Examples predator-prey

An innate ability to recognize natural predators is frequently tested in zoo animals, often offering contradictory results (e.g. Buchanan-Smith, Anderson and Ryan 1993 Boon 2003). Some authors only advocate the use of scents that are relevant to a zoo animal in the wild for example, natural prey and adversary species faeces, as used for olfactory enrichment in African lions (Baker, Campbell and Gilbert 1997 Schuett and Frase 2001). Most scents used occur in some form in the natural environment, although not necessarily the natural environment of the test... 

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

In biological dissipative structures, self-oiganization may be related to the attractors in the phase space, which correspond to ordered motions of the involved biological elements (De la Fuenta, 1999). When the system is far from equilibrium, ordering in time or spontaneous rhythmic behavior may occur. The Lotka-Volterra model of the predator-prey interactions is a simple example of the rhythmic behavior. The interactions are described by the following kinetics... 

The Lotka-Volterra model of the predator-prey interactions is a simple example of the rhythmic behavior. The interactions are described by the following kinetics... 

The Lotka-Volterra model is often used to characterize predator-prey interactions. For example, if R is the population of rabbits (which reproduce autocatalytically), G is the amount of grass available for rabbit food (assumed to be constant), L is the population of lynxes that feeds on the rabbits, and D represents dead lynxes, the following equations represent the dynamic behavior of the populations of rabbits and lynxes ... 

Any effects on populations may ultimately be manifested as effects on communities because, by definition, communities are collections of interacting populations of several species (e.g., an aquatic community may consist of populations of fish, worms, plants, insects). Individual populations within a community may interact by competing for resources (food, habitat, etc.) or by predator/prey relationships. Environmental contaminants can affect the structure of communities as well as the interactions of species within them. For example, it is well known that exposure to chemicals may cause a reduction in community diversity (e.g., relative number of species), and changes in community composition. In addition, the trophic structure of fish and invertebrate communities may also be affected by exposure to anthropogenic chemicals. Changes in community structure and diversity may be determined by field sampling or manipulative studies. Alternatively, computer simulations using food web or linked population models may be used to assess community-level effects. 

Such models describe the life history of animals as propagation through the different size or mass classes and need a sophisticated formulations of predator-prey interaction. There are several approaches to describe life histories of copepods by models (Carlotti et al., 2000). A new theoretical formulation to allow the consistent embedding of dynamical copepod models into three-dimensional circulation models was given in Fennel (2001). Examples of simulations for the Baltic were given in Fennel and Neumann (2003). The basic idea is that both biomass and abundance of different stages or mass classes are used as state variables, while the process control is related to mean average individuals in each mass class, that is the ratio of biomass over abundance. 

Example 14.2. Foxes and rabbits. Predator-prey fluctuations are well-understood periodic phenomena in nature as well as the basis of board games such as Struggle or Foxes and Rabbits [9]. In terms of these Grass grows as available area permits, rabbits feast on grass and multiply when doing so, foxes feast on rabbits and multiply when doing so, and hunters in constant number shoot foxes. 

A reaction may be periodic if its network provides for restoration of a reactant or intermediate that has been depleted, while conversion of main reactants to products continues. Periodic behavior often results from competition of two or more contending mechanisms. Predator-prey fluctuations in ecology (Lotka-Volterra mechanisms) provide an easily visualized example. The Belousov-Zhabotinsky reaction—catalyzed oxidation of malonic acid by bromate—involves a similar competition between two pathways. 

Examples include multiple steady states in isothermal CSTRs, predator-prey fluctuations, the Belousov-Zhabotinsky reaction, and a test for stability of quasi-stationary states in reactions with a self-accelerating intermediate steps. 

The term f(P)Z in (3.71), when f P) is given by (3.74), leads formally to the Michaelis-Menten dynamics (3.39), if Et is identified with the predator density and P with the substrate. This analogy has been elaborated in the literature. For example Real (1977) describes predator-prey dynamics with the Michaelis-Menten scheme (3.27), with S the prey, C the intermediate state of the prey when it is eaten, E is the predator searching for food and P is the new predator biomass produced during the consumption process, so that Et = E + P is the total amount of predator. This leads to a justification... 

The presence of the same or closely related compounds in multiple phyla in instances in which a predator/prey relationship cannot be established for the organisms. The isolation of p3oidinoacndine alkaloids, such as dercitamide (Scheme 24), from both the sponge Dercitus sp. and the ascidian Cystodytes (47) is an example of this. 

Parts III, IV and V deal with the distribution of trace elements in biota and reservoirs (soils and sediments). In this context, it should be noted that organisms, populations, biocenoses and finally the entire ecosystem are influenced by a number of different biotic and abiotic stressors under natural conditions. These are for example climatic changes, variations in radiation regimes or availability of food resources, predator-prey relationships, parasites, diseases, intraspecific and interspecific competition. Stress is an existential prerequisite for all biological levels of organization, as it... 

Some biological responses are periodic, varying in a predictable manner between two limits. The firing of certain nerve cells and the levels of circulating hormones are two examples of periodic responses. Another example is predator-prey population dynamics (see also Section 6.20.3). Oscillatory behavior (Figure 4.3.2) is described mathematically by combinations of sines and... 

KainmHMies. Name, derived from the Greek kairos (= favorable condition, advantage + hormone), for signalling substances ( semiochemicals) acting between individuals of different species with attractant effects, in contrast to within-species pheromones (see also al-lelochemicals, allomones, insect attractants), providing an advantage for the recipient. Example Predators of bark beetles locate their prey on the basis of the attractants produced by the latter to attract members of their own species. 

Now the question is how to construct the simplest model of a chemical oscillator, in particular, a catalytic oscillator. It is quite easy to include an autocatalytic reaction in the adsorption mechanism, for example A+B—> 2 A. The presence of an autocatalytic reaction is a typical feature of the known Bmsselator and Oregonator models that have been studied since the 1970s. Autocatalytic processes can be compared with biological processes, in which species are able to give birth to similar species. Autocatalytic models resemble the famous Lotka-Volterra equations (Berryman, 1992 Valentinuzzi and Kohen, 2013), also known as the predator-prey or parasite-host equations. 

In a forest, the rabbit and wolf populations balance each other, including many other components of the overall ecosystem. For the sake of simplicity, we will focus only on the rabbits and foxes. The growth rate of the rabbit population is a function of two parameters the birth rate of the rabbits and the rate that rabbits expire. The latter depends strongly on the wolf population, if the wolves are the only predators of the rabbits in this virtual environment. If the wolf population is large, they consume a large amount of rabbits, which brings the rabbit population to a level of extinction. Eventually, the wolf population declines due to the scarcity of the rabbits. Once the wolf population declines, without the predators, the rabbit population increases, which then improves the wolf population. In this particular example, the prey has a constant supply of food (open systan) otherwise, the system rapidly reaches equilibrium. 

Dynamic behavior and oscillations are also found in nature, such as predator-prey interactions. A classical example of interacting populations is shown in Figure 4.10.30 for the snowshoe hare and the Canadian lynx, a specialist predator. The lynx-hare... 

Sometimes chemical problems can be answered using the knowledge from other sciences that are not related to chemistry at first sight. For example, some information about a complex reactions flow can be gained from the mathematical models of the interspecific competition. A classical example is the predator-prey model, which describes the population trends for predators and prey in living conditions... 

Even though the predator-prey model is rather idealized, many kinetic models for real chemical systems are based on it. For example, D.A. Frank-Kamenetsky used the Lotka-Volterra model to explain the processes of higher hydrocarbon oxidation. 

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