A note on the onset of synchrony in avian ovulation cycles

Henson, Shandelle M.; Burton, Danielle L.

doi:10.1080/10236198.2013.870564

Cited by 4 publications

(4 citation statements)

References 5 publications

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“…Burton & Henson (2014) analyzed the following egg‐laying model:

\begin{matrix} true0.33em \\ right x_{t + 1} & center = & left b e^{- c x_{t}} + p y_{t} \\ right y_{t + 1} & center = & left x_{t} . \end{matrix}

Here, the time step is one day,

x

is the number of gulls in the first day of the ovulation cycle,

y

is the number of gulls in the second day of the ovulation cycle,

b > 0

is the inherent number of birds that enter the system each day,

e^{- c x}

is the probability of the incoming gulls joining the

x

class,

c > 0

represents colony density (number of nests per unit area),

p \in (0, 1)

is the probability that a bird in the

y

class returns to the

x

class, and

1 - p

is the probability that a bird leaves the system. The value of

p

controls the expected number of ovulation cycles experienced per female, which is empirically three.…”

Section: Introductionmentioning

confidence: 99%

“…The value of

p

controls the expected number of ovulation cycles experienced per female, which is empirically three. Burton & Henson (2014), using

c

as a bifurcation parameter, proved the existence and uniqueness of an equilibrium solution which bifurcates at a critical value

c_{c r}

into a two‐cycle that becomes increasingly synchronous as colony density

c

increases.…”

Section: Introductionmentioning

confidence: 99%

“…A major shortcoming in model (1) is that the synchronizing mechanism

e^{- c x}

depresses the average number of eggs laid per day when

c

is large. Thus, Burton and Henson were not able to compare the effect of cannibalism on synchronous (

c > c_{c r}

) and nonsynchronous (

c < c_{c r}

) colonies (Burton & Henson, 2014; Gallos et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

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Cannibalism and synchrony in seabird egg‐laying behavior

Nurhan

Henson

2021

Natural Resource Modeling

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During years of high sea surface temperature, food resources for glaucous‐winged gulls (Larus glaucescens) are scarce. In response, male gulls cannibalize the eggs of neighbors. When this occurs, female gulls in dense areas of the colony adopt a tactic of egg‐laying synchrony, in which they lay eggs synchronously on an every‐other‐day schedule. Field observations show that the first‐laid egg of each clutch is the most likely to be cannibalized. In this paper, we analyzed a discrete‐time model of egg‐laying behavior that tracks egg order in the nest. Using Jury conditions, we found that the equilibrium destabilizes into a two‐cycle as colony density (nests per unit area) increases through a critical value, and that the two‐cycle becomes increasingly synchronous as density increases further. We demonstrated that more eggs survive cannibalism in synchronous colonies than in nonsynchronous colonies. Recommendations for Resource Managers In colonial gulls, increased egg cannibalism and every‐other‐day egg‐laying synchrony are two behavioral consequences of rising sea surface temperature. As nest density (nests per unit area) increases, equilibrium egg laying destabilizes into increasingly synchronous two‐cycles. More eggs survive cannibalism in synchronous colonies than in nonsynchronous colonies.

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“…Burton & Henson (2014) analyzed the following egg‐laying model:

\begin{matrix} true0.33em \\ right x_{t + 1} & center = & left b e^{- c x_{t}} + p y_{t} \\ right y_{t + 1} & center = & left x_{t} . \end{matrix}

Here, the time step is one day,

x

is the number of gulls in the first day of the ovulation cycle,

y

is the number of gulls in the second day of the ovulation cycle,

b > 0

is the inherent number of birds that enter the system each day,

e^{- c x}

is the probability of the incoming gulls joining the

x

class,

c > 0

represents colony density (number of nests per unit area),

p \in (0, 1)

is the probability that a bird in the

y

class returns to the

x

class, and

1 - p

is the probability that a bird leaves the system. The value of

p

controls the expected number of ovulation cycles experienced per female, which is empirically three.…”

Section: Introductionmentioning

confidence: 99%

“…The value of

p

controls the expected number of ovulation cycles experienced per female, which is empirically three. Burton & Henson (2014), using

c

as a bifurcation parameter, proved the existence and uniqueness of an equilibrium solution which bifurcates at a critical value

c_{c r}

into a two‐cycle that becomes increasingly synchronous as colony density

c

increases.…”

Section: Introductionmentioning

confidence: 99%

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Cannibalism and synchrony in seabird egg‐laying behavior

Nurhan

Henson

2021

Natural Resource Modeling

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“…We have considered several low-dimensional, proof-of-concept population and evolutionary dynamic models designed to study the effects of cannibalism on a population's reproductive timing, the nature of its dynamics, and its prospect for survival in a deteriorating environment (Burton and Henson 2014;Henson et al 2011;Cushing et al 2015;Veprauskas and Cushing 2017). Using bifurcation theoretic techniques to study the bifurcation that occurs when the extinction equilibrium destabilizes, we have established several theoretical possibilities: a cannibalistic population can asymptotically persist in a deteriorated environment in which it would go extinct if it did not engage in cannibalism; reproductive synchrony can be a response to increased cannibalism activity; and cannibalism can be an evolutionarily stable strategy.…”

Section: Introductionmentioning

confidence: 99%

Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population

Cushing

Henson

2018

J. Math. Biol.

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For structured populations with an annual breeding season, life-stage interactions and behavioral tactics may occur on a faster time scale than that of population dynamics. Motivated by recent field studies of the effect of rising sea surface temperature (SST) on within-breeding-season behaviors in colonial seabirds, we formulate and analyze a general class of discrete-time matrix models designed to account for changes in behavioral tactics within the breeding season and their dynamic consequences at the population level across breeding seasons. As a specific example, we focus on egg cannibalism and the daily reproductive synchrony observed in seabirds. Using the model, we investigate circumstances under which these life history tactics can be beneficial or non-beneficial at the population level in light of the expected continued rise in SST. Using bifurcation theoretic techniques, we study the nature of non-extinction, seasonal cycles as a function of environmental resource availability as they are created upon destabilization of the extinction state. Of particular interest are backward bifurcations in that they typically create strong Allee effects in population models which, in turn, lead to the benefit of possible (initial condition dependent) survival in adverse environments. We find that positive density effects (component Allee effects) due to increased adult survival from cannibalism and the propensity of females to synchronize daily egg laying can produce a strong Allee effect due to a backward bifurcation.

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A note on synchronous egg laying in a seabird behaviour model

Henson

Gallos

et al. 2018

Journal of Difference Equations and Applications

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A note on the onset of synchrony in avian ovulation cycles

Cited by 4 publications

References 5 publications

Cannibalism and synchrony in seabird egg‐laying behavior

Cannibalism and synchrony in seabird egg‐laying behavior

Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population

A note on synchronous egg laying in a seabird behaviour model

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