Transcript Fish Population abd Fished Population Dynamics

Stock Assessment Workshop
19th June -25th June 2008
SPC Headquarters
Noumea
New Caledonia
Day 1 Session 2
Fish and “fished” populations – basic
principles
“To understand how populations will respond to exploitation, we
need to appreciate how they will behave when unexploited.”
Hillborn and Walters, 1992
Key Definitions
What is a population? Does it differ from a stock?
Definition and use of terms “population” and “stock” tends to be
a bit rubbery in fisheries science…..often taken to mean the
same thing, however…..
Population: A group of individuals of the same species living in
the same area at the same time and sharing a common gene
pool, with little or no immigration/emmigration
Stock: 1. The part of a fish population which is under
consideration from the point of view of actual or potential
utilization. Ricker W.E. (1975)
2. A group of fish of one species which shares common
ecological and genetic features. The stocks defined for the
purposes of stock assessment and management do not
necessarily coincide with self-contained population. Restrepo
V. (1999)
Examples of natural variation in
populations over time – non fisheries data
Industrialised
fishing
Session overview
Fish populations
•
Life cycles and life history strategies
•
Basic population dynamic – recruitment, natural mortality and
growth
•
Simple population models
•
Movement, physiology and the environment
Fished populations
1. Adding “fishing mortality” to the population dynamics equation
2. Natural variability v fishing based impacts
3. Behaviour of exploited stocks
a. Stability, instability, cyclicity, resilience,
b. Boundaries and regime shifts
4. Overfishing
Growth overfishing
Recruitment overfishing
5. “Fished” population models
Tuna Life cycle
Adults
Spawning and
fertilisation
Maturation
Eggs
Hatching
Larvae
Juvenile stages
Variations in fish life cycles
Within this basic strategy there is some variation, even across large
pelagic species taken by tuna fisheries. Two well known species
groups with very contrasting life histories are the tunas and sharks.
Big implications for population dynamics and for resilience to fishing.
107
Adults
104
Juveniles
Numbers
105
Eggs/Larvae
106
Sharks (generalised)
Tuna (generalised)
103
102
101
Days
Months
Years
Basic population dynamics
We’ve seen that life history strategies vary between species, but within
species, what are the processes that drive population fluctuations?
Closed animal population (no immigration or emmigration)
Population
Births
Size
(numbers of
individuals)
Deaths
(Natural mortality)
Nt+1 = Number of animals in one year,
Nt+1=Nt+B-M
Nt = Current Number of animals;
B= Births after one year
M = Deaths after one year.
Basic population dynamics
Biomass model
Closed population (no immigration or emmigration) with no fishing
Recruitment
Biomass
Growth
Death
(Natural mortality)
Basic population dynamics
Bt+1=Bt+R+G-M
Bt+1 = Biomass of fish in one year,
Bt = Current biomass;
R= Biomass of new recruits in one years time,
G= Additional biomass due to growth of current fish
M = Biomass of fish from current population that died.
Each of the processes of recruitment, growth and mortality, are effected
by numerous factors, both endogenous (relating to the fishes
genetics, physiology and behaviour) and exogenous (determined by
the fishes environment and external influencing factors)
We need to understand these factors to create realistic population
models
Recruitment (R)
Bt+1=Bt+R+G-M
Recruitment is a bit of a rubbery concept….the point at which
one considers a fish “recruited” is often determined by the
point at which individuals can be detected ie counted or
estimated
Recruitment definitions:
1. For demographic purposes recruitment refers to the maturing
of individuals into the adult age classes (Valiela, 1995)
2. In fishery publications, recruitment is defined as the
appearance of a cohort into the catch due to it becoming of a
size vulnerable to the fishery.” (Valiela, 1995)
3. The population still alive at any specified time after the egg
stage (Haddon, 1997)
4. The number of fish [of a cohort] alive in a population at any
arbitrarily defined point in time after the subsidence of initial
high mortality (Rothschild, 1987)
Bt+1=Bt+R+G-M
Recruitment (R)
What are the processes that
effect recruitment?
Adult production of gametes
Spawning and fertilisation
Firstly, we need to remind ourselves
of the stages leading from when
an adult population spawns, to
individuals from that spawning
event/year entering (recruiting
to) the adult population.
What factors influence the production
of eggs, and the probability of
progression through each of the
subsequent stages??
Larval development within eggs
Hatching
Larval stage
Metamorphosis
Juvenile stage
Maturation
Adult phase
Bt+1=Bt+R+G-M
Recruitment (R)
Processes that effect larval and
juvenile survival
Biotic (e.g.)
