Filter Extinct Species

Description

Filter Extinct Species

Usage

.filter_extinct(df, model)

Arguments

Details

Set to zero species biomass that are below the extinction threshold.

Value

df with values below th set to zero.

Internal function to remove species from a Scaled model

Description

Internal function to remove species from a Scaled model

Usage

.remove_Scaled(species, model)

Internal function to remove species from a Unscaled model

Description

Internal function to remove species from a Unscaled model

Usage

.remove_Unscaled(species, model)

Internal function to remove species from a Unscaled_nuts model

Description

Internal function to remove species from a Unscaled_nuts model

Usage

.remove_Unscaled_nuts(species, model, nuts = NULL)

Store parameters and functions associated to the scaled version of ATN

Description

Type the name of the class to see its methods

Fields

nb_s

Total number of species

nb_b

Number of basal species

c

double: interference competition

X

Vector of metabolic rates (length = number of species)

max_feed

Vector of maximum feeding rates (length = number of consumers)

e

Vector of assimilation efficiencies (length = number of species)

r

Vector of producers maximum growth rates (length = number of basal species)

BM

Vector of body masses (length = number of species)

dB

Vector of local derivatives (length = number of species)

B0

Vector of half saturation densities (length = number of consumers)

fw

Adjacency matrix of the food-web (dim = number of species * number of species)

w

Matrix of relative consumption rates (dim = number of species * number of consumers)

F

Matrix of per-capita feeding rates (dim = number of species * number of consumers)

q

hill exponent for the type of functional response

K

Carrying capacity of basal species

ext

Extinction threshold for species

alpha

Plant resource competition

ODE

Calculate the derivatives for the scaled version of the ATN model

• Parameter: bioms - Local species biomasses

• Parameter: t - Integration time point

• Returns a vector of growth rate for each species at time t

Store parameters and functions associated to the scaled version of ATN

Description

To not use. For testing purpose only. Please use Rcpp_Scaled instead.

Calculate trophic level of species

Description

Calculate trophic level of species

Usage

TroLev(fw)

Arguments

Value

A numeric vector of species' trophic level.

Store parameters and functions associated to the unscaled version of ATN

Description

Type the name of the class to see its methods

Fields

nb_s

Total number of species

nb_b

Number of basal species

c

double: interference competition

X

Vector of metabolic rates (length = number of species)

a

Matrix of attack rates (dim = number of species * number of consumers)

h

Matrix of handling times (dim = number of species * number of consumers)

e

Vector of assimilation efficiencies (length = number of species)

r

Vector of producers maximum growth rates (length = number of basal species)

BM

Vector of body masses (length = number of species)

dB

Vector of local derivatives (length = number of species)

fw

Adjacency matrix of the food-web (dim = number of species * number of species)

F

Matrix of per-capita feeding rates (dim = number of species * number of consumers)

q

hill exponent for the type of functional response

K

Carrying capacity of basal species

alpha

Plant resource competition

ext

Extinction threshold for species

ODE

Calculate the derivatives for the scaled version of the ATN model

• Parameter: bioms - Local species biomasses

• Parameter: t - Integration time point

• Returns a vector of growth rate for each species at time t

Store parameters and functions associated to the unscaled version of ATN

Description

To not use. For testing purpose only. Please use Rcpp_Unscaled instead.

Store parameters and functions associated to the unscaled version of ATN including nutrient dynamics

Description

Type the name of the class to see its methods

Fields

nb_s

Total number of species

nb_b

Number of basal species

nb_n

Number of nutrient pool

c

double: interference competition

b

Matrix of attack rates (dim = number of species * number of consumers)

h

Matrix of handling times (dim = number of species * number of consumers)

X

vector of metabolic rates (length = number of species)

K

matrix of plant nutrient efficiencies (dim = number of nutrients * number of plants)

V

matrix of plant relative nutrient content (dim = number of nutrients * number of plants)

S

Vector of maximum nutrient concentration (length = number of plants)

r

Vector of maximum growth rate of plant species (length = number of plant species)

e

Vector of assimilation efficiencies (length = number of species)

