lv_interaction_log

Calculates dn/dt for n species in a Lokta-Volterra system, in log space,
following the form:
dlog(ni)/dt = (ri + aii * ni + sum_j(aij * nj))
This form can be helpful for optimization routines where species abundances
are close to zero.

A collection of tools and data for analyzing the Gause microcosm experiments, and for fitting Lotka-Volterra models to time series data. Includes methods for fitting single-species logistic growth, and multi-species interaction models, e.g. of competition, predator/prey relationships, or mutualism. See documentation for individual functions for examples. In general, see the lv_optim() function for examples of how to fit parameter values in multi-species systems. Note that the general methods applied here, as well as the form of the differential equations that we use, are described in detail in the Quantitative Ecology textbook by Lehman et al., available at <http://hdl.handle.net/11299/204551>, and in Lina K. Mühlbauer, Maximilienne Schulze, W. Stanley Harpole, and Adam T. Clark. 'gauseR': Simple methods for fitting Lotka-Volterra models describing Gause's 'Struggle for Existence' in the journal Ecology and Evolution.

Adam Clark

gauseR

Lotka-Volterra Models for Gause's 'Struggle for Existence'

Lina Mühlbauer

Maximilienne Schulze

lv_interaction_log function

<dl><dt>time</dt>
<dd>The time steps corresponding to each observation - exists to interface with ode function, but should be left blank.</dd>
<dt>n_log</dt>
<dd>A vector of species abundances, in log space</dd>
<dt>parms</dt>
<dd>A vector of parameters - the first n elements should be the growth rates r1, r2, ... rn for all n species.
The remaining terms should be the elements of the interaction matrix A, listed in the order a11, a12, ... a1n, a21, a22, ... a2n, ... an1, an2, ... ann.</dd></dl>

Arguments

Lotka-Volterra Interactions in Log Space — lv_interaction_log

<dl>

<dt>time</dt>
<dd>The time steps corresponding to each observation - exists to interface with ode function, but should be left blank.</dd>


<dt>n_log</dt>
<dd>A vector of species abundances, in log space</dd>


<dt>parms</dt>
<dd>A vector of parameters - the first n elements should be the growth rates r1, r2, ... rn for all n species.
The remaining terms should be the elements of the interaction matrix A, listed in the order a11, a12, ... a1n, a21, a22, ... a2n, ... an1, an2, ... ann.</dd>

</dl>

lv_interaction_log: Lotka-Volterra Interactions in Log Space

Description

Usage

Value

Arguments