Starvation/Competition
Predation/Cannabalism
Disease
Abiotic (e.g.)
Temperature
Salinity
Oxygen
Adult production of gametes
Spawning and fertilisation
Larval development within eggs
Hatching
Larval stage
Metamorphosis
Juvenile stage
Small variations in survival = big
variations in recruitment
Maturation
*Age to maturity also important for total
egg production rate by population
Adult phase
Bt+1=Bt+R+G-M
Recruitment (R)
Processes that effect egg
production, condition and
survival
Fecundity
Adult condition
Environment
Adult production of gametes
Spawning and fertilisation
Larval development within eggs
Hatching
Larval stage
Metamorphosis
Juvenile stage
Maturation
Adult phase
Recruitment (R)
Bt+1=Bt+R+G-M
In summary…
Many different factors can impact the survival of marine fish at any of the
different stages in the recruitment process….
So….
How do we measure recruitment?
1. Sampling regimes targeted at juveniles.
2. Size specific indices of abundance from catch/effort data.
3. Assume a relationship with adult stock size
Where information pertaining to 1 and 2 above aren’t available, scientists
require a predictive relationship that is based on other available data.
The most commonly used, and debated, of these, is the stock-recruitment
relationship.
Recruitment (R)
Bt+1=Bt+R+G-M
The Stock-Recruitment Relationship
Two theories
1. Recruitment is density dependant, i.e. is dependant on the stock size.
2. Recruitment is density independant, i.e. is independant of the stock size
The latter theory was once very popular due to a lack of correlation in
plotted relationships (and previously discussed impacting factors)
Bigeye tuna
Yellowfin tuna
Bt+1=Bt+R+G-M
Recruitment (R)
Stock-Recruitment Curves – Basic Properties
Key point – SRR can vary depending on species.
Recruitment
Stock
Recruitment
Stock
Overcompensation
Recruitment
Recruitment
Density Dependance
Stock
Depensation
Compensation
Recruitment
Density Independance
Stock
Stock
Recruitment (R)
Bt+1=Bt+R+G-M
The Stock-Recruitment Relationship
However….
•
These results could be due in part to measurement error
•
Significant evidence that recruitment is reduced in overfished stocks
•
We also know if there is zero stock, there is zero recruitment!
•
Many examples where there is reasonable evidence for a stockrecruitment relationship
What is natural mortality (M)?
• Is the process of mortality (death) of fish due to natural causes
such as predation, disease, etc.
• Think of it as the removal of fish from a population
•Typically we are referring to mortality post recruitment (as
mortality in early stages is dealt with in recruitment estimation)
•Expressed as a rate (i.e. natural mortality rate).
• Rate is usually in proportions of the size/age class that suffer
natural mortality per time period
• Natural mortality rates are critical in understanding of the
relative impacts of fishing (e.g. compare natural v fishing
mortality rates)
• Permits some understanding of the “resilience” of a stock to
fishing (*More on this tommorow)
Natural mortality (M) [e.g. Hampton 2000]
BET
• M tends to decrease with age
[Fish ‘out-grow’ predators]
• May increase again in older fish
[‘Stress’ associated with reproduction]
SKJ
YFT
Why does M fluctuate?
• Natural mortality varies throughout the life-cycle of a
species
• Size/age – fish may “out-grow” predators (e.g. range
of predators of larval v juvenile v adult marlin)
• Senescence processes and Reproductive stresses
• Movement away from areas of high mortality
• Behavioural changes (e.g. formation of schools)
• Changes in ecosystem status (e.g. prey availability,
habitat availability)
• Changes in abundance (e.g. density-dependence
influences, like cannibalism, prey limitations)
•More on this later in the week!!
Growth
• All fish (organisms) grow
• Critical to fish as growth will influence a range of
biological characteristics (e.g. mortality, maturity etc)
• Critical to stocks as adds to biomass and influences
reproductive potential of a stock
• Critical to fisheries as influences catches (selectivity)
• Critical to management as influence sustainability
and reference points
Fish growth
• Typically fish show a deterministic, asymptotic growth
schedule
• Overall,
• Each species has a characteristic size-at-age path
• There is individual variability in size-at-age
• Each species can only attain a species-specific maximum
size
Fish growth
• Length – several periods (phases) of growth
Onset of maturity
Reduced growth of adults
Rapid growth of young fish
Growth
Thus, there are several factors in describing fish growth
• Maximum size that the species can obtain
• The rate of growth
• A starting size (e.g. hatching size)
•More on this later in the week!!
