Mid-Project Update.txt

The question we are trying to answer with our simulation is does a population with a high r (intrinsic growth rate) or a high K (carrying capacity) expand their range faster. We hypothesize that species with a higher r will be able to expand their range faster. This is a different question and hypothesis than presented in the proposal due issues in our original data set and question  and guidance from the course instructors.


The ‘world’ is being created as a nested list with each patch, containing the n (population) of both populations. The parameters (r, K) for each population are contained on a separate list ‘params’. The initial state of the ‘world’ will contain an equal number of individuals from population 1 and 2 in the same patch while all other patches remain uninhabited. This initial population will be put through a simulator function, which contains several smaller functions inside that simulate year to year population growth, species competition and movement between patches, in order to generate our final data. In order to simulate year to year growth a logistic growth equation will be applied to each population. To simulate migration the rbinom function will be applied to each population in order to determine a random number of emigrants for each time step. To redistribute the emigrants the sample function will be used to randomly select either -1 or +1. This will be applied to the index of their current patch enabling them to move to the patch to the right or to the left of their current patch. The ending point of our simulation will be based on when the furthest patch on either side from the initial inhabited patch becomes inhabited. At the end of the simulator we will have a winner counter that will count the number of wins for each population (this has yet to be added). 
In order to analyze the data produced by our simulator we plan to plot the win rate of each population as a function of r and K. This will allow us to see any trends that manipulating the values of r and K may produce in the win rate. We are also able to examine the effects of r and K both independently and combine, through manipulating the values accordingly and faceting plots. To achieve this will run multiple simulations with a large variety of r and K values.


The assumptions of our simulation are:
* The populations are growing logistically before the effect of migration is applied
* The populations are moving in 1-dimensional space (eg. North to South, East to West or island to island regardless of direction)
* Carrying capacity is fixed (per round of simulation)
* Consistent habitat quality across patches
* Constant r within the populations(per round of simulation)
* There is an equal sex ratio in both populations
* Ne = N (The effective population equals the total population)


Within each patch the possibilities for each population during a single time step are:
* The population can grow according to the logistic growth equation function
* Some, none, or the entire population may be selected as migrators 
* Random walk occurrs only at a one patch range
* A given population within a given patch may or may not recieve any immigrants depending on how the random walk occurred 
* A previously uninhavited patch can be colonized due to immigration
* An abandoned patch can be recolonized due to immigration
* A patch can remain uninhabited


note that we have pivoted from our initial proposal because over time we were able to streamline what question we were really interested in and discovered that movement dynamics generally were more interesting to us than what one specific plankton species was potentially doing, and we believe that the answers we can get from the project at its current iteration will be more broadly applicable.

Future directions:
* We will add the wins counter
* Once all the functions have been properly implemented we will then analyze how the simulation outcomes will change as we cary the parameter values (of r and k)
* Depeding on how our analysis ends up, we can also potentially explore using Lotka-Volterra growth models(instead of pure Logistic growth for each) to see if more direct competition intractions can change our outcomes.

Previous work:
https://academic.oup.com/ismej/article/17/12/2140/7506661
* Discusses trade off between r and K 
   * Typically found that r increases with K and vice versa, unless r and K and are affected by density dependent.
   * Provides an interesting equation to potentially look at the relationship between r and K 
https://pubmed.ncbi.nlm.nih.gov/24763335/
* Uses a mechanistic model to look at the role of r and K selection in colonization-competition tradeoff.
* They also include a figure of that explains the different steps in their model
* The model is specific to plant growth
* In the model they change the values of r selection and K selection not the value of r or K directly
* Model found that r selection favors colonizers while K selection tends to favor competitors