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

# of adults at x in time t+1 # of adults harvested Natural mortality of un-harvested adults Fecundity Larval survival Larval 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 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:  T sp = duration of spawning season (days):  T l = 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 (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 rockfish M= yr -1 Fecundity increases with age & weight Abundant but not heavily fished on California coast

Growth Von Bertalanffy growth  asymptotic weight (g)  K = instantaneous growth coefficient  T = age (yr)  t 0 = x-intercept Weight (g) Age (yr) (Ralston et al 2003)

Fecundity (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