Study design for Linear Mixed Models seminar, Fall 2010
Isabel Schmidt
I am studying an herbaceous plant (Syngonanthus nitens, Eriocaulaceae) known as golden
that occurs in humid grasslands in the savanna in Central Brazil. The plant’s flower stalks are
harvested by hundreds of local harvesters to produce handicrafts. Traditional management of the
humid grasslands involves burning every other year, during the dry season, since harvesters state
that golden grass flowering increases a year after burning.
Purpose: To understand effects of fire season and harvesting of flower stalks on the growth,
survival and reproduction (both sexual and clonal) on individuals plants of Syngonanthus nitens
(Eriocaulaceae). I am looking at the effects of fire season and harvest at the plant population
level using matrix models, I would like to look at the fate of individuals to better understand the
mechanisms behind the population level responses.
Study design: I have a crossed factorial design replicated in 6 sites; monitored for four years
interval (2006-2010). In each site I have areas subjected to the following treatments: (i) ‘early
fire’, fires in June of 2007 and 2009; (ii) ‘late fire’, fires in September of 2007 and 2009; (iii)
‘fire + harvest’, harvest and late fires in alternate years: harvest in 2006, 2008 and 2010; late
fires in 2007 and 2009; (iv) ‘harvest’ harvest every year, although, flower stalks were rarely
produced after 2008, in the absence of fire and (v) ‘control’, no harvest and no fire since 2005.
Late fire and harvest treatments are fully crossed, whereas the early fire treatment is aimed to
compare the effects of fire season on the populations.
In these areas (or superplots) where my treatments are applied, I tagged plants inside 0.5
x 0.5m plots, the plots were established to tag at least 200 plants/treatment, so number of plots
per treatment (superplot) vary from 4 to 9. Since this is a clonal species and I am considering
each ramet as an individual, ramets are nested within genets (many plants are solitary ramets, i.e.
one ramet is a genet by itself).
For my matrix models, I am analyzing each year separately and using multiple years to
create modeling scenarios. For the individual level analysis, I am also intending to consider a
yearly interval. If that is possible and interesting I could use different years as replications, for
example, fire in September 2007 and fire in September 2009 as replicates of the late fire
treatment, but I am not sure this would be very useful and wise, considering the amount of
variation in both space and time.
1) Response variables: (i) survival – binomial; (ii) growth - continuous, close to normal
distribution; note that growth can be negative; (iii) sexual reproduction, i.e. flowering rate continuous, but very skewed, since plants can produce 1 to 20 or more flower stalks, but the
more common is to produce 1 to 3 flower stalks; (iv) clonal reproduction – continuous and
skewed, plants can produce one to four new ramets, more commonly just one new ramet per
year.
2.1) Fixed Factors: (i) Fire – with three levels: ‘no fire’, ‘early fire’ and ‘late fire’; (ii) Harvest with two levels ‘no harvest’ and ‘harvest.’
2.2) Random factors: My initial thought was that only site, and maybe year, if I consider multiple
years as repetition of the same treatment, would be my random factors. But due to spatial
variation, plot and genet might be worth considering as random factors too. So my possibly
worthy considering random factors would be: (i) site; (ii) year; (iii) plot; (iv) genet.