Plot birth pulse data: last capture in December 2015

There are 32 births overall; 5 in 2013, 15 in 2014, 12 in 2015. First birth in July 2013; last in April 2015 Observations started July 2013 (t=0.54), ended June 2015 (t=2.46). Set t0= 1 Jan 2013; birth times approximated as midway through the month.

Plot birth pulse data of animals surviving to at least 6 months

6 births were excluded by this criteria; all born January-April 2015 No temporal trend in death of calves; use full dataset.

Plot birth pulse data from Ryan et al. 2008

Plot hazard of birth pulse: mu=0.443

dark line: sigma=1; light gray lines: sigma=1.1-1.5 (dashed), 0.6-0.8 (dotted) So with larger values of sigma, the pulse is sharper

Plot probability of birth over time: distribution depends on t0… so will need to estimate cv & t0

dark lines, cv=1; exp(get_log_birth_like(time, t0=0, sigma=1))

Test: plot Likelihood function and estimate CV assuming t0=0

Set t0=0 = January 1 2013

Estimate CV and t0

Plot predicted number of monthy births to determine realistic range of sigma.

I still don’t really understand t0 (other than that it should be the peak if the pusle is symmetric), so fixed.

Figures for Anna: Pulse by year