Analyzing the pattern in the growth of organisms using discrete data in R I have data of the size of 200 individuals of a particular plant species. But the size was measured in an indirect way, counting the number of leaves (discrete data), monthly during a total of 14 months. The germination, growth and death of the plants are very irregular, with some plants having a long life span, other dying quickly, and also the germination in time is irregular: new plants kept germinating during all the study period and being incorporated into the study. Here is an example of my data (numbers inside cells refer to the number of leaves):





Month.1
Month.2
Month.3
Month.4
Month.5
Month.6
Month.7




plant.1
3
21
15
-
-
-
-


plant.2
-
7
14
-
-
-
-


plant.3
-
8
12
10
-
-
-


plant.4
-
-
1
3
5
-
-


plant.5
-
3
6
18
13
4
-


.....
...
...
...
...
...
...
...




I'm interested in checking if there is some pattern in their growth, I mean if they first show an increase in the number of leaves, if they then get stable, and if they suddenly die or gradually decrease the number of leaves before dying.
(Next step, a different but related question, would be to investigate their phenology, i.e. when they mainly germinate, when there are a greater number of alive plants, etc.)
I've been looking for phenology analysis in R, but what I've found so far is mainly related to climate change, global parameters, etc. On the other hand, growth analysis considering time series is focused on long sequence of data of a particular variable, not several individuals.
Please, I'd appreciate any tips on how to analyze my data.

Longitudinal ordinal regression using Markov models can deal with the situations you described.  For example in a first-order Markov proportional odds logistic model the current count has the previous count as a covariate, and the way in which you model the previous count can give rise to increasing, decreasing, or stable current counts.  A large amount of background information, detailed case studies, and R code may be found at https://hbiostat.org/proj/covid19.  Examples show how to marginalize over the previous count to get the unconditional distributions over time.  For that purpose the Bayesian examples are most relevant because they easily allow you to get posterior probabilities and uncertainty intervals about any derived quantities you want, including mean counts and mean time in states.
Ordinal models don't assume a distribution for the counts.