Basic population models
So far we have considered the processes that contribute to
change in population size over time, being:
1. Recruitment
2. Growth
3. Mortality
And placed them in a simple “model”:
Bt+1 = Bt + R + G – M
However, this is not a form of model that is typically used for
anything other than explaining the concept.
We will now discuss some simple population models commonly
used in studying population dynamics of many organisms.
Understanding these will lay the foundation for understanding
the more complex models we will spend a lot of time discussing
later in the workshop
Basic Population Models
Population growth models
1. Expontential growth model:
a. The simplest growth model
b. Growth rate proportional to population size!
c. Expressed as:
Nt = N0ert
140
Population size (nos)
120
Where r is the the intrinsic rate
of increase (or, rate of
natural increase, or,
population growth rate).
100
80
60
r = birth rate (recruit rate for
fish) – death rate (mortality)
40
20
0
1
2
3
4
5
Years
6
7
8
d. However, we know that most
populations have limited
resources!
Basic Population Models
2. Logistic growth model:
12000
dB/dt = rB(1-Bt/k)
Population size
10000
8000
6000
4000
2000
0
1
3
5
7
9
11
Year
13
15
17
19
Populations might show expontential growth pattern until resources become
limited and individuals compete for food….thus growth rate slows until
the upper limit, carrying capacity (K) is reach (zero growth)
Basic Population Models
**Excel Based Examples**
Other factors to consider in population
dynamics
Movements!
Which are in large part dictated by their ….
1. Physiology
2. Interactions with physical environment
Population model may often look at a population by sub area
and as such considering movement is important to understand
exchange between those parts.
Movement
Bt+1=Bt+R+G-M-C
Influences estimates of biomass etc at time, depending
on the balance of;
Movement = Immigration – Emigration
These estimates may vary with size/age, time of year,
etc
Critical in understanding dynamics, especially for HMS
In stock assessment we are typically assuming no
movement in or out of the total stock and therefore
consideration of movement mainly pertains to within
stock movement for spatially structured models
Why do fish move?
Biology
Maintain preferred habitat, oxygen flow, follow prey,
counter negative buoyancy
Ecology
Migration to spawning areas (e.g. SBT), ontogenetic
change in locations (e.g. albacore), response to seasonal
(e.g. albacore) or long term changes (e.g. skipjack) in
environmental/oceanographic conditions
Why are movement estimates important?
• Effects the distribution of biomass
•Movement is simply estimating the balance between
immigration and emigration of fish between model
regions in order to estimate biomass within an area or
model region
How is movement monitored?
0:1
1993
n = 622
0:1
1994
n = 1220
1. Size –frequency analyses
0:1
0:1
1995
n = 2371
0:1
0:1
1996
n = 2912
0:1
0:1
1997
n = 14582
Proportion
0:1
0:1 at length
0:1
0:1
0:1
1999
n = 22931
0:1
2000
n = 27188
0:1
2001
n = 40844
0:1
2. CPUE analyses
1998
n = 18962
0:1
0:1
2002
n = 29050
0:1
0:1
3. Tagging analyses
2003
n = 21350
0:1
0:1
2004
n = 16679
0:1
0.00 0.10
0:1
2005
n = 16162
0:1
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150
Length
(cm)
0:1
0
20S
10
20
0
30
40
20N
50
60
40N
Albacore
140E
160E
180
160W
140W
120W
100W
80W
1994
1996
1998
10
Bigeye
8
120E
d hooks)
40S
1992
2000
2002
2004
Summary
“To understand how populations will respond to exploitation, we
need to appreciate how they will behave when unexploited.”
Hillborn and Walters, 1992
Fish populations have natural variability, and depending on their
life history characteristics (fecundity, growth rates, natural
mortality) and the impacts of environment and stock on
these, can vary from extremely variable to showing relatively
small fluctuations in population size.
….you just cant escape the biology of the species! We’ll see in
tommorow mornings session just how critical species biology
is to their vulnerability to overfishing
Fished Populations
Accounting for fishing mortality in population dynamics
Bt+1=Bt+R+G-M -C
Recruitment
(+)
Death
(Natural mortality)
Whole population
(-)
(-)
Growth
(+)
Catch
(Fishing mortality)
Fishing and the “balance of nature” myth
The idea that nature (ecosystems and their living populations) is
in balance is a myth:
Ecosystems and the interactions between there components are
variable, and the range of variability itself varies depending
on the system and the component
The degree of variability very much depends on the time scale
we are considering a population over:
Fishing and the “balance of nature” myth
Sardine and Anchovy – Study of Scale deposition
in marine sediments
Environmental impacts on recruitment
tend to be significant drivers of
population variability for pelagic
species
Bigeye tuna – fishery impacts analyses of
estimated biomass with and without the
impacts of fishing (SC2 – SA WP-2, 2006)
Fishing impacts: Nature v Man
The relative impacts of natural factors versus fishing on fish
stocks has been debated for many decades:
Four key points:
1. It is dangerous to automatically ascribe changes in fishing
success to fishing itself….
