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Excessive flower production as an anti-predator strategy: when is random flower abortion favored?

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Population Ecology

Abstract

Many plant species produce excessive flowers but abandon most of them halfway to maturation. Several hypotheses have been proposed to explain adaptive significances of this behavior. To understand this phenomenon, I developed a resource allocation model between flower and fruit/seed production to examine a new hypothesis that excessive flower production is favored to “dilute” predation pressures in plant–pre-dispersal seed predator systems. First, I compared the efficiencies of three abortion strategies: (1) no abortions: the plant matures all pollinated flowers; (2) selective abortions: the plant aborts all flowers oviposited by predators and only intact flowers mature; (3) random abortions: the plant indiscriminately aborts a fraction of the pollinated flowers irrespective of seed-predator oviposition. I assumed that the timing of selective abortions was later than that of random abortions owing to delays in response to feeding damage (the cost of selective abortion). I showed that the reproductive efficiencies of the random-abortion and selective-abortion strategies were much higher than that of the no-abortion strategy when resources were poor, predators were abundant, and the cost of flower production was low. In addition, the reproductive efficiency of the random-abortion strategy was greater than that of the selective-abortion strategy when the cost of selective abortion was high. Second, I examined a mixed-abortion strategy in which plants aborted flowers randomly earlier and selectively later. The proportion of random abortions increased as the amount of resources decreased, density of seed predators increased, flower production cost decreased, and cost of selective abortion increased.

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References

  • Augspurger CK (1981) Reproductive synchrony of a tropical shrub: experimental studies on effects of pollinators and seed predators in Hybanthus prunifolius (Violaceae). Ecology 62:775–788

    Article  Google Scholar 

  • Bonal R, Muñoz A, Díaz M (2007) Satiation of predispersal seed predators: the importance of considering both plant and seed levels. Evol Ecol 21:367–380

    Article  Google Scholar 

  • Brody AK (1992) Oviposition choices by a pre-dispersal seed predator (Hylemya sp.). Oecologia 91:56–62

    Article  PubMed  Google Scholar 

  • Brody AK, Mitchell RJ (1997) Effects of experimental manipulation of inflorescence size on pollination and pre-dispersal seed predation in the hummingbird-pollinated plant Ipomopsis aggregata. Oecologia 110:86–93

    Article  PubMed  CAS  Google Scholar 

  • Crawley MJ (2000) Seed predators and plant population dynamics. In: Fenner M (ed) Seeds: the ecology of regeneration in plant communities, 2nd edn. CAB International, Wallingford, pp 167–182

    Chapter  Google Scholar 

  • Ezoe H (2017) Optimal resource allocation model for excessive flower production in a pollinating seed-predator mutualism. Theor Ecol 10:105–115

    Article  Google Scholar 

  • Fenner M, Cresswell J, Hurley R, Baldwin T (2002) Relationship between capitulum size and pre-dispersal seed predation by insect larvae in common Asteraceae. Oecologia 130:72–77

    Article  PubMed  CAS  Google Scholar 

  • Ghazoul J, Satake A (2009) Nonviable seed set enhances plant fitness: the sacrificial sibling hypothesis. Ecology 90:369–377

    Article  PubMed  Google Scholar 

  • Gómez JM, Zamora R (1994) Top-down effects in a tritrophic system: parasitoids enhance plant fitness. Ecology 75:1023–1030

    Article  Google Scholar 

  • Higaki M (2016) Prolonged diapause and seed predation by the acorn weevil, Curculio robustus, in relation to masting of the deciduous oak Quercus acutissima. Entomol Exp Appl 159:338–346

    Article  Google Scholar 

  • Holland JN, DeAngelis DL (2006) Interspecific population regulation and the stability of mutualism: fruit abortion and density-dependent mortality of pollinating seed-eating insects. Oikos 113:563–571

    Article  Google Scholar 

  • Holland JN, Bronstein JL, DeAngelis DL (2004a) Testing hypotheses for excess flower production and low fruit-to-flower ratios in a pollinating seed-consuming mutualism. Oikos 105:633–640

    Article  Google Scholar 

  • Holland JN, DeAngelis DL, Schultz ST (2004b) Evolutionary stability of mutualism: interspecific population regulation as an evolutionarily stable strategy. Proc R Soc Lond B 271:1807–1814

