Flying foxes create extensive seed shadows and enhance germination success of pioneer plant species in deforested Madagascan landscapes

Seed dispersal plays a significant role in forest regeneration and maintenance. Flying foxes are often posited as effective long-distance seed dispersers due to their large home ranges and ability to disperse seeds when flying. We evaluate the importance of the Madagascan flying fox Pteropus rufus in the maintenance and regeneration of forests in one of the world’s priority conservation areas. We tested germination success of over 20,000 seeds from the figs Ficus polita, F. grevei and F. lutea extracted from bat faeces and ripe fruits under progressively more natural conditions, ranging from petri-dishes to outdoor environments. Seeds from all fig species showed increased germination success after passing through the bats’ digestive tracts. Outside, germination success in F. polita was highest in faecal seeds grown under semi-shaded conditions, and seeds that passed through bats showed increased seedling establishment success. We used data from feeding trials and GPS tracking to construct seed shadow maps to visualize seed dispersal patterns. The models use Gaussian probability density functions to predict the likelihood of defecation events occurring after feeding. In captivity, bats had short gut retention times (often < 30 mins), but were sometimes able to retain seeds for over 24h. In the wild, bats travelled 3–5 km within 24–280 min after feeding, when defecation of ingested seeds is very likely. They produced extensive seed shadows (11 bats potentially dispersing seeds over 58,000 ha over 45 total days of tracking) when feeding on figs within their large foraging areas and dispersed the seeds in habitats that were often partially shaded and hence would facilitate germination up to 20 km from the feeding tree. Because figs are important pioneer species, P. rufus is an important dispersal vector that makes a vital contribution to the regeneration and maintenance of highly fragmented forest patches in Madagascar.


S1 Supporting Information
Methods for calculation of seed shadows using Gaussian probability density functions

Feeding times
In addition to space-time values, each recorded trajectory contains information indicating whether the animal was assumed to be feeding at each recorded time step. During a single trajectory there can be several feeding events and the first analytic step is to extract the number of feeding events and time interval during which they occurred. A feeding event can be defined by the time interval [t↓, t↑], where t↓ is the beginning and t↑ is the end of such event. The time stamps t↓ and t↑ vary both in number and time of the day for each individual. Feeding events are determined by when bats become stationary as detected by the GPS loggers.

Defaecation probabilities
Four individuals from the GRT experiment provided sufficient data to establish the period over which bats can produce seeded faeces after food ingestion (with no further food ingestion). These data were used to calculate Gaussian probability density functions that predict the likelihood of defecation events occurring after feeding. The probability density functions (or distributions) were used to calculate seed shadows.
The recorded data describe when the flying foxes defecated for the first, second, third and fourth times after ingesting food. To construct a probability distribution associated with the events of dropping seeds from the raw data in Fig 3 (main text) we generated histograms weighted by the average number of seeds found in the faeces and we separated the events by considering whether they were the first, second, third, or fourth episode after a feeding event. We term the resulting distributions the defecation probability distributions, which we plot in S1 Fig. Two Gaussian probability density functions, P1(t) and P2(t), have been fitted to these data, (see S1 Fig), such that P1(t) is the probability density of the first defecation event occurring at time t after eating. For simplicity the probability densities of a second, third or fourth defecation event have been grouped together and so that P2(t) represents the combined probability density of a subsequent (second, third or fourth) defecation event occurring at time t. These fitted distributions are: Here Ɲ (µ, σ) represents the normal distribution with mean µ and standard deviation σ, where µ times, called t*1 and t*2 respectively, for each feeding event the probability density of first defecation is maximal at time T1=t↑ + t*1, and is also maximal at time T2=t↑ + t*2 for any of the other defecation events).
Finding the seeds requires knowledge of the location of the animal at these times. As the trajectory data provides the location of the animal at the end of feeding, time t↑, a linear interpolation allowed us to estimate the position of the animal at times T1 and T2.

Diffusive displacement
The knowledge of the peak probability distributions P1(T1) and P2(T2) for the first and subsequent defecation events need to be supplemented with some assumption about the way in which animals explore space.
By assuming that individuals roam randomly over the terrain, it is possible to extract a diffusion coefficient from the data, which can then be used to calculate the average area occupied by the animals in a given time interval.
To calculate the diffusion coefficient, D, we use the relationship between the mean squared displacement (

Combining space and time
By choosing an overall defecation probability, P" 1 and P" 2, we determine the times T1 -and T1 + , T2and T2 + centred around their respective mean such that From the interpolated spatial position at time T1 and T2 and the time intervals ΔT1=T1 + -T1 -and ΔT2=T2 + -T2 -the average area an animal has explored is a disc of radius R1,2 given by πR 2 1,2=4D ΔT1,2. We are thus able to estimate a probability equal to P" 1,2 that an animal defecated (and dropped seeds) within a circle of radius, R1,2 , centred at the interpolated location at time T1,2.
In Fig 5 and 6 of the main text we show the actual animal trajectories associated, respectively, with S2 and S3 Figs with circles of radius R1,2 around the location with the maximum probability distribution of defecation occurring at time T1,2 after each feeding event. The circles for the first and subsequent defecation events are plotted, respectively, in blue and green. Although the natural choice for P" 1 and P" 2 would be to select a value equal for both, the great disparity in the width of the distribution P1(t) and P2(t) forced us to have P" 1>P" 2. The actual choice, that is P" 1=0.9 and P" 2=0.3, was ultimately arbitrary, but it was dictated by the clarity of the display in S2 Fig and   Fig 3 in the main text. With these choices of P" 1 and P" 2 we obtained the values ΔT1=32 min and ΔT2=76 min. The blue and green circles thus represent the average area that a flying fox would cover over 32 and 76 minutes, respectively. S1 Figure. The recorded data for first, second, third and fourth defecation events plotted as a function of time after food ingestion. Two fitted Gaussian curves are also plotted corresponding to the 'first event', and the 'subsequent event' defecation probability density functions (pdfs).

S2 Figure
Feeding and defecation event probabilities for the first sample trajectory with only one feeding event.
S3 Figure. Feeding and defacation event probabilities for the second sample trajectory with several feeding events.
S4 Figure. Squared displacement as a function of the time step interval. Each data point has been constructed by binning the values from different individuals. The red curve is the straight line fit through the origin to determine the diffusion coefficient.