The effects of the elastic stage on the population abundance of Dutchman’s Breeches
(Dicentra cucullaria)
Kalamazoo Nature Center March 2006
Introduction
An understanding of the dynamics of a population leads to more effective conservation.
Understanding factors that affect the growth of a population of species similar to those at risk can
also aid in the protection of those more in danger more difficult to study. In addition to this
McLachlan and Bazely found that spring ephemerals are a good indicator of forest recovery due
to their reduced vulnerability to be re-colonized (2001). This was due to traits seen in their life
histories that affected colonization.
When studying the life histories of ephemerals, different stages have been found to have
a greater importance in the growth of a population. The determinant stage to population growth
is measured through elasticity. Elasticity measurements dictate which transition from one stage
to another is most vital to the survival to the population. Ephemerals tend to have elastic stages
in the juvenile or adult stages. This finding is supported in the study of the ephemeral Allium
tricoccum where germination was found to have no effect on population growth rate (Nault and
Gagnon, 1993).
Through investigating the growth dynamics through matrix models and growth
trajectories in populations of Dutchman’s Breeches (Dicentra cucullaria), a spring ephemeral
found in Western Michigan, this study looked at what traits lead to successful re-colonization. In
this study the growth rate and elasticity of four populations of Dutchman’s Breeches (Dicentra
cucullaria) were determined. This study hypothesized that 1.) the four populations were stable
2.) more individuals would be found at earlier developmental stages but the most elastic stage
would occur later in development and 3.) that with a decrease in survival in this elastic stage a
hypothetical growth trajectory would depict a decrease in population size leading to extinction.
Methods
The abundance of four different populations of Dutchman’s Breeches was recorded using
0.5m x 0.5m quadrats at the Kalamazoo Nature Center. Plants found within the quadrat were
divided into stages based on their development. Development was divided into 4 stages, plants
with 1 stalk, 2 stalks, 3 or more stalks, small flowering plants (1 or 2 stalks with flowers) and
large flowering plants (3 or more stalks with flowers). Abundance was recorded by counting the
number of plants in each category along with the number of flowers found on each flowering
plant. A description of the area was taken taking into account size of the patch, other plant
species found in the patch, light, direction of slope and moisture of the soil.
The data collected was analyzed using matrix models in RAMAS. The matrix models
were set up through the calculation of survival rate from one stage to the next and reproductive
rates of each stage. Survival rate was assumed to have a one-way progression through the stages.
When the number of plants exceeded the number of plants in the previous stage the additional
plants were assumed to have remained from the previous year. It was noticed in the field that
smaller flowering plants were found to have more flowers than larger flowering plants.
Reproductive rates were determined with two thirds being contributed by the small flowering
plants and one third from the larger flowering plants. Life history strategies were drawn using
survival percentages and reproductive rates. Using the matrices, population trajectories were
created for each population predicting population growth for the next 15 years along with the
final age and stage abundances at the end of the projection period. Population trajectories were
also made for 50 years if little change was seen in 15 years. Growth rate of the population,
elasticity, and stable age distribution in 15 years was determined. A hypothetical population
growth rate was created for population three after manipulating the most elastic life stage
transition to test the effects of elasticity on population growth.
Results
Growth Rate
The growth rate of the composite of all four populations studied was 0.9999, slightly
decreasing but basically stable as seen in the population trajectory (Figure 1). When looking at
the four populations individually population three was slightly increasing (1.0176) while
populations one, two, and four were decreasing with lambdas respectively 0.9986, 0.9962, and
0.998. Similar plot characteristics were seen in each site.
Figure 1. Trajectory summary for 50 years of the growth of a composite of four Dicentra cucullaria populations.
Abundance is measured in number of individuals versus time in years.
Elasticity
Along with the population growth rate, the elastic stage was determined for each population
individually and also from the combined data from all four populations (Table 1). The elastic
stage was the juvenile stage or young adult stage but not the reproduction stage in the majority of
populations. Many seedlings, young stages, were measured in the abundance measurements and
were seen in the final age distributions.
Table 1. Intrinsic growth rate, elastic stage and stage with highest final age distribution for the
four populations, composite, and hypothetical population.