    Article  Google Scholar 

  • Janzen DH (1971a) Escape of Cassia grandis L. beans from predators in time and space. Ecology 52:964–979

    Article  Google Scholar 

  • Janzen DH (1971b) Seed predation by animals. Ann Rev Ecol Syst 2:465–492

    Article  Google Scholar 

  • Janzen DH (1978) Seedling patterns of tropical trees. In: Tomlinson PB, Zimmermann MH (eds) Tropical trees as living systems. Cambridge University Press, Cambridge, pp 83–128

    Google Scholar 

  • Jones FA, Comita LS (2010) Density-dependent pre-dispersal seed predation and fruit set in a tropical tree. Oikos 119:1841–1847

    Article  Google Scholar 

  • Kelly D (1994) The evolutionary ecology of mast seeding. Trends Ecol Evol 9:465–470

    Article  PubMed  CAS  Google Scholar 

  • Klank C, Pluess AR, Ghazoul J (2010) Effects of population size on plant reproduction and pollinator abundance in a specialized pollination system. J Ecol 98:1389–1397

    Article  Google Scholar 

  • Ohashi K, Yahara T (2000) Effects of flower production and predispersal seed predation on reproduction in Cirsium purpuratum. Can J Bot 78:230–236

    Google Scholar 

  • Peguero G, Bonal R, Espelta JM (2014) Variation of predator satiation and seed abortion as seed defense mechanisms across an altitudinal range. Basic Appl Ecol 15:269–276

    Article  Google Scholar 

  • Sakai S, Kojima T (2009) Overproduction and selective abortion of ovules based on the order of fertilization revisited. J Theor Biol 260:430–437

    Article  PubMed  Google Scholar 

  • Shibata M, Tanaka H, Nakashizka T (1998) Causes and consequences of mast seed production of four co-occurring Carpinus species in Japan. Ecology 79:54–64

    Article  Google Scholar 

  • Stephenson AG (1981) Flower and fruit abortion: proximate causes and ultimate functions. Ann Rev Evol Syst 12:253–279

    Article  Google Scholar 

  • Traulsen A, Iwasa Y, Nowak MA (2007) The fastest evolutionary grajectory. J Theor Biol 249:617–623

    Article  PubMed  PubMed Central  Google Scholar 

  • Traveset A (1993) Deceptive fruits reduce seed predation by insects in Pistacia terebinthus L. (Anacardiaceae). Evol Ecol 7:357–361

    Article  Google Scholar 

  • Xu Y, Shen Z, Li D, Guo Q (2015) Pre-dispersal seed predation in a species-rich forest community: patterns and the interplay with determinants. PLoS One 10:e0143040

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Zangerl AR, Berenbaum MR, Nitao JK (1991) Parthenocarpic fruits in wild parsnip: decoy defense against a specialist herbivore. Evol Ecol 5:136–145

    Article  Google Scholar 

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Acknowledgements

I would like to thank Yusuke Ikegawa for his many valuable comments.

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Correspondence to Hideo Ezoe.

Appendices

Appendix 1

To find the optimal number of flowers produced n3 = n3* and the optimal abortion rate w3 = w3* for the reproductive success of the random-abortion strategy ϕ3 when q0 = 1 and qi = 0 for i ≥ 1, I applied the Lagrange multiplier method, an optimization technique for finding local maxima of a function with equality constraints (e.g., Traulsen et al. 2007).

We first constructed the following function from Eqs. 1c and 3c:

$$\begin{aligned} F({n_3},{w_3},\lambda ) & ={n_3}(1 - {P_0})(1 - {w_3}){Q_0} \\ & \quad +\lambda \{ R - {n_3}f - {n_3}s(1 - {P_0})(1 - {w_3})\} \\ \end{aligned}$$
(8)

where λ is a Lagrange multiplier and Q0 = Q0(n3). From Eq. 8 we had:

$$\begin{aligned} \frac{{\partial F}}{{\partial {n_3}}} & =(1 - {w_3})\left\{ {(1 - {P_0})\left( {{Q_0}+{n_3}\frac{{\partial {Q_0}}}{{\partial {n_3}}}} \right) - {n_3}\frac{{\partial {P_0}}}{{\partial {n_3}}}{Q_0}} \right\} \\ & \quad - \lambda \left\{ {f+(1 - {w_3})s\left(1 - {P_0} - {n_3}\frac{{\partial {P_0}}}{{\partial {n_3}}} \right)} \right\}=0, \\ \end{aligned}$$
(9)
$$\frac{{\partial F}}{{\partial {w_3}}}={n_3}(1 - {P_0})( - {Q_0}+\lambda s)=0$$
(10)

From Eqs. 10 and 1c, we obtained λ = Q0/s and w3 = 1 − (R − n3f)/{n3s(1 − P0)} respectively, which we substituted into Eq. 9 to numerically calculate n3 = n3*. The optimal abortion rate was w3* = 1 − (R − n3*f)/{n3s(1 − P0)}.