BM

Vector of body masses (length = number of species)

dB

Vector of local derivatives (length = number of species)

fw

Adjacency matrix of the food-web (dim = number of species * number of species)

w

Matrix of relative consumption rates (dim = number of species * number of consumers)

F

Matrix of per-capita feeding rates (dim = number of species * number of consumers)

q

hill exponent for the type of functional response

ext

Extinction threshold for species

ODE

Calculate the derivatives for the scaled version of the ATN model

• Parameter: bioms - Local species biomasses

• Parameter: t - Integration time point

• Returns a vector of growth rate for each species at time t

Store parameters and functions associated to the unscaled version of ATN

Description

To not use. For testing purpose only. Please use Rcpp_Unscaled_nuts instead.

Make L matrix

Description

Make L matrix

Usage

create_Lmatrix(BM, nb_b, Ropt = 100, gamma = 2, th = 0.01)

Arguments

Details

The L matrix contains the probability for an attack event to be successful based on allometric rules and a Ricker function defined by Ropt and gamma. If at least one species has not resource or consumer (i.e. it is an isolated species), another food web is generated, until a maximum of 100 iterations.

Value

A numeric matrix with the probability for an attack event between two species to be successful.

Examples

set.seed(123)
mass <- sort(10 ^ runif(30, 2, 6))
L <- create_Lmatrix(mass, nb_b = 10, Ropt = 100)
image(t(L))

Make parameter matrix

Description

Make parameter matrix

Usage

create_matrix_parameter(BM, b0, bprey, bpred, E, T.K, T0, k)

Arguments

Details

Make a parameter matrix that depends on both predators and prey and that is used to define attack rates and handling times based on the general allometric equation:

p_{i,j} = b_0 * BM_i^{bprey} * BM_j^{bpred} * exp(-E * (T0-T.K) / (k * T.K * T0))

Value

A matrix filled with estimated values for a model parameter that depends on prey and predator body masses (see details)

Initialize an ATN model, following Delmas et al. 2017, Methods in Ecology and Evolution

Description

Initialize an ATN model, following Delmas et al. 2017, Methods in Ecology and Evolution

Usage

create_model_Scaled(nb_s, nb_b, BM, fw)

Arguments

Details

A model is defined by the total number of species (nb_s), the number of basal species (nb_b), the number of nutrients (nb_n), the body masses (BM) of species, and the adjacency matrix (fw) representing species interactions.

Value

An object of class ATN (Rcpp_parameters_prefs).

References

Delmas, E., Brose, U., Gravel, D., Stouffer, D.B. and Poisot, T. (2017), Simulations of biomass dynamics in community food webs. Methods Ecol Evol, 8: 881-886. https://doi.org/10.1111/2041-210X.12713

Examples

library(ATNr)
set.seed(123)
n_species <- 50
n_basal <- 20
masses <- sort(10^runif(n_species, 2, 6)) #body mass of species
L <- create_Lmatrix(masses, n_basal)
fw <- L
fw[fw > 0] <- 1
mod <- create_model_Scaled(n_species, n_basal, masses, fw)

Initialize an ATN model, following Binzer et al. 2016, Global Change Biology

Description

Initialize an ATN model, following Binzer et al. 2016, Global Change Biology

Usage

create_model_Unscaled(nb_s, nb_b, BM, fw)

Arguments

Details

A model is defined by the total number of species (nb_s), the number of basal species (nb_b), the number of nutrients (nb_n), the body masses (BM) of species, and the adjacency matrix (fw) representing species interactions.

Value

An object of class ATN (Rcpp_parameters_prefs).

References

Binzer, A., Guill, C., Rall, B.C. and Brose, U. (2016), Interactive effects of warming, eutrophication and size structure: impacts on biodiversity and food-web structure. Glob Change Biol, 22: 220-227. https://doi.org/10.1111/gcb.13086 Gauzens, B., Rall, B.C., Mendonca, V. et al. Biodiversity of intertidal food webs in response to warming across latitudes. Nat. Clim. Chang. 10, 264-269 (2020). https://doi.org/10.1038/s41558-020-0698-z

