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Mobility and extinction risk in human-altered landscapes

by Amanda E. Martin (Submitted: 03/21/2016)

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#OVERVIEW

This model was designed to simulate the evolution of dispersal characteristics and species mobility in a landscape context, and the population response to habitat loss. Here _mobility_ refers to the tendency to leave the current home range or territory (i.e. _emigration_) and the likelihood of settling in a different habitat patch (i.e. _immigration_). In particular, the model was used to test four hypotheses that might explain contradictory findings on the role of mobility in extinction risk, because in some empirical studies mobility appears to increase species extinction risk, while other studies report the opposite.

The four hypotheses were:

>**Metric type hypothesis**: The mobility-risk relationship depends on how you measure mobility. This is because extinction risk increases with increasing mobility when mobility is measured as emigration, but decreases with increasing mobility when mobility is measured as immigration.

>**Metric context hypothesis**: The most mobile species (whether measured by emigration or immigration) in unaltered landscapes are least mobile in human-altered landscapes, so the relationship between mobility and extinction risk is opposite when mobility is measured in unaltered and altered landscapes.

>**Metric range hypothesis**: The mobility-risk relationship is ∩-shaped, thus the mobility-risk relationship will be apparently positive when the study includes sedentary species to moderately mobile species, but the mobility-risk relationship will be negative when the study includes moderately mobile species to highly mobile species.

>**Landscape context hypothesis**: The mobility-risk relationship depends on the landscapes of the studied species. This is because some landscape structures drive evolution of dispersal characteristics that increase both mobility and risk, while others drive evolution of characteristics that increase mobility and decrease risk.

For full details, please refer to our peer-reviewed paper:

* Amanda E. Martin and Lenore Fahrig. _In press_. Reconciling contradictory relationships between mobility and extinction risk in human-altered landscapes. Functional Ecology. DOI: 10.1111/1365-2435.12632

##HOW TO CITE

We ask that you cite both our peer-reviewed paper and the NetLogo software:

* Amanda E. Martin and Lenore Fahrig. _In press_. Reconciling contradictory relationships between mobility and extinction risk in human-altered landscapes. Functional Ecology.DOI: 10.1111/1365-2435.12632

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

##COPYRIGHT

Copyright 2015 Amanda E. Martin. All rights reserved.

For information on the copyright associated with the published paper, please see http://www.functionalecology.org/view/0/copyright.html

# MODEL STRUCTURE

This model simulates:

1. evolution of dispersal characteristics in the historic landscape, and
1. the population response to habitat loss.

The model allows simulation of either the full model (parts 1 + 2), or part 2 alone. If only the habitat loss portion of the simulation model is run, the starting landscape and population are loaded from space-delimited text files saved in a previous simulation run. This feature allows the user to, for example, simulate the effects of different rates of habitat loss on a given population, because you can load the same historic population and landscape and run the simulation with different rates of habitat loss.

##EVOLUTION OF DISPERSAL CHARACTERISTICS IN THE HISTORIC LANDSCAPE

A simulation run is initiated by creating an artificial landscape and populating it with individuals, each with a random set of values for its four, heritable dispersal characteristics (defined below). This part of the simulation run continues for a user-specified number of generations in the historic landscape (or until the population goes extinct).

Note that we use **habitat cell** and **matrix cell** when referring to a single habitat or matrix cell, respectively. Matrix (i.e. non-habitat) differs from habitat because matrix (a) does not support reproduction, and (b) is associated with a greater risk of dispersal mortality than habitat. **Habitat patch** refers to a contiguous group of habitat cells surrounded by matrix, where habitat cells are grouped based on a Moore (8-neighbor) neighborhood rule.

Each generation involves:

1. **habitat disturbance**, causing some local population extinctions, i.e. death of all individuals in a given habitat patch,

1. **reproduction**, including transfer and mutation of dispersal genotypes, and

1. **dispersal**, i.e. movement of individuals from their birth place, resulting in either dispersal mortality or settlement in a new location.

