## Annual plants with a seed bank

It is instructive to ask what happens to our annual plant population in the first year that seed production fails completely, so that l = 0. Since N(t +1) = l ■ N(t), the answer, of course, is that the population goes extinct. In the absence of immigration, it would stay extinct. If, however, there is a long-lived bank of seeds in the soil then recruitment could fail for many years in a row, yet the population would bounce back as soon as conditions favouring recruitment returned. Seeds in the soil bank are 'temporarily opting out of the struggle for existence' (Harper, 1977). Most of the seeds in the bank are not technically dormant, and would germinate as soon as conditions were conducive (typically, when the soil was moist enough, warm enough, and light enough). Genuine dormancy requires some specific process to break it: seeds may be under innate dormancy, enforced dormancy, or induced dormancy (Harper, 1977; Thompson, 2000).

Existence of a seed bank can have a profound stabilizing effect on plant population dynamics as well as reducing the likelihood of local extinction. For instance, systems with parameter values such that they would exhibit chaotic dynamics in the absence of a seed bank show damped oscillations or a stable point equilibrium as the fraction of current seed production entering the seed bank is increased (Rees, 1997). We model the size of the seed bank (B(t) seeds per unit area) and the above-ground population of mature plants N(t) separately, using a pair of coupled difference equations:

where next year's plant population is the germination rate, g, multipled by the size of the surviving seed bank (survival = 1 — d, where d is the death rate of seeds in the bank),

B(t + 1)= B(t)(1 — g)(1 — d)+N(t) f (N(t)) (6.7)

and next year's seed bank comprises the survivors from this year's seed bank (seeds that did not germinate or die), topped up by this year's seed production (which is a density-dependent function of this year's mature population size). To act as a stabilizing mechanism on plant dynamics, the essential requirement is that the loss of seeds from the soil (death plus germination) is sufficiently low that, given the characteristic return time of good conditions, u years, and fecundity in a good year F:

If seed banks are such a good idea, then why don't all annual plant species have a seed bank? The most obvious explanation lies in the trade-off between seed size and seed number. Large seeds give rise to competitive seedlings, but large seeds would suffer very high death rates in a seed bank (they would be too attractive as food for granivores, for instance). But not all small-seeded annuals have seed banks, so this cannot be the whole answer. Perhaps there is a trade-off between strategies of escape in space (effective seed dispersal) and escape in time (effective seed-bank formation). Seed-bank formation would be favoured when fluctuations in reproductive success were positively correlated over large areas (e.g. because of large-scale weather patterns, like regional droughts), because there is no point in trying to disperse if everywhere is likely to be equally bad. Dispersal would be favoured when fluctuations in reproductive success were not spatially correlated, or were negatively correlated. In this case, the benefits of finding a suitable site elsewhere make dispersal advantageous, even though dispersal may be very risky. If these hypotheses are true, then dormancy and dispersal should be negatively correlated traits (Cook, 1980; Klinkhamer et al, 1987).

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