Predation is a form of carnivory in which food items (prey) are searched for (or waited for), caught and killed.The chart below can be helpful in separating the types (adapted from text)īoth predation and herbivory are +.- species interactions in which one species benefits from the contact and one is harmed. Parasitism - feeding on another organism's parts without killing the organism (a note: parasitism is very widespread and includes all kingdoms as both parasite and host).The larvae complete development on the host, usually killing the host as a result Parasitoids - usually insects that lay their eggs on other insects as hosts.Cannibalism - eating one's own species - a specialized form of predation.Carnivory - meat eaters (other carnivores or herbivores).Herbivory - plant eaters, algae not usually considered but included.Several flavors of interaction fall under the above rubric: Press, Oxford.An interaction between two species in which one is harmed and the other helped Introduction to Ordinary Differential Equations with Mathematica. Cyclical behavior of predator and prey densities ( reasonable)īut cycle amplitude determined entirely by initial conditions ( unreasonable).(conversion of prey into baby predators - term b(aV)P in Eqn 23.2. Simple (unrealistic) assumption of linear numerical response of predator.Simple (unrealistic) assumption of linear functional response of predator to prey density (term aV in Eqn 23.1).Simple (unrealistic) assumption of exponential growth of prey in absence of predator (term rV in Eqn 23.1).Summary of Lotka-Volterra system of Eqns 23.1 and 23.2: The outer loops will take longer to go all the way round and speeds will change in different parts of the loops (e.g., fast predator crashes onthe left-hand edge of the outermost egg-shaped trajectory). A 'movie' of the trajectories would show dots moving around each of the loops above in endlesscycles. Here, in contrast, every initial condition will have itsown closed loop around which it cycles endlessly. Previously, with our competition equationanalyses, many different initial conditions would converge on a single equilibriumpoint (either stable coexistence or extinction of one or the other of the two species).

23.2 is sensitive to/dependent upon initial conditions. Springer-Verlag, NY and its ODE.m package.The behavior shown by Fig. I calculated the trajectories with Mathematica routines, aided by the Mathematica-based book: Gray, A., M. Note that for these parameter values, and starting with just 20 prey as the initial condition, the predator crash occurs along a line that is very close to prey extinction. The cycle is: prey explosion, prey crash, predator crash (with a slower rise in the predators happening along the 'width' of the egg-shaped orbit). Note that the trajectories are not circular because the prey grow more quickly than do the predators (maximum prey abundance is 5 times equilibrium, whereas maximum predator abundance is three times equilibrium). would stay at the point of intersection of the two isoclines (because that is the equilibrium point that is the focus for all the orbits). Again, our previous numerical response example (Fig. Numerical response by the predator that is a constant times the functional response (tells us how prey consumption is converted into baby predators). Linear functional response by the predator (more prey mean more eaten) - remember we had a curved functional response in the Bay-breasted Warbler example (Fig. The Lotka-Volterra predator-prey equations/graphs (continuous, differential equations)Įxponential growth of the prey in the absence of predation (like Eqn 4.5 and Fig. The first will be unrealistically simple. We will concentrate on just a couple of models. Why analyze predators and prey jointly?It seems reasonable to expect that abundant prey lead to increased predator numbers and that the converse is true for prey. Now we will turn to the classic Lotka-Volterra equations for jointly analyzing predator and prey dynamics. Last time I introduced the topic of predation (types, importance and indirect effects) and explored:ġ) Mesopredator effects on birds in California scrublandsĢ) Functional and numerical responses and the case history of Bay-breasted Warblers as predators of spruce budworm

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Predator vs prey graph