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
What are the different assessment criteria?
Minimize sum of squared errors
Maximize likelihood of the observed data
Determine most probable hypothesis for observed data
What is the downside to Minimize sum of squared errors?
all data needs to be in the same units). Complicated models with many different units and scales can’t use this assessment criteria.
Exponential Population Growth
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
Exponential population growth equation:
Change in population is equal to the difference between birth and death rates multiplied by the number of individuals
Exponential population growth equation:
r is known as the intrinsic rate of increase or the instantaneous rate of population growth; it is independent of population size N
Relative values of b and d determine
whether the population is rapidly increasing (b>d), decreasing (b<d), or stable (b=d)
Dynamics can be specified as:
r > 0 → population increasing
r = 0 → population stable
r < 0 → population decreasing
Logistic population growth
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.
Logistic growth displays:
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)
Density dependence implies:
birth rates and/or death rates are a function of population size.
Births and deaths balance at equilibrium population size K
How does Logistic Growth accommodate resource limitations?
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.
Logistic population growth, what is “r”?
r is the instantaneous rate of growth when N is close to 0, i.e., bmax - dmin
Logistic population growth, what is “K”?
K is the equilibrium population size (when births = deaths), also known as carrying capacity
Carrying Capacity
→ Maximum number of individuals or biomass able to be sustained by the current environment
In logistic population growth, when is the population growing the fastest?
population is growing at its fastest rate at half of carry capacity. Steepest part of the curve is at half of capacity.
Some assumptions of logistic growth models?
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)
What are logistic growth models good at?
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.
