A large number of South Africa's elephants can be found on small wildlife reserves. The large nutritional demands and destructive foraging behavior of elephants can threaten rare species of vegetation. If conservation management is to protect threatened species of vegetation, knowing how long elephants will stay in one area of a reserve as well as which area they will move to next could be useful. The goal of this study was to train a recurrent neural network to predict an elephant herd's next position in the Pongola Game Reserve. Accurate predictions would provide a useful tool in assessing future impact of elephant populations on different areas of the reserve. Particle swarm optimization (PSO), PSO initialized backpropagation (PSO-BP) and PSO initialized backpropagation through time (PSO-BPTT) algorithms are used to adapt the recurrent neural network's weights. The effectiveness of PSO, PSO-BP and PSO-BPTT for training a recurrent neural network for elephant migration prediction is compared and PSO-BPTT produces the most accurate predictions at the expense of more computational cost.