Department of Biology, Grand Valley State University, Allendale, MI 49401, USA

Institute of Molecular BioSciences, Massey University, Palmerston North 4442, New Zealand

Allan Wilson Centre for Molecular Ecology and Evolution, Palmerston North, New Zealand

Bio-Protection Research Centre, Canterbury, New Zealand

Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, USA

Abstract

Background

Human activities, such as agriculture, hunting, and habitat modification, exert a significant effect on native species. Although many species have suffered population declines, increased population fragmentation, or even extinction in connection with these human impacts, others seem to have benefitted from human modification of their habitat. Here we examine whether population growth in an insectivorous bat (^{6 }individuals) and, in the modern era, major agricultural insect pests form an important component of their food resource. It is thus hypothesized that the growth of these insectivorous bat populations was coupled to the expansion of agricultural land use in North America over the last few centuries.

Results

We sequenced one haploid and one autosomal locus to determine the rate and time of onset of population growth in

Conclusions

Our analyses reject the hypothesis that

Background

Modern human populations and their activities have had a significant, and frequently negative, impact on other organisms ^{1}-10^{3 }versus 10^{4}-10^{5 }years;

Roosting colonies of Mexican free-tailed bats (^{7}-10^{8 }individuals, making it one of the most numerous known non-human mammals. The largest known aggregations of Mexican free-tailed bats are in nursery colonies, primarily hosting reproductive adult females and their young. During the energetically demanding period of pregnancy and lactation, females ingest up to two-thirds of their body weight in insects every night

A number of studies have documented strong links between Mexican free-tailed bats and important agricultural pest insects, especially

This predator-prey relationship between Mexican free-tailed bats and agricultural pest insects suggests that we should observe population growth in bats coupled to increases in insect prey in connection with human agricultural practices in the Americas. Population growth would most likely be associated with the widespread expansion of European agriculture during the last few centuries, or as an outside possibility, with the emergence of Native American agriculture during the last few thousand years

Population growth leaves distinct patterns of variation in genetic data, and these patterns can be used to infer effective sizes and growth rates, as well as estimate the time at which growth commenced

Results

Approximate maximum likelihood

Summary statistics suggest that Mexican free-tailed bat populations have experienced growth (Table _{W }
_{W }
^{-8 }and 8.6 × 10^{-10}/bp/year, respectively). More tellingly, singleton polymorphisms - a signal of population growth - are frequent in both datasets, accounting for 40% of all polymorphisms in the mtDNA control region and 32% of all polymorphisms in the

Summary statistic information for the haploid mtDNA control region and the autosomal

**Summary Statistic**

**Symbol**

**Control region (mtDNA)**

**
RAG2
**

**(autosomal)**

Sample size (chromosomes)

94

150

Sequence length (bp)

474

686

Segregating sites

S

154

25

Watterson's theta (per bp)

θ_{W}

0.068

0.0065

Pairwise differences (per bp)

θ_{π}

0.038

0.0047

Tajima's

TD

-1.5

-0.82

Singletons

η_{1}

62

8

Haplotypes

h

86

52

We turned to approximate Maximum Likelihood to explore a two-phase population growth model (Figure _{A}
_{0}
_{A}
_{0}
_{0 }
_{A}
_{A }
_{0}
_{A}
_{0 }
_{0 }

Two-phase model of population growth

**Two-phase model of population growth**. An early period of constant size (Phase 1) is followed by a period of population growth (Phase 2). The dotted line reflects the time of onset of growth, during which the effective population size increases exponentially from ancestral to modern levels.

