Model of minority cytotype exclusion in polyploidy.

When there is a population with mixed ploidy, inter-ploidy cross can create infertile offspring. This create a competition between ploidy levels. Implement a stochastic model simulating this process, and analyze the outcome. For examples, you can analyze how the initial frequencies influence the final outcome, how time till exclusion by one ploidy is influenced by different parameter values, whether coexistence of two ploidy levels can be possible under certain parameter combinations. Or you can start from a diploid population and introduce a tetraploid individual, and see when the tetraploid individual can invade into the population.

Parameters: gMeanOvuleNum
gStddevOvuleNum
gSelfRate
gMeanPolVisit
gPopSize
gInitFreq4x

Qualitiative Findings

• In a large population, the minority ploidy is liekly to lose.

  Parameters: meanOvNum = 10.000000, stddevOvNum = 5.000000, selfRate = 0.800000, meanPolVisit = 3.000000, initFreq4x = 0.2
  Changing pop size

  paraVal	4xWin	2xWin	PopExtinct	Coexist
  10	7179	42821	0	0
  20	5211	44789	0	0
  30	3640	46360	0	0
  40	2534	47466	0	0
  50	1764	48236	0	0
  60	1295	48705	0	0
  70	824	49176	0	0
  80	593	49407	0	0
  90	372	49628	0	0
  100	272	49728	0	0

• In a small population, the probability of invasion is higher if the initial frequency is higher.
  
• High selfing can increase the chance of invasion.
• Lower mean number of pollination visit somewhat influence the chance of invasion.

  Parameters: meanOvNum = 10.000000, stddevOvNum = 5.000000, selfRate = 0.200000, meanPolVisit = 3.000000, initNum2x = 16, initNum4x = 4
  Changing Mean pol visit

  paraVal	4xWin	2xWin	PopExtinct	Coexist
  1.000000	517	49483	0	0
  3.000000	115	49885	0	0
  5.000000	79	49921	0	0
  7.000000	81	49919	0	0
  9.000000	61	49939	0	0

• Mean number of pollination visit has a smaller effect on invasion when the plants are mostly selfing.

  Parameters: meanOvNum = 10.000000, stddevOvNum = 5.000000, selfRate = 0.800000, meanPolVisit = 3.000000, initNum2x = 16, initNum4x = 4
  Changing Mean pol visit

  paraVal	4xWin	2xWin	PopExtinct	Coexist
  1.000000	6422	43578	0	0
  3.000000	5027	44973	0	0
  5.000000	5031	44969	0	0
  7.000000	4988	45012	0	0
  9.000000	4946	45054	0	0
  11.000000	4813	45187	0	0
  13.000000	4983	45017	0	0
  15.000000	5003	44997	0	0
  17.000000	5014	44986	0	0
  19.000000	4855	45145	0	0