Using maths to predict the movement of animals 🐆🦓🦍🐘

We can use mathematical modelling to predict the movements of many species in the wild 🐾🐾. But first…why is it important for us to be able to do this?! 🤔Well, knowing how and why animals move through their environment has huge ecological, behavioural and evolutionary ramifications such as those in social interactions, spread of disease, gene flow and migration.
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Now for the maths! 🤗 To make a model, we start by collecting some data through tracking the animal in question 💻. This technology may, for example, give us the position of the animal at each minute during an hour 🕰. We can then plot these movements in (x,y) coordinates. Since we only have the position of the animal every minute (and not every second or nano second etc), the path we obtain will be jagged where each ‘step’ goes to the next in a straight line with a given distance and angle📉📈. Using this path, we can create graphs📊 (histograms) showing the likelihood’s of different step distances and angles.
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We use this information to
make our model by telling the computer each of the step lengths and angles that are possible, but also that some should be more likely to be chosen than others! 💻✔️
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While this is the basis of our model, we can also include other information we know about the preferences of how a particular animal in question moves. For example, leopards 🐆 like to be on their own so may be more likely to move away from areas with other leopards, but elephants 🐘🐘🐘 are social and live in groups so are more likely to be looking for their friends. Jaguars like hiding in the cover of the trees so may be more likely to head deep into forests 🌳; however, meerkats would more likely prefer to sunbath in the open ☀️. Many other factors could also be considered, including predation risk, weather, foraging ability etc!
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To make our model a little easier, we break up the area we are looking at into a grid 🌐 (to reduce the number of spots the animal can move to from its current position). We give each square of the grid a value for each of the characteristics above between 0-1 i.e. close to 0 = low foraging ability (not much food in the area) and near to 1 = very good foraging ability (lots of food here!)🥜
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Finally we can assign a probability that the animal will move to each of the squares by…multiplying the probability of its distance ✖️ by the probability of its angle ✖️ by the values for the other preferences (numbers between 0-1) and divide ➗ this by the sum of the probabilities of each square in the grid. By repeating this method our model is able to make predictions about an animals route, providing essential knowledge for a wildlife conservationist 🐾🐾🐾
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#appliedmathematics #usingmaths #mathbiology #ecology #conservation #evolution #helpinganimals #stem #keeplearning #scicomm