Maximum likelihood estimates for modern and ancestral effective population sizes, time of onset of growth and population growth rates

**Demographic**

**Parameter**

**mtDNA**

**
RAG2
**

**Combined**

**MLE**

**95% CI**

**MLE**

**95% CI**

**MLE**

**95% CI**

N_{A }(×10^{3})

120

10-890

340

120-560

230

120-450

N_{0 }(×10^{6})

11

6-50

6

6-50

11

6-50

τ (kya)

330

110-500

110

0-500

220

110-500

α (×10^{-5}/generation)

5.4

2.5-18

10

2.6->>100

7

2.6-18

Fold growth

93

10-3900

16

10-420

48

16-320

**Log-likelihood surface ( N**.

Click here for file

**Log-likelihood surface ( N**.

Click here for file

Combined log-likelihood surface (_{A }

**Combined log-likelihood surface ( N**. Black and white points indicate the grid of sampling locations. Log-likelihoods at these points are known with certainty, whereas log-likelihoods in the intervening spaces are interpolated. Regions of the parameter space with highest likelihood are shaded black. Only highlighted white points (circles and triangles) fall within the 95% confidence interval. The maximum likelihood estimate (MLE) is indicated by a white triangle.

**Grid points forming the 95% confidence interval of the three-dimensional parameter space ranked by likelihood value**.

Click here for file

**Profile likelihood curves drawn from the combined likelihood surface for the haploid mtDNA control region and autosomal RAG2 locus**.

Click here for file

Note too that our three demographic parameters (i.e., _{A}
_{0}
_{A }
_{0}
_{s }
_{A }
_{s }
_{0 }
_{s }

Validation

Even though we used only standard methods, we still validated our inference technique using data simulated under known demographic histories. To do so, we generated coalescent trees and ancestral recombination graphs (ARG) at 10^{3 }values of _{A}
_{0}
_{1}
_{A}
_{0}
_{A}
_{0}
_{A}
_{0}

Discussion

We set out to determine whether Mexican free-tailed bat populations have experienced population growth and, if so, whether their onset of growth was concurrent with the expansion of human agricultural activity. The approximate Maximum Likelihood method applied here is a flexible and powerful analytical tool for testing hypotheses about historical demography. Similar methods have been applied previously to demographic analyses of human populations

Several key points emerge from our analyses. First, a scenario whereby Mexican free-tailed bat populations are not growing (i.e., they are constant sized) is statistically unlikely. Considering the data points contained within the 95% confidence intervals for the demographic parameters (Additional file _{0 }
_{A}
^{-5}/generation) is equivalent to a doubling of the bat population approximately every 31 kyr (or ~7,725 generations). Such values do not suggest the extremely rapid growth that would be expected if Mexican free-tailed bat populations expanded from a small population size to their current numbers in response to human agricultural activity during the last few hundred years. Third, although we have little statistical power to place an upper bound on the time of onset of growth, our analysis has considerable power to infer the lower bound (cf. Additional file

Several factors might confound our analysis, although none of these materially affect our main conclusions. First, coalescent analyses assume selective neutrality. There is no evidence for balancing selection (or equivalently, population structure) in our dataset; in such cases, Tajima's _{W}, or the number of segregating sites) are not consistent with positive, directional selection, which tends to considerably reduce genetic diversity

Second, both visual inspection of the sequence alignment and tests of the four-gamete rule ^{-8 }and 10^{-10 }- are sufficiently small that homoplasy should have only minor effects on either dataset, and consequently, on the demographic parameters that we infer.

Third, we may have over- or underestimated generation times. If the average generation interval is actually larger than we assume (i.e.,

Conclusions

Our analyses firmly support population growth in Mexican free-tailed bats, but reject a direct co-evolutionary connection with the development of human agriculture. We are then left asking what may have caused this increase in Mexican free-tailed bat numbers. The question is complicated by the fact that our data lack sufficient power to place an upper bound on the time of the onset of growth. However, since we are able to confidently infer a lower bound for this parameter (i.e., growth was no more recent than ~120 ka), we find it likely that the signals of population growth observed in our data may be attributable to range expansion out of Pleistocene refugia.

