Quantitative Models in Fisheries Science Flashcards
What is the goal of a model?
convey important pieces of information without unnecessary distractions.
What is common about all models?
Models are simplified versions of reality.
Models are useful and simplify a complex process. Almost all models are wrong because they make some assumptions.
Why do we need models in fisher science?
Before WWII, management believed that humans had very little impact on a fishery. However, no one predicted the technological advancements after the War.
Recognition that in response to exploitation, populations can exhibit a variety of changes:
Total numbers, total biomass
Size-frequency, age-structure
Growth patterns, age-at-maturity
Spatial distribution
Behavior, species’ interactions
Quantitative Models in fisheries science
Mathematics is the natural language to express (model) fish populations, natural processes (growth, mortality, etc.), and related ecosystems (including humans)
Quantitative models include:
Drivers:
Growth
Recruitment
Mortality
Dynamics:
Population & production models
Integrated bioeconomic models
Ecosystem models
Models have gotten more complicated over time. Why?
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.
Fisheries management is a somewhat conservative process still. Why?
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.
A simple model of fish populations
Box models:
Populations are represented as boxes and there are flows in and out of the box.
Four basic forces act on fishable biomass:
Reproduction and growth → increase biomass
Fishing and natural mortality → reduce biomass
Introducing dynamics
Can’t do a ton with models with just graphs in the sense of making predictions or probabilities
Drawing a standard dynamic model
Dynamic Population Models Include:
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)
State Variables
The information that we track through time. Biomass over time or population over time.
Parameters
Fixed values that affect the trajectory of the state variable. Growth and carry capacity.
Rules of Change
Internal relationship
Forcing Functions
External Shock
Dynamic Population Models can be:
random or deterministic;
continuous or discrete;
aggregate or individual based;
age, size, sex, spatially structured
Dynamic Model Example:
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)
Contemporary areas of research:
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
Fitting models to data
Models represent hypotheses about nature and underlying relationships
Data used to evaluate competing hypotheses (relative comparisons determine which is more “true”)
When fitting models to data, you need:
competing models/hypotheses, data, search algorithm/fitting procedure, assessment criterion
What does different parameter values represent in dynamic models?
Different parameter values (a, b in the length-weight model) represent different hypotheses and yield predictions that can be compared to actual data
Is this Allometric or Isometric Growth and why?
Allometric
3.14- Allometric Growth – not exactly 3
Isometric Growth – Direct scaling between length and weight
- exponent would be exactly 3
