Yield-per-recruit analysis

Answer 50

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)

Question 51

f msy

Answer 51

fishing pressure

Question 52

What is YPR analysis used for

Answer 52

When growth overfishing is a potential, YPR is the analysis often used.