Evolution of complex flowering strategies: an age– and size–structured integral projection model

We explore the evolution of delayed age– and size–dependent flowering in the monocarpic perennial Carlina vulgaris, by extending the recently developed integral projection approach to include demographic rates that depend on size and age. The parameterized model has excellent descriptive properties both in terms of the population size and in terms of the distributions of sizes within each age class. In Carlina the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy (ESS) approach. Despite accurately predicting the mean size of flowering individuals, the model predicts a step–function relationship between the probability of flowering and plant size, which has no age component. When the variance of the flowering–threshold distribution is constrained to the observed value, the ESS flowering function contains an age component, but underpredicts the mean flowering size. An analytical approximation is used to explore the effect of variation in the flowering strategy on the ESS predictions. Elasticity analysis is used to partition the agespecific contributions to the finite rate of increase (λ) of the survivalndash;growth and fecundity components of the model. We calculate the adaptive landscape that defines the ESS and generate a fitness landscape for invading phenotypes in the presence of the observed flowering strategy. The implications of these results for the patterns of genetic diversity in the flowering strategy and for testing evolutionary models are discussed. Results proving the existence of a dominant eigenvalue and its associated eigenvectors in general sizendash; and agendash;dependent integral projection models are presented.

[1]  S. Geritz,et al.  WHY BIENNIALS DELAY FLOWERING: AN OPTIMIZATION MODEL AND FIELD DATA ON CIRSIUM VULGARE AND CYNOGLOSSUM OFFICINALE , 1989 .

[2]  J. Schwartz,et al.  Linear Operators. Part I: General Theory. , 1960 .

[3]  EVOLUTION IN THE REAL WORLD: STOCHASTIC VARIATION AND THE DETERMINANTS OF FITNESS IN CARLINA VULGARIS , 2002, Evolution; international journal of organic evolution.

[4]  M. Mangel,et al.  Evolution of Size‐Dependent Flowering in Onopordum illyricum: A Quantitative Assessment of the Role of Stochastic Selection Pressures , 1999, The American Naturalist.

[5]  P. Klinkhamer,et al.  THRESHOLD SIZE FOR FLOWERING IN DIFFERENT HABITATS: EFFECTS OF SIZE‐DEPENDENT GROWTH AND SURVIVAL , 1997 .

[6]  L. A. Goodman.  The analysis of population growth when the birth and death rates depend upon several factors. , 1969, Biometrics.

[7]  Stephen P. Ellner,et al.  Simple Methods for Calculating Age‐Based Life History Parameters for Stage‐Structured Populations , 1992 .

[8]  P. Karlsson,et al.  Onset of reproduction in Rhododendron lapponicum shoots: the effect of shoot size, age, and nutrient status at two subarctic sites. , 2001 .

[9]  Simon N. Wood,et al.  PARTIALLY SPECIFIED ECOLOGICAL MODELS , 2001 .

[10]  J. S. Wang.  Statistical Theory of Superlattices with Long-Range Interaction. I. General Theory , 1938 .

[11]  H. Caswell.  Matrix population models : construction, analysis, and interpretation , 2001 .

[12]  P. Klinkhamer,et al.  Threshold size for vernalization in Senecio jacobaea: genetic variation and response to artificial selection , 1996 .

[13]  P. Klinkhamer,et al.  An eight-year study of population dynamics and life-history variation of the biennial Carlina vulgaris , 1996 .

[14]  R. Nisbet,et al.  How should we define 'fitness' for general ecological scenarios? , 1992, Trends in ecology & evolution.

[15]  P. Klinkhamer,et al.  Delay of flowering in the biennial Cirsium vulgare: size effects and devernalization , 1987 .

[16]  L. C. Cole.  The Population Consequences of Life History Phenomena , 1954, The Quarterly Review of Biology.

[17]  Mark Rees,et al.  Evolutionary demography of monocarpic perennials. , 2003 .

[18]  P. Holgate,et al.  Matrix Population Models. , 1990 .

[19]  J. Weiner,et al.  How important are environmental maternal effects in plants? A study with Centaurea maculosa , 1997 .

[20]  M. Johnston,et al.  Plasticity and the genetics of reproductive behaviour in the monocarpic perennial, Lobelia inflata (Indian tobacco) , 2000, Heredity.

[21]  T. J. Jong,et al.  Bidirectional selection on threshold size for flowering in Cynoglossum officinale (hound's-tongue) , 1995, Heredity.

[22]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[23]  William N. Venables,et al.  Modern Applied Statistics with S-Plus. , 1996 .

[24]  O. Eriksson,et al.  Population dynamics and the effect of disturbance in the monocarpic herb Carlina vulgaris (Asteraceae). , 2000 .

[25]  N. Sletvold.  Effects of plant size on reproductive output and offspring performance in the facultative biennial Digitalis purpurea , 2002 .

[26]  J. McGraw.  Effects of age and size on life histories and population growth of Rhododendron maximum shoots , 1989 .

[27]  J. Koerts.  Generalized linear models: Monographs on Statistics and Applied Probability, Chapman and Hall, London, 1983, xiii + 261 pages, £15.00 , 1984 .

[28]  G. Bell.  The Costs of Reproduction and Their Consequences , 1980, The American Naturalist.

[29]  P. Slim,et al.  The contrasting dynamics of two populations of Plantago lanceolata L. classified by age and size. , 1988 .

[30]  N. Kachi,et al.  Population dynamics of Oenothera glazioviana in a sand-dune system with special reference to the adaptive significance of size-dependent reproduction , 1985 .

[31]  M. A. Krasnoselʹskii,et al.  Positive Linear Systems, the Method of Positive Operators , 1989 .

[32]  Odo Diekmann,et al.  On evolutionarily stable life histories, optimization and the need to be specific about density dependence , 1995 .

[33]  R. Law,et al.  Transient Dynamics of Populations with Age‐ and Size‐Dependent Vital Rates , 1990 .

[34]  H. B. Wilson,et al.  Dynamics and evolution: evolutionarily stable attractors, invasion exponents and phenotype dynamics. , 1994, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[35]  M. Rees,et al.  The Analysis and Interpretation of Seedling Recruitment Curves , 1993, The American Naturalist.

[36]  P. Werner.  Predictions of fate from rosette size in teasel (Dipsacus fullonum L.) , 1975, Oecologia.

[37]  K. Gross.  Predictions of fate from rosette size in four “biennial” plant species: Verbascum thapsus, Oenothera biennis, Daucus carota, and Tragopogon dubius , 1981, Oecologia.

[38]  M. Rees,et al.  Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[39]  S. Ellner,et al.  SIZE‐SPECIFIC SENSITIVITY: APPLYING A NEW STRUCTURED POPULATION MODEL , 2000 .

[40]  P. Klinkhamer,et al.  The evolution of generation time in metapopulations of monocarpic perennial plants: some theoretical considerations and the example of the rare thistle Carlina vulgaris , 2000, Evolutionary Ecology.

[41]  S. Wright,et al.  Evolution in Mendelian Populations. , 1931, Genetics.

[42]  P. Klinkhamer,et al.  The Control of Flowering in the Monocarpic Perennial Carlina vulgaris , 1991 .

[43]  Richard Law,et al.  A Model for the Dynamics of a Plant Population Containing Individuals Classified by Age and Size , 1983 .

[44]  O. Eriksson,et al.  Seedling recruitment in semi-natural pastures: the effects of disturbance, seed size, phenology and seed bank , 1997 .

[45]  S. Wright.  Evolution in mendelian populations , 1931 .