Examples

library(ATNr)
set.seed(123)
n_species <- 50
n_basal <- 20
masses <- sort(10^runif(n_species, 1, 6)) #body mass of species
L <- create_Lmatrix(masses, n_basal)
fw <- L
fw[fw > 0] <- 1
mod <- create_model_Unscaled(n_species, n_basal, masses, fw)

Initialize an ATN model, following Schneider et al. 2016, Nature Communication

Description

Initialize an ATN model, following Schneider et al. 2016, Nature Communication

Usage

create_model_Unscaled_nuts(nb_s, nb_b, nb_n = 2, BM, fw)

Arguments

Details

A model is defined by the total number of species (nb_s), the number of basal species (nb_b), the number of nutrients (nb_n), the body masses (BM) of species, and the adjacency matrix (fw) representing species interactions. Nutrients are not counted as species.

Value

An object of class ATN (Rcpp_parameters_prefs).

Examples

library(ATNr)
set.seed(123)
n_species <- 50
n_basal <- 20
n_nutrients <- 2
masses <- sort(10^runif(n_species, 2, 6)) #body mass of species
L <- create_Lmatrix(masses, n_basal)
fw <- L
fw[fw > 0] <- 1
mod <- create_model_Unscaled_nuts(n_species, n_basal, n_nutrients, masses, fw)

Create a food web based on the niche model

Description

Function to generate a food web based on the niche model (Williams and Martinez, 2000) based on the number of species and connectance. Corrections from Allesina et al. (2008) are used.

Usage

create_niche_model(S, C)

Arguments

Details

If at least one species has not resource or consumer (i.e. it is an isolated species), another food web is generated, until a maximum of 100 iterations.

Value

A (square) matrix with zeros (no interaction) and ones (species j consume species i).

References

Williams, R. J., & Martinez, N. D. (2000). Simple rules yield complex food webs. Nature, 404(6774), 180-183.

Allesina, S., Alonso, D., & Pascual, M. (2008). A general model for food web structure. science, 320(5876), 658-661.

Examples

set.seed(123)
web_niche <- create_niche_model(30, .1)
image(t(web_niche))

Default parameters for the scaled version of ATN as in Delmas et al. 2016

Description

Initialise the default parametrisation for the scaled version of the ATN model as in Delmas et al. (2016).

Usage

initialise_default_Scaled(model)

Arguments

Value

An object of class Rcpp_Scaled with default parameters as in Delmas et al. (2017).

References

Delmas, E., Brose, U., Gravel, D., Stouffer, D.B. and Poisot, T. (2017), Simulations of biomass dynamics in community food webs. Methods Ecol Evol, 8: 881-886. https://doi.org/10.1111/2041-210X.12713

Examples

library(ATNr)
set.seed(123)
masses <- runif(20, 10, 100) #body mass of species
L <- create_Lmatrix(masses, 10, Ropt = 10)
L[L > 0] <- 1
mod <- create_model_Scaled(20, 10, BM = masses, fw = L)
mod <- initialise_default_Scaled(mod)

Default parameters for the scaled version of ATN as in Binzer et al. 2016, with updates from Gauzens et al. 2020

Description

Initialise the default parametrisation for the scaled version of the ATN model as in Binzer et al. (2016), with updates from Gauzens et al. 2020

Usage

initialise_default_Unscaled(model, temperature = 20)

Arguments

Value

An object of class ATN (Rcpp_Unscaled) with default parameters as in Delmas et al. (2017).

References

Binzer, A., Guill, C., Rall, B. C. & Brose, U. Interactive effects of warming, eutrophication and size structure: impacts on biodiversity and food-web structure. Glob. Change Biol. 22, 220-227 (2016). Gauzens, B., Rall, B.C., Mendonca, V. et al. Biodiversity of intertidal food webs in response to warming across latitudes. Nat. Clim. Chang. 10, 264-269 (2020). https://doi.org/10.1038/s41558-020-0698-z

Examples

 library(ATNr)
 set.seed(123)
 masses <- runif(20, 10, 100) #body mass of species
 L <- create_Lmatrix(masses, 10, Ropt = 10)
 L[L > 0] <- 1
 mod <- create_model_Unscaled(20, 10, masses, L)
 mod <- initialise_default_Unscaled(mod)

Default model parameters as in Schneider et al. 2016

Description

Initialise the default parametrisation for the model for Schneider et al. (2016).