Finally, we cannot completely exclude the possibility that growth rates of Mexican free-tailed bat populations may have increased (or indeed decreased) relative to previous levels in response to extremely recent human activity, such as the development of large wind farms or the advent of wide-scale industrialized agriculture following the Second World War. A very recent uptick in the rate of growth on the background of a population that is already growing is extremely difficult to detect

Methods

Samples and sequences

Mexican free-tailed bats (_{S }
_{2}, 0.8 mM dNTP Blend (Applied Biosystems) 2.5 ng each primer (Integrated DNA Technologies), and 0.0625 U AmpliTaq Gold DNA polymerase (Applied Biosystems). The PCR amplification profile consisted of initial hot start denaturation for 10 min at 95°C, followed by 35 cycles of denaturation at 95°C for 30 s, annealing at 55°C for 30 s, and elongation at 72°C for 1 min, with a final extension at 72°C for 10 min.

Diploid

Summary statistics

A suite of summary statistics was assembled to describe patterns of variation at each locus. Watterson's theta _{W}
_{π }
_{e}μ_{e }
_{π}
_{W}
_{1 }
_{W }
_{π}

The ^{-10 }substitutions/site/year was estimated by comparing data for ^{-8 }substitutions/site/year;

Population growth model

To provide more nuanced inference than is possible from simple observation of summary statistics, we compared the data to a two-phase population growth model (Figure _{A}
_{0}

where _{0 }
_{A}

Demographic inference

To infer demographic parameters under the two-phase population growth model, we employed an inference procedure based on the Maximum Likelihood framework. Likelihood functions for complex demographic histories are too intractable to be derived analytically, and we therefore determine likelihoods by simulation with the _{1 }
_{1}
**ℕ**), which significantly raises the number of instances where the values of these summary statistics are identical in both observed and simulated datasets (see below). This characteristic greatly simplifies the calculation of likelihoods.

To explain the method simply, we aim to estimate the likelihood of a set of observed summary statistics _{1, }
_{
A
}, _{0}, _{A}
_{0 }
_{A }
^{4}, 10^{6}}, _{0 }
^{4}, 5×10^{7}}, and ^{5}}. We produced a uniform 10 × 10 × 10 grid across this 3-dimensional parameter space, although to ensure coalescence, we constrained the parameter space such that _{0 }
_{A }
^{6 }coalescent trees for the haploid locus and 10^{6 }ancestral recombination graphs (ARGs) for the autosomal locus using the simulation software _{1}
_{1 }

where _{λ }
_{ij}
_{ij }

As is traditional, we report the natural log of likelihoods in preference to the likelihoods themselves; that is, values are reported on the scale (-∞, 0) rather than (0, 1). Confidence intervals were constructed using standard methods. In brief, confidence intervals incorporate all values

Because we consider a parameter space with three independent demographic parameters, the quartile of the χ^{2 }distribution with 3 degrees of freedom and a one-tailed probability of 0.05 was applied. Profile likelihoods were also calculated using standard methods; however, because these confidence intervals represent only a single dimension (i.e., each demographic parameter is considered separately), we applied a χ^{2 }distribution with only 1 degree of freedom.

Validation

Our inference method was validated by generating 10^{3 }coalescent trees and ARGs using values of _{A}
_{0 }
_{1 }
_{A}
_{0 }

Authors' contributions

ALR, MPC, and GFM conceived of the study and participated in its design. ALR and VAB carried out the molecular genetic studies. ALR aligned the sequence data and performed initial statistical analyses. MPC wrote code for and performed the approximate Maximum Likelihood analyses. ALR and MPC drafted the manuscript. All authors read and approved the final manuscript.

Acknowledgements

Funding for this study was provided by the Department of Ecology and Evolutionary Biology of the University of Tennessee, Bat Conservation International, Sigma Xi, and the American Museum of Natural History. We thank Arizona Research Laboratories at the University of Arizona for computational support, Grand Valley State University for logistical support, and Liliana Dávalos for critical comments on the manuscript.