…….there are many factors that can influence either stock
size, or the indicators used to track stock size, that are not
directly related to fishing
e.g. Case of South Pacific albacore) that are not
related to fishing.
Bt+1=Bt+R+G-M-C
Fishing impacts: Nature v Man
2. It is equally dangerous to assume that natural variability is
the key factor.
One might then miss an opportunity to implement changes to
the fishery that might ensure sustainability of catches and
stock recovery
3. The fact is, changes in populations over time are likely to be
influence by both fishing and by environment/other factors
e.g. Sardine in the Eastern Pacific Ocean
Fishing impacts: Nature v Man
4. It is the job of stock assessment to determine which factors
are having the highest impact (or at least, the impact of
fishing). The relative impacts of man will be dependant on
many different factors, which we will now discuss…….
5. A population’s response to its environment may in fact be
changed by the impacts of fishing so the two processes are
interrelated
e.g Increased growth and reproduction from reduced
competition for resources)
Population “states”
1. Stability versus instability of fished populations
Stability
Instability
Time
Time
Population size
Fishing catch
Skipjack
Population “states”
Resilience
“Natural systems are not stable but do exhibit changes within
certain bounds or regions of stability. A system with a large
region of desirable behaviour is called resilient”. (Hilborn and
Walters, 1991)
If a population has shown a capacity to regularly recover from
low population levels then it can be thought of as resilient.
If a population naturally varies within a fairly narrow population
range then reduceing the population below its lower
“boundary” (e.g. by introducing fishing) carries high risk….it
takes the population into a state where we have no idea how
it might react or whether it can recover.
Resilience in a fishing context is the capacity of a population to
sustain itself in the long term despite the added impact of
fishing at some given level.
Population “states”
How do we know how stable or resilient a population might be
without fishing it?.....we don’t!
Cant determine where or if a boundary state exists till you have
pushed past it.
However, we can learn from history!
We can also learn from our understanding of species biology!
Stability and Resilience
Examples:
Tropical Tunas
Sharks
Reproductive mode
Broadcast spawning
Internal fertilisation
Fecundity
Millions of eggs
~2-40 eggs/young
Growth rate
Fast
Varies, typically slower
Age to maturity
1-5 years (most spp)
6-7 years, up to 20 for
some
Life span
4-12 years
20-30 years
What can we imply or predict from these parameters regarding the relative
resilience of these species to fishing pressure?
Ref: Last and Stevens (1994)
Variations among WCPO tuna
Reproductive mode
Fercundity
Growth rate
Age to maturity
Life span
Recruitment to fishery
Reproductive mode
Fercundity
Growth rate
Age to maturity
Life span
Recruitment to fishery
Yellowfin
Bigeye
Serial spawning
2 million+
45-50cm (1yr)
2-3yr (100-110cm)
7-8yr
0.5-1yr(PS), ~2+yr(LL)
Multiple spawners
2 million+
40cm (1yr), 80cm (2yr)
3yr+ (100-130cm)
12+
0.5-1yr(PS), 2+yr(LL)
Albacore
Skipjack
?
0.8-2.6 million
30cm (1yr)
4-5yrs (80cm)
~9yr
~2yr(troll), 5+(LL)
Serial spawners
2 million+
44-48cm (1yr), 61-68 (2yr)
<1yr (44cm)
~4yr
0.5-1yr(PS)
Resilience: Importance of biology
Fish A
Fish B
Age to maturity: 1 years 2 years
Fishing Mortality: 2 per year (quota)
Natural Mortality: 0
Recruitment: 3/6 per year
Growth: 0
Fish A
1 years
Fish B
2 years
3 years
4 years
5 years
Resilience: Importance of biology
Fish A
Fish B
Age to maturity: 1 years
1 years
Fishing Mortality: 2 per year (quota)
Natural Mortality: 0
Recruitment:
3/6
1/6
Growth: 0
Fish A
1 years
Fish B
2 years
3 years
4 years
5 years
Adding “fishing” to our logistic
population model
We have already introduced some simple models for
unexploited populations. One of these was a logistic model,
which was adapted by Schaefer (1954) to account for the
impacts of fishing on a population over time:
Bt+1 = Bt + rB(1-Bt/k)-Ct
Where…
Ct = qEB
q = catchability = proportion of the stock
taken by one unit effort
E = Fishing effort
There are number of variations on this equation (e.g. Pella and Tomlinson
model)
Adding fishing to our logistic population
model
Ct = qEB
q = catchability = proportion of the stock
taken by one unit effort
E = Fishing effort
For example:
If we have a stock of 100 fish, and on average each unit of effort will take one
fish, then q = 1/100 = 0.01.
