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 a b c c b
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
standardized regression analysis Path diagram for standardized regression analysis Size Herbivory Neighbours [Fruits] Survival
standardized regression analysis Path diagram for standardized regression analysis Size Herbivory Neighbours [Fruits] Relative growth
standardized regression analysis Path diagram for standardized regression analysis Size Herbivory Neighbours [Fruits] Inflore- scences
1982 1983 Seedlings Juveniles 1984 Pre-reproductives 1985 Separate analyses for each dependent variable by stage and year (total of 55 analyses!) 1982 1983 1984 1985 1986 Seedlings Juveniles Pre-reproductives Reproductives
Effects on Survival
Effects on Survival Fisher’s combined probability statistic, -2lnP across years for a stage STB, standardized regression coefficient
Effects on Survival P< 0.0001 (Fisher’s combined probability statistic, -2lnP, across years for a stage) P< 0.05 (STB, standardized regression coefficient)
Results Growth Reproduction Survival Size: + for seedlings and juveniles Competition: - for seedlings Competition temporal pattern: - in 1983 (highest year) Herbivory temporal pattern: - in 1985 (NOT highest!)
Effects on Relative Growth P< 0.0001, P<0.05, P<0.001 (Fisher’s combined probability statistic, -2lnP, 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 Size: - for all stages Herbivory temporal pattern: - in 1985 (NOT highest!) Competition: - for juveniles Competition: - in 1984 Fruit: + Reproduction
Effects on Inflore-scences Produced (Fisher’s combined probability statistic, -2lnP, 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 Size: - for all stages Herbivory temporal pattern: - in 1985 (NOT highest!) Competition: - for juveniles Competition: - in 1984 Fruit: + Reproduction Size: + for pre-reproductives and reproductives Competition: - only for reproductives in 1983 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