anm.LV {asbio} | R Documentation |
Animated depictions of Lotka-Volterra competition and exploitation models
Description
Creates animated plots of two famous abundance models from ecology; the Lotka-Volterra competition and exploitation models
Usage
anm.LVcomp(n1, n2, r1, r2, K1, K2, a2.1, a1.2, time = seq(0, 200), ylab =
"Abundance", xlab = "Time", interval = 0.1, ...)
anm.LVexp(nh, np, rh, con, p, d.p, time = seq(0, 200), ylab = "Abundance",
xlab = "Time", interval = 0.1, circle = FALSE, ...)
anm.LVc.tck()
anm.LVe.tck()
Arguments
n1 |
Initial abundance values for species one. To be used in the competition function |
n2 |
Initial abundance values for species two in the competition function, i.e., |
r1 |
Maximum intrinsic rate of increase for species one, i.e., |
r2 |
Maximum intrinsic rate of increase for species two in the competition model |
K1 |
Carrying capacity for species one, i.e., |
K2 |
Carrying capacity for species two, i.e., |
a2.1 |
The interspecific effect of species one on species two, i.e., the term |
a1.2 |
The interspecific effect of species two on species one, i.e., the term |
nh |
Initial abundance values for the host (prey) species. To be used in the the exploitation model |
np |
Initial abundance values for the predator species in the the exploitation model, i.e., the term |
rh |
The intrinsic rate of increase for the host (prey) species, i.e., the term |
con |
The conversion rate of prey to predator, i.e., the term |
p |
The predation rate, i.e., the term |
d.p |
The death rate of predators, i.e., the term |
time |
A time sequence for which competition or exploitation is to be evaluated. |
ylab |
Y-axis label. |
xlab |
X-axis label. |
interval |
Animation speed per frame (in seconds). |
circle |
Logical, if |
... |
Additional arguments from |
Details
The Lotka-Volterra competition and exploitation models require simultaneous solutions for two differential equations. These are solved using the function rk4
from odesolve
.
The interspecific competition model is based on:
\frac{dN_1}{dt}=r_{max1}N_1\frac{K_1-N_1-\alpha_{12}}{K_1},
\frac{dN_2}{dt}=r_{max2}N_2\frac{K_2-N_2-\alpha_{21}}{K_2},
where N_1
is the number of individuals from species one, K_1
is the carrying capacity for species one, r_{max1}
is the maximum intrinsic rate of increase of species one, and \alpha_{12}
is the interspecific competitive effect of species two on species one.
The exploitation model is based on:
\frac{dN_h}{dt} = r_hN_h-pN_hN_p,
\frac{dN_p}{dt} = cpN_hN_p-d_pN_p,
where N_h
is the number of individuals from the host (prey) species, N_p
is the number of individuals from the predator species, r_h
is the intrinsic rate of increase for the host (prey) species, p
is the rate of predation, c
is a conversion factor which describes the rate at which prey are converted to new predators, and d_p
is the death rate of the predators.
The term r_hN_h
describes exponential growth for the host (prey) species. This will be opposed by deaths due to predation, i.e. the term pN_hN_p
. The term cpN_hN_p
is the rate at which predators destroy prey. This in turn will be opposed by d_pN_p
, i.e. predator deaths. Loading package tcltk allows one to run the GUIs in anm.LVe.tck
and anm.LVc.tck
.
Value
The functions return descriptive animated plots
Author(s)
Ken Aho, based on a concept elucidated by M. Crawley
References
Molles, M. C. (2010) Ecology, Concepts and Applications, 5th edition. McGraw Hill.
Crawley, M. J. (2007) The R Book. Wiley
Examples
## Not run:
#---------------------- Competition ---------------------#
##Species 2 drives species 1 to extinction
anm.LVcomp(n1=150,n2=50,r1=.7,r2=.8,K1=200,K2=1000,a2.1=.5,a1.2=.7,time=seq(0,200))
##Species coexist with numbers below carrying capacities
anm.LVcomp(n1=150,n2=50,r1=.7,r2=.8,K1=750,K2=1000,a2.1=.5,a1.2=.7,time=seq(0,200))
#----------------------Exploitation----------------------#
#Fast cycles
anm.LVexp(nh=300,np=50,rh=.7,con=.4,p=.006,d.p=.2,time=seq(0,200))
## End(Not run)