In a similar way, we found the optimal flower production n4 = n4* and the random abortion rate w4 = w4* of the mixed-abortion strategy when q0 = 1 and qi = 0 for i ≥ 1. From Eqs. 4 and 5, we constructed the function:

$$\begin{aligned} G({n_4},{w_4},\mu ) & ={n_4}(1 - {P_0})(1 - {w_4}){Q_0} \\ & \quad +\mu \left[ {R - {n_4}f - {n_4}s(1 - {P_0})(1 - {w_4})\{ u+(1 - {Q_0})u\} } \right] \\ \end{aligned}$$
(11)

where λ is a Lagrange multiplier and Q0 = Q0(n4). From Eq. 11 we had:

$$\begin{aligned} \frac{{\partial G}}{{\partial {n_4}}} & =(1 - {w_4})\left\{ {(1 - {P_0})\left( {{Q_0}+{n_4}\frac{{\partial {Q_0}}}{{\partial {n_4}}}} \right) - {n_4}\frac{{\partial {P_0}}}{{\partial {n_4}}}{Q_0}} \right\} - \mu f \\ & \quad - \mu (1 - {w_4})s\left[ {\left\{ {(1 - {P_0}) - {n_4}\frac{{\partial {P_0}}}{{\partial {n_4}}}} \right\}\{ u+(1 - u){Q_0}\} +{n_4}(1 - {P_0})(1 - \mu )\frac{{\partial {Q_0}}}{{\partial {n_4}}}} \right] \\ & =0 \\ \end{aligned}$$
(12)
$$\frac{{\partial G}}{{\partial {w_4}}}={n_4}(1 - {P_0})[ - {Q_0}+\mu s\{ u+(1 - u){Q_0}\} ]=0$$
(13)

From Eqs. 4 and 13, we had:

$${w_4}=1 - \frac{{R - {n_4}f}}{{{n_4}s(1 - {P_0})\left\{ {u+(1 - u){Q_0}} \right\}}},$$
(14)
$$\mu =\frac{{{Q_0}}}{{s\{ u+(1 - u){Q_0}\} }}.$$
(15)

By substituting Eqs. 14 and 15 into Eq. 12, we had an equation with respect to n4. We could numerically calculate its solution n4 = n4*. The optimal random-abortion rate w4* was calculated with Eq. 14.

Appendix 2

From Eq. 2, we obtained:

$$\frac{{d{Q_i}}}{{dn}}=\frac{1}{n}(k - 1){(\alpha {n^{k - 1}})^i}(i - \alpha {n^{k - 1}})\exp ( - \alpha {n^{k - 1}}),$$
(16)

where the subscript of n was omitted. When k = 1, ΣqiQi was clearly independent of n. When k > 1, the sign of that derivative depended only on the sign of i − αnk−1. Considering Σ(dQi/dn) = 0 (because ΣQi = 1), there should be a positive integer I such that dQi/dn ≤ 0 and dQi/dn > 0 if i ≤ I and i > I, respectively. Then, we had:

$$\frac{d}{{dn}}\sum\limits_{i} {{q_i}{Q_i}} =\sum\limits_{{i \leq I}} {{q_i}\frac{{d{Q_i}}}{{dn}}+} \sum\limits_{{i>I}} {{q_i}\frac{{d{Q_i}}}{{dn}} \leq {q_I}} \sum\limits_{i} {\frac{{d{Q_i}}}{{dn}}} =0$$
(17)

as {qi} was a non-negative decreasing sequence. Thus ΣqiQi was independent of or decreased with the number of flowers n if k ≥ 1.

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Ezoe, H. Excessive flower production as an anti-predator strategy: when is random flower abortion favored?. Popul Ecol 60, 275–286 (2018). https://doi.org/10.1007/s10144-018-0625-6

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