Usage

initialise_default_Unscaled_nuts(model, L.mat, temperature = 20)

Arguments

Value

An object of class ATN (Rcpp_Unscaled_nuts) with default parameters as in Schneider et al. (2016).

References

Schneider, F. D., Brose, U., Rall, B. C., & Guill, C. (2016). Animal diversity and ecosystem functioning in dynamic food webs. Nature Communications, 7(1), 1-8.

Examples

library(ATNr)
set.seed(123)
masses <- runif(20, 10, 100) #body mass of species
L <- create_Lmatrix(masses, 10, Ropt = 10)
L[L > 0] <- 1
mod <- create_model_Unscaled_nuts(20, 10, 3, masses, L)
mod <- initialise_default_Unscaled_nuts(mod, L)

Detect whether a food web is composed of several disconnected sub-networks

Description

Run a deep search first algorithm (DFS)

Usage

is_connected(fw)

Arguments

Value

Boolean: TRUE if the food web is connected, FALSE if several disconnected sub-networks are detected.

Examples

library(ATNr)
set.seed(123)
# number of species, nutrients, and body masses
n_species <- 20
n_basal <- 5
n_nutrients <- 3
masses <- sort(10^runif(n_species, 2, 6)) #body mass of species
# create food web matrix
L <- create_Lmatrix(masses, n_basal)
L[, 1:n_basal] <- 0
fw <- L
fw[fw > 0] <- 1
connected <- is_connected(fw)

Estimate the Jacobian matrix of a ODE system

Description

Estimate the Jacobian matrix of a ODE system

Usage

jacobian(bioms, ODE, eps = 1e-06)

Arguments

Details

The function provides a numerical estimation of the Jacobian matrix based on the 5 points stencil method. The precision of the method is in

O(h^5)

, where

h = eps*bioms

. The choice of eps should ensure that

h^5

is always lower to the extinction threshold.

The dimension of the Jacobian matrix are not always matching the number of species in the system. This is because we considered that a perturbation can not correspond to the recolonisation of an extinct species. Therefore, extinct species are removed from the system to calculate the Jacobian matrix.

Value

A matrix corresponding to the Jacobian of the system estimated at the parameter biomasses

Examples

library(ATNr)
set.seed(123)
# first run a model to reach equilibrium
masses <- runif(20, 10, 100) #body mass of species
L <- create_Lmatrix(masses, 10, Ropt = 10)
L[L > 0] <- 1
mod <- create_model_Unscaled_nuts(20, 10, 3, masses, L)
mod <- initialise_default_Unscaled_nuts(mod, L)
biomasses <- masses ^ -0.75 * 10 ^ 4 #biomasses of species
biomasses <- append(runif(3, 20, 30), biomasses)
times <- seq(0, 100, 1)
sol <- lsoda_wrapper(times, biomasses, mod)
# get the final biomasses
final.bioms = sol[nrow(sol), -1]
# estimate jacobian
jacobian(final.bioms, mod$ODE)

Wrapper for lsoda

Description

This is a wrapper to call lsoda from deSolve and solve the ODE. Package deSolve needs to be installed to run this wrapper.

Usage

lsoda_wrapper(t, y, model, verbose = FALSE, ...)

Arguments

Value

A matrix for the ODE solution with species as columns and times as rows.

Examples

library(ATNr)
set.seed(123)
masses <- runif(20, 10, 100) #body mass of species
L <- create_Lmatrix(masses, 10, Ropt = 10)
L[L > 0] <- 1
mod <- create_model_Unscaled_nuts(20, 10, 3, masses, L)
mod <- initialise_default_Unscaled_nuts(mod, L)
biomasses <- masses ^ -0.75 * 10 ^ 4 #biomasses of species
biomasses <- append(runif(3, 20, 30), biomasses)
times <- seq(0, 100, 1)
sol <- lsoda_wrapper(times, biomasses, mod)
range(sol[, -1])
mod$ext <- 1e-3
sol <- lsoda_wrapper(times, biomasses, mod)

Plot food web dynamics

Description

Plot solution of the ODE for the food web. Currently only species and not nutrients are plotted.