So if we put 20 units of effort in the water:
C = 0.01 x 20 x 100
= 20
If the fishers efficiency increased (e.g. they could catch two fish per unit effort)
then q increases, and C increases with it
C = 0.02 x 20 x 100 = 40
Adding “fishing” to our logistic
population model
Today we have discussed two key issues:
1. The importance of biological characteristics of species and
how these might relate to vulnerability to fishing pressure
2. The adaptation of population models to account for fishing
based exploitation of fish populations
We are now going to look at some Excel based examples of
some basic logistic models that encorporate fishing
impacts, and at how varying biological parameters can
influence how a population reacts to a given level of fishing
pressure.
1. Recruitment rate
2. Natural Mortality rate
Sustainability and overfishing
In the Excel based examples we have just looked at you will have
noticed:
Population size
R>Z
R=Z
R<Z
Time
When a population is at equiliberium, any further increase in Z (due to
fishing) will clearly cause the population to decline, continuously if
there is no other change in the system.
Hence fishing mortality at a level that keeps R = Z is sustainable over
time, fishing mortality that causes R<Z is not sustainable.
Sustainability and overfishing
A sustainable catch can exist at many different levels of stock size. If stock
size declines, sustainable catches might still be made, but at a lower level
than previously.
As we all know, one of the most common objectives in fisheries management
is to achieve Maximum Sustainable Yield (MSY).
This is the highest amount of catch that can sustainably be taken without
impacting the stock to such a degree that catch subsequently declines.
Sustainability and overfishing
An overfished fishery generally considered to be one in which the
current biomass (B) is less than that which would produce MSY. A
stock is considered “overfished” when exploited beyond an explicit limit
beyond which its abundance is considered "too low" to ensure safe
reproduction.
Overfishing is said to be occuring when the level of fishing mortality
(F) is greater than the level that would produce MSY. In general,
action of exerting a fishing pressure (fishing intensity) beyond agreed
optimum level. A reduction of fishing pressure would, in the medium
term, lead to an increase in the total catch.
These concepts will be discussed in depth further on in the workshop,
however it is useful to remind ourselves of them now
There are some problems with the use of MSY as an objective, but
these will also be discussed later
Sustainability and overfishing
Recruitment overfishing
A situation in which the rate of fishing is
(or has been) such that annual
recruitment to the exploitable stock
has become significantly reduced.
The situation is characterized by a greatly
reduced spawning stock, a decreasing
proportion of older fish in the catch,
and generally very low recruitment
year after year.
If prolonged, recruitment overfishing can
lead to stock collapse, particularly
under unfavourable environmental
conditions. Restrepo V. (1999):
Figure ref: http://www.oceansatlas.com/
Sustainability and overfishing
Growth overfishing occurs when too many small fish are being
harvested, usually because of excessive effort and poor selectivity (e.g. too
small mesh sizes) and the fish are not given the time to grow to the size at
which the maximum yield-per-recruit would be obtained from the stock.
A reduction of fishing mortality on juveniles, or their outright protection,
would lead to an increase in yield from the fishery.
Growth overfishing, by itself, does not affect the ability of a fish population
to replace itself.
Ecosystem overfishing
Occurs when the species composition and dominance is significantly
modified by fishing (e.g. with reductions of large, long-lived, demersal
predators and increases of small, short-lived species at lower trophic
levels).
Summary
Bt+1=Bt+R+G-M-C
1. Populations vary naturally. The scale of that variation often
depends on the time scale considered.
2. The impact of fishing on a populations dynamics and size
over time will depend in part on the inherent biological
properties of the population and what that confers about
resilience.
3. A key task for stock assessment scientists is to be able to
estimate the relative impact of fishing on the stock….whether
declines are due to fishing or environment will effect the
management decisions made
4. Understanding the likely impact of fishing on a population
requires understanding the biology of the species itself