Historic landscapes vary in:

1. **habitat amount**: the proportion of the grid cells in habitat; smaller values mean less habitat

1. **habitat fragmentation**: the level of patchiness of habitat, for a given habitat amount, modeled as the Hurst exponent of the midpoint displacement algorithm used to assign locations of habitat and matrix cells (Saupe 1988); smaller values produce more fragmented habitat

1. **matrix quality**: probability of mortality during movement across a matrix cell; smaller values indicate higher matrix quality

1. **disturbance frequency**: mean number of generations until local population extinction, for a Poisson distribution; smaller values indicate more frequent disturbance

Four dispersal characteristics are modeled as independent, heritable traits:

1. **dispersal probability**: probability that the individual leaves its natal habitat cell and disperses

1. **probability of boundary crossing**: probability that the individual will cross from habitat to matrix, when it encounters a boundary

1. **path shape in matrix**: correlation in movement direction between successive movement steps originating in matrix, modeled as the concentration parameter for a wrapped Cauchy distribution with a mean of zero

1. **path shape in habitat**: correlation in movement direction between successive movement steps originating in habitat, modeled as the concentration parameter for a wrapped Cauchy distribution with a mean of zero

##POPULATION RESPONSE TO HABITAT LOSS

Habitat loss is simulated for a user-specified number of generations, or until the population goes extinct. Habitat disturbance, reproduction, and dispersal are simulated as described above. In each generation prior to reproduction, a proportion of the remaining habitat cells is converted to matrix. This habitat loss is simulated as encroachment of matrix into habitat; cells converted from habitat to matrix are on the edges of habitat patches, i.e. they have at least one neighbouring matrix cell.

# MODEL INTERFACE

## MAIN ACTIONS

* **SET UP**: prepares for a simulation run; pust be pressed prior to the simulation run

* **RUN MODEL**: runs a single simulation run

##MODEL INPUT-OUTPUT

* **file-directory**: directory where model input and output are saved

* **output-file**: name of the file where model output is saved (if **save-output** = ON, see below)

* **run-id**: identifier for a simulation run; _if saving multiple runs to the same directory, the run number should be unique to each simulation run_

* **load-existing-simulation**: ON = only the habitat loss portion of the simulation model is run; the starting landscape and population are loaded from space-delimited text files (as saved by the model when **save-final-generation** = ON, see below); OFF = full simulation model is run (evolution of dispersal characteristics + response to habitat loss)

* **previous-generations**: _Only used if load-existing-simulation = ON;_ identifies the number of generations simulated in the simulation data set to be loaded

* **previous-rate-of-loss**: _Only used if load-existing-simulation = ON;_ identifies the rate of habitat loss in the simulation data set to be loaded

* **save-output**: ON = model output is saved to a space-delimited plain text file, adding a row to the file (specified by **output-file**) in each simulated generation (see MODEL DATA below); OFF = no data are saved

* **save-final-generation**: ON = data for the final landscape and population model are saved to space-delimited plain text files, at the end of a simulation run (see MODEL DATA below). If the full simulation model is run, also saves the historic landscape and population (in the generation before habitat loss begins); OFF = no data are saved

##MODEL PARAMETERS
_Users must pay attention to the accepted range of values for each parameter. Acceptable parameter values are given below, in brackets. If values are invalid, the model run will be stopped, and a message identifying the problem parameter(s) will be printed to the ‘Command Center’._

###Evolution of dispersal characteristics in the historic landscape
* **initial-generations**: number of generations without habitat loss _(>= 1)_

* **lambda**: variable in the equation used to calculate the mean number of offspring produced by each adult inhabiting a habitat cell (Hassell 1975) _(>=1)_

* **carring-capacity**: variable in the equation used to calculate the mean number of offspring produced by each adult inhabiting a habitat cell (Hassell 1975); also determines whether a dispersing individual settles or continues moving (it can only settle if the habitat cell is below capacity) _(>=1)_

* **habitat-cost**: probability of mortality during movement across a habitat cell _(0 - 1)_

* **competition-type**: variable in the equation used to calculate the mean number of offspring produced by each adult inhabiting a habitat cell (Hassell 1975); 1 = contest competition, >1 = scramble competition _(>= 1)_

* **mutation-rate**: probability of mutation for a given dispersal characteristic _(0 - 1)_

