Transcript Spatial and Temporal Patterns in Modeling Marine Fisheries

Spatial and Temporal Patterns
in Modeling Marine Fisheries
Heather Berkley
Outline
 Chapter 1: Spatial and temporal patterns in a spatial
fisheries model with stochastic dispersal
 Spatial & temporal patterns of model with and without fishing
 How the spatial pattern of fishing impacts population dynamics
 Find optimal harvest level for each harvest strategy
 Chapter 2: Age-structured population model with spatial
and age-targeted harvest
 Add age-structure to population model
 Impose age/size-specific harvest
 Determine optimal harvest strategy for age-structured model
 Chapter 3: Multi-species fishery: spatial and temporal
patterns impacting coexistence & storage effect
 Model 2 interacting species
 Determine requirements for coexistence
 Evaluate management strategies, including separate policies
Motivation for Research
Fisheries are in decline due to overfishing
Questions:
How to maintain sustainable levels of fish
How and where fish disperse
How different fishing policies impact the
populations
How spatial & temporal variability impacts
population dynamics
Use the answers to better inform fisheries
management
This Fisheries Model
Single species, near shore fishery
Linear coastline
Sessile adults
Dispersal only in larval stage
Homogeneous ocean with realistic ocean
velocity statistics
An integro-difference model describing
coastal fish population dynamics:
# of adults at x
in time t+1
# of adults
harvested
Natural mortality of
un-harvested adults
Axt 1  Axt  H xt  M (Axt  H xt )
  (A  H ) Fx ' L K x  x ' R
t
x'
t
x'
t
x
all x '
Fecundity
Larval survival
Larval dispersal
# of larvae that successfully recruit
to location x from everywhere
Fraction of
settlers that
recruit at x
Stochastic Dispersal
 Physical oceanographers (Davis 1985, Poulain and Niiler
1989, Dever et al. 1998) say:
 On average, flows become decorrelated
 on a temporal scale of about 3 days
 on a spatial scale of 10-50 km
 So, larvae released in a region within a few days tend to
travel together
 Annual recruitment may be a small sampling of a Gaussian
dispersal kernel
 E.g. From 100 independent releases, 10% may make it back to shore
within competency window
 This “spiky” recruitment better fits empirical larval settlement data
 If there is larger spatial correlation in dispersal,
 Groups of larvae are larger
 “Packets” will be released from a region and settle together
 Connections among sites are stochastic and intermittent
Basis for Packet Model
 Number of packets released:
 Tsp  D 
  S
N  
 Tl  r 
 Tsp = duration of spawning season
(days):
 Tl = Lagrangian decorrelation time
scale (days):
 D = size of the domain (km)
 r = Rossby radius (km)
 S = survival probability of packet
“Spiky” or “Packet” vs. Diffusive Dispersal
 In “spiky” model, single
locations serve as
sources & destinations
 In “packet” model,
many adjacent
locations serve as
sources & settlement
locations
Spatial & Temporal Patterns
 Packet model has spatial autocorrelation the size of
the settlement “packet”
 Positive temporal autocorrelation for long-lived adults
for 3-4 years
(B)
Fishing policies
 1. Constant Effort
 Same fraction of adults is harvested (H) at all locations
 2. Constant TAC
 TAC set for the whole region: (H) (virgin K) (size of
domain)
 effort concentrated on locations with most fish
 3. Constant Escapement
 Escapement level same for each location: (1 - H)
(virgin K)
 4. Constant Local Harvest
 TAC set for the whole region, divided equally among
all locations
Pattern of Spatial Variance
For all 4 harvest policies:
Variance in Recruitment increases with harvest
due to decrease in post-settlement density
dependence
Combination of variance in Recruitment and
Escapement determines variance in Adults
Spatial pattern of harvest determines how
variance in escapement changes with
increased fishing pressure
Future steps
 Determine optimal harvest level for each policy
Plot mean harvest vs. harvest fraction and take
maximum
 Investigate the impact of different types of
density dependence
Post-settlement recruitment due to adult density
Post-settlement recruitment due to larval density
Reduced adult survival due to adult density
Reduced adult fecundity due to adult density
Chapter 2. Age-Structured Model
 Demographic characteristics are not constant
throughout life
 Especially important in fisheries b/c older
females can produce many more larvae than
younger, smaller females
 Age-Structured model allows different ages to
have different demographic parameters
 Often used when evaluating marine reserves,
but also applicable to evaluating other types of
management
Age-Structured Rockfish model
Sebastes jordani, shortbelly rockfish
M=0.2 - 0.35 yr -1
Fecundity increases with age & weight
Abundant but not heavily fished on
California coast
Growth

W  W 1  e
 K T t0 


 W  asymptotic weight (g)
 K = instantaneous growth
coefficient
 T = age (yr)
 t0 = x-intercept
W  248.11  e
 K 0.285 T 1.48 
Weight (g)
 Von Bertalanffy growth

Age (yr)
2.98
(Ralston et al 2003)
Fecundity
logF   log   logW 
logF   3.8155  1.1416 logW 
(Ralston et al 2003)
Size-Specific Harvest
 Use age and size relationships to assign a
length to fish
 Allow harvest of specific sizes:
Minimum size limit
Maximum size limit
Slot limit
 Harvest will change age-structure of population,
which will impact the future productivity of the
population
Size-Specific Harvest
Determine optimal size limits for different
size-specific management
Compare to 4 non size-related
management and marine reserves
Evaluate the value of using an agestructured model vs. more simple model
Ch 3. Multi-Species Fisheries
 Many species of fish and invertebrates in
nearshore communities are fished
 Interactions through a shared resource can
impact the population dynamics of other species
 Changing the abundance through fishing alters
the intensity of the interactions between species
 It is important to study how these interactions
are influenced by stochastic dispersal
Temporal Variability
 Temporal variability in settlement and
recruitment propagates up through age classes
 Long-lived adults buffer the population against
drastic decline when recruitment does not occur
consistently
 Inter & intraspecifc competition decreases
recruitment of all species
 Temporal changes in settlement alters the
intensity of competition
Eg. good environmental conditions promote settlement,
which increases the competition between larvae
This is called “covariance between environment and
competition”
Storage Effect
 Species at high density experiences more
intraspecific competition
 Species at lower density experiences mostly
interspecific competition, but its density is low
Higher growth rate
Allows for coexistence
 Storage Effect occurs when long-lived adults
buffer against too much variation and difference
in population sizes and gives a growth rate
advantage for the species at lower density
Spatial Variability
 Species have different preferences to environmental
conditions
 Overtime, population size will increase in the most
favorable locations
 Spatial pattern of habitat suitability generates differences
in the strength of competition between species of
different densities
 Species at low density experiences less interspecific
competition in good habitat locations because the other
species is more likely to be somewhere else
 Higher growth rate
 Allows for coexistence
Spatial Storage Effect
 Covariance between environmental conditions
and competition is stronger for the species at
higher density
 Difference in between the covariances
establishes the “spatial storage effect” and
facilitates coexistence
 Short-distance dispersal increases the
covariance because it causes populations to
build up in nearby locations
Multi-Species Model
 2 species with similar life-histories
 Test the impact of temporal & spatial variability
on coexistence by changing:
Duration of spawning
Dispersal distance
 Evaluate the impact of different spatial patterns
of harvest on both fisheries
With same type of management
With different types of management
Marine Reserves