Path analysis of the effects of
biotic interactions on
fruit production and demographic fates
in a neotropical herb
Carol Horvitz
University of Miami, Coral Gables, FL 33124, USA
and
Douglas Schemske,
Michigan State University, East Lansing, MI 48824,
USA
Effects of biotic interactions on
“fitness”?
Within the year: within season fruit production
Between years: demographic fates from t to t+1
Population growth rate (for single time step of 1
year, time-invariant population projection matrix)
Long run growth rate, e.g. stochastic growth rate
(for multiple time steps, varying population
projection matrix)
Regression analysis and causality
No regression model is assumption-free about
causality among a set of variables
Only the correlation matrix makes no assumption
about the causal relationships among variables
The model of causal relationships comes from
biological insights external to the data at hand
Causal relationships are depicted in path diagrams
a
b
c
a
b
c
Regression analysis and causality, 2
The “direct effects” leading from one cause to one
effect are depicted by straight, single-headed
arrows
Unresolved correlations are depicted by curved,
two-headed arrows
Correlations in the data set can be decomposed into
linear combinations more than one way
Matrix algebra facilitates the process
Both direct and indirect causal effects can thus be
quantified
Regression analysis and causality, 3
The path coefficients for the direct effects are
standardized regression coefficients
They quantify “the average change in standard
deviation units of the dependent variable for one
standard deviation unit of each independent
variable” (Sokal and Rohlf 1981, p. 623)
The study system
 Calathea ovandensis (Marantaceae)
Laguna Encantada, Los Tuxtlas, Veracruz, MX
Natural variation in parameters quantified for individual
plants in the field
Two studies
Within year: pollinator visits, antguards, herbivore of reproductive
tissues, flowers, initiated and mature fruits (2 yrs)
Between years: size, herbivore damage to leaves, competition,
fruits, survival, growth, inflorescence production (5 yr to yr steps)
Biotic interactions
Antguards
An herbivore of reproductive tissues
Pollinators
Size
Herbivory of leaf tissues
Neighbours
Fruits
Biotic interactions
Antguards
An herbivore of reproductive tissues
Pollinators
Size
Herbivory of leaf tissues
Neighbours
Fruits
Biotic interactions acting on fruit
production within a season
Antguards (many taxa)
Herbivory of reproductive tissues
Eurybia elvina (Riodinidae)
Pollinator visits
Euglossa spp
Eulaema cingulata
Eulaema polychroma
Exaerete smaragdina
Rhathymus sp
Conclusions for effects of biotic
interactions on fruit production
 Ants:
+ direct on flower production,
both yrs
 Ants:
+ indirect on fruit production,
both yrs
 Eurybia: - direct on flower production,
both yrs
 Eurybia: - direct on fruit production,
both yrs
Pollinators: + direct on fruit initiation,
one yr only (the year with more abundant
high quality visitors)
Biotic interactions
Antguards
An herbivore of reproductive tissues
Pollinators
Size
Herbivory of leaf tissues
Neighbours
Fruits
Biotic interactions at time t acting
on demographic fates at t+1
Current size (leaf area, cm2)
Herbivory of leaf tissues (% leaf area gone)
Neighbourhood competition (leaf area, cm2)
Fruits produced
Biotic interactions at time t acting
on demographic fates at t+1
Current size (leaf area, cm2)
Herbivory of leaf tissues (% leaf area gone)
Lema bipsitulata, L. plumbea (Chrysomelidae)
Saliana sp, Podalia sp (Lepidoptera)
Unidentified Orthopterans in rolled leaf
Neighbourhood competition (leaf area, cm2)
conspecifics in area
radius defined by leaf length
Fruits produced
no. of inflorescences and biotic interactions
Path diagram for
standardized regression analysis
Size
Herbivory
Neighbours
[Fruits]
Survival
Path diagram for
standardized regression analysis
Size
Herbivory
Neighbours
[Fruits]
Relative
growth
Path diagram for
standardized regression analysis
Size
Herbivory
Neighbours
[Fruits]
Inflorescences
Separate analyses for each dependent variable
by stage and year (total of 55 analyses!)