* **mutation-increment**: change in the value of a dispersal characteristic, when mutation occurs _(0 - 0.5)_

* **minimum-** and **maximum-habitat-amount**: defines the range of values for habitat amount in the historic landscape _(>0 - 1)_

* **minimum-** and **maximum-fragmentation**: defines the range of values for habitat fragmentation in the historic landscape _(0 - 1)_

* **minimum-** and **maximum-matrix-cost**: defines the range of values for matrix quality in the historic landscape _(0 - 1)_

* **minimum-** and **maximum-disturbance-interval**: defines the range of values for the disturbance parameter in the historic landscape _(>=1)_

###Response to habitat loss
* **habitat-loss-generations**: number of generations with habitat loss _(>= 0)_

* **rate-habitat-loss**: proportion of habitat converted to matrix in a given generation _(0 - 1)_

##VISUAL OUTPUT
Onscreen output includes:

* the value for each of the four landscape attributes

* the simulated grid landscape (green = habitat, black = matrix) and population (yellow)

* a plot of the population size in each generation

* a plot of the population mean trait value for each of the four dispersal characteristics in each generation

* a plot of the **emigration rate**, i.e. proportion of the population that left the natal habitat cell and did not return, per generation, and **immigration rate**, i.e. proportion of the population that settled in a different habitat patch, per generation

# MODEL OUTPUT

##SAVE-OUTPUT

_The following values are saved in a space-delimited text file (.txt) each generation, if _**save-output** = ON. A row is added to this file in each generation.

* **run**: identifier for the simulation run

* **generation**: current generation

* **rate_habitat_loss**: rate of habitat loss; in generations prior to habitat loss, this is set to zero

* **model parameters**: parameter values used in the simulation run

* **evolved dispersal characteristics**: population mean dispersal trait values

* **population size**: number of individuals before dispersal (**pre_disperse_n**) and after dispersal (**post_disperse_n**)

* **n_patches**: number of habitat patches (i.e. continuous groupings of habitat cells, completely surrounded by matrix)

* **emigration**: number of dispersers that left the natal habitat cell and did not return

* **immigration**: number of dispersers that left the natal habitat patch and settled in a new habitat patch

* **natal_patch_settlement**: number of dispersers that left the natal habitat cell and settled in a new habitat cell within the natal habitat patch

* **natal_habitat_mortality**: number of dispersers that died during dispersal through the natal habitat patch

* **new_habitat_mortality**: number of dispersers that died during dispersal through any habitat patch that was not the natal habitat patch

* **matrix_mortality**: number of dispersers that died during dispersal through matrix

* **recolonization**: proportion of unoccupied habitat patches that were recolonized in that generation; set as "NA" if all patches were occupied at the beginning of the generation

* **local_extinction**: proportion of occupied habitat patches that became unoccupied in that generation

##SAVE-FINAL-GENERATION

_Saves three space-delimited plain text files after the final simulated generation, if_ **save-final-generation** = ON.

Each file is identified by the run-id, rate of habitat loss, and generation. For example, if run 50 ran for 1000 generations, and the rate of habitat loss was 0.03, the model would save files:

* run_50_parameters_rate_0.03_gen_1000.txt

* run_50_population_rate_0.03_gen_1000.txt

* run_50_landscape_rate_0.03_gen_1000.txt

These files can be used to continue a simulation run (using **load-existing-simulation** = ON). Note that these files are only saved if the population persists for the user-specified number of generations.

###PARAMETER VALUES

Saves the habitat amount, fragmentation, matrix quality, disturbance frequency, habitat cost, competition type, mutation increment, mutation rate, carrying capacity, lambda, and population size for the simulation run.

###FINAL POPULATION
Saves the location (x and y coordinates), heading, and evolved dispersal characteristics (dispersal probability, probability of boundary crossing, path shape in matrix, and path shape in habitat) for each individual.

###FINAL LANDSCAPE
Saves the location (x and y coordinates), cell color (where habitat = color code 55, matrix = code 0), dispersal cost (with a different cost associated with habitat and matrix cells), time to disturbance, and unique habitat patch ID (identifies which habitat cells belong to each habitat patch) for each grid cell.

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