1
Department of Geography and Environmental science, 2 School of Biological Sciences, 3 CEFAS, 4 SPFA
Modelling mackerel using remotelysensed estimates of plankton and
temperature
Rob Boyd1 | Shovonlal Roy 1 | Richard Sibly 2 | Robert Thorpe 3 | Kieran Hyder 3 | Steve Mackinson 4
Emergent population dynamics
Mackerel are a commercially important fish in the northeast Atlantic.
Management of the stock has become difficult, as changing sea
temperature and the availability of plankton (food) has expanded its
range north-westwards into waters outside of current fishing
agreements. Here we present an Individual-Based Model (IBM), in
which the effects of plankton availability and temperature on
individual mackerel are described. From this emerge the population
dynamics and spatial distribution, which can be used to inform
management, help make predictions about future change and better
understand the system.
Food and temperature
08/03/12
Biomass (tonnes)
Introduction
24/03/12
16/03/12
Figure 3a) a typical year’s fluctuation in Total Stock Biomass (TSB) and Spawning Stock Biomass (SSB), b)
a preliminary comparison of predicted TSB vs that from the stock assessment and c) the same for SSB
Figure 1) the model interface on 3 dates in March 2012, showing the change in SST
Remotely-sensed data on plankton and temperature is used to create a
spatio-temporally changing map, in which the mackerel live. The
spatial extent spans most of the stock’s geographical range in the
northeast Atlantic.
The model is close to describing population characteristics like the
biomass of spawners (SSB) or of the whole stock (TSB), recruitment, the
number of eggs produced and the size distribution.
Emergent spatial distribution
How does an individual’s environment affect its success?
Maintenance
Reserves
Ingestion
Assimilation
𝑎𝑋
𝐼𝑅 =
𝑀2/3 𝐴(𝑇)
1+𝑎ℎ𝑋
Reproduction
Growth
𝑀𝑅 =
3
𝑆0 𝑀4
⃝Overwintering
⃝ Feeding
⃝ Spawning
𝐴 𝑇 , 𝑛𝑜𝑡 𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑛𝑔
3
𝐴0 𝑀 4
𝑆𝑎 𝐴(𝑇) , 𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑛𝑔
Proportion of available energy
𝐹𝑝 𝑀0 (𝐸𝑐 + 𝐸𝑠
𝑅𝑝 =
𝐴(𝑇)
𝐷𝑟
∆𝑀 = 𝐾 𝐴 𝑇 (𝐿00 − 𝐿)
Figure 2) the energy budget through which the acquisition and distribution of energy is described. A(T)
is the Arrhenius function which describes the effect of temperature on each of the rates
The acquisition and use of energy from food is described using an energy
budget. The order of priority given to the processes depends upon life
stage and the time of year, and all depend upon temperature. Metabolic
costs must be covered, but growth and reproductive rates can be
adjusted if energy is limited.
Figure 4a) Current model zones and adult migration route and b) landings per unit effort data in the
overwintering area (red) and the mean no. of adults in the model overwintering area by year and quarter.
(datasets are on different scales)
Adults cycle between spawning, feeding and overwintering grounds.
Arrival times in each area emerge from an individual’s swimming speed,
which is a function of body length and thus growth. The effects of
temperature on migrations are soon to be incorporated.
What next?
• Expansion of the spatial extent to encompass all feeding areas
Contact information
• Department of Geography and Environmental Sciences, University of Reading, Whiteknights, RG6 6AH
• Email: [email protected]
• Website: ibmreading.wordpress.com/
• Incorporation of temperature-driven migration rules
• Calibration of the parameter set using Approximate Bayesian
Computation (ABC)