Seedlings
Juveniles
Pre-reproductives
Reproductives

1982
1983
1984
1985
1986
Effects
on
Survival
Effects
on
Survival
Fisher’s
combined
probability
statistic,
-2lnP across
years for a
stage
STB,
standardized
regression
coefficient
Effects
on
Survival
P< 0.0001
(Fisher’s
combined
probability
statistic,
-2lnP,
across years
for a stage)
P< 0.05
(STB,
standardized
regression
coefficient)
Results
 Growth
 Survival
Size: + for seedlings and
juveniles
Competition: - for
seedlings
Competition temporal
pattern: - in 1983
(highest year)
Herbivory temporal
pattern: - in 1985 (NOT
highest!)
 Reproduction
Effects
on
Relative
Growth
P< 0.0001,
P<0.05,
P<0.001
(Fisher’s
combined
probability
statistic,
-2lnP,
across years
for a stage)
P< 0.05
(STB,
standardized
regression
coefficient)
Results
 Survival
Size: + for
seedlings and
juveniles
Herbivory
temporal pattern:
- in 1985 (NOT
highest!)
Competition: - for
seedlings
Competition
temporal pattern:
- in 1983 (highest
year)
 Growth
 Reproduction
Size: - for all
stages
Herbivory
temporal pattern:
- in 1985 (NOT
highest!)
Competition: - for
juveniles
Competition: - in
1984
Fruit: +
Effects
on
Inflorescences
Produced
P< 0.0001
(Fisher’s
combined
probability
statistic,
-2lnP, across
years for a
stage)
P< 0.05
(STB,
standardized
regression
coefficient)
Results
 Survival
Size: + for
seedlings and
juveniles
Herbivory
temporal pattern:
- in 1985 (NOT
highest!)
Competition: - for
seedlings
Competition
temporal pattern:
- in 1983 (highest
year)
 Growth
 Reproduction
Size: - for all
Size: + for prestages
reproductives
and
Herbivory
reproductives
temporal pattern:
- in 1985 (NOT
Competition: highest!)
only for
reproductives in
Competition: - for
1983
juveniles
Fruit: +
Competition: - in
1984
Fruit: +
Conclusions for effects of biotic
interactions on demographic fates
Size: important for all stages, improving survival
(of smallest ones) and improving reproduction, but
slowing down relative growth.
Herbivory: very low in general; it had mysterious
negative effects in 1985, not the year it was
highest.
Competition: strongest negative impact on
seedlings, but also had temporal pattern (partially)
consistent with its strength.
Fruit production: positive impacts on future growth
and future reproduction.
Biotic interactions
Antguards
An herbivore of reproductive tissues
Pollinators
Size
Herbivory of leaf tissues
Neighbours
Fruits
Tying the two studies together
plus...
Standardized regression coefficients (path
coefficients) are a great tool for summarizing the
magnitudes of effects over many analyses
The stage-specific demographic influence of an
animal may not be predicted its magnitude
Animals affecting fruit production may also
influence future demographic fates in unpredicted
ways (beyond “cost of reproduction” sorts of ideas)
Tying the two studies together
plus...placing them into broader context
Within and between season effects: population
projection matrix growth rate sensitivity
Variable environments: a set of matrices
appropriately linked and analyzed to determine
stochastic growth rate sensitivity
References and ongoing
collaborations
Schemske, D.W. and C.C. Horvitz, 1988. Plant-animal
interactions and fruit production in a neotropical
herb: a path analysis. Ecology 69: 1128-1137
Horvitz, C.C. and D.W. Schemske, 2002. Effects of
plant size, leaf herbivory, local competition and
fruit production on survival, growth and future
reproduction of a neotropical herb. Journal of
Ecology 90: 279-290
Plant-animal interactions in random environments:
ongoing collaborations with Tuljapurkar, Pascarella,
Ehrlen and Matlaga