Mathematical models can be used to simulate the spreading of exotic marine species. Marine environments around the world are being threatened by exotic species of moon jellyfish being dispersed by international shipping and trade, according to research by staff at the School of Mathematics and Statistics, UNSW.

Using genetic data and computer simulations of ocean currents and water temperatures, researchers from the School of Mathematics and Statistics, UNSW and the University of California, Davis, have revealed that the jellyfish could not have migrated naturally. The species of Jellyfish studied are known as Aurelia (Fig. 1) and these are found over much of the world’s temperate oceans.

By simulating the movement of the jellyfish (shown in Fig. 2) over a 7,000-year period the study provides strong evidence that the world-wide dispersal post-dates European global shipping and trade, which began almost 500 years ago.

To investigate the limits of natural dispersion of species of the moon jellyfish over multi century time scales, the researchers developed a global Lagrangian model incorporating representative life-history characteristics of the moon jellyfish.

The researchers used both the known lifecycle of the moon jellyfish and climate and ocean current information to create a mathematical model of their dispersion over time. Each experiment was based on the virtual release of 20 000 lavae from known moon jellyfish zones of occurrence (see red coastal zones of Fig. 2). The model can be summarised by:

In the formula x_t is the moon jellyfish location at time of t, U is the current speed, Δt is time, R_n is a normal distributed random number, and K_h is a lateral mixing rate and C_mix is tidal mixing near the coast. The model is then integrated and the results can be shown on a global map of dispersal (Fig. 2 below). During the model integration, biological processes such as temperature limits, mortality, re-settlement and spawning are included to take account of the life cycle of the jellyfish. The red areas show virtual release points off the coast of Australia, around Japan, United States and Europe.

Unnatural migration occurs via ballast water from international shipping and because of international trade of marine species.

About 3,000 species of marine organisms are believed to travel the world in ships' ballast water on a daily basis. Ships take in water for stability before a voyage and, despite preventative measures such as mid-ocean exchange/ flushing, this 'foreign' water and its contents can find its way into bays and harbours at the ships destination.

The computer model could answer similar questions about the migration and introduction of any suspected non-native marine creatures, according to its developers Professor Matthew England and Alex Sen Gupta.

"Up until now our knowledge of natural and human-assisted dispersal of species has been insufficient to confidently track and predict the spread of non-indigenous marine species," Now we have a tool that can include data on currents, geography and the biology of an organism to help separate natural dispersal from that which happens through shipping and trade," says Professor England.

Dawson M.N., A. Sen Gupta, and M.H. England, 2005: Coupled biophysical global ocean model and molecular genetic analyses identify multiple introductions of cryptogenic species. Proc. Nat. Acad. Sciences, 102, 11968-11973. - http://www.maths.unsw.edu.au/~matthew/DSGE_2005.pdf

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