In population dynamics, the term "zero-growth isocline" refers to the set of population sizes at which the rate of change for one population in a pair of interacting populations is zero. [1] However, this is rare and a more common term is nullcline .
What is a zero-growth isocline?
The zero-growth isocline describes expected equilibrium population sizes of one species if abundance of the second species is held constant, and vice versa. The relationship between the two species is assumed to be linear, i.e., the isoclines for species 1 and species 2 can be written as equations for a straight line (y = a + bx).
What is isocline in ecology?
Other uses. In population dynamics, the term "isocline" refers to the set of population sizes at which the rate of change for one population in a pair of interacting populations is zero. Hanski, I. (1999) Metapopulation Ecology.
What is the meaning of ISO line?
Other uses. In population dynamics, the term "isocline" refers to the set of population sizes at which the rate of change for one population in a pair of interacting populations is zero.
How do you find the isocline of an equation?
Isocline. In an equation of the form y' = f ( x, y ), the isoclines are lines in the ( x, y) plane obtained by setting f ( x, y) equal to a constant. This gives a series of lines (for different constants) along which the solution curves have the same gradient. By calculating this gradient for each isocline, the slope field can be visualised;
What does an isocline represent?
The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation is, a curve with equation for some constant is known as an isocline. In other words, all the solutions of the ordinary differential equation intersecting that curve have the same slope. .
What is isocline in Lotka Volterra?
The isocline for each species i is the line on the N 1 / N 2 phase plane where dN i / dt = 0. Joint equilibria are shown as. Source publication. The struggle for existence: How the notion of carrying capacity, K, obscures the links between demography, Darwinian evolution, and speciation.
What is an isocline biology?
isocline A line joining points on a graph at which combinations of resource levels or population densities produce a similar rate of population growth for a particular species. A Dictionary of Ecology.
What is an isocline map?
An isocline is a curve that starts from the origin and passes through the isoquant map of the firm, and along which the marginal rate of technical substitution of input X for input Y, i.e., the numerical slope of the isoquants is constant.
How is isocline calculated?
An isocline is a set of points in the direction field for which there is a constant c with dy dx = c at these points. Geometrically, the direction field arrows at the points of the isocline all have the same slope. Algebraically, we find the isocline for a constant c by solving f(x, y) = c.
What is the Lotka-Volterra model used for?
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
How do you graph an isocline?
0:512:49Sketch an Isocline for a Differential Equation - YouTubeYouTubeStart of suggested clipEnd of suggested clipThese 4 horizontal lines well the best way to do it would be with this vertical line right here andMoreThese 4 horizontal lines well the best way to do it would be with this vertical line right here and this line would be the isocline. So again sometimes it ends up being a curve.
How is an isocline applied in economics?
Each isocline line reflects all points with the same slope of gradients (the term "isocline lines" is also known as "expansion path" in economics). The maximum growth line (or stream line) shows the optimal path defined by changing the slope of the gradient.
What will be the outcome of the competition if zero growth isocline of species 2 lies outside to zero growth isocline of species 1?
Again, if the number of species 2 is below is zero growth isocline, the growth rate will be positive and the population will increase towards the equilibrium. If the number of species 2 is above is zero growth isocline the growth rate will be negative and the population will decrease towards its isocline.
Can an isocline be a curve?
Generally, an isocline will itself have the shape of a curve or the union of a small number of curves.
What are some examples of isolines?
A line of constant value on a map or chart. Examples include isobar (equal barometric pressure), isotherm (equal temperature), and isohyet (equal precipitation).
What is the another name of isolines?
Isolines, also referred to as contour lines, can be used to represent elevation on a map by connecting points of equal elevation, for instance. These imaginary lines provide a good visual representation of the terrain.
What is intraspecific level?
Intraspecific competition is an interaction in population ecology, whereby members of the same species compete for limited resources. This leads to a reduction in fitness for both individuals, but the more fit individual survives and is able to reproduce.
What does intraspecific predation mean?
Intraspecific predation, the process of both killing and eating an individual. of the same species, is a significant and widespread process that until re- cently has not received the attention it merits.
What is intraspecific exploitation?
Exploitation (contest) intraspecific competition. This occurs between individuals of the same population exploiting the same resources and reducing or depleting its availability to others. This competition is indirect interactions between individuals such as deleting of a food source.
What is intraspecific evolution?
Intraspecific variation, which includes the genomic and phenotypic diversity found within and among populations, is threatened by local extinctions, abundance declines, and anthropogenic selection. However, biodiversity assessments often fail to highlight this loss of diversity within species.
What is the shape of an isocline?
Generally, an isocline will itself have the shape of a curve or the union of a small number of curves. Isoclines are often used as a graphical method of solving ordinary differential equations. In an equation of the form y' = f ( x , y ), the isoclines are lines in the ( x , y) plane obtained by setting f ( x , y) equal to a constant.
How is an isocline formed?
Given a family of curves, assumed to be differentiable, an isocline for that family is formed by the set of points at which some member of the family attains a given slope. The word comes from the Greek words ἴσος (isos), meaning "same", and the κλίνειν, meaning "make to slope". Generally, an isocline will itself have the shape ...
Which set of points in the phase plane at which the vectors of the phase velocity are collinear is an is?
the set of points in the phase plane at which the vectors of the phase velocity are collinear is an isocline of the equation
Can $0 $- isocline lie on the curve?
can lie on the $ 0 $- isocline only, and the points of inflection of the solution can lie only on the curve
What is isoclines in math?
Isoclines can be used as a graphical method of solving an ordinary differential equation . The term is also used to refer to points on maps of the world having identical magnetic inclinations. Hollis, S. Differential Equations with Boundary Value Problems. Upper Saddle River, NJ: Prentice Hall, p. 53, 2002.
What is the name of the equation that intersects a curve with the same slope?
Isocline. The term isocline derives from the Greek words for "same slope.". For a first-order ordinary differential equation is, a curve with equation for some constant is known as an isocline. In other words, all the solutions of the ordinary differential equation intersecting that curve have the same slope .
