estimating number of new recruits per survey in Dail-Madsen N-mixture model

[David Rosenbaum]

Hi all,

I have been fitting Dail-Madsen N-mixture models in unmarked using function pcountOpen(), and with dynamics set to "constant." I have a covariate of gamma/immigration, which changes value during each primary period (I am not modeling closed/secondary survey periods). This covariate has a unimodal relationship with survey dates, so immigration rate and abundance increase during middle surveys and decrease during ending survey periods (ranef() and bup() show abundances gradually increasing and then dropping again through time across surveys.

I would like to estimate the number of gains to the population each survey period. Using predict() with values of my immigration covariate, I've outputted model-estimated immigration rate for each survey. I was under the impression that if I multiplied predicted gamma at survey 2 * lambda at survey 1, this would grant an estimate of the mean number of new recruits in survey 2. 

Continuing this line of thought throughout surveys, If I multiplied gamma of survey 3 by the calculated number of individuals estimated in survey 2 ( (survey 2 recruitment rate* lambda) + (survival rate * lambda) ), and gamma at survey 4 by the number of individuals estimated in survey 3 ((survey 3 recruitment rate * survey 2 abun.) + (survival rate * survey 2 abu.n) ), I figured I could continue down and estimate number of recruits for all surveys. However, this leads to abundance estimates that continue to increase through time, when according the the model, abundance should drop in the latter surveys since predicted immigration rate drops towards the end of the survey window.

Would anyone be able to provide insight on what I may be missing here? Am I miscalculating recruitment rate or misunderstanding the relationship between the model parameters? 

Thank you,

David

[Marc Kery]

Dear David,

I think you confuse dynamics = "constant" with dynamics = 'autoreg'. See here in the help text of the function:

"Character string describing the type of population dynamics. "constant" indicates that there is no relationship between omega and gamma. "autoreg" is an auto-regressive model in which recruitment is modeled as gamma*N[i,t-1]."

[On a side-note, I wonder whether 'omega' should be replaced with lambda or possibly N ?].

So, your predictions should yield directly what you want.

Best regards  --- Marc

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From: unma...@googlegroups.com <unma...@googlegroups.com> on behalf of David Rosenbaum <rsnb...@gmail.com>
Sent: Monday, November 24, 2025 20:54
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Subject: [unmarked] estimating number of new recruits per survey in Dail-Madsen N-mixture model

 

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