Predator-prey

In 1914, F. W. Lanchester introduced a set of coupled ordinary differential equations-now commonly called the Lanchester Equationsl (LEs)-as models of attrition in modern warfare. Similar ideas were proposed around that time by [chaseSS] and [osip95]. These equations are formally equivalent to the Lotka-Volterra equations used for modeling the dynamics of interacting predator-prey populations [hof98]. The LEs have since served as the fundamental mathematical models upon which most modern theories of combat attrition are based, and are to this day embedded in many state-of-the-art military models of combat. [Taylor] provides a thorough mathematical discussion. 

Figure 11.4. (a) Flow-model scheme for a simple food chain with one predator-prey relationship. See text for discussion, (b) The steps involved whereby atoms from prey collagen (i.e., the diet) may be transferred to a predator s collagen (i.e., the consumer tissue). Each arrow represents a potential change in carbon isotopic composition, complicating the relationship between prey collagen 5 C and predator 5 C. 

In a similar way, an integrated biomarker approach has a role when carrying out experiments in mesocosms. Under these controlled conditions, behavioral effects of neurotoxic pollutants, acting singly or in combination, can be monitored and compared with data on predator-prey relationships and effects at the population level. The employment of mechanistic biomarker assays can facilitate comparisons between results obtained in mesocosms and other data obtained in the field or in laboratory tests. Here is one way of attempting to answer the difficult question— how comparable are mesocosms to the real world ... 

Section 4.5). Of these, mesocosms have stimulated the greatest interest. In these, replicated and controlled tests can be carried out to establish the effects of chemicals upon the structure and function of the (artihcial) communities they contain. The major problem is relating effects produced in mesocosms to events in the real world (see Crossland 1994). Nevertheless, it can be argued that mesocosms do incorporate certain relationships (e.g., predator/prey) and processes (e.g., carbon cycle) that are found in the outside world, and they test the effects of chemicals on these. Once again, the judicious use of biomarker assays during the course of mesocosm studies may help to relate effects of chemicals measured by them with similar effects in the natural environment. 

Internal regulatory processes (e.g. predator-prey interactions) Large habitat areas and spatial linkages between ecosystem Ecological gradients... 

Elvira B, Nicola GG, Almodovar A (1996) Pike and red swamp crayfish a new case on predator-prey relationship between aliens in central Spain. J Fish Biol 48 437 146... 

Ham, L., R. Quinn, and D. Pascoe. 1995. Effects of cadmium on the predator-prey interaction between the turbellarian Dendrocoelum lacteum (Muller, 1974) and the isopod crustacean Asellus aquaticus (L.). Arch. Environ. Contam. Toxicol. 29 358-365. 

Many scents are chosen on the basis of assumed relevance to the test subject. Interest in the scent of a predator, prey, mate or natural environment will be affected by the animal s familiarity (previous experience) with the scent, and the motivation to... 

Calderisi, D. (1997) Different scents for different responses in predator-prey relationships as a form of enrichment in captive animals. In V. Hare and K. Worley (Eds.), Proceedings of the Third International Conference on Environmental Enrichment, Sea World, Florida, pp. 155-161. 

Brizzi, R., Delfino, G. and Pellegrini, R. (2002) Specialized mucous glands and their possible adaptive role in the males of some species of Rana (Amphibia, Anura). J. Morph. 254, 328-341. Chen, C. and Osuch, M. V. (1969) Biosynthesis of bufadienolides - 3Bhydroxycholonates as precursors in Bufo marinus bufadienolides synthesis. Biochem. Pharmacol. 18, 1797-1802. Chivers, D. P. and Smith, R. J. F. (1998) Chemical alarm signalling in aquatic predator-prey systems a review and prospectus. Ecosci. 5, 338-352. 

A particularly large and varied class of eavesdroppers includes prey species that learn of impending danger from chemical signals disseminated by their predators. Prey responses to these warning... 

We demonstrate the use of Matlab s numerical integration routines (ODE-solvers) and apply them to a representative collection of interesting mechanisms of increasing complexity, such as an autocatalytic reaction, predator-prey kinetics, oscillating reactions and chaotic systems. This section demonstrates the educational usefulness of data modelling. 

Figure 3-35. The concentration of wolves plotted versus the concentration of sheep in the Lotka-Volterra predator-prey kinetics.

A detailed predator-prey analysis of the chemical relations between the carabid Pasimachus subsulcatus and the skink Eumeces inexpectus proved that the latter were repelled by constituents of the carabids secretions, indicating that the beetles are chemically protected from attacks by the lizards [85]. 

How is Le Chatelier s principle related to predator-prey interactions in ecosystems ... 

An inventory of known biomacromolecules is provided in Table 22.3. Many of these play essential metabolic roles in enabling growth and reproduction, such as the carbohydrates, lipids, proteins, and polynucleotides. Others are components of cell walls and exoskeletons. Some organisms, such as bacteria, plankton, plants, and lower invertebrates, synthesize biomolecules, called secondary metabolites, that are used to control ecological relationships, including predator/prey, host/symbiont, mating/spawning, and competition for food or space. 

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]. 

From a mathematical point of view, the onset of sustained oscillations generally corresponds to the passage through a Hopf bifurcation point [19] For a critical value of a control parameter, the steady state becomes unstable as a focus. Before the bifurcation point, the system displays damped oscillations and eventually reaches the steady state, which is a stable focus. Beyond the bifurcation point, a stable solution arises in the form of a small-amplitude limit cycle surrounding the unstable steady state [15, 17]. By reason of their stability or regularity, most biological rhythms correspond to oscillations of the limit cycle type rather than to Lotka-Volterra oscillations. Such is the case for the periodic phenomena in biochemical and cellular systems discussed in this chapter. The phase plane analysis of two-variable models indicates that the oscillatory dynamics of neurons also corresponds to the evolution toward a limit cycle [20]. A similar evolution is predicted [21] by models for predator-prey interactions in ecology. 

R. M. May, Limit cycles in predator-prey communities. Science 111, 900-902 (1972). 

Dicke M, Vanbeek TA, Posthumus MA, Bendom N, Vanbokhoven H, Degroot AE (1990) Isolation and identification of volatile kairomone that affects acaiine predator-prey interactions -involvement of host plant in its production. J Chem Ecol 16 381-396... 

Acidification of acid-sensitive waters is accompanied by severe changes in biological communities. Effects range from reductions in diversity without changes in total biomass to elimination of all organisms. In many cases the immediate cause of the changes is unknown. Some effects are the result of H" toxicity itself or of the toxicity of metals mobilized from the watershed, others have more indirect causes such as changes in predator-prey interactions or in physical conditions of lakes (ex. transparency). [14]... 

Prey fish may mask their own odors. Some marine fish avoid predation by covering their body odors. Some parrot fish (Scaridae) sleep in a mucus cocoon. It is believed that this covers up its scent and protects it from predation. Table 12.1 summarizes some chemical predator-prey relationships in marine fish. 

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