The two choices for each species are local (nearest neighbor), or global (entire lattice). If seed dispersal distance of each species differs by at least an order of magnitude, set the better disperser to global and the poorer disperser to local. Setting both species to local allows strong spatial dynamics and patch formation, whereas setting both species to global essentially removes spatial processes.
Seed dispersal can be estimated either by dispersal mode - wind dispersed seeds (like dandelions) can initially be assumed to be global whereas seeds that simply drop can be assumed to local. Animal dispersed seeds are trickier to estimate and depend also on predation loss. Some grass seeds, for example, can be carried long distances by catching in the fur of mammals whereas other seeds can be ingested and excreted latter far away - these may or may not be considered relatively rare events relative to the majority of seeds produced.
Quantifying seed dispersal can be challenging but it can be measured using seed traps, wind-tunnels, or fluorescent markers.
Each species has a feedback parameter which is simply the percent decrease in its germination and/or growth in the other species soil relative to when it is grown in its own soil. These values can be estimated based on experience and observation or they can be quantified experimentally. Values up to about 30% have been documented (Levine, J. M., E. Pachepsky, B. E. Kendall, S. G. Yelenik, and J. Hille Ris Lambers. 2006. Plant-soil feedbacks and invasive spread. Ecology Letters 9:1005-1014).
If quantitative estimates of feedback are not available, a range of feedback values can be run to explore the potential contribution of positive feed back to invasion dynamic. An initial guess about the potential of the species to produce positive feedback can be made based on published studies indicating a difference between the two species effects on soil nutrient dynamics, litter production or chemistry, or allelopathy. Species producing high root biomass, large amounts of litter, or secondary compounds are potential candidates for generating positive feedback. Likewise, experience can be very useful in identifying such species. It may be observed that an invasive species leads to observable alteration of soil properties or that soils under removed individuals are slower to re-colonize.
Feedback effects can be quantified using cultured soils either
collected from established populations in the field or from
Note that the model is designed to explore the effects of positive feedback. As such, it assumes that the net effect of negative and positive feedbacks is greater than or equal to zero. Because negative feedback is required for stable coexistence and because the model is stochastic, the model will always lead to eventual exclusion of one of the species. If neither species produces feedback effects and both have the same dispersal values, the model reduces to a neutral case in which initial abundance and stochasticity determine the winner.
The percent annual chance of dying (equal to 100% minus survival probability). This can be estimated, and longevity estimates often can be found in the literature. Here, we ssume it to be constant throughout the life of an individual: the model does not currently take into account age-dependent differences in life history traits. Annuals have 100% mortality each year. If an annual and a perennial are to be compared, consider whether the annual has a seed production advantage (see next parameter) to offset the mortality disadvantage.
Ratio of Exotic/Native Seed Production
Allows for orders of magnitude differences between the two species. For example does the exotic produce about the same amount of seed or 10 or 100 times more? This can be a bal-park guess based on observation or it can be measured and could also take into account seed viability.
Initial Soil State
Does the system start out with exotic soils, which give the exotic an initial advantage? Alternatively it can start with native soils or neutral soils.
Initial Percent Native
What percent of the lattice is initially occupied by the native?
This can be used to represent the expected relative abundance of native
species following restoration. The exotic will be 100% minus Native%.
External Seed Source
Make one edge of the lattice a permanent population of exotics. The default is that all four edges are absorbing: they do not contribute seeds of either species.
How many cells wide should the lattice be? This will result in a square NxN size lattice. Bigger lattices will take longer to run and to plot.
How long should the model run? Each time steps represents one growing season or year. Longer runs will show the eventual outcome but also take longer. Also, shorter runs can be more representative of the shorter-term dynamics that are relevant to managers.