Quantitative Models in Fisheries Science

Question 1

What is the goal of a model?

Answer 1

convey important pieces of information without unnecessary distractions.

Question 2

What is common about all models?

Answer 2

Models are simplified versions of reality.

Models are useful and simplify a complex process. Almost all models are wrong because they make some assumptions.

Question 3

Why do we need models in fisher science?

Answer 3

Before WWII, management believed that humans had very little impact on a fishery. However, no one predicted the technological advancements after the War.

Question 4

Recognition that in response to exploitation, populations can exhibit a variety of changes:

Answer 4

Total numbers, total biomass

Size-frequency, age-structure

Growth patterns, age-at-maturity

Spatial distribution

Behavior, species’ interactions

Question 5

Quantitative Models in fisheries science

Answer 5

Mathematics is the natural language to express (model) fish populations, natural processes (growth, mortality, etc.), and related ecosystems (including humans)

Question 6

Quantitative models include:

Answer 6

Drivers:
Growth
Recruitment
Mortality

Dynamics:
Population & production models
Integrated bioeconomic models
Ecosystem models

Question 7

Models have gotten more complicated over time. Why?

Answer 7

Technological advances easier
More accurate models
More data collection
Better data collection

The most simplified model but no simpler is not as applicable now because of the above.

Question 8

Fisheries management is a somewhat conservative process still. Why?

Answer 8

Most models we use now were developed in the 1950s and 1970s.

Conservative in terms that progress is slow, defaulting to what is known, and/or needs to have a lot of convincing to prove change is needed.

Question 9

A simple model of fish populations

Answer 9

Box models:
Populations are represented as boxes and there are flows in and out of the box.

Question 10

Four basic forces act on fishable biomass:

Answer 10

Reproduction and growth → increase biomass

Fishing and natural mortality → reduce biomass

Question 11

Introducing dynamics

Answer 11

Can’t do a ton with models with just graphs in the sense of making predictions or probabilities

Question 12

Drawing a standard dynamic model

Answer 12

Question 13

Dynamic Population Models Include:

Answer 13

state variables, parameters, rules of change, forcing functions

Understand how state variables evolve given some set of fixed conditions (parameters), internal relationships (rules of change), and external shocks (forcing functions)

Question 14

State Variables

Answer 14

The information that we track through time. Biomass over time or population over time.

Question 15

Parameters

Answer 15

Fixed values that affect the trajectory of the state variable. Growth and carry capacity.

Question 16

Rules of Change

Answer 16

Internal relationship

Question 17

Forcing Functions

Answer 17

External Shock

Question 18

Dynamic Population Models can be:

Answer 18

random or deterministic;
continuous or discrete;
aggregate or individual based;
age, size, sex, spatially structured

Question 19

Dynamic Model Example:

Answer 19

State variables: number of animals (N)
Parameters: intrinsic rate of increase (r) and carrying capacity (K)
Rules of change: density dependent logistic growth
Forcing functions: harvest (H)

Question 20

Contemporary areas of research:

Answer 20

Resolve key parameters within rules of change (e.g., r, K; rates of natural mortality, fishing mortality, growth)

Estimate current and future state variables

Estimate/incorporate additional factors omitted from the simple model

Question 21

Fitting models to data

Answer 21

Models represent hypotheses about nature and underlying relationships

Data used to evaluate competing hypotheses (relative comparisons determine which is more “true”)

Question 22

When fitting models to data, you need:

Answer 22

competing models/hypotheses, data, search algorithm/fitting procedure, assessment criterion

Question 23

What does different parameter values represent in dynamic models?

Answer 23

Different parameter values (a, b in the length-weight model) represent different hypotheses and yield predictions that can be compared to actual data

Question 24

Is this Allometric or Isometric Growth and why?

Answer 24

Allometric

3.14- Allometric Growth – not exactly 3
Isometric Growth – Direct scaling between length and weight
- exponent would be exactly 3

Question 25

What are the different assessment criteria?

Answer 25

Minimize sum of squared errors
Maximize likelihood of the observed data
Determine most probable hypothesis for observed data

Question 26

What is the downside to Minimize sum of squared errors?

Answer 26

all data needs to be in the same units). Complicated models with many different units and scales can’t use this assessment criteria.

Question 27

Exponential Population Growth

Answer 27

density independent -> proportional rate of increase does not depend on population level.

assumes environmental and biological factors are not limiting (e.g. colonizing species).

Generally not true for most species

Constant rates of birth (b) and death (d) leads to constant proportional increase in population size

Question 28

Exponential population growth equation:

Answer 28

Change in population is equal to the difference between birth and death rates multiplied by the number of individuals

Question 29

Exponential population growth equation:

Answer 29

r is known as the intrinsic rate of increase or the instantaneous rate of population growth; it is independent of population size N

Question 30

Relative values of b and d determine

Answer 30

whether the population is rapidly increasing (b>d), decreasing (b<d), or stable (b=d)

Question 31

Dynamics can be specified as:

Answer 31

r > 0 → population increasing
r = 0 → population stable
r < 0 → population decreasing

Question 32

Logistic population growth

Answer 32

Population grows slowly at first (in absolute numbers), reaches maximum growth at an intermediate level, then slows down again as it reaches an asymptote.

More realistic for resource dependent systems. Slows as it reaches carry capacity.

Question 33

Logistic growth displays:

Answer 33

density dependence

Food/resource availability, competition, disease, predator refuge, and other factors limit population growth and size

Birth rates increase and/or death rates decrease at low population levels (compensation)

Question 34

Density dependence implies:

Answer 34

birth rates and/or death rates are a function of population size.

Births and deaths balance at equilibrium population size K

Question 35

How does Logistic Growth accommodate resource limitations?

Answer 35

Coordination of N and K. If N is far from K, the population grows exponentially. If N is close to K, the population stops growing.

Question 36

Logistic population growth, what is “r”?

Answer 36

r is the instantaneous rate of growth when N is close to 0, i.e., bmax - dmin

Question 37

Logistic population growth, what is “K”?

Answer 37

K is the equilibrium population size (when births = deaths), also known as carrying capacity

Question 38

Carrying Capacity

Answer 38

→ Maximum number of individuals or biomass able to be sustained by the current environment

Question 39

In logistic population growth, when is the population growing the fastest?

Answer 39

population is growing at its fastest rate at half of carry capacity. Steepest part of the curve is at half of capacity.

Question 40

Some assumptions of logistic growth models?

Answer 40

Environmental factors are constant

All members of population affected by limiting factors identically (e.g., food, refuge)

Birth and death rates respond instantly to changes in density (no lagged effects)

Density dependence is a smooth process; population growth rate affected by even small densities

Age, size, and sex distributions are stable

No Allee effect (e.g., females always able to find mates)

Question 41

What are logistic growth models good at?

Answer 41

The logistic population growth curve is broadly characteristic of a lot of things. Simplifies a lot of nuances away. The point of a model is to be as simple as possible but no simpler. Logistic growth does a good job of explaining population trajectories.