Intrinsic growth rate
Elastic Stage
Population 1 Population 2 Population 3
0.9986
0.9962
1.0176
Population 4 Total Populations Hypothetical Population
0.9998
0.9999
0.5919
stage2-3
stage 5
stage 1-2 and 3-4
stage 3-4
stage 3-4
stage 2-3
stage 1
stage 1
stage 3
stage 1
stage 1
stage 2
Stage with highest
Final Age Distribution
Hypothetical Model
A hypothetical trajectory was generated using data from population three where survival in stage
two to three, the elastic stage, was reduced from 0.62 to 0.01. The intrinsic growth rate was
reduced to 0.5919. As seen in Figure 2, this change in the elastic stage greatly altered the
population trajectory and the population died in 8 years. As seen in Table 1 above, this also
altered the final age distribution to stage 2.
Figure 2. Hypothetical trajectory summary for the growth of Dicentra cucullaria where the survival in the elastic
stage was reduced to 0.01.
Discussion
The population of Dutchman’s Breeches (Dicentra cucullaria) included in the study were
found to be stable (λ= 0.9999). There were not an abundance of plants seen in the area
suggesting little intraspecific and interspecific competition over resources. There was little
competition for light as the canopy was open and the densities in the quadrats were low
suggesting little competition over resources in the soil. With little competition the population
remains stable.
The elastic stage varied slightly from one population to the next. This was due to
assumptions made when generating the matrices. The plants were assumed to progress only
forward through the stages which may not be accurate for this species. Due to this plants found
in a stage the exceeded the number of plants in the previous stage were assumed to have
remained from the previous season. In the populations where the elastic stages differed, there
was a high percentage of plants that had remained in that stage from the previous season. This
was seen in population two where the elastic stage was stage 5 and population three where there
was tie for the elastic stage between stages one to two and two to three.
One characteristic seen in the data of Dutchman’s Breeches (Dicentra cucullaria) is a
trade-off in selection to produce many less fit offspring in comparison to few better-fit offspring.
Many seedlings were counted in each of the population patches. In the final stage trajectory, the
highest abundance was predicted for the youngest stage. Because fewer individuals are found in
later stages, there is a high mortality rate at this stage. As seen in the elasticity, the younger
stages, germination, did not have the greatest effect on the population growth. Growth in this
population is more important to survival of the population than reproduction. This was further
tested with an alteration of the survival in the elastic stage.
From the reduction of survival to 0.01 from stage two to stage three in population three,
the importance of this elastic stage in the growth of the population is seen. This change is evident
in the final age distribution. In the final stage the majority of individuals were found in stage
two. Due to the low survival rate from this stage into stage three there was a high number of
individuals in the stage at extinction. In less than 8 years the population is driven to extinction.
Like the Allium tricoccum, germination is not seen to affect the growth of the population in
Dicentra cucullaria. Survival in the juvenile and young adult stages is more important. This life
history strategy allows spring ephemerals to be good indicators of successful re-colonization.
More thorough future studies on this population are needed to confirm the conclusions
drawn. This study was limited by time by small sample size. Many assumptions were made that
could have affected the results. Elastic stages may have been altered due to the linearly
progression assumption, when the abundance of individuals exceeded the abundance of
individuals in the previous stage they were assumed to have remained from the previous year.
Only through collection of more data would these relationships become clearer.
For successful rehabilitation after a disturbance certain characteristics are found to be
more favorable. As seen in this study, elastic stages in the juvenile or adult stages are a factor
that aids in successful re-colonization. In the process of human aided succession the first steps in
bringing species back to an area is re-colonization. After re-colonization, the first colonizing
species are replaced until the area returns once again to its original state.
Works Cited
Nault, Andree and Gagnon, Daniel. Ramet Demography of Allium Tricoccum, A Spring
Ephemeral, Perennial Forest Herb. The Journal of Ecology, Vol. 81, No. 1. (Mar., 1993), pp.
101-119.
McLachlan, Stephane M. and Bazely, Dawn R. Recovery Patterns of Understory Herbs and
Their Use as Indicators of Deciduous Forest Regeneration. Conservation Biology, Vol. 15, No. 1.
(Feb., 2001), pp. 98-110.