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 dynamicsUse the answers to better inform fisheries

management

This Fisheries Model

Single species, near shore fisheryLinear coastlineSessile adultsDispersal only in larval stageHomogeneous ocean with realistic ocean

velocity statistics

'''''

all x

txxxx

tx

tx

tx

tx

tx

tx

1tx

R L K) FH(A

)HM (AHAA

# of adults at x in time t+1

# of adults harvested

Natural mortality of un-harvested

adults

FecundityLarval survivalLarval dispersal

Fraction of settlers

that recruit at x

# of larvae that successfully recruit to location x from

everywhere

An integro-difference model describing coastal fish population

dynamics:

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 = 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

Sr

D

T

TN

l

sp

“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

(B)

Packet model has spatial autocorrelation the size of the settlement “packet”

Positive temporal autocorrelation for long-lived adults for 3-4 years

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 rockfishM=0.2 - 0.35 yr -1

Fecundity increases with age & weightAbundant but not heavily fished on

California coast

Growth

Von Bertalanffy growth

asymptotic weight (g) K = instantaneous growth

coefficient T = age (yr) t0 = x-intercept

0tTKe1WW

982481T2850Ke11248W....

Wei

ght

(g)

W

Age (yr)

(Ralston et al 2003)

Fecundity

WF logloglog W1416181553F log..log

(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 age-structured 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