Bird & Mammal Populations

All life history models in Bird & Mammal Populations (BMP) are at equilibrium with zero population growth. These are extended into simulations in the Population Dynamic Simulator using the selection-regulated model of Witting (2023).

For the simple case with non-overlapping generations, the selection-regulated model reduces to the following form

n_t+1 = n_t [n_t / n^*]^-γ / q_twithq_t = q_t-1 [n_t-1 / n^*]^γ_ι

where n is population density with equilibrium n^*, q the competitive quality of individuals with growth rate λ=1/q, and γ and γ_ι population regulation by density and population dynamic feed-back selection.

The age-structured parameters of the dynamic models are given by the life history models, and the density (γ) and selection (γ_ι) regulation parameters are estimated by statistical fits to time-series data. The γ and γ_ι estimates are then extrapolated to approximate models for species with no time-series data (using the method in Witting, 2024).

Time-series data

Almost 4000 population specific models are obtained by maximum likelihood fits to time-series of abundance estimates. Most of these data are obtained from the Living Planet Index, the North American Breeding Bird Survey, the PanEuropean Common Bird Monitoring Scheme, the Netwerk Ecologische Monitoring, Sovon, the Swiss Breeding Bird Index, the British Trust for Ornithology, the Danish Ornithological Society, and Svensk Fågeltaxering.

Density regulation vs. selection regulation

Population dynamic studies have traditionally incorporated density regulation. By allowing also for regulation by population dynamic feed-back selection, the selection-regulated models of BMP cover a broader range of dynamics (Fig. 1).

Fig. 1 Left: The Daubenton’s myotis is a rather rare example of density-regulated-like population growth, where the abundance returns more or less monotonically to an equilibrium. Right: The general population dynamics in birds and mammals behave more like selection-regulated dynamics, with population cycles that are more or less stable: illustrated here by a population of ovenbirds. Data from the Living Planet Index and the North American Breeding Bird Survey.

An essential question is whether natural populations are predominantly density or selection regulated. Figure 2 shows the estimated distribution of the importance of selection regulation (γ_ι) relative to total regulation (γ+γ_ι) across models that explain more than 50% of the variance in the data. With median estimates of 0.60 (se:0.01) for birds and 0.69 (se:0.02) for mammals, selection regulation is found to be more important than density regulation in most cases. While the distribution of estimates covers the range from almost pure selection regulation to almost pure density regulation, only 6% of the bird and 5% of the mammal populations have selection regulation below 10% of total regulation by density and selection. There is no support for the hypothesis that natural populations are exclusively density-regulated.

Fig. 2 The distributions of the relative importance of selection regulation [γ_ι/(γ+γ_ι)] among time-series where the best population dynamic model explains more than 50% of the population dynamic variance of the data.

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References

• Witting, L. 2023. On natural selection regulation in the population dynamics of birds and mammals. Preprint at bioRxiv https://dx.doi.org/10.1101/2021.11.27.470201.
• Witting, L. 2024. Population dynamic life history models of the birds and mammals of the world. Ecological Informatics 80:102492.