Usage

plot_odeweb(x, nb_s)

Arguments

Value

No return value, called for side effects.

Examples

## Not run: 
library(ATNr)
library(deSolve)
set.seed(123)
# number of species, nutrients, and body masses
n_species <- 20
n_basal <- 5
n_nutrients <- 3
masses <- sort(10^runif(n_species, 2, 6)) #body mass of species
# create food web matrix
L <- create_Lmatrix(masses, n_basal)
L[, 1:n_basal] <- 0
fw <- L
fw[fw > 0] <- 1
model <- create_model_Unscaled_nuts(
  n_species,
  n_basal,
  n_nutrients,
  masses,
  fw
)
# initialize model as default in Schneider et al. (2016)
model <- initialise_default_Unscaled_nuts(model, L)
# defining integration time
times <- seq(0, 500, 5)
biomasses <- runif(n_species + n_nutrients, 2, 3)
sol <- lsoda_wrapper(times, biomasses, model, verbose = FALSE)
plot_odeweb(sol, model$nb_s)

## End(Not run)

Function to remove species from a model class

Description

Function to remove species from a model class

Usage

remove_species(species, model, nuts = NULL)

Arguments

Value

A model object where the data structure has bee updated to remove the species in parameters.

Run checks on model parameters

Description

Check if the dimensions of vectors and matrices used in the model are correct. If any dimension is not correct, an error message is returned.

Usage

run_checks(model, verbose = TRUE)

Arguments

Value

No return value, only throw an error if parameters are inconsistent.

Default parameters as in Schneider et al. (2016)

Description

A dataset containing the default parameters as in the Schneider et al. (2016) and used to parametrize the default models. See also create_model_Unscaled_nuts, create_Lmatrix, initialise_default_Unscaled_nuts.

Usage

schneider

Format

A list with the default parameters:

Temperature

ambient temperature in Celsius

T.K

default temperature, 20 degree Celsius in Kelvin

k

Boltzmann's constant

T0

20 degree Celsius in Kelvin, used to estimate scaling law of metabolic rates

q

Hill's exponent of the functional response

Ropt

consumer/resource optimal body mass ratio

gamma

shape of the Ricker function

mu_c

average predator interference

sd_c

standard deviation of predator interference

E.c

Activation energy for interference

h0

scaling constant of the power-law of handling time with consumer and resource body mass

hpred

exponent associated to predator body mass for the allometric scaling of handling time

hprey

exponent associated to prey body mass for the allometric scaling of handling time

E.h

Activation energy for handling time

b0

normalisation constant for capture coefficient

bprey

exponent associated to prey body mass for the allometric scaling of capture coefficient

bpred

exponent associated to predator body mass for the allometric scaling of capture coefficient

E.b

Activation energy for capture coefficient

e_P

Assimilation efficiency associated to the consumption of a plant species

e_A

Assimilation efficiency associated to the consumption of an animal species

x_P

scaling constant of the power-law of metabolic demand per unit of plant biomass

x_A

scaling constant of the power-law of metabolic demand per unit of animal biomass

E.x

Activation energy for metabolic rates

expX

TBD

D

turnover rate of nutrients

nut_up_min

Minimum uptake efficiency of plants

nut_up_max

Maximum uptake efficiency of plants

mu_nut

Average maximum nutrient concentration

sd_nut

standard deviation of maximum nutrient concentration

v

relative content of nutrient 1 in plant biomass

References

Schneider, F. D., Brose, U., Rall, B. C., & Guill, C. (2016). Animal diversity and ecosystem functioning in dynamic food webs. Nature Communications, 7(1), 1-8.

Sort custom input

Description

Sort custom input

Usage

sort_input(BM, fw)

Arguments

Details

Body masses and food web matrix should be arranged with the first elements/columns being for basal species. This is a requirement for the Cpp class and must be enforced before initializing the Rcpp_Schneider and Rcpp_Delmas objects.

Value

A list with sorted body masses (body.mass) and food web matrix (food.web).

Examples

bm <- runif(10, 10, 50)
fw <- matrix(as.numeric(runif(100) > .9), 10, 10)
sort_input(bm, fw)